- #1
emob2p
- 56
- 1
All derivations of the Lorentz Transformations I've seen assume a linear transformation between coordinates. Why must this be the case? Thanks.
I used to say to my students that the LET should be linear because to a pair of space-time coordinates in one inertial reference frame should correspond a single pair of space-time coordinates in an other one.emob2p said:All derivations of the Lorentz Transformations I've seen assume a linear transformation between coordinates. Why must this be the case? Thanks.
That happens with any 1-1 transformation...a pair of space-time coordinates in one inertial reference frame should correspond a single pair of space-time coordinates in an other one.
of couse! in any consistent theory.Hurkyl said:LET? Oh, you mean Lorentz-Einstein transforms, not Lorentz Ether Theory.
That happens with any 1-1 transformation...
Yes, the LT is linear so that if there is no accelartion in one LF, there will no acceleration in any other LF. But, don't talk about F=ma in SR.emob2p said:So if the transformation were not linear, then an object would appear to be accelerating in one inertial frame but moving at a constant velocity in another. This would mean F=ma doesn't hold in both frames, a violation of a relativity assumption. Does that argument sound good to you guys?
emob2p said:So if the transformation were not linear, then an object would appear to be accelerating in one inertial frame but moving at a constant velocity in another. This would mean F=ma doesn't hold in both frames, a violation of a relativity assumption. Does that argument sound good to you guys?
The Lorentz Transformations are a set of mathematical equations that relate space and time coordinates between two reference frames in special relativity. They must be linear in order to accurately describe the behavior of objects moving at high speeds, as non-linear transformations would lead to inconsistencies and paradoxes in our understanding of space and time.
Linearity in mathematics refers to a relationship between two variables in which a change in one variable leads to a proportional change in the other variable. In the context of the Lorentz Transformations, this means that the equations must maintain their form and obey the laws of physics regardless of the reference frame used to measure them.
The Lorentz Transformations were derived from Einstein's theory of special relativity, which states that the laws of physics must be the same for all observers in uniform motion. By being linear, the transformations allow for the consistent measurement of space and time between two reference frames, ensuring that the laws of physics hold true for all observers.
No, the Lorentz Transformations must be linear in order to accurately describe the behavior of objects moving at high speeds. If they were non-linear, it would lead to contradictions and inconsistencies in our understanding of space and time, violating the principles of special relativity.
The Lorentz Transformations were first derived mathematically by Hendrik Lorentz and Joseph Larmor in the late 19th century. They were later refined and incorporated into Einstein's theory of special relativity. These transformations have been extensively tested and validated through experiments and observations, such as the famous Michelson-Morley experiment, which confirmed the constancy of the speed of light and the validity of the Lorentz Transformations.