Lorentz Transforms: Question About Inverting LT Frames

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In summary, the conversation discusses constructing a transformation (LT) from an un-prime frame to a prime frame and then to a double prime system, followed by inverting the first transformation and substituting it into the second. It is noted that this process does not result in the same transformation as directly going between the double and single prime frames. The question is asked about the velocity used in going from S' to S'', and it is explained that the relative velocity of S' and S'' is not simply v'' - v'. The conversation concludes with the realization that the SRT addition of velocities must be used.
  • #1
exmarine
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If I construct a LT from an un-prime frame to a prime fame: S':=LT(S,v') and another to a double prime system: S":=LT(S,v"), then invert the first: S:=LT(S',-v') and substitute it into the second: S":=LT([LT(S',-v')],v"), I do NOT get the same transform as going directly between the double and single prime frames: LT([LT(S',-v')],v") ≠LT(S',[v"-v']). Does this question make any sense? What am I missing?

Thanks.
 
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  • #2
When going from S' to S'', what velocity did you use?

Realize that if v' is the relative velocity of S and S' and v'' is the relative velocity of S and S'', then the relative velocity of S' and S'' is not simply v'' - v'.
 
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  • #3
Oh? I thought it would be v"-v'. What is it then?

Thanks.
 
  • #4
Ok, I get it. I have to use the SRT addition of velocities. Thanks!
 
  • #5
exmarine said:
Ok, I get it. I have to use the SRT addition of velocities.
Right!
 

1. What are Lorentz Transforms?

Lorentz Transforms are mathematical equations that describe how space and time coordinates change from one frame of reference to another. They are a fundamental part of Einstein's theory of Special Relativity.

2. Why do we need to invert Lorentz Transforms?

Inverting Lorentz Transforms allows us to go from one frame of reference to another, and then back again. This is important because it allows us to compare measurements from different frames of reference and understand how they relate to each other.

3. How do you perform an inverse Lorentz Transform?

An inverse Lorentz Transform is performed by taking the inverse of the matrix that represents the original Lorentz Transform. This involves taking the transpose of the matrix and then dividing each element by the determinant of the original matrix.

4. What are some applications of Lorentz Transforms?

Lorentz Transforms are used in many areas of modern physics, including particle physics, cosmology, and GPS technology. They are also important in understanding the behavior of objects traveling at high speeds, such as space shuttles and satellites.

5. Are there any limitations to Lorentz Transforms?

Lorentz Transforms are only accurate for objects moving at constant speeds in a straight line. They do not account for acceleration or curved paths, and therefore cannot be used for objects in non-inertial reference frames. Additionally, Lorentz Transforms only apply to objects moving in a vacuum, and do not take into account the effects of external forces such as gravity.

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