Galilean transform and Lorentz transform questions

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SUMMARY

The discussion focuses on the distinctions between the Galilean transform and the Lorentz transform in the context of relative motion between two observers, Alice and Bob. The Galilean transform is used to determine the position of one observer from the perspective of another, specifically when one is stationary and the other is in motion. The Lorentz transform, applicable in special relativity, also relates the coordinates of events in different inertial frames but incorporates time dilation effects. Both transformations allow for switching between rest frames, but they are used in different physical contexts.

PREREQUISITES
  • Understanding of classical mechanics and special relativity
  • Familiarity with the concepts of inertial frames
  • Knowledge of the equations for Galilean and Lorentz transformations
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the derivation and applications of the Galilean transform
  • Learn the implications of the Lorentz transform on time and space in special relativity
  • Practice problems involving both Galilean and Lorentz transformations
  • Explore the concept of time dilation and its mathematical representation
USEFUL FOR

Students of physics, educators teaching classical mechanics and relativity, and anyone interested in understanding the mathematical foundations of motion in different reference frames.

rgtr
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Homework Statement
I am just curious about the Galilean transform and the Lorentz Transform
Relevant Equations
## x = x'+vt ##
## x = gamma(x'+vt') ##
I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position.

If I want Bob moving and Alice stationary that is not what the Galilean transform does. Is this correct?

I have not gotten to it yet but previously have read a little bit about the Lorentz transform for position the same logic applies as above.

If I want Bob moving and Alice stationary that is not what the Lorentz transform does. Is this correct?
 
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rgtr said:
The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position.
No, it will not. It will tell you how the coordinates of an event in Alice and Bob’s rest frames relate to each other.
rgtr said:
Homework Statement:: I am just curious about the Galilean transform and the Lorentz Transform
Relevant Equations:: ## x = x'+vt ##
## x = gamma(x'+vt') ##

If I want Bob moving and Alice stationary that is not what the Lorentz transform does. Is this correct?
No. Both going back and forth between their rest frames are Galilean/Lorentz transformations (which depending on whether you do classical mechanics or special relativity).
 
Thanks for that clarification. Any idea where I could practice a few questions about Galilean transforms?
 

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