Galilean transform and Lorentz transform questions

In summary, the Galilean transform relates the positions of two objects in different rest frames, while the Lorentz transform takes into account the effects of special relativity. Both transformations can be used to switch between the rest frames of two objects, but they are not interchangeable. To practice questions about Galilean transforms, you can try searching for practice problems online or consulting a textbook on classical mechanics.
  • #1
rgtr
92
8
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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  • #2
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).
 
  • #3
Thanks for that clarification. Any idea where I could practice a few questions about Galilean transforms?
 

FAQ: Galilean transform and Lorentz transform questions

What is the difference between Galilean transform and Lorentz transform?

The Galilean transform is a mathematical equation used to describe the relationship between the position, velocity, and time of an object in different reference frames. It assumes that time and space are absolute and do not change. On the other hand, the Lorentz transform is a mathematical equation used in special relativity to describe the relationship between the space and time coordinates of an event in different inertial frames. It takes into account the fact that time and space are relative and can be affected by the speed of an object.

How do the Galilean transform and Lorentz transform differ in their predictions?

The Galilean transform predicts that the laws of physics are the same in all inertial frames, regardless of their relative motion. This means that the speed of light is constant and time and space are absolute. However, the Lorentz transform predicts that the laws of physics are the same for all observers moving at a constant velocity, but the speed of light is always constant and time and space are relative.

Can the Galilean transform and Lorentz transform be used interchangeably?

No, the Galilean transform and Lorentz transform cannot be used interchangeably. The Galilean transform is only valid for objects moving at low speeds, while the Lorentz transform is used for objects moving at any speed, including the speed of light. The Lorentz transform also takes into account the effects of time dilation and length contraction, which are not accounted for in the Galilean transform.

What is the significance of the Lorentz factor in the Lorentz transform?

The Lorentz factor, denoted by γ, is a mathematical term that appears in the Lorentz transform equation. It represents the factor by which time, length, and mass change for an object moving at a high speed. It is also used to calculate the time dilation and length contraction effects predicted by special relativity.

How do the Galilean transform and Lorentz transform impact our understanding of space and time?

The Galilean transform assumes that time and space are absolute and do not change, while the Lorentz transform takes into account the fact that time and space are relative and can be affected by the speed of an object. This has significant implications for our understanding of space and time, as it shows that they are not fixed, but rather, can be influenced by the laws of physics and the observer's frame of reference.

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