Phase Velocity of Information

Discussion in 'Physics & Math' started by Reiku, Dec 2, 2007.

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  1. Reiku Banned Banned

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    I thought it would be best to re-establish the notion of faster than light here in the physics dep. It was removed before, because i added old work which was moved. Therefore, there shouldn't be any problem with me adding this back, with a small extra. There is math that describes waves moving at ''c'' - the phase of information. This is different though for physical particles, because we need to give them group equations. But this shouldn't hold back any of the notions that certain information can travel at v>c.

    This wave equation,

    d^2u/dt^2 -c^2 d2u/dx2 + w2 u = 0

    has a set of solutions:

    u = A cos( ax - bt )

    c^2 a^2 - b^2 + w^2 = 0

    Which are sine waves propagating with a speed,

    v = b/a = sqrt(c^2 + (w/a)^2)

    The problem here, is that they are moving at a speed which exceeds ''c''. These are normal equations for any wave form or particle. The problem can be removed, by distinguishing this velocity which is known as the phase velocity v_ph from another velocity known as the group velocity v_gr which is given by,

    v_gr = c / v_ph

    Now, this basically means that a wave packet will have a velocity at the value of ''c'' when in a group. But here is the problem, we can apply the same values for actual information waves in space and time, and when you measure an entangled photon, the other photon is instantly determined: despite any group variables. We could apply the phase veclocity equation to an information wave which would allow instantaneous action at a very spooky distance. The equations just shown, say that is it is only possible to send information with such a wave equation at a group velocity ''c'', but it doesn't account for possible information determining the action at great distances.

    The Phase Velocity however, does in itself, describe faster-then-light communication. It begs the question to what kind of information we are dealing with, without resorting to a group factor. If there isn't anything which describes this phase velocity, then the phase velocity is just a lame example of a speed faster than light which cannot carry a message.

    This doesn't seem right, especially when we have top physicists, such as Dr Cramer who's interpretations describe faster-than-light travel for certain information, the Wheeler-Choice Experiment, which even proves in itself backwards through time travel, and the well known phenomena of action at spooky distances which could be answered for by superluminal phase waves.

    ** Which is why i wrote the following. After some confusion by someone, concerning the phase and group velocity equations, it should now be quite clear that information is predicted to move faster than light, but it depends on what information we are referring to.

    So what is information?
    It turns out that information isn't real at all, but it has real effects on the universe. Information doesn't have any mass or energy, and neither can we see it, smell it or touch it... It exists in absolutely everything, but it doesn't seem to have a position, or substance.

    This is because information is what gives rise to substance and texture. It also gives rise to every property that makes up the intrinsic qualities of all of matter. It even makes up the intrinsic information of space and time... So information plays the biggest role known. Now, information will take on different roles, and that must mean that some information will have different properties themselves, such as speed. Some of these information waves will travel at lightspeed. According to Einstein, nothing can travel faster-than-light... Let's investigate this.

    The phase velocity of a wave is the rate at which a ''phase'' of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave will propagate. You could pick one particular phase of the wave and it would appear to move at the phase velocity. The phase velocity is given in terms of the wave's angular frequency, which is represented as w and wave vector k by:

    V_p = w/k

    It turns out though, that the phase velocity of electromagnetic radiation may exceed the velocity of ''c'' > the speed of light in a vacuum under some special circumstances, but (according to general thought) this does not indicate any superluminal information or energy transfer. This is called anomalous dispersion.
    Is it possible to break the lightspeed barrier?

    Well, no. Exceeding the speed of light, 186,000 miles per second, is supposed to be completely impossible according to Einstein’s relativity papers. According to Einstein, it would require an infinite amount of energy. As we have already been told as well, superluminal speeds also hold some strange consequences when time is involved. And how strange is this? An astronaut moving beyond light speed would theoretically arrive at his destination before leaving! Thus, if you go far and fast enough, you end up exactly where you began...

    Now, two German physicists have claimed to make light particles exceed its own velocity using the strange phenomenon known as quantum tunneling. Quantum tunneling is a well known phenomenon that occurs as a direct result of the strange uncertainty which pervades nature at very small scales. Tunneling is also involved in radioactivity and nuclear fusion, and according to theory, quantum tunneling helps make the sun shine, and according to the minority, tunneling also had something to do with the existence of the universe.

    Their research involved an experiment in which microwave photons, which are just another one of the several wavelengths of photons, appeared to travel "instantaneously" between two prisms forming the halves of a cube placed a meter apart. When the prisms were placed together, photons fired at one edge passed straight through them, as expected. After they were moved apart, most of the photons reflected off the first prism they encountered and were picked up by a detector. But, and here is the amazing part, a few photons appeared to "tunnel" through the gap separating them as if the prisms were still held together.

    Stranger still is that these photons had traveled a much longer distance, and yet, they seem to have arrived at their detector at exactly the same time as the reflected photons! If photons all travel at the same speed, and they made a journey that was longer than what was taken by the other photons, and yet turned up at the finishing end at the same time, can only indicate that these photons traveled faster-than-light. Now, this begs the same question for information.

    Einstein, as we are all aware, was highly critical of quantum mechanics. He was very displeased with the course it was inexorably taking. In response to his dislike, Einstein, Nathan Rosen and Boris Podolsky set up a thought experiment which has now come to be known as the EPR-Paradox.
    Their experiment consisted of dealing with a measurement performed on one half of a quantum system. Note however, that this quantum system being measured was actually part of another quantum system, which is now detached, and left alone. When one half of the system (A) is measured should instantly affect the other half of the system (B) at the very instant of measurement, even though there is no longer any connection between parts A and parts B. One can apply these systems as photons, and if the two photons are created from a single source, then any measurement made on one photon will instantly determine the state of the other photon, even if they are billions of light years apart. Einstein dismissed such long-distance communication as ''spooky,'' but a talented Irish physicist called John Bell mathematically proved that ''entanglement'' as it was coined, could be observed in the lab. Then in 1996 Alain Aspect and colleagues solved the EPR-Paradox, and witnessed for the first time quantum entanglement.
    But this is very strange. If a measured photon at x distance can instantly determine another photon, then this must suggest that information must travel at superluminal speeds. The only other answer came from physicist David Bohm, suggesting that the results where of a local result in the system called ''hidden variables.''

    But we must consider superluminal speeds... not just for quantum entanglement, but also for other applications concerning physics. One of these stems from the theory that the past and the future form the present. John G. Cramer introduced this idea, suggesting that quantum information comes from the past and from the future, and multiplies in the present, creating a collapse in the wave function.

    Might it be that Einstein was wrong again about quantum theory?
     
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  3. superluminal I am MalcomR Valued Senior Member

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    Interesting. You should quote the passages that you paste from another source and attribute the source. Which I suspect covers your entire post.
     
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  5. Reiku Banned Banned

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    What source?
     
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  7. superluminal I am MalcomR Valued Senior Member

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    We'll see. Maybe you really did write all of that.
     
  8. Reiku Banned Banned

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    But i did write all of this. The equations are not mine - they are standard equations of relativity and quantum mechanics. That much would be known.
     
  9. superluminal I am MalcomR Valued Senior Member

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    Well then. Nicely done.
     
  10. Reiku Banned Banned

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    Thank you.
     
  11. saudade Unfiltered perspective... Registered Senior Member

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    Isn't it true that mass increases as velocity increases? That would tell me that given an energetic enough push, massless particles could easily break the speed of light since their mass would not increase and the energy needed to push them so hard would not be extraordinary. If information isn't even a particle, it doesn't push my imagination too hard to see them going way faster than light.
     
  12. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    Reiku---

    You are not right. The phase carries no information. In order to observe the wavefunction, you must take the modulous squared. The modulous destroys any information about the phase.

    So no information can be propogated in the phase velocity.
     
  13. saudade Unfiltered perspective... Registered Senior Member

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    Can you be more specific?
     
  14. superluminal I am MalcomR Valued Senior Member

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    Right. But I'm suprised at how well he actually write sometimes...
     
  15. saudade Unfiltered perspective... Registered Senior Member

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    Why, specifically, is he wrong... I'm sure you guys are right, but I don't know what you mean... When you say "phase" what do you mean? The fact that I'm used to electrical engineering is probably not helping me in this case...
     
  16. superluminal I am MalcomR Valued Senior Member

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    Interesting... I'm an EE...

    Here is what I think is a very good description of the issue:

    http://www.mathpages.com/home/kmath210/kmath210.htm
     
  17. saudade Unfiltered perspective... Registered Senior Member

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    Well I'm by no means graduated, but every time I see or hear the word "phase" I think phase to phase in industrial motor control settings... Thanks for the link.
     
  18. saudade Unfiltered perspective... Registered Senior Member

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    hey hey, i get it!
     
  19. superluminal I am MalcomR Valued Senior Member

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    Sure. It's all the same thing. The phase of anything is just the relationship of one part of something to another. In this case (in my understanding) since the refractive index of vacuum is constant, the phase and group velocity are equal. In other media under the right conditions, the group velocity can exceed the phase velocity. But as the author states, this is no big deal since the limiting speed of c (light speed in a vacuum) is never exceeded.
     
  20. superluminal I am MalcomR Valued Senior Member

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    Awesome.
     
  21. saudade Unfiltered perspective... Registered Senior Member

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    okay... Now what is the modulous, why are we squaring it, and why is that eliminating all of our information regarding phase velocity?
     
  22. superluminal I am MalcomR Valued Senior Member

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    Well, Ben's the physicist. But here's my current understanding of it.

    In QM the modulus (I also think it's called the amplitude) is a complex number that is part of the wave function (which describes the probability distribution of a given event happening in a certain way), and when squared, gives the classical probability of an event happening. Anytime you make a measurement of a quantum system, you disturb the wave function and "collapse" it. In other words, what was a probability distribution becomes an actual instance of the event, selected by the very act of observation. Any information in the wave function, including phase velocity, is lost when it ceases to be a wave function and becomes "realized".

    I really hope Ben will correct me here if I've really screwed it up...
     
  23. saudade Unfiltered perspective... Registered Senior Member

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    Oh that's funny... I knew what a modulous was, but I didn't know the word for it...
     
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