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I had a thought the other day about a connection between special relativity and the uncertainty principle. According to special relativity, you need an infinite amount of energy to accelerate a particle not moving the speed of light to the speed of light. According to the uncertainty principle, the uncertainty in the energy involved with a process is inversely related to the timescale of the process. So an infinite fluctuation in energy would need to occur instantaneously and then disappear (?). Photons "experience" no passage of time because they have infinite time dilation. Are these concepts linked at all in a fundamental way?

Edit: I guess I was wondering if a massive particle could somehow move at the speed of light via an instantaneous energy fluctuation, at which point it would have infinite time dilation, thus extending that instant infinitely? I assume that if something like this did exist, I would've heard of it, so presumably something prevents this from occurring, but what is it? Is there something that disallows this sort of infinite energy fluctuation?

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    $\begingroup$ "According to special relativity, you need an infinite amount of energy to accelerate a particle not moving the speed of light to the speed of light." -- Only if the particle is massive. Massless particles are in fact required to travel at precisely $c$. $\endgroup$
    – zeldredge
    Commented May 5, 2015 at 23:03
  • $\begingroup$ I agree! But massive particles can be converted into massless particles via particle decay processes, can't they? $\endgroup$
    – Eli Lilleskov
    Commented May 5, 2015 at 23:18
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    $\begingroup$ @EliLilleskov no $\endgroup$
    – Jimmy360
    Commented May 5, 2015 at 23:31

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No, because you need an infinite amount of energy to make a massive particle go at light speed. Photons are massless, therefore there is no relation.

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