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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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Spacetime distances and perception
My question is about how things appear in human perception vs how things are in spacetime.
Take as an example my perception of the laptop screen while I am writing this. …
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Perception of simultaneous events
I have a two-fold question about the light-cone structure of spacetime, specifically about space-like separated events. …
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Common properties of all spacetime metrics
I understand that spacetime (in GR) has many possible metrics, all of which are calculated via the Einstein Field Equations. … The Minkowski metric (from SR) is one solution of the EFEs; it is a solution of the EFEs for a flat spacetime in a vacuum. …
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What does the spacetime interval measure?
I know that the spacetime interval is the analog of the (square of the) Euclidean distance in spacetime. … Case 3: spacetime events E and F are timelike separated, and the spacetime interval between them is 5. …
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Is spacetime isomorphic to a metric space?
The label "pseudo" is due to the fact that the metric of spacetime entails not only positive distances, but also negative and null distances (resulting in the three kinds of spacetime intervals: space-like … Thus, spacetime has a very different geometry than any metric space. …
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Difference between spacetime interval and metric
I understand that the spacetime interval $(Δs)^2$ is the analog of the Euclidean distance in spacetime.
But what exactly is the relation between the spacetime interval and the spacetime metric? …
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The effects of Lorentz transformation on shape
Imagine a solid 3D cube. Now imagine that this cube is traveling close to the speed of light. To what degree will the spatial geometric properties of this object (or in general of any 3D object) chang …
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The metric of world lines in Newtonian and Galilean spacetimes
Consider a flat Newtonian or a flat Galilean 2+1 spacetime. So, mainly a flat 2D Euclidean space, evolving over time, where each time-slice is connected with the next one by a world line. …