Neutrino speed - Page 2

There are a number of things which can go "faster than light" without breaking relativity. http://en.wikipedia.org/wiki/Faster-than-light

Also, I did 10% of my third year Physics degree on a report about the OPERA faster than light experiment - so it's cool to see you guys talking about it here. :D

^theoretically things may be able to go faster than light, however they would not be able to carry or transmit information at FTL speed

On June 11 2012 20:21 palak wrote: ^theoretically things may be able to go faster than light, however they would not be able to carry or transmit information at FTL speed

They would be able to carry and transfer information. They can not transfer this information to subluminal/slower than light particles though, only to other superluminal particles. A particle in itself is transferring and carrying information by its very existence , if it can be seen by an observer.

^if/could be true would be wonderfully hard to prove experimentally

On June 11 2012 20:41 palak wrote: ^if/could be true would be wonderfully hard to prove experimentally

If the particle exists and can be observed by someone/something, then it is carrying and delivering information by its very existence alone.

Maybe the particle would travel slower than light in a certain medium, just like light needs a vacuum to travel at full speed. Then perhaps we could observe them.

^once you are over c, you can't drop back below c, at least not with physics as we know it.

One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when approaches infinity. (For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light). Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.

http://en.wikipedia.org/wiki/Tachyon

On June 11 2012 20:58 palak wrote: ^once you are over c, you can't drop back below c, at least not with physics as we know it. Show nested quote + One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when approaches infinity. (For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light). Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below. http://en.wikipedia.org/wiki/Tachyon

But the speed of light is not a constant in every medium, in a different medium the FTL speed may be slower than the speed of light outside that medium. Thus in a different medium, FTL particles may be observable from the outside, because the particle still travels faster than light in that specific medium.

"Light, which normally travels the 240,000 miles from the Moon to Earth in less than two seconds, has been slowed to the speed of a minivan in rush-hour traffic -- 38 miles an hour. "

http://www.news.harvard.edu/gazette/1999/02.18/light.html

http://en.wikipedia.org/wiki/Slow_light

c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second

On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second

If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster.

someone make a troll physics comic of slowing down light so we can travel faster than light.

On June 11 2012 21:31 Zorglub wrote: Show nested quote + On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster.

it may travel slower than it normally would and if you want to say pretend world of say tachyon 1,2,3 where 3=6c faster than 2=4c faster than 1=2c in a vacuum there could be a medium where tachyon 1 would travel faster than tachyon 3...so say tachyon 3 would get slowed to 1.5c while tachyon 1 continues on at 2c...but all 3 would need to always travel faster than c at all times

On June 11 2012 21:44 palak wrote: Show nested quote + On June 11 2012 21:31 Zorglub wrote:   On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster. it may travel slower than it normally would and if you want to say pretend world of say tachyon 1,2,3 where 3=6c faster than 2=4c faster than 1=2c in a vacuum there could be a medium where tachyon 1 would travel faster than tachyon 3...so say tachyon 3 would get slowed to 1.5c while tachyon 1 continues on at 2c...but all 3 would need to always travel faster than c at all times

Why is that? C is the speed of light in a vacuum, it is not some magical number. If you run a light particle and a tachyon through a "slowing medium", the tachyon would remain at the relativistic faster than light speed (in that medium). The tachyon stays the same compared to light in that medium. Speed and velocity are dependent on reference frames, they are "nothing" on their own, they are only meaningful if you compare them to something else.

On June 11 2012 21:56 Zorglub wrote: Show nested quote + On June 11 2012 21:44 palak wrote:   On June 11 2012 21:31 Zorglub wrote:   On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster. it may travel slower than it normally would and if you want to say pretend world of say tachyon 1,2,3 where 3=6c faster than 2=4c faster than 1=2c in a vacuum there could be a medium where tachyon 1 would travel faster than tachyon 3...so say tachyon 3 would get slowed to 1.5c while tachyon 1 continues on at 2c...but all 3 would need to always travel faster than c at all times Why is that? C is the speed of light in a vacuum, it is not some magical number. If you run a light particle and a tachyon through a "slowing medium", the tachyon would remain at the relativistic faster than light speed (in that medium). The tachyon stays the same compared to light in that medium. Speed and velocity are also dependent on reference frames, they are "nothing" on their own, they are only meaningful if you compare them to something else.

C is a constant number that doesn't change. Something that lowers lights speed to v=C/n may slow a tachyon from v'=xC to v'=xC/n but x/n will still always need to be >1 so the tachyon speed is above 1 so v'>C always.
Think about it how the wiki article says...or well my simplified version...
A normal particle you add energy to speed it up, in order to speed a particle with mass up to C you need to add an infinite amount of energy to it (impossible to duo), to slow it down you obviously remove energy from it (which can be done to zero)
A tachyon as above C to begin with has the effects of energy addition reversed...as you remove energy from a tachyon it speeds up, in order to slow down a tachyon you need to add energy to it, slowing the tachyon down to C requires the addition of infinite energy (impossible to do)

longer explanation + Show Spoiler +

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

On June 11 2012 22:18 palak wrote: Show nested quote + On June 11 2012 21:56 Zorglub wrote:   On June 11 2012 21:44 palak wrote:   On June 11 2012 21:31 Zorglub wrote:   On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster. it may travel slower than it normally would and if you want to say pretend world of say tachyon 1,2,3 where 3=6c faster than 2=4c faster than 1=2c in a vacuum there could be a medium where tachyon 1 would travel faster than tachyon 3...so say tachyon 3 would get slowed to 1.5c while tachyon 1 continues on at 2c...but all 3 would need to always travel faster than c at all times Why is that? C is the speed of light in a vacuum, it is not some magical number. If you run a light particle and a tachyon through a "slowing medium", the tachyon would remain at the relativistic faster than light speed (in that medium). The tachyon stays the same compared to light in that medium. Speed and velocity are also dependent on reference frames, they are "nothing" on their own, they are only meaningful if you compare them to something else. C is a constant number that doesn't change. Something that lowers lights speed to v=C/n may slow a tachyon from v'=xC to v'=xC/n but x/n will still always need to be >1 so the tachyon speed is above 1 so v'>C always. Think about it how the wiki article says...or well my simplified version... A normal particle you add energy to speed it up, in order to speed a particle with mass up to C you need to add an infinite amount of energy to it (impossible to duo), to slow it down you obviously remove energy from it (which can be done to zero) A tachyon as above C to begin with has the effects of energy addition reversed...as you remove energy from a tachyon it speeds up, in order to slow down a tachyon you need to add energy to it, slowing the tachyon down to C requires the addition of infinite energy (impossible to do) longer explanation + Show Spoiler +   It is a well known fact that nothing can travel faster than the speed of light. At best, a massless particle travels at the speed of light. But is this really true? In 1962, Bilaniuk, Deshpande, and Sudarshan, Am. J. Phys. 30, 718 (1962), said "no". A very readable paper is Bilaniuk and Sudarshan, Phys. Today 22, 43 (1969). Here is a brief overview. Draw a graph, with momentum (p) on the x-axis, and energy (E) on the y-axis. Then draw the "light cone", two lines with the equations E = ±p. This divides our 1+1 dimensional space-time into two regions. Above and below are the "timelike" quadrants, and to the left and right are the "spacelike" quadrants. Now the fundamental fact of relativity is that E² &#8722; p² = m² where E is an object's energy, p is its momentum, and m is its rest mass, which we'll just call 'mass'. In case you're wondering, we are working in units where c=1. For any non-zero value of m, this is a hyperbola with branches in the timelike regions. It passes through the point (p,E) = (0,m), where the particle is at rest. Any particle with mass m is constrained to move on the upper branch of this hyperbola. (Otherwise, it is "off shell", a term you hear in association with virtual particles — but that's another topic.) For massless particles, E² = p², and the particle moves on the light-cone. These two cases are given the names tardyon (or bradyon in more modern usage) and luxon, for "slow particle" and "light particle". Tachyon is the name given to the supposed "fast particle" which would move with v > c. Tachyons were first introduced into physics by Gerald Feinberg, in his seminal paper "On the possibility of faster-than-light particles" [Phys. Rev. 159, 1089—1105 (1967)]. Now another familiar relativistic equation is E = m[1&#8722;(v/c)²]&#8722;½. Tachyons (if they exist) have v > c. This means that E is imaginary! Well, what if we take the rest mass m, and take it to be imaginary? Then E is negative real, and E² &#8722; p² = m² < 0. Or, p² &#8722; E² = M², where M is real. This is a hyperbola with branches in the spacelike region of spacetime. The energy and momentum of a tachyon must satisfy this relation. You can now deduce many interesting properties of tachyons. For example, they accelerate (p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is "transcendent", or moves infinitely fast. This has profound consequences. For example, let's say that there were electrically charged tachyons. Since they would move faster than the speed of light in the vacuum, they should produce Cherenkov radiation. This would lower their energy, causing them to accelerate more! In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy. This suggests that coming up with a sensible theory of anything except free (noninteracting) tachyons is likely to be difficult. Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable. To treat this precisely requires quantum field theory, which gets complicated. It is not easy to summarize results here. However, one reasonably modern reference is Tachyons, Monopoles, and Related Topics, E. Recami, ed. (North-Holland, Amsterdam, 1978). However, tachyons are not entirely invisible. You can imagine that you might produce them in some exotic nuclear reaction. If they are charged, you could "see" them by detecting the Cherenkov light they produce as they speed away faster and faster. Such experiments have been done but, so far, no tachyons have been found. Even neutral tachyons can scatter off normal matter with experimentally observable consequences. Again, no such tachyons have been found. How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity? It's worth noting that when one considers the relativistic quantum mechanics of tachyons, the question of whether they "really" go faster than the speed of light becomes much more touchy! In this framework, tachyons are waves that satisfy a wave equation. Let's treat free tachyons of spin zero, for simplicity. We'll set c = 1 to keep things less messy. The wavefunction of a single such tachyon can be expected to satisfy the usual equation for spin-zero particles, the Klein-Gordon equation: (&#9633; + m²)&#966; = 0 where &#9633; is the D'Alembertian, which in 3+1 dimensions is just &#9633; = &#8706;²/&#8706;t² &#8722; &#8706;²/&#8706;x² &#8722; &#8706;²/&#8706;y² &#8722; &#8706;²/&#8706;z². The difference with tachyons is that m² is negative, and so m is imaginary. To simplify the math a bit, let's work in 1+1 dimensions with co-ordinates x and t, so that &#9633; = &#8706;²/&#8706;t² &#8722; &#8706;²/&#8706;x². Everything we'll say generalizes to the real-world 3+1-dimensional case. Now, regardless of m, any solution is a linear combination, or superposition, of solutions of the form &#966;(t,x) = exp(&#8722;iEt + ipx) where E² &#8722; p² = m². When m² is negative there are two essentially different cases. Either | p | &#8805; | E |, in which case E is real and we get solutions that look like waves whose crests move along at the rate | p/E | &#8805; 1, i.e., no slower than the speed of light. Or | p | < | E |, in which case E is imaginary and we get solutions that look like waves that amplify exponentially as time passes! We can decide as we please whether or not we want to consider the second type of solution. They seem weird, but then the whole business is weird, after all. (1) If we do permit the second type of solution, we can solve the Klein-Gordon equation with any reasonable initial data — that is, any reasonable values of &#966; and its first time derivative at t = 0. (For the precise definition of "reasonable", consult your local mathematician.) This is typical of wave equations. And, also typical of wave equations, we can prove the following thing: if the solution &#966; and its time derivative are zero outside the interval [&#8722;L, L] when t = 0, they will be zero outside the interval [&#8722;L&#8722; | t |, L + | t |] at any time t. In other words, localized disturbances do not spread with speed faster than the speed of light! This seems to go against our notion that tachyons move faster than the speed of light, but it's a mathematical fact, known as "unit propagation velocity". (2) If we don't permit the second sort of solution, we can't solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [&#8722;| m |, | m |]. By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [&#8722;L, L]! In other words, we can no longer "localize" our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is "unit propagation velocity" in the precise sense of part (1). Of course, the crests of the waves exp(&#8722;iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place! The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal. futher note...when the paper says   | p/E | &#8805; 1, i.e., no slower than the speed of light he has already set c=1 during the derivation so the answer with c set to a constant is c*|p/E| > c http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Yes I am aware of that simplified explanation, but C is only a constant from a specific reference frame or point of view. If you are a photon yourself, the speed of light is not 299,792,458 metres per second. If you are travelling towards the light at high speed, the speed of the photons hitting you would be more than 299,792,458 metres per second and vice versa if you travel away from it. (Redshift/Blueshift). If you are moving at close to the speed of light, a tachyon travelling at say 1½ times the speed of light passing by you from behind, would not travel faster than 299,792,458 metres per second from your point of view, because of your already inherent speed compared to that particle.

Na Tesla still rules. Turn on a light and you'll see I'm right.

On June 11 2012 22:50 Zorglub wrote: Show nested quote + On June 11 2012 22:18 palak wrote:   On June 11 2012 21:56 Zorglub wrote:   On June 11 2012 21:44 palak wrote:   On June 11 2012 21:31 Zorglub wrote:   On June 11 2012 21:22 palak wrote: c is not "speed of light"...c is the speed of light in a vacuum, the absolute max speed of any known particle...saying a particle can't go below c means no matter what it will be traveling above our current maximum speed limit of 299,792,458 metres per second If light is travelling slower in some media compared to others, why would this not be the case for a tachyon also? It would still remain at the same relativistic speed compared to light. Maybe a tachyon only would be able to travel faster. it may travel slower than it normally would and if you want to say pretend world of say tachyon 1,2,3 where 3=6c faster than 2=4c faster than 1=2c in a vacuum there could be a medium where tachyon 1 would travel faster than tachyon 3...so say tachyon 3 would get slowed to 1.5c while tachyon 1 continues on at 2c...but all 3 would need to always travel faster than c at all times Why is that? C is the speed of light in a vacuum, it is not some magical number. If you run a light particle and a tachyon through a "slowing medium", the tachyon would remain at the relativistic faster than light speed (in that medium). The tachyon stays the same compared to light in that medium. Speed and velocity are also dependent on reference frames, they are "nothing" on their own, they are only meaningful if you compare them to something else. C is a constant number that doesn't change. Something that lowers lights speed to v=C/n may slow a tachyon from v'=xC to v'=xC/n but x/n will still always need to be >1 so the tachyon speed is above 1 so v'>C always. Think about it how the wiki article says...or well my simplified version... A normal particle you add energy to speed it up, in order to speed a particle with mass up to C you need to add an infinite amount of energy to it (impossible to duo), to slow it down you obviously remove energy from it (which can be done to zero) A tachyon as above C to begin with has the effects of energy addition reversed...as you remove energy from a tachyon it speeds up, in order to slow down a tachyon you need to add energy to it, slowing the tachyon down to C requires the addition of infinite energy (impossible to do) longer explanation + Show Spoiler +   It is a well known fact that nothing can travel faster than the speed of light. At best, a massless particle travels at the speed of light. But is this really true? In 1962, Bilaniuk, Deshpande, and Sudarshan, Am. J. Phys. 30, 718 (1962), said "no". A very readable paper is Bilaniuk and Sudarshan, Phys. Today 22, 43 (1969). Here is a brief overview. Draw a graph, with momentum (p) on the x-axis, and energy (E) on the y-axis. Then draw the "light cone", two lines with the equations E = ±p. This divides our 1+1 dimensional space-time into two regions. Above and below are the "timelike" quadrants, and to the left and right are the "spacelike" quadrants. Now the fundamental fact of relativity is that E² &#8722; p² = m² where E is an object's energy, p is its momentum, and m is its rest mass, which we'll just call 'mass'. In case you're wondering, we are working in units where c=1. For any non-zero value of m, this is a hyperbola with branches in the timelike regions. It passes through the point (p,E) = (0,m), where the particle is at rest. Any particle with mass m is constrained to move on the upper branch of this hyperbola. (Otherwise, it is "off shell", a term you hear in association with virtual particles — but that's another topic.) For massless particles, E² = p², and the particle moves on the light-cone. These two cases are given the names tardyon (or bradyon in more modern usage) and luxon, for "slow particle" and "light particle". Tachyon is the name given to the supposed "fast particle" which would move with v > c. Tachyons were first introduced into physics by Gerald Feinberg, in his seminal paper "On the possibility of faster-than-light particles" [Phys. Rev. 159, 1089—1105 (1967)]. Now another familiar relativistic equation is E = m[1&#8722;(v/c)²]&#8722;½. Tachyons (if they exist) have v > c. This means that E is imaginary! Well, what if we take the rest mass m, and take it to be imaginary? Then E is negative real, and E² &#8722; p² = m² < 0. Or, p² &#8722; E² = M², where M is real. This is a hyperbola with branches in the spacelike region of spacetime. The energy and momentum of a tachyon must satisfy this relation. You can now deduce many interesting properties of tachyons. For example, they accelerate (p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is "transcendent", or moves infinitely fast. This has profound consequences. For example, let's say that there were electrically charged tachyons. Since they would move faster than the speed of light in the vacuum, they should produce Cherenkov radiation. This would lower their energy, causing them to accelerate more! In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy. This suggests that coming up with a sensible theory of anything except free (noninteracting) tachyons is likely to be difficult. Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable. To treat this precisely requires quantum field theory, which gets complicated. It is not easy to summarize results here. However, one reasonably modern reference is Tachyons, Monopoles, and Related Topics, E. Recami, ed. (North-Holland, Amsterdam, 1978). However, tachyons are not entirely invisible. You can imagine that you might produce them in some exotic nuclear reaction. If they are charged, you could "see" them by detecting the Cherenkov light they produce as they speed away faster and faster. Such experiments have been done but, so far, no tachyons have been found. Even neutral tachyons can scatter off normal matter with experimentally observable consequences. Again, no such tachyons have been found. How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity? It's worth noting that when one considers the relativistic quantum mechanics of tachyons, the question of whether they "really" go faster than the speed of light becomes much more touchy! In this framework, tachyons are waves that satisfy a wave equation. Let's treat free tachyons of spin zero, for simplicity. We'll set c = 1 to keep things less messy. The wavefunction of a single such tachyon can be expected to satisfy the usual equation for spin-zero particles, the Klein-Gordon equation: (&#9633; + m²)&#966; = 0 where &#9633; is the D'Alembertian, which in 3+1 dimensions is just &#9633; = &#8706;²/&#8706;t² &#8722; &#8706;²/&#8706;x² &#8722; &#8706;²/&#8706;y² &#8722; &#8706;²/&#8706;z². The difference with tachyons is that m² is negative, and so m is imaginary. To simplify the math a bit, let's work in 1+1 dimensions with co-ordinates x and t, so that &#9633; = &#8706;²/&#8706;t² &#8722; &#8706;²/&#8706;x². Everything we'll say generalizes to the real-world 3+1-dimensional case. Now, regardless of m, any solution is a linear combination, or superposition, of solutions of the form &#966;(t,x) = exp(&#8722;iEt + ipx) where E² &#8722; p² = m². When m² is negative there are two essentially different cases. Either | p | &#8805; | E |, in which case E is real and we get solutions that look like waves whose crests move along at the rate | p/E | &#8805; 1, i.e., no slower than the speed of light. Or | p | < | E |, in which case E is imaginary and we get solutions that look like waves that amplify exponentially as time passes! We can decide as we please whether or not we want to consider the second type of solution. They seem weird, but then the whole business is weird, after all. (1) If we do permit the second type of solution, we can solve the Klein-Gordon equation with any reasonable initial data — that is, any reasonable values of &#966; and its first time derivative at t = 0. (For the precise definition of "reasonable", consult your local mathematician.) This is typical of wave equations. And, also typical of wave equations, we can prove the following thing: if the solution &#966; and its time derivative are zero outside the interval [&#8722;L, L] when t = 0, they will be zero outside the interval [&#8722;L&#8722; | t |, L + | t |] at any time t. In other words, localized disturbances do not spread with speed faster than the speed of light! This seems to go against our notion that tachyons move faster than the speed of light, but it's a mathematical fact, known as "unit propagation velocity". (2) If we don't permit the second sort of solution, we can't solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [&#8722;| m |, | m |]. By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [&#8722;L, L]! In other words, we can no longer "localize" our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is "unit propagation velocity" in the precise sense of part (1). Of course, the crests of the waves exp(&#8722;iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place! The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal. futher note...when the paper says   | p/E | &#8805; 1, i.e., no slower than the speed of light he has already set c=1 during the derivation so the answer with c set to a constant is c*|p/E| > c http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html Yes I am aware of that simplified explanation, but C is only a constant from a specific reference frame or point of view. If you are a photon yourself, the speed of light is not 299,792,458 metres per second. If you are travelling towards the light at high speed, the speed of the photons hitting you would be more than 299,792,458 metres per second and vice versa if you travel away from it. (Redshift/Blueshift). If you are moving at close to the speed of light, a tachyon travelling at say 1½ times the speed of light passing by you from behind, would not travel faster than 299,792,458 metres per second from your point of view, because of your already inherent speed compared to that particle.

This is part of the fun of relativity, relativistic velocity and independence. The speed of light in a vacuum,c, is independent of the observers reference frame. If you are traveling at 5 mph in a vacuum you will see light pass you at 299,792,458 m/s, if you are going 299,700,000 m/s you will still observe light passing you at 299,792,458 m/s. This is extremely counter-intuitive.
you are doing this exact problem

It is tempting to extrapolate one or other of these results to light: if light is like little arrows, Jasper should measure v+c. If light is like sound, and if its medium is stationary with respect to Jasper, than Zoe should measure its speed as c−v. (We discuss the possibility of a medium for light later.) If we are really careful in our thinking, however, we should also say that light may be neither like arrows nor like sound. The extrapolation mentioned above is tempting, but it would be a huge extrapolation: light travels nearly a million times faster than sound. And extrapolations are always dangerous. For instance, very near where you are now, the temperature and other physical conditions are (I hope) fairly comfortable. But the further you go from your familiar surroundings - suppose for instance you go 20 kilometers up or down - the more likely things are to be different in surprising ways. The further you go from the familiar, the more likely we shall be surprised. And the speed of light is a very unfamiliar speed. Indeed, the speed of light (about 300,000 km/s - over a billion k.p.h.) is so great that our intuition is of little use. All the observations about speed that you have ever made, all of the experience upon which your common sense is based, are in a tiny area of physical reality that we could label "extremely low speed" compared with light. It is often the case that one can make approximations that apply over a limited region of reality, but that fail when we examine a larger range. For instance, objects fall at 9.8 metres per second per second in the lab. Also in the basement or on the roof. But this is not true in high orbits, or at the centre of the Earth.

furhter explained y that is wrong http://www.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm

Another assumption on the laws of physics made by the SI definition of the metre is that the theory of relativity is correct. It is a basic postulate of the theory of relativity that the speed of light is constant. This can be broken down into two parts: The speed of light is independent of the motion of the observer. The speed of light does not vary with time or place.

http://math.ucr.edu/home/baez/physics...vity/SpeedOfLight/speed_of_light.html
experiment done http://www.phys.unsw.edu.au/einsteinlight/jw/module3_is_it_true.htm

Even if you are traveling in a vacuum at say 99999% the speed of light and an object if fired directly at you going 99999% the speed of light by Einein velocity addition you would only observe the object flying at you as going 9999999999499994% the speed of light, still not 100% the speed of light.

Relativistic velocity calculator (note the blank boxes need a decimal place since you are going at a percent of c, so .5 for 50% c instead of putting 50 http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html#c2

Key is no matter what reference frame or objects, a person will never observe an object going faster than light in a vacuuum and a person will never be able to slow the speed of light in a vacuum relative to themselves.

Palak is right 200 000 km/s + 200 000 km/s =/= 400 000 km/s, that is relativity.

On June 11 2012 08:55 D_smart_S wrote: So some conspiracy theorist concluded that there will be a new disaster soon and nothing happens[b], then they said they were wrong and that is enough for you to conclude that they are now correct [b]on their new conspiracy theory ? Don't you think that they might be wrong a second time?

fyp

Interesting. I dont quite get that Einstein Velocity Addition though. It seems to me in the explanation they talk about velocity, which has a vector and thus it is able to be negative. Speed on the other hand has no vector and is therefore not negative. A photon at negative speed would be travelling back in time.

The speed of an object is the magnitude of its velocity (the rate of change of its position).

Now this confuses me, they write: "How will A and B measure their relative speeds? This is an example of Einstein velocity addition. In the calculation below, velocities to the right are taken as positive." They write how will A and B measure their relative speeds, yet they go on by calling it velocities instead and naming one of them negative. I don't see the logic in that. How would one of them suddenly have a negative velocity, when they talk about relative speeds?

I understand that the speed of light is fixed due to time dilation for the observer.

B is moving to the left therefore it's velocity vector is taken to be negative. Instead of saying it's coming at you with speed x, they just rephrase it as "it's traveling at -x velocity" since there is no worry of the problem situation changing they are lazy w/ exact wording. Speed and Velocity are used nearly interchangeably in the problem since it's just a 1 dimensional example problem.

Also a photon (or any object) traveling faster than light under relativity is also going backwards in time