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Is this description of superluminal speeds correct?

  1. Oct 29, 2012 #1
    Most of us know that Einstein came up with the theory that superluminal speed was impossible. And most physicists nowadays believe that and have accepted that as fact. I just want to know if this is a technically correct way of stating this:

    Light travels at approx. 299,800 km/s in a vacuum. And "light" can be described as being composed of (in some senses) photons. Massless particles that travel as particles AND waves. Now, since these particles are massless, they travel at the speed of light. All of it's energy can be used for "traveling the speed of light." And for mass to exist, that mass needs to have a energy content. That energy content cannot be used for the "motion" which would be traveling at the speed of light, so therefore, that particle with mass just doesn't have enough energy that can be used in motion to travel faster than the speed of light.

    Now, I know I'm thinking in a very mechanical sense, thinking of particles' energy contents as used for motion and whatnot, but is that technically a correct way of stating that? And if not, what would be a more correct way of stating that? Or is this statement just completely wrong, and I should just completely drop this notion completely?
  2. jcsd
  3. Oct 29, 2012 #2
    It has nothing to do with how much "energy" a particle has. A photon can have any energy it wants depending on wavelength, and the frame you measure it in.

    Feynman described it in a fairly intuitive way (the only intuitive way I know of at least). What he said was that the faster you accelerate something, the more energy it takes to continue accelerating it, and in fact it takes and infinite amount of energy to accelerate something to the speed of light, which is absurd, and hence must be impossible.

    It's all fairly straight forward mathematically, but thinking of it in terms of hand-wavy arguments usually doesn't work out very well.
  4. Oct 30, 2012 #3
    Actually, I think that is a good way to formulate it. The ratio between the kinetic energy and rest mass energy is related to velocity, and approaches infinity as velocity approaches c. Infinite ratio can only have a realistic meaning with zero mass.

    But in general I do not like light speed limit explanations that involve energy at all. For me there are more convincing reasons that explain the limit. The math quite obviously says that it is impossible to have a reference frame with a velocity above c relative to some other reference frame. No need to involve any energy.

    The best argument for me is the division of spacetime into distinct regions by any event's lightcones. I find the classification of event pairs into spacelike separated, timelike separated and null-separated that is independent of actual reference frame chosen to be a very beautiful aspect of the theory. Especially the possible relation with causality seems to be very interesting. Namely that spacelike separated events can not be causally related, putting a limit not just on literal "travel" but also on information transfer or any kind of interaction or dependance. That gives birth to the concept of locality, etc.

    [edit: I will explain in more details if you want, but for now I will assume you are familiar with these concepts and not bother you with possibly redundant explanations.]
    Last edited: Oct 30, 2012
  5. Oct 30, 2012 #4
    For the purposes of this explaination you are in motion and I am a stationary observer. 1 second (bold) is what I see when watching the tick of my own clock. 1 second is what I see when watching your clock tick.

    The most intuitive way for me to think of it is in terms of 4 velocity. It is a fundamental law of nature that all things travel at the same rate through space-time. The conversion rate between spacial dimensions and the time dimension is 299,792,485 meters = 1 second. The spacial dimensions are all at right angles to the time dimension so you could simplifiy the thought to motion along one space dimension and one time dimension. Total motion through space-time is always 1c. If you have a spacial velocity of 0 then your time velocity is 1 (second per second). If your spacial velocity is .5c then your time velocity must be about .866 (second per second). This is just the pythagerian therom. 0.52+.8662=12.

    If you try to accelerate to the speed of light you run into a problem. Acceleration is change in velocity per unit time. The faster you are traveling through a space dimension the slower you are traveling through the time dimension and the more seconds tick by on my clock for each second on your clock. If you are accelerating at .1c/second then I will count more and more seconds for each .1c change in your spacial velocity. The problem will get progressively worse until I count an infinite number of seconds between .9c and 1c. Hence, you will never reach c.
  6. Oct 31, 2012 #5
    Anyway, thanks to Einstein we know what happens when anything approaches the speed of light, but this doesn't mean yet superluminal propagation is impossible. For example, absolute zero is also an asymptotic value, but negative absolute temperature can be achieved.
  7. Nov 1, 2012 #6
    No, and no.
    If you accept locality, as I explained above, then no superluminal propagation is possible. If you don't, then you lose determinism, and even logic.
    And negative absolute temperature? Just a matter of definition of "temperature", the energy is not negative and the zero temperature for such materials is nothing special with that definition.
  8. Nov 4, 2012 #7
    I would say that it is just you loosing logic based on your own knowledge. Who would say some decades ago that we would now speak about strings existing in more than 3 dimensions ? Or about Universes outside the limits of our own universe? By the way, there is intense research being carried out on superluminal propagation.
  9. Nov 4, 2012 #8

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    That is a very bad analogy. Those negative temperatures are a weird beast, a consequence of the fact that inverse temperature is sometimes a better thermodynamic variable than temperature. Those negative temperatures don't represent temperatures colder than absolute zero. They are *hot*, hotter than anything with a positive temperature. Heat flows from a substance with a positive temperature to one with a negative temperature.
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