Questions tagged [spacetime]
Within relativity (both special and general), changes of reference frames can change both the notions of space and of time, with one depending on the other as well. As a consequence, it is necessary to treat both concepts in a unified manner. Hence the term spacetime.
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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
$$
...
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How to motivate that in presence of gravity the spacetime metric must be modified to $ds^2=g_{ab}(x)dx^adx^b$?
In the presence of a gravitational field, the spacetime metric, $$ds^2=\eta_{ab}dx^a dx^b,$$ should be changed to, $$ds^2=g_{ab}(x)dx^adx^b.$$ What are the convincing physical arguments that motivate ...
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Is there a location in the universe with the minimum rate of time dilation?
According to general relativity, time dilation occurs due to strong gravitational fields and high relative velocities, causing time to pass more slowly compared to observers in weaker gravitational ...
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Apparent paradox in general relativity wrt relative gravity, spacetime curvature and time dilation [closed]
Imagine Alice is near a massive black hole and Bob is on the Earth.
Obviously their gravitational fields are different for each other. In other words, their spacetime is flat for themselves but curved ...
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Clarification on Representing Distances and Trajectories in Minkowski Spacetime
In the context of Minkowski spacetime, where the metric has a signature of (-, +, +, +), the $x-t$ plane (spacetime diagram) is commonly used to visualize events and their evolution in both space and ...
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Train example of special relativity
My friend Eric is at the center of the train. The train is moving forward. The front end and back end of the train flash a light at the same time. From Eric's perspective, both light arrives at him at ...
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Implications of quantized space (a la LQG) on defining "realistic" number systems [duplicate]
Disclaimer: not a professional physicist or mathematician, so (deserved) tomato-throwing is welcome.
I've been pondering the "naturalness" of real numbers for some time now, in the sense of ...
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Does the Weyl tensor amount to tidal effects of gravity?
The Ricci tensor, for the spacetime surrounding the Earth, is zero, so the spacetime around the Earth is Ricci-flat.
The Riemann tensor though is not zero since spacetime certainly is curved. This ...
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Relativity explained using sound instead of light
A friend of mine asked me to explain Einstein relativity to him, and I tried to use a methaphore using sound, however for some reason it does’t quite work:
imagine there are 2 people with a clock, ...
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Regarding the signature of special relativity
in special relativity we add time as a dimension and replace euclidean space $ \mathbb{R}^4 $ with a pseudo-euclidean space $ \mathbb{R}^{1,3} $ of signature $ (1,3) $ by defining a quadratic form $\...
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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 ...
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Types of singularities
I am confused about the types of singularities. According to my limited knowledge there are two types of singularity. One is space like singularity ( a curvature singularity enclosed within a null ...
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How small can we measure space? [closed]
I got this question after looking into transcendental numbers and I noticed how there are some distinctions that should be made from numbers and reality especially in measurement of length for example ...
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Why does the warping of spacetime make objects move closer together?
I understand why the warping of spacetime affects moving objects, but why would it affect stationary ones if it even does? Would two completely stationary objects not move closer together because they ...
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How does null infinity differ from ordinary infinity?
Null infinity is the diagonal lines on the edge of a Penrose diagram. It seems to be the place where beams of light go if they never bump into anything, but only light can go there. It appears to be ...
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