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According to Einstein's thought experiment, imagine a clock but this time the distance between mirrors is one Planck length $\ell_p$. If we move the spaceship (with clock on board) at velocity $v$. What is the distance that the photon wavefunction must go to reflect from the point of view of an external observer? Obviously it should be $n\ell_p,n\in\mathbb{N}$ and can't be a non-integral multiple.

By the way I'm not a physicist so I will be glad if you explain with less math.

Qmechanic
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Alberto
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    Obviously it should be n×(planck length) {n=1,2,3,4,...} and can't be for example 1.5×(planck length) From this, I am guessing that you think that spacetime is discrete, with "block "units of Planck length? I don't think there is any evidence for that, apologies if I have misunderstood you....https://en.m.wikipedia.org/wiki/Planck_length –  Aug 15 '16 at 11:41
  • Please suppose that space is discrete. Then what is the answer? – Alberto Aug 15 '16 at 11:44
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    Space(time) is not discrete in any of the currently accepted theories (supposing it is would destroy e.g. the Lorentz invariance crucial for relativistic QFT), but only in some speculative models. You'll have to be more precise about what you want to know for this question to be answerable. – ACuriousMind Aug 15 '16 at 11:50
  • I heard that in some theories like loop quantum gravity space is discrete and I realized that a discrete space can solve many problems in my mind. So my question is simple. If spacetime be discrete how can we calculate the distance the photon travels between mirrors? – Alberto Aug 15 '16 at 11:54
  • @ACuriousMind: I wanted to ask a simple question because always I can't get my answer but because you want me be more precise my original question in my head is that the time dilation formula in SR how changes when we consider quantum mechanic and discrete spacetime. – Alberto Aug 15 '16 at 12:00
  • @Alberto If the distance between the mirrors at rest is the Planck length then there exists a reference frame in which the distance between them is smaller than this. Einstein relativity just doesn't work with a minimum length scale. – Mark Mitchison Aug 15 '16 at 12:01
  • If you want to know how special relativity and quantum mechanics can be reconciled, you need to look at standard QFT, not discrete spacetimes. – ACuriousMind Aug 15 '16 at 12:03
  • Thanks for replys. I don't need a exact answer. Maybe there is no answer yet about this situation. I want just an easy analogy like Einstein clock that I can calculate and extract the formula myself. My problem is reconciling SR and QM in a discrete spacetime. – Alberto Aug 15 '16 at 12:08
  • Possible duplicates: http://physics.stackexchange.com/q/185939/2451 and links therein. – Qmechanic Aug 15 '16 at 12:14
  • No l read the link and my question is not that space is discrete or not. I know according to relativity spacetime is not discrete. My question is about theories like LQG that assume spacetime discrete. I read the wikipedia about LQG but it is very complicated (mathematically). – Alberto Aug 15 '16 at 12:24
  • This is how this site works. When you don't have the answer mark it as duplicate. Any idiot knows these questions are not the same. – Alberto Aug 16 '16 at 05:17

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