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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What is the manifold topology of a spinning Cosmic String?
Given the following metric which is that of a rotating Cosmic String:
$$g=-c^2 dt^2 + d\rho^2 + (\kappa^2 \rho^2 - a^2) d\phi^2 - 2ac d \phi dt + dz^2.$$
can one determine the manifold topology ...
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Geometry of spacetime at different length scales [closed]
Does spherical geometry govern physics at the quantum scale?
My motivation for this question came from studying non-Euclidean geometry. When we go down from general relativistic length scales to ...
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Relativistic force correction factor for time-dilated continuous entities
How does gravitational time dilation affect the transmission of mechanical forces in a hypothetical scenario where a tether extends from a less gravitationally influenced region, like the edge of the ...
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Geometric Construction of Minkowski Space and Proper Time
In Minkowski spacetime, we define a tangent space at each point and using the metric, we calculate a real number that is the infinitesimal invariant interval between two points. This real number, ...
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Whether nonlinear coordinate transformations are symmetries of flat spacetime
I am editing this question after the answers are posted just to present my question a little clearly (without changing the main theme of the question). Moreover, this question is solely about flat ...
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Confusion with the Lorentz contraction as explained in "Introduction to Elementary Particles" by D. Griffiths
I am trying to understand how to derive the Lorentz contraction equation using the Lorentz transformations and while I know of a way to do this, I am still confused by a number of things, including ...
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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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