All Questions
10
questions
0
votes
1
answer
54
views
Proof of the invariance of $c$ using the Lorentz group
Apologies if this question was already asked a few times but i could only find proofs of the invariance of $ ds^2 $.
Is there any way of proving the 2nd postulate (that $c$ is invariant in all ...
- 309
2
votes
1
answer
776
views
The value of speed of light in different regions of spacetime
This question of mine started shaping in my head first while I was looking for the most fundamental answer for the speed of light's value and its property of being the limit.
I have convinced myself ...
- 23
0
votes
3
answers
200
views
Is it possible to prove from relativity that massless things have proper time of zero?
Is it possible to come to the conclusion that something massless has proper time of zero, thus moves at $c$? I have seen many arguments for why moving at the speed of light means proper time is zero, ...
- 1,261
2
votes
3
answers
444
views
Why does $ds^2=0$ for a light signal's worldline in general relativity?
I know that in special relativity, the invariant interval $ds^2$ for a light signal's worldline is $$ds^2=\eta_{\mu\nu}dx^\mu dx^\nu=0$$ where the flat metric $\eta_{\mu\nu}=\text{diag}(-1,1,1,1)$.
...
- 4,235
1
vote
2
answers
1k
views
Is the magnitude of the four-velocity vector in spacetime arbitrary?
I know that the squared magnitude of the four-velocity vector is plus or minus $c^2$, but I’m a little confused on whether or not this vector has been normalised arbitrarily, since it is often claimed ...
- 2,123
0
votes
1
answer
415
views
Difficulty in understanding the three classes of events of light-cone
Recently I'm reading Chapter 2: Space and Time of A Brief History of Time. The paragraph that follows the light cone says:
Given an event P, one can divide the other events in the universe into ...
- 103
2
votes
1
answer
80
views
Is spacetime defined mathematically without using $c$ speed?
Is there a mathematical definition of spacetime that does not use $c$ speed as a conversion factor or involve the spacetime interval? If not why?
3
votes
2
answers
3k
views
Why is $ds^2=0$ along the path of a light ray in any spacetime, in any reference frame, specifically non-inertial?
In the Minkowski spacetime of special relativity it is apparent that along the path of a light ray $ds^2=0$ in any inertial reference frame given the Lorentz transformations and the invariance of $ds^...
- 281
2
votes
1
answer
538
views
Deriving the Minkowski Metric from homogeneity of space-time and the isotropy of space
In this wikipedia page, it says that one can derive the spacetime interval between 2 arbitrary events from the second postulate of special relativity, together with the homogeneity of spacetime and ...
- 504
17
votes
3
answers
3k
views
Proving invariance of $ds^2$ from the invariance of the speed of light
I've started today the book of Landau and Lifshitz Vol.2: The Classical Theory of Fields $\S 2$. They start from the invariance of the speed of light, express it as the fact that $$c^2(\Delta t)^2-(\...
- 171