Wednesday, 4 January 2012
Ow. I woke up today with my left eye swollen as I was rubbing my eyes quite badly as it was itching badly. Not a wise thing to do. I had to endure the uncomfortable feeling of not having both eyes open fully at the same time. Even now, at night, as I am typing this, my left eye is still swollen, albeit less than that in the morning.
So today, the second day of school, was when actual lessons began. However it was a short school day today, so no problems there :) We had a lesson on philosophy, and I almost fell asleep trying to comprehend what the teacher was trying to explain. And then it was literature, we are studying MacBeth. Almost fell asleep yet again, because of the Shakespearean language used...
Anyway like other days its a normal, ordinary school day. The stress isn't here yet, but soon will be. If only I had taken some pictures today of random stuff. But then again my phone's camera sucks, evident from the recent set of photos I uploaded on the blog (or rather, on imageshack). Ah well.
Right now, there's no motivation for me to study. Nothing pushes me to study. Of course, having that thought for the entire year would be disastrous, so I'm looking for motivation. And there's still the scholarships. I can work hard for them, but I hate facing failures. After all, it's not the first time I've competed nationwide and intra-school, and seriously, I wasn't somewhere up there for every single thing I sat for. First there's this secondary school that I initially applied for, the NUS high school of math and science, and there was an entry test. I didn't even make it through the first round :/
And then I remember sitting for a nationwide chemistry olympiad test, and naturally I wasn't selected to enter the semi-finals. There was a intra-school physics olympiad test, and yeah, you know the outcome. There was this scholarship I tried out (rather I had the opportunity to try out) which was from the Government, to reduce my school fees (it's expensive) and I wasn't selected yet again.
I remember those four, but there are, of course, more.
So right now, the scholarships can't work as motivation for me, unless my friends, along with the entire school, turns stupid. Or I become the only student in the level ^^ then there won't be problems being the first.
To end off, here's my favourite quote. I heard it somewhere in my brain.
"Life's not a journey, it's a series of competitions you'll ultimately lose one day" ~Darrell Tay :)
:/
Well, so a year has passed, but I'm not at all ecstatic...
Now school's starting in two days, and my life would be shit once again. I'd rather stay in 2011 and not move on. Ah well. Perhaps I'm afraid of the future and what it would bring to me. After all, we all fear the unknown.
Now, back to the usual, one post per month "Life sucks" again...
:(
On a slightly happier note, happy new year everyone!
:/
*edit* I changed the audio in the blog to my favourite soundtrack so far - the reunion theme from the tearjerking movie Windstruck (K-movie, 2004). I set it to loop, but the only thing that is missing is a nice rain-like sound backdrop. If you don't understand what I mean, go to http://www.rainymood.com and leave this blog open. Its a soothing experience :)
Wow. My post after a long break.
Anyway, here's a question for you people. What do you think makes a good melody in all songs? Dont tell me the chord progression and scales crap. You could tell me through the tagboard, but no crap please.
And, if you have nothing better to do, you can go hear songs from Weird Al. He's a parodist, and sings present songs with their lyrics changed. Perhaps you would know this eBay song that sounds like "I want it that way" by the Backstreet Boys. If you really dont know the song, then play the song from this player below this line of words.
Well, there are more. Perhaps you know the song "American Idiot" by Green Day?
Here's the Weird Al version of American Idiot:
And lastly, a parody of You're Beautiful by James Blunt.
Dont forget to find out other songs from Weird Al.
As I checked my past emails ranging from Yi Ling's constant sending of emails in my hotmail account all the way to the present, I get this feeling. A very strange feeling. Even now, after Thursday's outing, that strange feeling to turn spacetime negative and travel back into time stays in me. They say treasure your childhood. Now I understand what they meant. Now I'm having this intense feeling of wanting to be 11 or 12 again and stay at that age forever. That was the time when my life was the happiest, and it was the time when most memories, happy and sad, stays in me.
Unfortunately, I didnt treasure that time, thinking it was the most stressful time ever with the PSLE drawing near. (Of course I was wrong, Sec sch's worse.) Try it. Enter your email inbox and open the very first email that you have ever received after you made an email account to send junk and chain mail as well as other sorts of important email. Perhaps you wouldnt have such a feeling, but I suppose most of you would want to travel back into the past. The time when you have all your friends, where you knew your friends would never backstab you; it would be more like a home to you. And moving on to a new life, to a new Secondary school, would be more like moving out of the house sometimes with some of your friends. Or in my case, none at all. A totally new and different life.
So, treasure the time you had. Even it's too late, your secondary school would be your new home and one day you will get use to the life in Sec school. Then, treasure that, for after Prom Night, you may be on a new road alone, regretting. And let's sit back and wait for someone on earth to disprove the theory of special relativity, so that we can travel back into time.
Meanwhile, hear this song:
This is a very good song indeed, but I seriously wonder why West Grove didnt feature this song. Well, that's all for now, till then!
I've changed the picture, it seems to overlap the post, but who in the world cares?
Have you ever thought of a world without technology?
Of course, most people cant live without technology. Many would go "No!!! Cannot play games!!!". Imagine a communication breakdown among every single human on Earth. Things like SMS will not even exist, no email, nothing. This will make the Earth seem soo much larger than before. No link? Well, with technology, humans at the opposite ends of the Earth can communicate with each other, this would make it seem the Earth is very small. But, without technology, is it really that bad? We could live without technology. And without technology, in my opinion, we will be much much smarter than we are now.
Of course, less time or none spent on playing computer games will give you more time to study and revise your homework. That could make you smarter. Or you could spend time on the computer doing online studies. But the latter wasn't what I was trying to mean.
Picture yourself in the stone age. That's what I mean.
Say the calculator. Now with the calculator, we can square root non perfect squares, do statistical calculations, etc. But every human's brain is a million times better than any calculator. Even the best of calculators are still much lousier than our brain power. But can we find out the square root of 5 correct to the 1000th significant figure?
Of course we cant.
But imagine the calculator didnt exist. We would be using so much of our brain to solve mathematical calculations. Wouldnt that be a million times better? We grow smarter just because we didnt use a calculator. Of course, with today's people having easy access to calculators, a mathematical problem comprising 10 positive and negative numbers with square roots and powers will be extraordinarily tough to people now. But will people of the past think it's tough? Maybe, it all depends if the person uses too much technology or not.
So, maybe this original article by me will set your mind thinking on whether the use of technology decrease our brain power. Of course, there are many other exceptions too. This will make a very good debate topic indeed. Happy thinking! =D
-Article is by Darrell Tay Jun Jie, owner of this blog. Copy this article if you want to; there's no stopping you.
Hear the extraordinary hard rock song Steelheart on the left.
It starts with fast singing followed by SCREAMS!!!
YAY SCREAMS!!!
(Just nth better to do)
On the night of 26th December 2008, horses down with viruses were sent to Singapore, Block 744, Jurong West Street 73, in one apartment by Mr Trojan. The horses went wild and started destroying files in thumb drives in that particular apartment. Mr Trojan was on one of the horses, and within minutes Mr McAffee shot Mr Trojan down, clearing his dead body. The horses were isolated, but files were destroyed already.
Says Darrell Tay, the victim, "The horses were everywhere, destroying files with their 'deadly' viruses. One file was even corrupted, and it could not be deleted. No matter how many times I tried deleting it (from the thumb drive), it kept coming back. I could only format it. And the computer said I do not have sufficent rights to format the thumb drive. I did it on another computer, and it worked."
Darrell Tay says the horses were probably summoned when he found an application that he never created but was already there. When he opened it, he saw the word 'virus' and exited the application, but it was too late. The horses were summoned into his house, and caused considerable damage, but computers were fine.
"Curiosity killed the files," quotes Darrell Tay.
-Report done by Darrell Tay
There arent many things to post about. However, there is one very serious thing to post about, and it's a warning.
Antivirus 2009.
Sounds familiar?
Yes, it's a FAKE antivirus software. And instead of scanning your computer it adds viruses to it. They will prompt you to scan your computer with the software by any means, so watch out.
This isnt anything important as compared to Ryan's new blog.
His blog is going to add viruses to computers that visits his blog.
So watch out.
Virtual particle
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article needs additional citations for verification.Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (August 2007)
In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle. (Indeed, because energy and momentum in quantum mechanics are time and space derivative operators, then due to Fourier transforms their spans are inversely proportional to time duration and position spans, respectively).
Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws. If a single particle is detected, then the consequences of its existence are prolonged to such a degree that it cannot be virtual. Virtual particles are viewed as the quanta that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields, such as a simple electric or magnetic fields, or any field that exists without excitations that result in its carrying information from place to place.
Contents[hide]
1 Properties
2 Manifestations
3 History
4 Virtual particles in Feynman diagrams
5 Virtual particles in vacuo
6 Pair production
7 External links
8 References
9 See also
//
[edit] Properties
The concept of virtual particles necessarily arises in the perturbation theory of quantum field theory, where interactions (essentially, forces) between real particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram which facilitates understanding of calculations.
A virtual particle is one that does not precisely obey the m2c4 = E2 − p2c2 relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity — indeed, it can be negative. The probability amplitude for them to exist tends to be canceled out by destructive interference over longer distances and times. They can be considered a manifestation of quantum tunnelling. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artefact of perturbation theory, and do not appear in a nonperturbative treatment. As such, their objective existence as "particles" is questionable;[citation needed] however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms.[citation needed]
There are two principal ways in which the notion of virtual particles appear in modern physics. They appear as intermediate terms in Feynman diagrams; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles cause the effect, or that the effect occurs because of the existence of virtual particles.[citation needed]
[edit] Manifestations
There are many observable physical phenomena resulting from interactions involving virtual particles. All tend to be characterized by the relatively short range of the force interaction producing them. Some of them are:
The Coulomb force between electric charges. It is caused by exchange of virtual photons. In symmetric 3-dimensional space this exchange results in inverse square law for force.
The so-called near field of radio antennas, where the magnetic effects of the current in the antenna wire and the charge effects of the wire's capacitive charge are detectable, but both of which effects disappear with increasing distance from the antenna much more quickly than do the influence of conventional electromagnetic waves, for which E is always equal to cB, and which are composed of real photons.
The strong nuclear force between quarks - it is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.
The weak nuclear force - it is the result of exchange by virtual W bosons.
The spontaneous emission of a photon during the decay of an excited atom or excited nucleus; such a decay is prohibited by ordinary quantum mechanics and requires the quantization of the electromagnetic field for its explanation.
The Casimir effect, where the ground state of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates.
The van der Waals force, which is partly due to the Casimir effect between two atoms,
Vacuum polarization, which involves pair production or the decay of the vacuum, which is the spontaneous production of particle-antiparticle pairs (such as electron-positron).
Lamb shift of positions of atomic levels.
Hawking radiation, where the gravitational field is so strong that it causes the spontaneous production of photon pairs (with black body energy distribution) and even of particle pairs.
Most of these have analogous effects in solid-state physics; indeed, one can often gain a better intuitive understanding by examining these cases. In semiconductors, the roles of electrons, positrons and photons in field theory are replaced by electrons in the conduction band, holes in the valence band, and phonons or vibrations of the crystal lattice. A virtual particle is in a virtual state where the probability amplitude is not conserved.
Antiparticles should not be confused with virtual particles or virtual antiparticles.
[edit] History
Paul Dirac was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of virtual electron-positron pairs, known as the Dirac sea. The Dirac sea has a direct analog to the electronic band structure in crystalline solids as described in solid state physics. Here, particles correspond to conduction electrons, and antiparticles to holes. A variety of interesting phenomena can be attributed to this structure.
[edit] Virtual particles in Feynman diagrams
One particle exchange scattering diagram
The calculation of scattering amplitudes in theoretical particle physics requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as Feynman diagrams. The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with real, on-shell particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". Mathematically, they correspond to the propagators appearing in the diagram.
In the image above and to the right, the solid lines correspond to real particles (of momentum p1 and so on), while the dotted line corresponds to a virtual particle carrying momentum k. For example, if the solid lines were to correspond to electrons interacting by means of the electromagnetic interaction, the dotted line would correspond to the exchange of a virtual photon. In the case of interacting nucleons, the dotted line would be a virtual pion. In the case of quarks interacting by means of the strong force, the dotted line would be a virtual gluon, and so on.
One-loop diagram with fermion propagator
It is sometimes said that all photons are virtual photons. This is because the world-lines of photons always resemble the dotted line in the above Feynman diagram: the photon was emitted somewhere (say, a distant star), and then is absorbed somewhere else (say a photoreceptor cell in the eyeball). Furthermore, in a vacuum, a photon experiences no passage of (proper) time between emission and absorption. This statement illustrates the difficulty of trying to distinguish between "real" and "virtual" particles as mathematically they are the same objects and it is only our definition of "reality" which is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in particle detectors, whereas virtual photons are not directly detected; only their average or side-effects may be noticed, in the form of forces or (in modern language) interactions between particles.
Virtual particles need not be mesons or bosons, as in the example above; they may also be fermions. However, in order to preserve quantum numbers, most simple diagrams involving fermion exchange are prohibited. The image to the right shows an allowed diagram, a one-loop diagram. The solid lines correspond to a fermion propagator, the wavy lines to bosons.
[edit] Virtual particles in vacuo
Formally, a particle is considered to be an eigenstate of the particle number operator where is the particle annihilation operator and the particle creation operator (sometimes collectively called ladder operators). In many cases, the particle number operator does not commute with the Hamiltonian for the system. This implies the number of particles in an area of space is not a well-defined quantity but like other quantum observables is represented by a probability distribution. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy. In a certain sense, they can be understood to be a manifestation of the time-energy uncertainty principle in a vacuum, which bears some similarity to Aether theories.
An important example of the "presence" of virtual particles in a vacuum is the Casimir effect. Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together. Thus, although the virtual particles themselves are not directly observable in the laboratory, they do leave an observable effect: their zero-point energy results in forces acting on suitably arranged metal plates or dielectrics.
[edit] Pair production
Main article: Pair production
In order to conserve the total fermion number of the universe, a fermion cannot be created without also creating its antiparticle; thus many physical processes lead to pair creation. The need for the normal ordering of particle fields in the vacuum can be interpreted by the idea that a pair of virtual particles may briefly "pop into existence", and then annihilate each other a short while later.
Thus, virtual particles are often popularly described as coming in pairs, a particle and antiparticle, which can be of any kind. These pairs exist for an extremely short time, and mutually annihilate in short order. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles.
This may occur in one of two ways. In an accelerating frame of reference, the virtual particles may appear to be real to the accelerating observer; this is known as the Unruh effect. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of real particles in thermodynamic equilibrium. The Unruh effect is a toy model for understanding Hawking radiation, the process by which black holes evaporate.
Another example is pair production in very strong electric fields, sometimes called vacuum decay. If, for example, a pair of atomic nuclei are merged together to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the fine structure constant), the strength of the electric field will be such that it will be energetically favorable to create positron-electron pairs out of the vacuum or Dirac sea, with the electron attracted to the nucleus to annihilate the positive charge. This pair-creation amplitude was first calculated by Julian Schwinger in 1951.
The restriction to particle-antiparticle pairs is actually only necessary if the particles in question carry a conserved quantity, such as electric charge, which is not present in the initial or final state. Otherwise, other situations can arise. For instance, the beta decay of a neutron can happen through the emission of a single virtual, negatively charged W particle that almost immediately decays into a real electron and antineutrino; the neutron turns into a proton when it emits the W particle. The evaporation of a black hole is a process dominated by photons, which are their own antiparticles and are uncharged.
It is sometimes suggested that pair production can be used to explain the origin of matter in the universe. In models of the Big Bang, it is suggested that vacuum fluctuations, or virtual particles, briefly appear. Then, due to effects such as CP-violation, an imbalance between the number of virtual particles and antiparticles is created, leaving a surfeit of particles, thus accounting for the visible matter in the universe.
Adapted from Wikipedia. Click the title link.
Ok, i managed to squeeze some time in posting. But I have nothing to post abt. Seriously. Fun times past like the wind, and bad times, well, they past like wind too. The most recent, most fun was the recent chalet i went to. Seemed a little late to post abt an event that happened long time ago. But if that's wat you want, i shall give it to you.
And so on a particular sunday, probably 19th oct, i went for a chalet. Organised by Jan and YL. More information abt this event can be found on Janice's blog, where the posts are in foreign languages.
And that's it. Dont complain. I've already posted.
Check out this website. Type in sth. YOu get rubbish. For example, Air.
uncyclopedia.org/wiki/Air
Try potato.
uncyclopedia.org/wiki/Potato
Try water.
uncyclopedia.org/wiki/Water
The first two were written by terroists. The third is saying RI found the year 1823. Haha. Oh yes Bryan left us. Then we three again took a bus back to the library where I met my dad. After some time at the library, I went home whereas Ming Wei and Yong Kuan went to the Jurong Point library.
Like any other days, boring, still awaiting the spam of LOL.......
No, I'm not giving out free rice. You wait. But the UN is giving out free rice to those in need. They ask you the synonyms of a word. Give the correct answer, and they donate 20 grain of rice. Thinking of helping the poor? This might be a good chance. The URL is : www.freerice.com
Dun noe the meaning of the word? Go to dictionary.reference.com
Remember wat Ms Yeo taught non Math olympiad pupils abt the grid thing? Pic this question.
There are 10000000000000000000000000000000000000! to the power of 10000000000000000000000000000000000000000000000000000000000000000000!
squares on one side of a grid and another 10000000000000000000000000000000000000! to the power of 10000000000000000000000000000000000000000000000000000000000000000000!
squares on the other side of the grid. There are two towns: town a and town b. adjacent to each other. You can only move towards B which is the upper right - hand corner of the grid. (Right or up.) How many possible routes are there from town a to town b, when town a is at the bottom left - hand corner of the grid?
Always think questions the hard way.
Like any other days, boring.
Let us see sth new (from http://en.wikipedia.org/wiki/Faster-than-light)
Faster-than-light
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Faster than the speed of light" redirects here. For other uses, see Faster than the speed of light (disambiguation).
Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. Science fiction style space travel, dubbed "True" FTL, in which matter exceeds the speed of light in its own frame of reference, defies known physics.
Under special theory of relativity, a particle (that has mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times. (see Tachyon)
On the other hand, what some physicists refer to as "apparent" or "effective" FTL[1][2][3][4] is the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations faster than what it would take light in the "normal" route (though still moving subluminally through the distorted region).
Apparent FTL is not excluded by general relativity. Examples of apparent FTL proposals are the Alcubierre drive and the traversable wormhole, although the physical plausibility of these solutions is uncertain.
Outside of mainstream physics, others (often without traditional physics training) have speculated on mechanisms that might allow FTL travel to be achieved, often relying on new theories of physics of their own invention, but their ideas have not gained significant acceptance in the physics research community. Fictional depictions of superluminal travel and the mechanisms of achieving it are also a staple of the science fiction genre.
Contents[hide]
1 Faster than light travel
2 Possibility of FTL
3 Justifications for FTL travel
3.1 Option A: Ignore special relativity
3.2 Option B: Get light to go faster (Casimir vacuum and quantum tunnelling)
3.3 Option C: Give up causality
3.4 Option D: Give up (absolute) relativity
3.5 Option E: Go somewhere where the speed of light is not the limit
3.6 Option F: Distort the space-time fabric
3.7 Option G: Make use of the fact that space and time are quantized
4 Tachyons
5 General relativity
6 Superficially FTL phenomena which do not carry information
6.1 Closing speeds
6.2 Phase velocities above c
6.3 Group velocities above c
6.4 Universal expansion
6.5 Astronomical observations
6.6 Quantum mechanics
6.6.1 Example 1 : Hartman effect
6.6.2 Example 2 : Casimir effect
6.6.3 Example 3 : EPR Paradox
6.6.4 Example 4 : Delayed choice quantum eraser
7 Variable speed of light
8 See also
8.1 In fiction
9 References
10 External links
//
[edit] Faster than light travel
In the context of this article, FTL is transmitting information or matter faster than c, a constant equal to the speed of light in a vacuum, 299,792,458 meters per second, or about 186,282 miles per second. This is not quite the same as travelling faster than light, since:
Some processes propagate faster than c, but cannot carry information (See below).
Light travels at speed c/n when not in a vacuum but travelling through a medium with refractive index = n (causing refraction), and in some materials other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation.
Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here.
[edit] Possibility of FTL
Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. According to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their relative velocity, will always measure zero-mass particles such as photons traveling at c in a vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by Poincaré transformations. These transformations have important implications:
The relativistic momentum of a particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
Either way, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not generally considered to be a sensible notion.
Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a space-like interval. In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference. Therefore any theory which permits "true" FTL also has to cope with time travel and all its associated paradoxes.
Albert Einstein elaborated that faster-than-light travel is impossible.
[edit] Justifications for FTL travel
Despite the established conclusion that relativity precludes FTL travel, some have proposed ways to justify FTL behavior:
[edit] Option A: Ignore special relativity
This option is popular particularly in science fiction. However, empirical and theoretical evidence strongly supports Einstein's theory of special relativity as the correct description of high-speed motion,[5] which generalizes the more familiar Galilean relativity, which is actually an approximation at conventional (much less than c) speeds. Similarly, general relativity is an overwhelmingly supported and experimentally verified theory of gravitation, except in the regime of very high energy densities over very short distances, where an as-yet-undeveloped theory of quantum gravity is necessary. Special relativity, however, is incorporated easily into quantum field theories. Therefore, even in the broader contexts of general relativity and quantum mechanics, conventional acceleration from subluminal to superluminal speeds is not possible.
[edit] Option B: Get light to go faster (Casimir vacuum and quantum tunnelling)
Einstein's equations of special relativity postulate that the speed of light is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light itself. That is an experimentally determined quantity, though it has an exact value because the units of length are defined using the speed of light.
The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called the vacuum energy. This vacuum energy can perhaps be changed in certain cases. When vacuum energy is lowered, light itself has been predicted to go faster than the standard value 'c'. This is known as the Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon travelling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036.[6] Accordingly there has as yet been no experimental verification of the prediction. A recent analysis[7] argued out that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze (with the hope that such a theory would guarantee the impossibility of a true time machine ever forming). Other authors argue that Scharnhorst's original analysis which seemed to show the possibility of faster-than-c signals involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.[8]
While getting light to go faster still doesn't mean one can travel faster than it, it just increases the speed limit from the standard one of 299,792,458 m/s. A comical variant of this explanation is used to justify the superluminal travel of starships on the animated sci-fi series, Futurama (The writers of the show justified ships travelling faster than the speed of light by explaining that the speed of light had been increased).
The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Koblenz, claim to have violated relativity experimentally by transmitting photons faster than the speed of light.[9] They say they have conducted an experiment in which microwave photons - relatively low energy packets of light - travelled "instantaneously" between a pair of prisms that had been moved up to 3ft apart, using a phenomenon known as quantum tunnelling. Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the train moves forward at each stop; in this way, the center of the train exceeds the speed of any of the individual cars.[10]
[edit] Option C: Give up causality
Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations, as can be seen in this graphical description of a tachyon's pistol duel. Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option.[citation needed] An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle.
An important point to note is that in general relativity it is possible for objects to be moving apart faster than light because of the expansion of the universe, in some reasonable choice of cosmological coordinates. This is understood to be due to the expansion of the space between the objects, and general relativity still reduces to special relativity in a "local" sense, meaning that two objects passing each other in a small local region of spacetime cannot have a relative velocity greater than c, and will move more slowly than a light beam passing through the region. (See Option F below)
[edit] Option D: Give up (absolute) relativity
Because of the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is doubly-special relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidence[citation needed] casts doubt on this theory, some physicists still consider it viable.[citation needed] However, even if this theory is accurate, it is still very unclear whether it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c.
There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis.
[edit] Option E: Go somewhere where the speed of light is not the limit
A very popular option in science fiction is to assume the existence of some other realm (typically called hyperspace, subspace, or slipspace) which is accessible from this universe, in which the laws of relativity are usually distorted, bent, or nonexistent, facilitating rapid transport between distant points in this universe, sometimes with acceleration differences - that is, not requiring as much energy or thrust to go faster. To accomplish rapid transport between points in hyperspace/subspace, special relativity is often assumed not to apply in this other realm, or that the speed of light is higher. Another solution is to posit that distant points in the mundane universe correspond to points that are close together in hyperspace.
This method of faster-than-light travel does not correspond to anything seriously proposed by mainstream science.
[edit] Option F: Distort the space-time fabric
Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light years from us today have a recession velocity which is faster than light.[11] Miguel Alcubierre theorized that it would be possible to create what is called an Alcubierre drive, in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally travelling faster than light. However, several objections raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the traversable wormhole, which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not locally move faster than light which travels through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.
[edit] Option G: Make use of the fact that space and time are quantized
As given by the planck length, there is a minimum amount of 'space' that can exist in this universe (1.616x10-35 meters). This limit can be used to determine a minimum time quantisation of 1.078x10-43 seconds, which corresponds to a beam of light with a wavelength approaching the planck length. This means that there is a physical limit to how much blue shift a beam of light can endure. According to general relativity there is no limit to this shift, and an infinitesimally small space can exist, but according to well accepted quantum theory these limits do exist.
This is precisely what happens towards the center of a black hole; the incoming light becomes blue shifted past the planck length as it approaches the region of discontinuity within our universe. The argument is: if a black hole with finite mass can create such a discontinuity in the fabric of space and time, why would people be unable to do the same thing using a finite amount of energy and acceleration? (According to general relativity, the space-time distortions caused by gravity are fundamentally identical to space-time distortions caused simply by accelerating your reference frame).
[edit] Tachyons
Main article: Tachyon
In special relativity, while it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light, it is not impossible for an object to exist which always moves faster than light. The hypothetical elementary particles that have this property are called tachyons. Their existence has neither been proven nor disproven, but even so attempts to quantise them show that they may not be used for faster-than-light communication.[12] Physicists sometimes regard the existence of mathematical structures similar to Tachyons arising from theoretical models and theories as signs of an inconsistency or that the theory needs further refining.[13]
[edit] General relativity
General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it. Another possible system is the wormhole, which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypothetical exotic matter or negative energy.
General relativity also agrees that any technique for faster-than-light travel could also be used for time travel.[citation needed] This raises problems with causality. Many physicists believe that the above phenomena are in fact impossible, and that future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In string theory Eric Gimon and Petr Hořava have argued[14] that in a supersymmetric five-dimensional Gödel universe quantum corrections to general relativity effectively cut off regions of spacetimes with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.
[edit] Superficially FTL phenomena which do not carry information
[edit] Closing speeds
An observer may conclude that two objects are moving faster than the speed of light relative to each other, by adding their velocities according to the principle of Galilean relativity.
For example, two fast-moving particles approaching each other from opposite sides of a particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator. This correctly reflects the rate at which the distance between the two particles is decreasing, from the observer's point of view and is called the closing speed. However, it is not the same as the velocity of one of the particles as would be measured by a hypothetical fast-moving observer travelling alongside the other particle. To obtain this, the calculation must be done according to the principle of special relativity. If the two particles are moving at velocities v and -v, or expressed in units of c, β and − β, where
then this relative velocity (again in units of the speed of light c) is
,
which is less than the speed of light.
[edit] Phase velocities above c
The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies[15]. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information[16]. Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.
[edit] Group velocities above c
The group velocity of a wave (e.g. a light beam) may also exceed c in some circumstances. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity above c. However, even this situation does not imply the propagation of signals with a velocity above c, even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind, the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than without this effect.
[edit] Universal expansion
The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.[17] Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10-36 seconds after the Big Bang to around 10-33 seconds), when the universe may have rapidly expanded by a factor of around 1020 - 1030.[18]
[edit] Astronomical observations
Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed.[citation needed], and can be explained as an optical illusion caused by the object moving in the direction of the observer,[citation needed] when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light.[citation needed] Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.
[edit] Quantum mechanics
Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. According to the No-communication theorem these phenomena do not allow true communication; they only let two observers in different locations see the same event simultaneously, without any way of controlling what either sees. Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment. Since the underlying behaviour doesn't violate local causality or allow FTL it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.
The uncertainty principle implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than c, even in a vacuum; this possibility must be taken into account when enumerating Feynman diagrams for a particle interaction. To quote Richard Feynman:
"… there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c"[19]
However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e. non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.
There have been various reports in the popular press of experiments on faster-than-light transmission in optics — most often in the context of a kind of quantum tunneling phenomenon. Usually, such reports deal with a phase velocity or group velocity faster than the vacuum velocity of light. But, recall from above, that a superluminal phase velocity cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point.
Quantum teleportation transmits quantum information at whatever speed is used to transmit the same amount of classical information, likely the speed of light. This quantum information may theoretically be used in ways that classical information can not, such as in quantum computations involving quantum information only available to the recipient. In science fiction, quantum teleportation is either used as a basis for teleportation of physical objects at the speed of light, presumably preserving some important aspect of the entanglement between the particles of the object, or else is misrepresented as allowing faster-than-light communication.
[edit] Example 1 : Hartman effect
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At the time of the crossing by tunnel effect it can prove that the top of the package of waves, associated with a particle, appears to cross the barrier of potential at an high speed with speed of light. The Hartman effect, thus named initially because described by Thomas E. Hartman in 1962, is associated with a very weak transmittivity which watch the barrier tunnel.
For the massive particles, it rather often is hidden or polluted by the filtering high frequency which the barrier constitutes, owed to the great dispersion of the transmittivity.
A study theoretical, or numerical, reveals easily that the time of crossing tunnel becomes independent the thickness of the barrier, driving at a supraluminic speed.[20] However, an analysis by Herbert Winful from the University of Michigan suggests that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than c, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".[21]
[edit] Example 2 : Casimir effect
In physics, the Casimir effect or Casimir-Polder force is a physical force exerted between separate objects due to resonance of vacuum energy in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, due to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Energy appears suddenly as if it came from the vacuum. See Option B above for a discussion of whether or not this effect could actually be used to send signals faster than c or violate causality.
[edit] Example 3 : EPR Paradox
We can also quote the spectacular case of the thought experiment of Einstein, Podolski and Rosen (EPR paradox) which could be realized in experiments for the first time by Alain Aspect in 1981 and 1982. In this case, the measurement of the state on one of the quantum systems of an entangled pair forces the other system to be measured in the complementary state. Thus functions quantum teleportation.
An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated nonlocal quantum correlations between particles separated by over 10 kilometers.[22] But as noted earlier, the nonlocal correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved; see no-communication theorem for further information.
[edit] Example 4 : Delayed choice quantum eraser
Delayed choice quantum eraser (The experiment of Marlan Scully) is an alternative of the paradox EPR in which the observation or not of interference after the passage of a photon through a double slit experiment depends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon, [23] which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it can't be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an FTL or backwards-in-time manner (see the delayed choice quantum eraser article for further information).
[edit] Variable speed of light
Main article: Variable speed of light
In conventional physics, the speed of light in a vacuum is assumed to be a constant. There exist theories which postulate that the speed of light is not a constant. The interpretation of this statement is as follows.
The speed of light is a dimensionful quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured.[24] Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when you measure the height of a mountain you really measure the ratio of its height to the length of a meterstick. The conventional SI system of units is based on seven basic dimensional quantities, namely distance, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity[25]. These units are defined to be independent and so cannot be described in terms of each other. As an alternative to using a particular system of units, one can reduce all measurements to dimensionless quantities expressed in terms of ratios between the quantities being measured and various fundamental constants such as Newton's constant, the speed of light and Planck's constant; physicists can define at least 26 dimensionless constants which can be expressed in terms of these sorts of ratios and which are currently thought to be independent of one another.[26] By manipulating the basic dimensional constants one can also construct the Planck time, Planck length and Planck energy which make a good system of units for expressing dimensional measurements, known as Planck units.
João's proposal used a different set of units, a choice which he justifies with the claim that some equations will be simpler in these new units. In the new units he fixes the fine structure constant, a quantity which some people, using units in which the speed of light is fixed, have claimed is time dependent. Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.
While it may be mathematically possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.
Ow. I woke up today with my left eye swollen as I was rubbing my eyes quite badly as it was itching badly. Not a wise thing to do. I had to endure the uncomfortable feeling of not having both eyes open fully at the same time. Even now, at night, as I am typing this, my left eye is still swollen, albeit less than that in the morning.
So today, the second day of school, was when actual lessons began. However it was a short school day today, so no problems there :) We had a lesson on philosophy, and I almost fell asleep trying to comprehend what the teacher was trying to explain. And then it was literature, we are studying MacBeth. Almost fell asleep yet again, because of the Shakespearean language used...
Anyway like other days its a normal, ordinary school day. The stress isn't here yet, but soon will be. If only I had taken some pictures today of random stuff. But then again my phone's camera sucks, evident from the recent set of photos I uploaded on the blog (or rather, on imageshack). Ah well.
Right now, there's no motivation for me to study. Nothing pushes me to study. Of course, having that thought for the entire year would be disastrous, so I'm looking for motivation. And there's still the scholarships. I can work hard for them, but I hate facing failures. After all, it's not the first time I've competed nationwide and intra-school, and seriously, I wasn't somewhere up there for every single thing I sat for. First there's this secondary school that I initially applied for, the NUS high school of math and science, and there was an entry test. I didn't even make it through the first round :/
And then I remember sitting for a nationwide chemistry olympiad test, and naturally I wasn't selected to enter the semi-finals. There was a intra-school physics olympiad test, and yeah, you know the outcome. There was this scholarship I tried out (rather I had the opportunity to try out) which was from the Government, to reduce my school fees (it's expensive) and I wasn't selected yet again.
I remember those four, but there are, of course, more.
So right now, the scholarships can't work as motivation for me, unless my friends, along with the entire school, turns stupid. Or I become the only student in the level ^^ then there won't be problems being the first.
To end off, here's my favourite quote. I heard it somewhere in my brain.
"Life's not a journey, it's a series of competitions you'll ultimately lose one day" ~Darrell Tay :)
:/
Labels: Darrell Tay
人之命，若无意，何生乎？22:36
Well, so a year has passed, but I'm not at all ecstatic...
Now school's starting in two days, and my life would be shit once again. I'd rather stay in 2011 and not move on. Ah well. Perhaps I'm afraid of the future and what it would bring to me. After all, we all fear the unknown.
Now, back to the usual, one post per month "Life sucks" again...
:(
On a slightly happier note, happy new year everyone!
:/
*edit* I changed the audio in the blog to my favourite soundtrack so far - the reunion theme from the tearjerking movie Windstruck (K-movie, 2004). I set it to loop, but the only thing that is missing is a nice rain-like sound backdrop. If you don't understand what I mean, go to http://www.rainymood.com and leave this blog open. Its a soothing experience :)
Labels: Darrell Tay
人之命，若无意，何生乎？22:28
Ah. Something interesting in my life today.
Well, I went for this outing. Four people including me - Cheryl Ong, Shiya Yong Kuan and one more person whom you should know. Since there were so few people going, we spent a short time outside. :(
But anyway, our first destination and final destination was Lot 1 Shoppers' Mall. We spent a freaking long time at the arcade, but at least I played there, so it isn't boring. I played:
- The car racing thing (1st!)
- The dancing thing where you step on the floor (somewhat forced to)
- Drumming (on a electronic drum set)
- The guitar thing, similar to Guitar Hero (I need to improve on my timing)
- The car thing, again.
And thn we waited for the two girls to finish their dancing game. After that we went to take neoprints. After the shots, while the Shiya and Cheryl were editing the photos, the entire system shut down. Amazing thing. We had to redo the decorations.
After staying at the arcade, we went to eat! While looking for the food court, I realised that the ceiling of the "stairway to ceiling" has been taken off. Here's a photo of it.
Well, Food Junction at Lot 1 Shoppers' Mall has good food, but they charge things at a high price. Very high. One can drink costs $1.50. That's a lot. Well, still, there's good food. And I tore my aluminium can, again. Last time it was green tea, now apple tea. :D
Then we went home. What a short journey, but still it is fun. :D
After this post which I posted on 17th May '09 I will attend a wedding dinner. I wonder how it will be like. Meanwhile, I have changed my playlist, I am using www.playlist.com now. Imeem decided to play 30 second long songs, no way am I going to allow these short songs to be played on my blog (if you want to listen to music, listen to it fully, not a part of it, and not with only one channel).
:D Till next time.
Labels: Darrell Tay
人之命，若无意，何生乎？15:14
Wow. My post after a long break.
Anyway, here's a question for you people. What do you think makes a good melody in all songs? Dont tell me the chord progression and scales crap. You could tell me through the tagboard, but no crap please.
And, if you have nothing better to do, you can go hear songs from Weird Al. He's a parodist, and sings present songs with their lyrics changed. Perhaps you would know this eBay song that sounds like "I want it that way" by the Backstreet Boys. If you really dont know the song, then play the song from this player below this line of words.
 | Weird Al Yankovic - eBay Song |  |
 | ||
 | Found at bee mp3 search engine |  |
Well, there are more. Perhaps you know the song "American Idiot" by Green Day?
Here's the Weird Al version of American Idiot:
| Weird Al Yankovic - Canadian Idiot | |
| | ||
| Found at bee mp3 search engine | |
And lastly, a parody of You're Beautiful by James Blunt.
| Weird Al Yankovic - You're Pitiful | |
| | ||
| Found at bee mp3 search engine | |
Dont forget to find out other songs from Weird Al.
Labels: Darrell Tay
人之命，若无意，何生乎？12:41
As I checked my past emails ranging from Yi Ling's constant sending of emails in my hotmail account all the way to the present, I get this feeling. A very strange feeling. Even now, after Thursday's outing, that strange feeling to turn spacetime negative and travel back into time stays in me. They say treasure your childhood. Now I understand what they meant. Now I'm having this intense feeling of wanting to be 11 or 12 again and stay at that age forever. That was the time when my life was the happiest, and it was the time when most memories, happy and sad, stays in me.
Unfortunately, I didnt treasure that time, thinking it was the most stressful time ever with the PSLE drawing near. (Of course I was wrong, Sec sch's worse.) Try it. Enter your email inbox and open the very first email that you have ever received after you made an email account to send junk and chain mail as well as other sorts of important email. Perhaps you wouldnt have such a feeling, but I suppose most of you would want to travel back into the past. The time when you have all your friends, where you knew your friends would never backstab you; it would be more like a home to you. And moving on to a new life, to a new Secondary school, would be more like moving out of the house sometimes with some of your friends. Or in my case, none at all. A totally new and different life.
So, treasure the time you had. Even it's too late, your secondary school would be your new home and one day you will get use to the life in Sec school. Then, treasure that, for after Prom Night, you may be on a new road alone, regretting. And let's sit back and wait for someone on earth to disprove the theory of special relativity, so that we can travel back into time.
Meanwhile, hear this song:
| Nickelback - Photograph | |
| | ||
| Found at bee mp3 search engine | |
This is a very good song indeed, but I seriously wonder why West Grove didnt feature this song. Well, that's all for now, till then!
Labels: Darrell Tay
人之命，若无意，何生乎？19:09
Yesterday was a damn fun day.
There was an outing, and we (Brandon, Thomas, Cheryl, Shiya, Carina, Kelly and I) proceeded to the basketball court. It wasnt quite fun at first (I couldnt play, I've just recovered). Thereafter we moved to this unknown fitness corner. Then I got hungry and went back to Jurong Point to eat. We crushed our drink cans and I tried to return it to its original shape, but the can tore instead and Thomas continued tearing the aluminium until it was like this:
There was an outing, and we (Brandon, Thomas, Cheryl, Shiya, Carina, Kelly and I) proceeded to the basketball court. It wasnt quite fun at first (I couldnt play, I've just recovered). Thereafter we moved to this unknown fitness corner. Then I got hungry and went back to Jurong Point to eat. We crushed our drink cans and I tried to return it to its original shape, but the can tore instead and Thomas continued tearing the aluminium until it was like this:
After hanging around in the arcade at Jurong Point, we headed for the MRT station. While waiting for the MRT, I told Brandon to play this song on the handphone and we both sang together (crazily):
We took the MRT to Choa Chu Kang and entered Lot 1 Shopper's Mall. After taking neoprints, Brandon, Thomas and I were about to head home, Thomas claimed to have seen an escalator to the ceiling(stairway to heaven (Led Zeppelin)... Haha). Here is the photo:
| Bon Jovi - Have A Nice Day | |
| | ||
| Found at bee mp3 search engine | |
We took the MRT to Choa Chu Kang and entered Lot 1 Shopper's Mall. After taking neoprints, Brandon, Thomas and I were about to head home, Thomas claimed to have seen an escalator to the ceiling(stairway to heaven (Led Zeppelin)... Haha). Here is the photo:
| Led Zeppelin - Stairway to Heaven | |
| | ||
| Found at bee mp3 search engine | |
Amazing right? They patched the hole.
So yesterday was extraordinarily fun. Hopefully that isnt the last time we're going out together.
Labels: Darrell Tay
人之命，若无意，何生乎？09:22
I've changed the picture, it seems to overlap the post, but who in the world cares?
Labels: Darrell Tay
人之命，若无意，何生乎？19:54
Have you ever thought of a world without technology?
Of course, most people cant live without technology. Many would go "No!!! Cannot play games!!!". Imagine a communication breakdown among every single human on Earth. Things like SMS will not even exist, no email, nothing. This will make the Earth seem soo much larger than before. No link? Well, with technology, humans at the opposite ends of the Earth can communicate with each other, this would make it seem the Earth is very small. But, without technology, is it really that bad? We could live without technology. And without technology, in my opinion, we will be much much smarter than we are now.
Of course, less time or none spent on playing computer games will give you more time to study and revise your homework. That could make you smarter. Or you could spend time on the computer doing online studies. But the latter wasn't what I was trying to mean.
Picture yourself in the stone age. That's what I mean.
Say the calculator. Now with the calculator, we can square root non perfect squares, do statistical calculations, etc. But every human's brain is a million times better than any calculator. Even the best of calculators are still much lousier than our brain power. But can we find out the square root of 5 correct to the 1000th significant figure?
Of course we cant.
But imagine the calculator didnt exist. We would be using so much of our brain to solve mathematical calculations. Wouldnt that be a million times better? We grow smarter just because we didnt use a calculator. Of course, with today's people having easy access to calculators, a mathematical problem comprising 10 positive and negative numbers with square roots and powers will be extraordinarily tough to people now. But will people of the past think it's tough? Maybe, it all depends if the person uses too much technology or not.
So, maybe this original article by me will set your mind thinking on whether the use of technology decrease our brain power. Of course, there are many other exceptions too. This will make a very good debate topic indeed. Happy thinking! =D
-Article is by Darrell Tay Jun Jie, owner of this blog. Copy this article if you want to; there's no stopping you.
Labels: Darrell Tay
人之命，若无意，何生乎？19:53
Hear the extraordinary hard rock song Steelheart on the left.
It starts with fast singing followed by SCREAMS!!!
YAY SCREAMS!!!
(Just nth better to do)
Labels: Darrell Tay
人之命，若无意，何生乎？21:03
On the night of 26th December 2008, horses down with viruses were sent to Singapore, Block 744, Jurong West Street 73, in one apartment by Mr Trojan. The horses went wild and started destroying files in thumb drives in that particular apartment. Mr Trojan was on one of the horses, and within minutes Mr McAffee shot Mr Trojan down, clearing his dead body. The horses were isolated, but files were destroyed already.
Says Darrell Tay, the victim, "The horses were everywhere, destroying files with their 'deadly' viruses. One file was even corrupted, and it could not be deleted. No matter how many times I tried deleting it (from the thumb drive), it kept coming back. I could only format it. And the computer said I do not have sufficent rights to format the thumb drive. I did it on another computer, and it worked."
Darrell Tay says the horses were probably summoned when he found an application that he never created but was already there. When he opened it, he saw the word 'virus' and exited the application, but it was too late. The horses were summoned into his house, and caused considerable damage, but computers were fine.
"Curiosity killed the files," quotes Darrell Tay.
-Report done by Darrell Tay
Labels: Darrell Tay
人之命，若无意，何生乎？11:04
There arent many things to post about. However, there is one very serious thing to post about, and it's a warning.
Antivirus 2009.
Sounds familiar?
Yes, it's a FAKE antivirus software. And instead of scanning your computer it adds viruses to it. They will prompt you to scan your computer with the software by any means, so watch out.
This isnt anything important as compared to Ryan's new blog.
His blog is going to add viruses to computers that visits his blog.
So watch out.
Labels: Darrell Tay
人之命，若无意，何生乎？10:13
Virtual particle
From Wikipedia, the free encyclopedia
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This article needs additional citations for verification.Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (August 2007)
In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle. (Indeed, because energy and momentum in quantum mechanics are time and space derivative operators, then due to Fourier transforms their spans are inversely proportional to time duration and position spans, respectively).
Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws. If a single particle is detected, then the consequences of its existence are prolonged to such a degree that it cannot be virtual. Virtual particles are viewed as the quanta that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields, such as a simple electric or magnetic fields, or any field that exists without excitations that result in its carrying information from place to place.
Contents[hide]
1 Properties
2 Manifestations
3 History
4 Virtual particles in Feynman diagrams
5 Virtual particles in vacuo
6 Pair production
7 External links
8 References
9 See also
//
[edit] Properties
The concept of virtual particles necessarily arises in the perturbation theory of quantum field theory, where interactions (essentially, forces) between real particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram which facilitates understanding of calculations.
A virtual particle is one that does not precisely obey the m2c4 = E2 − p2c2 relationship for a short time. In other words, their kinetic energy may not have the usual relationship to velocity — indeed, it can be negative. The probability amplitude for them to exist tends to be canceled out by destructive interference over longer distances and times. They can be considered a manifestation of quantum tunnelling. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artefact of perturbation theory, and do not appear in a nonperturbative treatment. As such, their objective existence as "particles" is questionable;[citation needed] however, the term is useful in informal, casual conversation, or in rendering concepts into layman's terms.[citation needed]
There are two principal ways in which the notion of virtual particles appear in modern physics. They appear as intermediate terms in Feynman diagrams; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles cause the effect, or that the effect occurs because of the existence of virtual particles.[citation needed]
[edit] Manifestations
There are many observable physical phenomena resulting from interactions involving virtual particles. All tend to be characterized by the relatively short range of the force interaction producing them. Some of them are:
The Coulomb force between electric charges. It is caused by exchange of virtual photons. In symmetric 3-dimensional space this exchange results in inverse square law for force.
The so-called near field of radio antennas, where the magnetic effects of the current in the antenna wire and the charge effects of the wire's capacitive charge are detectable, but both of which effects disappear with increasing distance from the antenna much more quickly than do the influence of conventional electromagnetic waves, for which E is always equal to cB, and which are composed of real photons.
The strong nuclear force between quarks - it is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.
The weak nuclear force - it is the result of exchange by virtual W bosons.
The spontaneous emission of a photon during the decay of an excited atom or excited nucleus; such a decay is prohibited by ordinary quantum mechanics and requires the quantization of the electromagnetic field for its explanation.
The Casimir effect, where the ground state of the quantized electromagnetic field causes attraction between a pair of electrically neutral metal plates.
The van der Waals force, which is partly due to the Casimir effect between two atoms,
Vacuum polarization, which involves pair production or the decay of the vacuum, which is the spontaneous production of particle-antiparticle pairs (such as electron-positron).
Lamb shift of positions of atomic levels.
Hawking radiation, where the gravitational field is so strong that it causes the spontaneous production of photon pairs (with black body energy distribution) and even of particle pairs.
Most of these have analogous effects in solid-state physics; indeed, one can often gain a better intuitive understanding by examining these cases. In semiconductors, the roles of electrons, positrons and photons in field theory are replaced by electrons in the conduction band, holes in the valence band, and phonons or vibrations of the crystal lattice. A virtual particle is in a virtual state where the probability amplitude is not conserved.
Antiparticles should not be confused with virtual particles or virtual antiparticles.
[edit] History
Paul Dirac was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of virtual electron-positron pairs, known as the Dirac sea. The Dirac sea has a direct analog to the electronic band structure in crystalline solids as described in solid state physics. Here, particles correspond to conduction electrons, and antiparticles to holes. A variety of interesting phenomena can be attributed to this structure.
[edit] Virtual particles in Feynman diagrams
One particle exchange scattering diagram
The calculation of scattering amplitudes in theoretical particle physics requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as Feynman diagrams. The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with real, on-shell particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles". Mathematically, they correspond to the propagators appearing in the diagram.
In the image above and to the right, the solid lines correspond to real particles (of momentum p1 and so on), while the dotted line corresponds to a virtual particle carrying momentum k. For example, if the solid lines were to correspond to electrons interacting by means of the electromagnetic interaction, the dotted line would correspond to the exchange of a virtual photon. In the case of interacting nucleons, the dotted line would be a virtual pion. In the case of quarks interacting by means of the strong force, the dotted line would be a virtual gluon, and so on.
One-loop diagram with fermion propagator
It is sometimes said that all photons are virtual photons. This is because the world-lines of photons always resemble the dotted line in the above Feynman diagram: the photon was emitted somewhere (say, a distant star), and then is absorbed somewhere else (say a photoreceptor cell in the eyeball). Furthermore, in a vacuum, a photon experiences no passage of (proper) time between emission and absorption. This statement illustrates the difficulty of trying to distinguish between "real" and "virtual" particles as mathematically they are the same objects and it is only our definition of "reality" which is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in particle detectors, whereas virtual photons are not directly detected; only their average or side-effects may be noticed, in the form of forces or (in modern language) interactions between particles.
Virtual particles need not be mesons or bosons, as in the example above; they may also be fermions. However, in order to preserve quantum numbers, most simple diagrams involving fermion exchange are prohibited. The image to the right shows an allowed diagram, a one-loop diagram. The solid lines correspond to a fermion propagator, the wavy lines to bosons.
[edit] Virtual particles in vacuo
Formally, a particle is considered to be an eigenstate of the particle number operator where is the particle annihilation operator and the particle creation operator (sometimes collectively called ladder operators). In many cases, the particle number operator does not commute with the Hamiltonian for the system. This implies the number of particles in an area of space is not a well-defined quantity but like other quantum observables is represented by a probability distribution. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy. In a certain sense, they can be understood to be a manifestation of the time-energy uncertainty principle in a vacuum, which bears some similarity to Aether theories.
An important example of the "presence" of virtual particles in a vacuum is the Casimir effect. Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together. Thus, although the virtual particles themselves are not directly observable in the laboratory, they do leave an observable effect: their zero-point energy results in forces acting on suitably arranged metal plates or dielectrics.
[edit] Pair production
Main article: Pair production
In order to conserve the total fermion number of the universe, a fermion cannot be created without also creating its antiparticle; thus many physical processes lead to pair creation. The need for the normal ordering of particle fields in the vacuum can be interpreted by the idea that a pair of virtual particles may briefly "pop into existence", and then annihilate each other a short while later.
Thus, virtual particles are often popularly described as coming in pairs, a particle and antiparticle, which can be of any kind. These pairs exist for an extremely short time, and mutually annihilate in short order. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles.
This may occur in one of two ways. In an accelerating frame of reference, the virtual particles may appear to be real to the accelerating observer; this is known as the Unruh effect. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of real particles in thermodynamic equilibrium. The Unruh effect is a toy model for understanding Hawking radiation, the process by which black holes evaporate.
Another example is pair production in very strong electric fields, sometimes called vacuum decay. If, for example, a pair of atomic nuclei are merged together to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the fine structure constant), the strength of the electric field will be such that it will be energetically favorable to create positron-electron pairs out of the vacuum or Dirac sea, with the electron attracted to the nucleus to annihilate the positive charge. This pair-creation amplitude was first calculated by Julian Schwinger in 1951.
The restriction to particle-antiparticle pairs is actually only necessary if the particles in question carry a conserved quantity, such as electric charge, which is not present in the initial or final state. Otherwise, other situations can arise. For instance, the beta decay of a neutron can happen through the emission of a single virtual, negatively charged W particle that almost immediately decays into a real electron and antineutrino; the neutron turns into a proton when it emits the W particle. The evaporation of a black hole is a process dominated by photons, which are their own antiparticles and are uncharged.
It is sometimes suggested that pair production can be used to explain the origin of matter in the universe. In models of the Big Bang, it is suggested that vacuum fluctuations, or virtual particles, briefly appear. Then, due to effects such as CP-violation, an imbalance between the number of virtual particles and antiparticles is created, leaving a surfeit of particles, thus accounting for the visible matter in the universe.
Adapted from Wikipedia. Click the title link.
Labels: Darrell Tay, maybe wikipedia too
人之命，若无意，何生乎？16:44
Ok, i managed to squeeze some time in posting. But I have nothing to post abt. Seriously. Fun times past like the wind, and bad times, well, they past like wind too. The most recent, most fun was the recent chalet i went to. Seemed a little late to post abt an event that happened long time ago. But if that's wat you want, i shall give it to you.
And so on a particular sunday, probably 19th oct, i went for a chalet. Organised by Jan and YL. More information abt this event can be found on Janice's blog, where the posts are in foreign languages.
And that's it. Dont complain. I've already posted.
Labels: Darrell Tay
人之命，若无意，何生乎？16:36
Check out this website. Type in sth. YOu get rubbish. For example, Air.
uncyclopedia.org/wiki/Air
Try potato.
uncyclopedia.org/wiki/Potato
Try water.
uncyclopedia.org/wiki/Water
Labels: Darrell Tay
人之命，若无意，何生乎？21:47
On 17th May, Yong Kuan, Ming Wei and I went for the first open house. (not nanyang girls', it's RI). Damn big.The first activity we tried was air rifle. Shot 6 times, all missed. (i have bad aiming)Next we had coffee and biscuits with a total stranger. Found out he was from the RI parents association. Then we went to the strings musical instruments where we were taught how to play the bass. The stick was made of horse hair. Oh my.
We then wandered around where we reach the auditorium and found out the talk abt to be over and we had to listen the Q & A session. Mr Ng Yong Kuan daringly asked the panel a question. When it was over we went to the atrium. Took some goodie bags and met Bryan. Moved to the Science Hub. Someone demonstrated Lycopodium powder with fire. In a tin can. It 'exploded' and the tin lid was sent flying out. Wow. The fire was extinguished. We were told it was a carbohydrate so it is flammable. Next we moved to crystal breeding grounds (take it easy sherman) where we placed certain salts like Iron nitrate in Sodium Silicate solution and it increased in size. were told as the salts reacted with sodium silicate it becomes less dense and rises. I grew mine and then washed the container. Juz at that time i found out the liquid was leaking but wanted to confirm it.
There came the boy. There were many containers of sodium silicate on a tray. He took one, and the whole tray dropped onto the floor. Sodium silicate was splashed all around. Some entered Yong Kuan's and my mouth. We ran for the toilet. B4 tat i took a last look at the boy. He showed no remorse. Rinsed our mouth and felt like vomitting. Luckily did not vomit.
It was 11.30 am then, and the next talk started. We ran for the auditorium and had to sit on the stairway. The same guy said if we are offered a place in RI we will still be able to enter RI unless it is out of the express range. YAY.
After the talk we went to the canteen. To eat. We saw the same boy again, and he showed no remorse. Heck. Ming Wei and I bought a book titled 'English as it is broken'. Quite weird. Btw RI has a bookshop which is called Popular bookshop(somewhat the ones you see at jurong point but smaller). Next we headed for Bishan Community Library. On our way out we saw these:
The first two were written by terroists. The third is saying RI found the year 1823. Haha. Oh yes Bryan left us. Then we three again took a bus back to the library where I met my dad. After some time at the library, I went home whereas Ming Wei and Yong Kuan went to the Jurong Point library.
Labels: Darrell Tay
人之命，若无意，何生乎？20:21
Like any other days, boring, still awaiting the spam of LOL.......
Labels: Darrell Tay
人之命，若无意，何生乎？20:44
No, I'm not giving out free rice. You wait. But the UN is giving out free rice to those in need. They ask you the synonyms of a word. Give the correct answer, and they donate 20 grain of rice. Thinking of helping the poor? This might be a good chance. The URL is : www.freerice.com
Dun noe the meaning of the word? Go to dictionary.reference.com
Labels: Darrell Tay
人之命，若无意，何生乎？18:36
Remember wat Ms Yeo taught non Math olympiad pupils abt the grid thing? Pic this question.
There are 10000000000000000000000000000000000000! to the power of 10000000000000000000000000000000000000000000000000000000000000000000!
squares on one side of a grid and another 10000000000000000000000000000000000000! to the power of 10000000000000000000000000000000000000000000000000000000000000000000!
squares on the other side of the grid. There are two towns: town a and town b. adjacent to each other. You can only move towards B which is the upper right - hand corner of the grid. (Right or up.) How many possible routes are there from town a to town b, when town a is at the bottom left - hand corner of the grid?
Always think questions the hard way.
Labels: Darrell Tay
人之命，若无意，何生乎？18:16
Like any other days, boring.
Labels: Darrell Tay
人之命，若无意，何生乎？18:04
Let us see sth new (from http://en.wikipedia.org/wiki/Faster-than-light)
Faster-than-light
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Faster than the speed of light" redirects here. For other uses, see Faster than the speed of light (disambiguation).
Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. Science fiction style space travel, dubbed "True" FTL, in which matter exceeds the speed of light in its own frame of reference, defies known physics.
Under special theory of relativity, a particle (that has mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times. (see Tachyon)
On the other hand, what some physicists refer to as "apparent" or "effective" FTL[1][2][3][4] is the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations faster than what it would take light in the "normal" route (though still moving subluminally through the distorted region).
Apparent FTL is not excluded by general relativity. Examples of apparent FTL proposals are the Alcubierre drive and the traversable wormhole, although the physical plausibility of these solutions is uncertain.
Outside of mainstream physics, others (often without traditional physics training) have speculated on mechanisms that might allow FTL travel to be achieved, often relying on new theories of physics of their own invention, but their ideas have not gained significant acceptance in the physics research community. Fictional depictions of superluminal travel and the mechanisms of achieving it are also a staple of the science fiction genre.
Contents[hide]
1 Faster than light travel
2 Possibility of FTL
3 Justifications for FTL travel
3.1 Option A: Ignore special relativity
3.2 Option B: Get light to go faster (Casimir vacuum and quantum tunnelling)
3.3 Option C: Give up causality
3.4 Option D: Give up (absolute) relativity
3.5 Option E: Go somewhere where the speed of light is not the limit
3.6 Option F: Distort the space-time fabric
3.7 Option G: Make use of the fact that space and time are quantized
4 Tachyons
5 General relativity
6 Superficially FTL phenomena which do not carry information
6.1 Closing speeds
6.2 Phase velocities above c
6.3 Group velocities above c
6.4 Universal expansion
6.5 Astronomical observations
6.6 Quantum mechanics
6.6.1 Example 1 : Hartman effect
6.6.2 Example 2 : Casimir effect
6.6.3 Example 3 : EPR Paradox
6.6.4 Example 4 : Delayed choice quantum eraser
7 Variable speed of light
8 See also
8.1 In fiction
9 References
10 External links
//
[edit] Faster than light travel
In the context of this article, FTL is transmitting information or matter faster than c, a constant equal to the speed of light in a vacuum, 299,792,458 meters per second, or about 186,282 miles per second. This is not quite the same as travelling faster than light, since:
Some processes propagate faster than c, but cannot carry information (See below).
Light travels at speed c/n when not in a vacuum but travelling through a medium with refractive index = n (causing refraction), and in some materials other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation.
Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here.
[edit] Possibility of FTL
Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. According to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their relative velocity, will always measure zero-mass particles such as photons traveling at c in a vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by Poincaré transformations. These transformations have important implications:
The relativistic momentum of a particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
Either way, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not generally considered to be a sensible notion.
Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a space-like interval. In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference. Therefore any theory which permits "true" FTL also has to cope with time travel and all its associated paradoxes.
Albert Einstein elaborated that faster-than-light travel is impossible.
[edit] Justifications for FTL travel
Despite the established conclusion that relativity precludes FTL travel, some have proposed ways to justify FTL behavior:
[edit] Option A: Ignore special relativity
This option is popular particularly in science fiction. However, empirical and theoretical evidence strongly supports Einstein's theory of special relativity as the correct description of high-speed motion,[5] which generalizes the more familiar Galilean relativity, which is actually an approximation at conventional (much less than c) speeds. Similarly, general relativity is an overwhelmingly supported and experimentally verified theory of gravitation, except in the regime of very high energy densities over very short distances, where an as-yet-undeveloped theory of quantum gravity is necessary. Special relativity, however, is incorporated easily into quantum field theories. Therefore, even in the broader contexts of general relativity and quantum mechanics, conventional acceleration from subluminal to superluminal speeds is not possible.
[edit] Option B: Get light to go faster (Casimir vacuum and quantum tunnelling)
Einstein's equations of special relativity postulate that the speed of light is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light itself. That is an experimentally determined quantity, though it has an exact value because the units of length are defined using the speed of light.
The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called the vacuum energy. This vacuum energy can perhaps be changed in certain cases. When vacuum energy is lowered, light itself has been predicted to go faster than the standard value 'c'. This is known as the Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon travelling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036.[6] Accordingly there has as yet been no experimental verification of the prediction. A recent analysis[7] argued out that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze (with the hope that such a theory would guarantee the impossibility of a true time machine ever forming). Other authors argue that Scharnhorst's original analysis which seemed to show the possibility of faster-than-c signals involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.[8]
While getting light to go faster still doesn't mean one can travel faster than it, it just increases the speed limit from the standard one of 299,792,458 m/s. A comical variant of this explanation is used to justify the superluminal travel of starships on the animated sci-fi series, Futurama (The writers of the show justified ships travelling faster than the speed of light by explaining that the speed of light had been increased).
The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Koblenz, claim to have violated relativity experimentally by transmitting photons faster than the speed of light.[9] They say they have conducted an experiment in which microwave photons - relatively low energy packets of light - travelled "instantaneously" between a pair of prisms that had been moved up to 3ft apart, using a phenomenon known as quantum tunnelling. Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the train moves forward at each stop; in this way, the center of the train exceeds the speed of any of the individual cars.[10]
[edit] Option C: Give up causality
Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations, as can be seen in this graphical description of a tachyon's pistol duel. Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option.[citation needed] An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle.
An important point to note is that in general relativity it is possible for objects to be moving apart faster than light because of the expansion of the universe, in some reasonable choice of cosmological coordinates. This is understood to be due to the expansion of the space between the objects, and general relativity still reduces to special relativity in a "local" sense, meaning that two objects passing each other in a small local region of spacetime cannot have a relative velocity greater than c, and will move more slowly than a light beam passing through the region. (See Option F below)
[edit] Option D: Give up (absolute) relativity
Because of the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is doubly-special relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidence[citation needed] casts doubt on this theory, some physicists still consider it viable.[citation needed] However, even if this theory is accurate, it is still very unclear whether it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c.
There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis.
[edit] Option E: Go somewhere where the speed of light is not the limit
A very popular option in science fiction is to assume the existence of some other realm (typically called hyperspace, subspace, or slipspace) which is accessible from this universe, in which the laws of relativity are usually distorted, bent, or nonexistent, facilitating rapid transport between distant points in this universe, sometimes with acceleration differences - that is, not requiring as much energy or thrust to go faster. To accomplish rapid transport between points in hyperspace/subspace, special relativity is often assumed not to apply in this other realm, or that the speed of light is higher. Another solution is to posit that distant points in the mundane universe correspond to points that are close together in hyperspace.
This method of faster-than-light travel does not correspond to anything seriously proposed by mainstream science.
[edit] Option F: Distort the space-time fabric
Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light years from us today have a recession velocity which is faster than light.[11] Miguel Alcubierre theorized that it would be possible to create what is called an Alcubierre drive, in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally travelling faster than light. However, several objections raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the traversable wormhole, which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not locally move faster than light which travels through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.
[edit] Option G: Make use of the fact that space and time are quantized
As given by the planck length, there is a minimum amount of 'space' that can exist in this universe (1.616x10-35 meters). This limit can be used to determine a minimum time quantisation of 1.078x10-43 seconds, which corresponds to a beam of light with a wavelength approaching the planck length. This means that there is a physical limit to how much blue shift a beam of light can endure. According to general relativity there is no limit to this shift, and an infinitesimally small space can exist, but according to well accepted quantum theory these limits do exist.
This is precisely what happens towards the center of a black hole; the incoming light becomes blue shifted past the planck length as it approaches the region of discontinuity within our universe. The argument is: if a black hole with finite mass can create such a discontinuity in the fabric of space and time, why would people be unable to do the same thing using a finite amount of energy and acceleration? (According to general relativity, the space-time distortions caused by gravity are fundamentally identical to space-time distortions caused simply by accelerating your reference frame).
[edit] Tachyons
Main article: Tachyon
In special relativity, while it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light, it is not impossible for an object to exist which always moves faster than light. The hypothetical elementary particles that have this property are called tachyons. Their existence has neither been proven nor disproven, but even so attempts to quantise them show that they may not be used for faster-than-light communication.[12] Physicists sometimes regard the existence of mathematical structures similar to Tachyons arising from theoretical models and theories as signs of an inconsistency or that the theory needs further refining.[13]
[edit] General relativity
General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it. Another possible system is the wormhole, which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypothetical exotic matter or negative energy.
General relativity also agrees that any technique for faster-than-light travel could also be used for time travel.[citation needed] This raises problems with causality. Many physicists believe that the above phenomena are in fact impossible, and that future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In string theory Eric Gimon and Petr Hořava have argued[14] that in a supersymmetric five-dimensional Gödel universe quantum corrections to general relativity effectively cut off regions of spacetimes with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.
[edit] Superficially FTL phenomena which do not carry information
[edit] Closing speeds
An observer may conclude that two objects are moving faster than the speed of light relative to each other, by adding their velocities according to the principle of Galilean relativity.
For example, two fast-moving particles approaching each other from opposite sides of a particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator. This correctly reflects the rate at which the distance between the two particles is decreasing, from the observer's point of view and is called the closing speed. However, it is not the same as the velocity of one of the particles as would be measured by a hypothetical fast-moving observer travelling alongside the other particle. To obtain this, the calculation must be done according to the principle of special relativity. If the two particles are moving at velocities v and -v, or expressed in units of c, β and − β, where
then this relative velocity (again in units of the speed of light c) is
,
which is less than the speed of light.
[edit] Phase velocities above c
The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies[15]. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information[16]. Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.
[edit] Group velocities above c
The group velocity of a wave (e.g. a light beam) may also exceed c in some circumstances. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity above c. However, even this situation does not imply the propagation of signals with a velocity above c, even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind, the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than without this effect.
[edit] Universal expansion
The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.[17] Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10-36 seconds after the Big Bang to around 10-33 seconds), when the universe may have rapidly expanded by a factor of around 1020 - 1030.[18]
[edit] Astronomical observations
Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed.[citation needed], and can be explained as an optical illusion caused by the object moving in the direction of the observer,[citation needed] when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light.[citation needed] Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.
[edit] Quantum mechanics
Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. According to the No-communication theorem these phenomena do not allow true communication; they only let two observers in different locations see the same event simultaneously, without any way of controlling what either sees. Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment. Since the underlying behaviour doesn't violate local causality or allow FTL it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.
The uncertainty principle implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than c, even in a vacuum; this possibility must be taken into account when enumerating Feynman diagrams for a particle interaction. To quote Richard Feynman:
"… there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c"[19]
However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e. non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.
There have been various reports in the popular press of experiments on faster-than-light transmission in optics — most often in the context of a kind of quantum tunneling phenomenon. Usually, such reports deal with a phase velocity or group velocity faster than the vacuum velocity of light. But, recall from above, that a superluminal phase velocity cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point.
Quantum teleportation transmits quantum information at whatever speed is used to transmit the same amount of classical information, likely the speed of light. This quantum information may theoretically be used in ways that classical information can not, such as in quantum computations involving quantum information only available to the recipient. In science fiction, quantum teleportation is either used as a basis for teleportation of physical objects at the speed of light, presumably preserving some important aspect of the entanglement between the particles of the object, or else is misrepresented as allowing faster-than-light communication.
[edit] Example 1 : Hartman effect
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At the time of the crossing by tunnel effect it can prove that the top of the package of waves, associated with a particle, appears to cross the barrier of potential at an high speed with speed of light. The Hartman effect, thus named initially because described by Thomas E. Hartman in 1962, is associated with a very weak transmittivity which watch the barrier tunnel.
For the massive particles, it rather often is hidden or polluted by the filtering high frequency which the barrier constitutes, owed to the great dispersion of the transmittivity.
A study theoretical, or numerical, reveals easily that the time of crossing tunnel becomes independent the thickness of the barrier, driving at a supraluminic speed.[20] However, an analysis by Herbert Winful from the University of Michigan suggests that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than c, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".[21]
[edit] Example 2 : Casimir effect
In physics, the Casimir effect or Casimir-Polder force is a physical force exerted between separate objects due to resonance of vacuum energy in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, due to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Energy appears suddenly as if it came from the vacuum. See Option B above for a discussion of whether or not this effect could actually be used to send signals faster than c or violate causality.
[edit] Example 3 : EPR Paradox
We can also quote the spectacular case of the thought experiment of Einstein, Podolski and Rosen (EPR paradox) which could be realized in experiments for the first time by Alain Aspect in 1981 and 1982. In this case, the measurement of the state on one of the quantum systems of an entangled pair forces the other system to be measured in the complementary state. Thus functions quantum teleportation.
An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated nonlocal quantum correlations between particles separated by over 10 kilometers.[22] But as noted earlier, the nonlocal correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved; see no-communication theorem for further information.
[edit] Example 4 : Delayed choice quantum eraser
Delayed choice quantum eraser (The experiment of Marlan Scully) is an alternative of the paradox EPR in which the observation or not of interference after the passage of a photon through a double slit experiment depends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon, [23] which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it can't be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an FTL or backwards-in-time manner (see the delayed choice quantum eraser article for further information).
[edit] Variable speed of light
Main article: Variable speed of light
In conventional physics, the speed of light in a vacuum is assumed to be a constant. There exist theories which postulate that the speed of light is not a constant. The interpretation of this statement is as follows.
The speed of light is a dimensionful quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured.[24] Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when you measure the height of a mountain you really measure the ratio of its height to the length of a meterstick. The conventional SI system of units is based on seven basic dimensional quantities, namely distance, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity[25]. These units are defined to be independent and so cannot be described in terms of each other. As an alternative to using a particular system of units, one can reduce all measurements to dimensionless quantities expressed in terms of ratios between the quantities being measured and various fundamental constants such as Newton's constant, the speed of light and Planck's constant; physicists can define at least 26 dimensionless constants which can be expressed in terms of these sorts of ratios and which are currently thought to be independent of one another.[26] By manipulating the basic dimensional constants one can also construct the Planck time, Planck length and Planck energy which make a good system of units for expressing dimensional measurements, known as Planck units.
João's proposal used a different set of units, a choice which he justifies with the claim that some equations will be simpler in these new units. In the new units he fixes the fine structure constant, a quantity which some people, using units in which the speed of light is fixed, have claimed is time dependent. Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.
While it may be mathematically possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.
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