Lorentz Transformation via Rotation

In summary, The easiest way to arrive at the Lorentz transformation is by rotation, using one dimension for space and the other for the product of time, the speed of light and the square root of minus one. This method is justifiable if one starts with the premise that ds^2 =ds'^2. Assuming that the speed of light is the same in both frames of reference, ds^2=0 implies ds'^2=0 (and vice versa). However, it is not clear why ds^2=ds'^2 in general and it is possible that one must find the Lorentz transformation in another way in order to arrive at this equality. Also, it should be noted that this method only works for flat spacetimes
  • #1
snoopies622
840
28
To me the easiest way to arrive at the Lorentz transformation is by rotation, using one dimension for space and the other for the product of time, the speed of light and the square root of minus one. This seems justifiable to me if one starts with the premise that ds^2 =ds'^2. I can see how if one assumes that the speed of light is the same in both frames of reference then ds^2=0 implies ds'^2=0 (and vice versa). But I don't know why ds^2=ds'^2 in general. Must one find the Lorentz transformation in some other way in order to arrive at this equality?
 
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  • #2
snoopies622 said:
To me the easiest way to arrive at the Lorentz transformation is by rotation, using one dimension for space and the other for the product of time, the speed of light and the square root of minus one. This seems justifiable to me if one starts with the premise that ds^2 =ds'^2. I can see how if one assumes that the speed of light is the same in both frames of reference then ds^2=0 implies ds'^2=0 (and vice versa). But I don't know why ds^2=ds'^2 in general. Must one find the Lorentz transformation in some other way in order to arrive at this equality?
Whatever works easiest for you!
But notice that this only works for flat spacetimes.
 
  • #3
ict was popular 100 years ago. It has lost fashion, because it can't be extended to GR, and it complicates relativistic QM, with two different i's.
 
  • #4
Thanks to you both. I didn't realize that ict wouldn't work for non-flat spacetimes, but I guess it would yield a complex ds^2 (and who wants that?).
 

1. What is Lorentz Transformation via Rotation?

Lorentz Transformation via Rotation is a mathematical formula used to describe the relationship between space and time in the theory of special relativity. It involves rotating coordinate systems to account for the effects of time dilation and length contraction on objects moving at high speeds.

2. Why is Lorentz Transformation via Rotation important?

Lorentz Transformation via Rotation is important because it helps us understand how time and space are relative and interconnected. It allows us to accurately describe the behavior of objects moving at high speeds, and is a fundamental concept in the theory of special relativity.

3. How does Lorentz Transformation via Rotation differ from other transformation formulas?

Lorentz Transformation via Rotation differs from other transformation formulas, such as Galilean transformations, because it takes into account the principles of special relativity, including the constancy of the speed of light and the relativity of simultaneity. It also includes a rotation component, which allows for the proper alignment of spatial and temporal coordinates.

4. Can Lorentz Transformation via Rotation be applied to any type of motion?

Yes, Lorentz Transformation via Rotation can be applied to any type of motion, as long as the objects are moving at speeds close to the speed of light. It is particularly useful for describing the behavior of particles in high energy physics experiments.

5. Are there any real-world applications of Lorentz Transformation via Rotation?

Yes, Lorentz Transformation via Rotation has a wide range of real-world applications, including GPS technology, particle accelerators, and space travel. It is also used in various fields of physics, such as astrophysics and quantum mechanics, to accurately describe the behavior of objects moving at high speeds.

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