All Questions
139
questions
2
votes
1
answer
44
views
Are non-point spacetime events partially ordered?
When describing events in spacetime, we usually use points. We then phrase the relation between points as a trichotomy: either they are timelike, spacelike, or lightlike separated, based on the ...
- 180
0
votes
0
answers
87
views
Nature of the spacetime trajectory (worldline) described by $\frac{d^2x^\mu}{d\tau^2}=0$
The covariant equation of motion of a free particle, in flat Minkowski spacetime and Cartesian coordinates, reads
$$
\frac{d^2x^\mu}{d\tau^2}=0, \tag{1}
$$
with $\mu=0,1,2,3$, and has the solution
$$
...
- 11.7k
0
votes
1
answer
177
views
How is special relativity explained by general relativity?
To be more specific about this, I am under the below assumptions and then will explain my question further. Please let me know if any of the assumptions are incorrect.
(1) Special relativity describes ...
0
votes
0
answers
60
views
How would you reparametrize a worldline in terms of proper time in 2-dimensional Minkowski spacetime?
In a 2-dimensional Minkowski spacetime i.e. $x^\mu=(t,x)$, you can define the metric simply by the Minkowski metric, $ds^2=-dt^2+dx^2$, and the Christoffel symbols vanish. If you have a worldline ...
- 51
0
votes
1
answer
104
views
In terms of gravitational waves, what terms or components are actually embedded within $h_{\mu\nu}$?
In terms of gravitational waves:
$$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\text{ with } |h_{\mu\nu}|\ll 1$$
The components of $\eta_{\mu\nu}$ are $[-1,1,1,1]$ which expresses flat Minkowski spacetime. ...
- 335
1
vote
0
answers
62
views
Visualizing CTC - is it related to a "periodic wick rotation"?
As far as I understand Wick rotation, it means the mathematical transformation $$ ct → jct $$
Where $j$ is imaginary unit. While reading on CTC (closed timelike curves) in the Gödel metric I came ...
- 421
1
vote
1
answer
56
views
Could you take a point on the surface of the earth as the frame of reference in the Hafele-Keating experiment?
I was recently reading about the Hafele-Keating experiment and asking, how does time in the plane which has flow westwards could have passed faster than on the surface of the earth if the frame of ...
- 13
1
vote
0
answers
106
views
Energy is the time component of 4-momentum in SR: Proof as per R. Wald's book
This is an excerpt fom R. Wald's book on General Relativity (page 61). I'm not able to understand how he deduces that $E$ must be the time component of $p^a$ with only the assertions made before this ...
- 107
2
votes
0
answers
100
views
Lorentz transformations in General Relativity confusion
Given a Minskowskian metric spacetime $(M,\mathcal{O},\mathcal{A}^{\uparrow},\nabla,g)$ and given two parametrized curves $\gamma:I\rightarrow M; \delta \rightarrow M$ such that they intersect in a ...
- 159
0
votes
1
answer
88
views
Radial Coordinate or Equivalence Principle: What Determines Time Dilation in Free Fall?
I have a question regarding the math of General Relativity. Let's consider an observer with two clocks attached to their head and feet. If the person is in free fall, their feet would have a lower ...
user364003
2
votes
2
answers
175
views
Do the Klein bottle and torus topologies break the Lorentz invariance?
According to this preprint, it seems that there are topologies (like the Klein bottle and the torus) that break some symmetries (like the Lorentz and translation invariances).
Is this right? Can they ...
- 2,472
-5
votes
4
answers
171
views
Is it possible to define time in a more universal way, such as, time is the outward manifestation of the activities inside an atom? [closed]
Is it possible to define time as the outward manifestation of the activities inside an atom?
For example,
one second is defined as the unperturbed ground state hyperfine
transition frequency of the ...
- 9
3
votes
2
answers
158
views
Are there non-smooth metrics for spacetime?
I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics:
Lorentz invariance holds locally in GR, but you're right that it no longer applies ...
- 2,472
0
votes
0
answers
27
views
Is it correct to say that acceleration slows the frequency of an oscillator?
My question is based on differential aging or differential timekeeping due to, 1) increased speed, and 2) proximity to center of gravitational field. As far as I know, both involve acceleration, and ...
- 1
1
vote
0
answers
170
views
Rindler Observers
In the process of transition from STR to GR, I'm trying to understand what Rindler observers actually are. Here is how one of the questions from our assignment defines them:
If the distance between B ...
- 67