Thursday, 24 April 2008

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

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"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.

K so ryan and i rejoined again. so did what i pointed out contradictory? it is right?

Woo hoo. i fell while running 1.6 km. the blood came out after a while. in fact if i did not fall i would have clocked a slower time. thats becoz i fell and touched the line (not toe the line).

In this lesson i will teach you how to count the number of possibilities in a code to help you in your mathematics equations. First, count the number of words or number and then count the code length. Put the number of code letters as whole numbers and then raise it to the component of the code length. For example,

-26 alphabetical letters

-5 bit key code length

so take 26 to the fith power equals to 11881376 different possibilities.....

Have a look at this:

Conservation of mass and energy

The concept of mass–energy equivalence unites the concepts of conservation of mass and conservation of energy, allowing rest mass to be converted to forms of active energy (such as kinetic energy, heat, or light) while still retaining mass. Conversely, active energy in the form of kinetic energy or radiation can be converted to particles which have rest mass. The total amount of mass/energy in a closed system (as seen by a single observer) remains constant because energy cannot be created or destroyed and, in all of its forms, trapped energy exhibits mass. In relativity, mass and energy are two forms of the same thing, and**neither one appears without the other.**

Wait, have a look at this first:

Mass–energy equivalence

From Wikipedia, the free encyclopedia

In physics, mass–energy equivalence is the concept that any mass has an associated energy and vice versa. In special relativity this relationship is expressed using the mass–energy equivalence formula

E-mc2

where

E = energy,

m = mass,

c = the speed of light in a vacuum (celeritas).

Two definitions of mass in special relativity may be validly used with this formula. If the mass in the formula is the rest mass, the energy in the formula is called the rest energy. If the mass is the relativistic mass, then the energy is the total energy.

The formula was derived by Albert Einstein, who arrived at it in 1905 in the paper "Does the inertia of a body depend upon its energy-content?", one of his Annus Mirabilis ("Wonderful Year") Papers.[1] While Einstein was not the first to propose a mass–energy relationship, and various similar formulas appeared before Einstein's theory, Einstein was the first to propose that the equivalence of mass and energy is a general principle, which is a consequence of the symmetries of space and time.

In the formula, c2 is the conversion factor required to convert from units of mass to units of energy. The formula does not depend on a specific system of units. In the International System of Units, the unit for energy is the joule, for mass the kilogram, and for speed meters per second. Note that 1 joule equals 1 kg·m2/s2. In unit-specific terms, E (in joules) = m (in kilograms) multiplied by (299,792,458 m/s)2.

The first part which i bolded, it adds on to my theory one of Enistein's theories had a flaw. Light has energy, which meant it has mass. then the special theory says something travvelling at the speed of light will have infinite mass and zero length. Light travels at the speed of light. light has mass and if it travels at the speed of light it will have infinite mass and our eyeballs will be squished, but they asren't squished. Then this excuse was given:

Meanings of the mass–energy equivalence formula

Mass–energy equivalence says that when a body has a mass, it has a certain energy, even when it isn't moving. In Newtonian mechanics, a massive body at rest has no kinetic energy, and it may or may not have other (relatively small) amounts of internal stored energy such as chemical energy or thermal energy, in addition to any potential energy it may have from its position in a field of force. In Newtonian mechanics, none of these energies contributes to the mass.

In relativity, all the energy which moves along with the body adds up to the rest energy of the body, which is proportional to the rest mass of the body. Even a single photon traveling in empty space has a relativistic mass, which is its energy divided by c2. If a box of mirrors contains light, the mass of the box is increased by the energy of the light, since the total energy of the box is its mass.

Although a photon is never "at rest", it still has a rest mass, which is zero. If an observer chases a photon faster and faster, the observed energy of the photon approaches zero as the observer approaches the speed of light. This is why photons are massless. They have zero rest mass even though they have varying amounts of energy and relativistic mass. But, systems of two or more photons moving in different directions (as for example from an electron–positron annihilation) may have zero momentum over all. Their energy E then adds up to an invariant mass m = E/c2, when they are considered as a system.

This formula also gives the amount of mass lost from a body when energy is removed. In a chemical or nuclear reaction, when heat and light are removed, the mass is decreased. So the E in the formula is the energy released or removed, corresponding to a mass m which is lost. In those cases, the energy released and removed is equal in quantity to the mass lost, times c2. Similarly, when energy of any kind is added to a resting body, the increase in the mass is equal to the energy added, divided by c2.

Contradictory dont you think so? And about the special theory of relativity: http://en.wikipedia.org/wiki/Introduction_to_special_relativity

Check it out. something is definitely wrong.

*All information is from Wikipedia, the free encyclopedia.

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

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"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.

Labels: Darrell Tay

人之命，若无意，何生乎？20:53

K so ryan and i rejoined again. so did what i pointed out contradictory? it is right?

Woo hoo. i fell while running 1.6 km. the blood came out after a while. in fact if i did not fall i would have clocked a slower time. thats becoz i fell and touched the line (not toe the line).

Labels: Darrell Tay

人之命，若无意，何生乎？20:41

A number of Guthix druids have discovered an unexplored cave under the lower Wilderness, just north of Varrock. Inside is a new, one-on-one, tactical PvP combat minigame, available to both members and free players!

The cave appears to have been left undisturbed since the time of the god wars, guarded over the years by Fiara, a giant earwig and protector of something called the Fist of Guthix. Great powers emanate from this 'Fist' and the druids have managed to convince Fiara to allow them to gather charges from it. Being light on numbers, they need others to help them, which is where you come in!

In the spirit of Guthix, Fiara has introduced a 'balance' to this minigame. For each adventurer looking to absorb the power of the fist, there is another trying to chop, range or cast spells at them!

You and another adventurer must each take a turn being the hunted or the hunter. The hunted's task is to survive as long as possible, storing charges in a stone of power as the time counts down, while the hunter simply has to defeat the hunted in as quick a time as possible!

The energy of this mysterious area has quite an impact on those who attempt to absorb the power from the Fist of Guthix. Even the mightiest of warriors will find themselves severely weakened as they avoid the hunter, making it incredibly difficult to survive for long. The cave does offer some help in the form of places to hide, but will this be enough?

After both you and your opponent have had a chance to be the hunted, victory is assigned to those who stored the most charges in their stone of power. Fist of Guthix tokens will then be given out, based on how well you did, with which you can purchase a wide variety of rewards, including magical gloves to help you boost your XP, spiked shields and many more.

Fist of Guthix is available to play on ALL free and members worlds. There is a list of recommended worlds on the Themed Worlds Knowledge Base page.

We have also put a cap on the number of players who can play Fist of Guthix on any world at any time, which is set at 250 players. This will maximise your enjoyment of Fist of Guthix and minimise any conflict from other ongoing matches!

人之命，若无意，何生乎？20:34

In this lesson i will teach you how to count the number of possibilities in a code to help you in your mathematics equations. First, count the number of words or number and then count the code length. Put the number of code letters as whole numbers and then raise it to the component of the code length. For example,

-26 alphabetical letters

-5 bit key code length

so take 26 to the fith power equals to 11881376 different possibilities.....

人之命，若无意，何生乎？08:12

Have a look at this:

Conservation of mass and energy

The concept of mass–energy equivalence unites the concepts of conservation of mass and conservation of energy, allowing rest mass to be converted to forms of active energy (such as kinetic energy, heat, or light) while still retaining mass. Conversely, active energy in the form of kinetic energy or radiation can be converted to particles which have rest mass. The total amount of mass/energy in a closed system (as seen by a single observer) remains constant because energy cannot be created or destroyed and, in all of its forms, trapped energy exhibits mass. In relativity, mass and energy are two forms of the same thing, and

Wait, have a look at this first:

Mass–energy equivalence

From Wikipedia, the free encyclopedia

In physics, mass–energy equivalence is the concept that any mass has an associated energy and vice versa. In special relativity this relationship is expressed using the mass–energy equivalence formula

E-mc2

where

E = energy,

m = mass,

c = the speed of light in a vacuum (celeritas).

Two definitions of mass in special relativity may be validly used with this formula. If the mass in the formula is the rest mass, the energy in the formula is called the rest energy. If the mass is the relativistic mass, then the energy is the total energy.

The formula was derived by Albert Einstein, who arrived at it in 1905 in the paper "Does the inertia of a body depend upon its energy-content?", one of his Annus Mirabilis ("Wonderful Year") Papers.[1] While Einstein was not the first to propose a mass–energy relationship, and various similar formulas appeared before Einstein's theory, Einstein was the first to propose that the equivalence of mass and energy is a general principle, which is a consequence of the symmetries of space and time.

In the formula, c2 is the conversion factor required to convert from units of mass to units of energy. The formula does not depend on a specific system of units. In the International System of Units, the unit for energy is the joule, for mass the kilogram, and for speed meters per second. Note that 1 joule equals 1 kg·m2/s2. In unit-specific terms, E (in joules) = m (in kilograms) multiplied by (299,792,458 m/s)2.

The first part which i bolded, it adds on to my theory one of Enistein's theories had a flaw. Light has energy, which meant it has mass. then the special theory says something travvelling at the speed of light will have infinite mass and zero length. Light travels at the speed of light. light has mass and if it travels at the speed of light it will have infinite mass and our eyeballs will be squished, but they asren't squished. Then this excuse was given:

Meanings of the mass–energy equivalence formula

Mass–energy equivalence says that when a body has a mass, it has a certain energy, even when it isn't moving. In Newtonian mechanics, a massive body at rest has no kinetic energy, and it may or may not have other (relatively small) amounts of internal stored energy such as chemical energy or thermal energy, in addition to any potential energy it may have from its position in a field of force. In Newtonian mechanics, none of these energies contributes to the mass.

In relativity, all the energy which moves along with the body adds up to the rest energy of the body, which is proportional to the rest mass of the body. Even a single photon traveling in empty space has a relativistic mass, which is its energy divided by c2. If a box of mirrors contains light, the mass of the box is increased by the energy of the light, since the total energy of the box is its mass.

Although a photon is never "at rest", it still has a rest mass, which is zero. If an observer chases a photon faster and faster, the observed energy of the photon approaches zero as the observer approaches the speed of light. This is why photons are massless. They have zero rest mass even though they have varying amounts of energy and relativistic mass. But, systems of two or more photons moving in different directions (as for example from an electron–positron annihilation) may have zero momentum over all. Their energy E then adds up to an invariant mass m = E/c2, when they are considered as a system.

This formula also gives the amount of mass lost from a body when energy is removed. In a chemical or nuclear reaction, when heat and light are removed, the mass is decreased. So the E in the formula is the energy released or removed, corresponding to a mass m which is lost. In those cases, the energy released and removed is equal in quantity to the mass lost, times c2. Similarly, when energy of any kind is added to a resting body, the increase in the mass is equal to the energy added, divided by c2.

Contradictory dont you think so? And about the special theory of relativity: http://en.wikipedia.org/wiki/Introduction_to_special_relativity

Check it out. something is definitely wrong.

*All information is from Wikipedia, the free encyclopedia.

Labels: Darrell Tay

人之命，若无意，何生乎？20:06

Morse Code

Quantum Entanglement

6G2008

JANICE

COUSIN XINYI

CARINA

LINGYIN

CHERYL HENG

JASPER

JOJ

TET

JULIE

EGI

MICHELLE

★★wendy

MAE

VILDA

SONIA

POPPIMESHI

TARA

SUSAN

sHeRrY

Amanda

Su Ann

Nisa

Karl

Selvi

I'm starting to clear those broken links, please do inform me if you have changed your blog URL. Thanks.

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