Discrete Relativity: Measuring Planck Units

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The discussion centers on the thought experiment involving four co-moving observers (A, B, C, D) and a flash of light emanating from a central point (P). It establishes that the light obeys Lorentz invariance, reaching all observers simultaneously only if they are stationary relative to point P. The conversation challenges the notion of reality being discrete, particularly in relation to Planck units, arguing that there is no empirical basis for measuring circumference in discrete Planck units rather than a continuous model described by 2πr.

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Consider the thought experiment involving four hypothetical perfectly equidistantly juxtaposed "co-moving" observers[A,B,C,D], with a flash of light eminating from their equidistant center-point[P]:


A_________B

_____P

C_________D

The flash of light obeys what is known as Lorentz invariance, and will reach all observers[A,B,C,D] simultaniously, since they are co-moving and at rest with respect to each other.

If reality is totally discrete then the expanding circle of light that reaches all observers simultaneously has a circumference that consists of discrete Planck units, not a continuous circle described by 2*pi*radius?

How can the circumference be determined experimentally?
 
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Russell E. Rierson said:
Consider the thought experiment involving four hypothetical perfectly equidistantly juxtaposed "co-moving" observers[A,B,C,D], with a flash of light eminating from their equidistant center-point[P]:A_________B

_____P

C_________D

The flash of light obeys what is known as Lorentz invariance, and will reach all observers[A,B,C,D] simultaniously, since they are co-moving and at rest with respect to each other.
The light will NOT reach all the observers at the same time unless they are stationary relative to P (which you may have intended but did not state).

Assuming they are moving right to left, the light will reach A and C at time T1, slightly blue shifted, and will later reach B and D at time T2, slightly red-shifted. ("slightly" => depending on the speed relative to P)

As for reality being discrete, there is no reason at all to believe that it is but IF it is, there is no reason at all to believe that it is discrete in Plank units since that's just a man-made unit of measure that nature doesn't care about at all, so I don't see your question as meaningful.
 

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