All Questions
Tagged with spacetime inertial-frames
28
questions with no upvoted or accepted answers
4
votes
0
answers
143
views
Linearity of Lorentz Transformations from Principle of Relativity
Many derivations of the Lorentz transformations assume they must be linear maps on $\mathbb R^4$, where we identify the components of $\mathbb R^4$ with orthogonal coordinate systems associated to ...
- 3,407
4
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0
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297
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How is time "homogeneous"?
My book$^1$ states:
Let's consider a clock moving freely over a curve such as:
\begin{equation}
\frac{dx^i}{dt}=\text{const} \tag{1.20}
\end{equation}
We define the proper time $\tau$ as the ...
- 740
2
votes
3
answers
115
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How does length contraction apply while distances increase in the Lorentz transformation?
I am having trouble settling the difference between the math in the length contraction equation and the Lorentz transformation. Say there is a piece of wood traveling near the speed of light and you ...
- 21
2
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3
answers
142
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What does it physically mean for the inverse of the metric tensor of inertial frames to be the metric tensor itself?
The metric tensor of inertial frames in S.R is given by $$g_{\alpha \beta}=diag(1,-1,-1,-1)$$
It's inverse $$(g_{\alpha \beta})^{-1}=g_{\alpha \beta}$$
I was wondering what this means geometrically. I ...
- 223
2
votes
2
answers
837
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Lorentz invariance of the Klein-Gordon equation action
What I will say is not exclusively true for the KG equation, but let's take it as a simple example.
When proving the invariance of its action under a Lorentz transformation, it suffices to show that ...
- 119
2
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62
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About General Relativity and Reference Frames
So, I came up with this question which is intriguing me since a bit. Maybe it's stupid, but it's always better to ask.
The question is about inertial reference frames (I'll name them IRF)
We know ...
- 3,705
2
votes
1
answer
210
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Lorentz Factor from Minkowski's Original Paper 'Space and Time'
Consider the following figure:
Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure.
He ...
2
votes
1
answer
285
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Does curved spacetime arise from inhomogeneity of gravitational field?
In general relativity textbooks such as Sean Carroll's Spacetime and Geometry, there is often a line of reasoning that goes like this:
Strong equivalence principle states that free falling frames are ...
- 2,997
1
vote
2
answers
113
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Trying understand the argument on Special Theory of relativity on Goldstein book
I am reading Goldstein and trying to understand the special theory of relativity. I am not sure how did he make this following argument.
The books explain that $ds^2$ is invariant in spacetime. He ...
- 19
1
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0
answers
52
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Contraction of distances in explanation of relativity of simultaneity in special relativity
I was going through my old college notes on special relativity and found a reasoning that a professor used to explain why the simultaneity of events is relative. But I believe there is a mistake in ...
- 293
1
vote
1
answer
58
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Why does light change its path in different frames of reference?
A similar question has previously appeared on this site:
Light in Different Reference Frames
But my question is slightly different in nature. The difference would be clear after a read of this ...
- 161
1
vote
1
answer
89
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Synchronizing clocks
In special theory of relativity, While deriving the Lorentz transformation equations we use spherical electromagnetic waves which start at $t=0$ when the origins of the two reference frames are ...
- 21
1
vote
1
answer
96
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"If something moves while you are measuring its length, it does not represent its length": why?
In minutepysics, while explaning length contraction, it is stated that
If something moves while you are measuring its length, it does not represent its length
Question:
Why?
I, somewhat, know ...
- 2,283
1
vote
2
answers
99
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What happens to the light you see as a far away object approaches you with constant velocity?
A rocket ship 1000 light years away from me approaches me with a constant velocity. At first the light i see is 1000 years old and the ship is closer than it appears. Later the difference between the ...
- 11
1
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0
answers
145
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Space and time variant? But together invariant?
I admit I'm having difficulty with spacetime. I don't understand how unifying space and time, seemingly variant quantities, results in an invariant spacetime. All texts and references talk about using ...
- 435