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Just a quick question to help me see if my reasoning is right. The speed of light is constant from all frames of reference. So does this mean that an observer travelling at the speed and taking into consider time dilation. Does this mean that observer observes the passage of time of every other observer to be the same rate relative to theres since every observer would be travelling at the speed of light toward them.


marked as duplicate by Qmechanic Jun 18 '17 at 10:34

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    $\begingroup$ "Observers at the speed of light" - I believe it's been stated here many times here that there are no inertial frames of reference (observers) with relative speed $c$. $\endgroup$ – Hal Hollis Jun 2 '17 at 19:27
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/16018/2451 and links therein. $\endgroup$ – Qmechanic Jun 2 '17 at 19:40

You're going to get the usual objections that we can't answer except in the limit as one goes faster and faster; obviously for massive entities like us actually attaining the speed of light is off-limits.

As one gets moving faster and faster (relative to some space-permeating lattice of clocks which are equidistant to each other and in sync in their coordinate system, say), many things happen:

  1. Everything that they can see "crowds into" the point right in front of them, except for the single point immediately behind them.
  2. The lattice also appears to be length-contracted; at higher rapidities $\alpha$ the speed these things are coming towards you is approximately a constant $c \tanh \alpha \approx c$ but the distance between them goes to zero like $\ell / \cosh \alpha.$ Therefore you appear to be passing more and more and more of them per second of your time.
  3. These two effects of the stars wanting to tilt "forward" and the things you're passing flying backwards past you seem to meet up at a definite distance behind you: your uniform acceleration effectively creates an event horizon at a fixed distance behind you; things which pass you appear to fall towards this and redshift into stasis rather than fully disappear. However this wall of death is actually an effect of your acceleration and if you were to stop accelerating it would fall back further and further behind you, as the tilt "forward" stopped increasing.
  4. Clocks which appear on the lattice appear to be getting time-dilated more and more, going slower and slower.

There is, technically speaking, no "limit where one accelerates all the way to the speed of light." The problem is that everyone measures light travel at the speed $c$ in their own local coordinates, so no matter how fast you start going, you still have an infinite distance to go! I like to refer to this as a "real-life Zeno paradox".

But we can try to stretch our imagination, to try to figure out what would be happening if you took these trends as far as they may go: for example, all of the stars crowding into the one point of the sky suggests a one-dimensional existence, but all of the inter-object distances shrinking also suggests that this line is only a handful of real honest-to-goodness points. So one might imagine that one needs to think of a sort of zero-dimensional three-point existence, there is the point where the photon "is" between emission and absorption, the entire future-pointing light cone of events appears as one point in front of it, and the emission event and its past-pointing light cone of events appears as one point behind it. There is no "time" per se as the photon hops from the first of these points to the middle to the end point; there are just the two transitions where it winks into existence and winks out, and as far as the photon is concerned they just happen one after the other.

  • $\begingroup$ thanks for the answer, was far more interesting than saying observers cannot travel at the speed of light. At least now I know someone's been thinking seriously about a picture of things as observers get close to the speed of light thanks again I've never heard that description before. $\endgroup$ – 8Mad0Manc8 Jun 2 '17 at 19:47
  • $\begingroup$ @Bobs, consider adding another identical accelerated observer to the above set-up; there is never a time when one observes the other to be length contracted or otherwise affected despite both 'being close to the speed of light'. My point is that it doesn't make since to say that an observer is close to the speed of light since motion is relative. It is meaningful to talk about how two observers with relative motion close to $c$ observe each other. $\endgroup$ – Hal Hollis Jun 2 '17 at 19:53
  • $\begingroup$ At the limit where one accelerates all the way to the speed of light You know you can't do that so please rephrase it so as not to give a potentially misleading impression to the uninformed. I get what you're trying to say, but the expression makes me cringe somewhat. $\endgroup$ – StephenG Jun 2 '17 at 21:27
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    $\begingroup$ OK, I added some caveat explaining why you can't do that. $\endgroup$ – CR Drost Jun 2 '17 at 21:52
  • $\begingroup$ My first intuition when an observers relative velocity gets closer to the speed of light was that every other observer would become an equal distance from them but I dismissed this intuition and my mind turned to the observer would observe every other observer to be coming more directly toward them and there time dilation to becoming more equal to one another and given your answer about the lattice I think it may be vindicated.The Members of the lattice relative velocity to each would become more equal as the observer accelerated and got closer to the speed of light I am correct about that? $\endgroup$ – 8Mad0Manc8 Jun 3 '17 at 0:19

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