Galilean Relativity & Inconsistency with Classical Physics

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SUMMARY

Galilean relativity transformations lead to inconsistencies in classical physics when applied to the expansion of a light sphere. The transformation equations, specifically x2 = x1 - vt1, y1 = y2, z1 = z2, and t1 = t2, do not hold true under the conditions of light propagation as described by the equations x12 + y12 + z12 - ct12 = 0 and x22 + y22 + z22 - ct22 = 0. The substitution of these transformations reveals contradictions, particularly when comparing the terms involving time and the speed of light, indicating a fundamental flaw in applying Galilean principles to relativistic scenarios.

PREREQUISITES
  • Understanding of Galilean transformations
  • Familiarity with the equations of light propagation
  • Knowledge of Lorentz contraction and its implications
  • Basic grasp of classical physics principles
NEXT STEPS
  • Study the implications of Lorentz transformations in special relativity
  • Explore the concept of simultaneity in different reference frames
  • Investigate the mathematical derivation of the speed of light as a constant
  • Review the differences between classical and relativistic physics
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Students of physics, particularly those studying relativity, educators explaining the inconsistencies between classical and modern physics, and anyone interested in the foundational principles of light propagation and reference frames.

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Hi, I am a novice here and i am trying to solve the following problem:
1.Show that Galilean relativity transformation produces inconsistent classical physics result when used with equation of expansion of light sphere. (2 different frames)



2. x2 = x1 - vt1
y1 = y2
z1 = z2
t1 = t2

expansion of light sphere: x12 + y12 + z12 - ct12 = 0
x22 + y22 + z22 - ct22 = 0



3. I have substituted the Galilean transformation equations in the later expansion of the light sphere equations:
x12 + y12 + z12 - ct12 = 0
x22 + y22 + z22 - ct22 = 0

x12 + y12 + z12 - ct12 = 0 = x22 + y22 + z22 - ct22

x12 + y12 + z12 - ct12 = x22 + y12 + z12 - ct22

x12 - ct12 = x22 - ct22

x12 - ct12 = (x1 - vt1)2 - ct22

x12 - ct12 = x12 - 2vt1 + v2t12 - c2t22

So far I have not been able understand the inconsistency and it's bothering me. I do know about Lorentz contraction, but don't know where the inconsistency is? Is there something wrong with my thought process? Thanks in advance.
 
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Hey,

An interesting problem, anyone have a solution to it?

Thanks,

-PFStudent
 

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