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Prophylaxis
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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.
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.