Galilean Relativity & Inconsistency with Classical Physics

AI Thread Summary
Galilean relativity transformations lead to inconsistencies in classical physics when applied to the expansion of light spheres, particularly when comparing two different frames. The equations of the light sphere, which involve the speed of light, do not align with the results derived from Galilean transformations, indicating a fundamental issue. The user has attempted to substitute Galilean equations into the light sphere equations but struggles to identify the source of the inconsistency. Understanding the role of Lorentz contraction is crucial, as it highlights the limitations of Galilean relativity in explaining phenomena at high speeds. The discussion invites insights or solutions to clarify these inconsistencies in the context of classical physics.
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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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