Questions tagged [spacetime]
As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.
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Is time relative because of the difference in distance traveled by the light inside the light clock [closed]
Are space and time then directly connected? Can someone just explain to me how the math translates this intuition or correct my intuition of the concept through the same thought experiment with the ...
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Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed
This is one of the exercises on Wald's General Relativity:
Chapter 8, Problem 8.b Find an example of a closed, achronal set $S$ in Minkowski spacetime such that $J^+(S)$ is not closed. (Hint: ...
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Expressing curvature invariants ($K_1, I_1, ... $), at any one event, through Synge's WF $\sigma$ (given of each event pair, in a suitable region)
Considering a set $\mathcal S$ of events such that for each pair $p, q \in \mathcal S$ Synge's world function $\sigma$ is defined and the corresponding value $\sigma[ ~ p, q ~ ]$ is given, and such ...
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Another dimensions [closed]
Just a science ponderer, and pretty much interested in physics. Please guide me if I am wrong.
There have been many statements made by the physicists about the existence of other dimensions (...
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Relationship between spacelike and timelike distances in General Relativity vs. Special Relativity
In Minkowski spacetime, the distance $d_S$ between two space-like separated events $x$ and $y$ can (up to constant) be given by a distance between the two time-like separated events $z$ and $w$ where $...
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Spatial separation in analogy to time separation in Lorentzian geometry?
O'Neill (Semi-Riemannian Geometry With Applications to Relativity, 1983, p. 409) defines time separation between two events as follows:
"If $p, q \in M$, the time separation $\tau(p, q)$ from $p$...
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Questions about E. Minguzzi's article on Synchronization (arXiv:1009.3005)
Only recently I learned of E. Minguzzi's article
"Clocks' synchronization without round-trip conditions", [gr-qc: arXiv:1009.3005] ...
(Notably, the article available for download is dated ...
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Since we observe stars, galaxies, etc in their past - is it correct to say that our present is only present for us but is in the past from afar? [closed]
So - I know that when we observe galaxies, we are observing their past. And that if the same past-them were to be looking at us, they would see our past. But when we look at their past - that is a ...
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How comes that we use space and time together in one manifold?
I know and understand that the speed of light is constant in vacuum. It's been the experiment of Michelson amd Morley that took us to this finding.
I know and understand Einsteins special and general ...
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Chose coordinates where $g_{01}=g_{02}=g_{03}=0$ to disentangle space and time?
$g_{\mu\nu}$ is the metric tensor. It describes the curvature of spacetime in general relativity. The choice of coordinates is completely arbitrary. It should be possible to find and chose coordinates ...
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When doing general relativity in practice, how do we choose the appropriate manifold describing the scenario?
The theory only deals with the local curvatures, not the global topology. Hence any manifold with an allowed metric is allowed. These can be infinitely many, especially for negative curvature space-...
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Is it possible to describe every possible spacetime in Cartesian coordinates? [duplicate]
Curvature of space-time (in General Relativity) is described using the metric tensor. The metric tensor, however, relies on the choice of coordinates, which is totally arbitrary.
See for example ...
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The limit of GR with infinite speed of light $c$
Just answer what you can. I don't mean the zero curvature flat space time version. I know that the Einstein Field equations use $c$ as a constant, but what would the universe be like if gravity was ...
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Books/resources for the study of non-flat spacetime shadows
I'm preparing a research paper (and possible review) on shadow calculation in asymptotically non-flat spacetime. I have been searching the internet for some references and the only thing I found was ...
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Compactification of Minkowski spacetime
I'm studying Ray D'Inverno's book "Introducing Einstein's relativity". I'm having trouble understanding Fig. 17.7 (pag. 236), which is an illustration of compactified Minkowski spacetime. ...
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According the theory of general relativity, what is the role of causality in the changes of the curvature of spacetime? [closed]
In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes ...
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Is it true to say that there is a single electric field and it is inhabited by and affected by all charges in the universe? [closed]
I don't see why or how this could be argued against or if it really matters, but that's why I ask the forum.
I am just trying to understand the nature of the fields in the universe. Am I correct in ...
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Is curvature localised in General Relativity?
Is the curvature of spacetime in General Relativy localised?
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How do we know the geometry of our physical world is made from real numbers and not rational numbers? [duplicate]
If I draw a line on a paper from point a to point b, how do we know that each point on the line exists in the real space, and not the rational space? How do we know if I randomly draw a dot, it won't ...
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Difference between timelike vector and causal vector
I don't understand the difference between time like vector and causal vector.(Are they same???)
\ My Knowledge : Time like vectors lie inside a light cone and null vectors lie on light cone. I came ...
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How to get metric tensor components?
I was wondering how do we get the components of the metric tensor? Why, in euclidian 3D space, the metric tensor is represented like this :
$$
g_{\mu\nu}=\left[\begin{matrix}1&0&0\\0&1&...
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Static spacetime and metric invariance
I'm studying General Relativity using Ray D'Inverno's book "Introducing Einstein's relativity". I don't understand what the author writes in paragraph 14.3 ("Static solutions") ...
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Isotropy of space doubts
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we ...
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Physical meaning of each component of the metric tensor in GR
I am searching, without success, what is the meaning of each component of the metric tensor in the context of General Relativity.
$$
g_{\mu\nu}=\left[\begin{matrix}g_{00}&g_{01}&g_{02}&g_{...
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Space expansion or generation [duplicate]
When physicists assert that space is expanding, does this imply the creation of new space? If so, why do they use the term "expansion" instead of "generation"?
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Can energy redistribution Influence Spacetime Warping According to General Relativity? [duplicate]
I have a question regarding the interplay between modern technology and Einstein's general theory of relativity. According to Einstein's theory, the warping of spacetime is directly related to the ...
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My question learning gravity [duplicate]
so einstein told us two things: number one matter curves spacetime so if you put the earth on you assume so einstein said assume that there is a curved sheet or a curved rubber sheet and if you put ...
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Homogeneity of space doubts [duplicate]
This question might have been asked so many times, but here we go again. I'm wondering what homogeneity of space means. All the descriptions say:
there's no special point in space, every point looks ...
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How does the covariant derivative satisfy the Leibniz rule?
In Carroll's "Spacetime and Geometry", he states on page 95 (section 3.2) that the covariant derivative, $\nabla$, is a map from $\left(k, l\right)$ tensor fields to $\left(k, l+1\right)$ ...
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How to relate Riemannian and Lorentzian tetrad fields on the same manifold/spacetime?
Consider Gibbons and Hawkings paper wherein a Riemannian metric $\overset{\mathcal{R}}{g}_{\mu\nu}$ and everywhere well defined normalized line field $l_{\mu}$ on spacetime $M$ may be used to ...
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Why doesn't Galilean relativity lead to a contradiction in SR?
Two identical spaceships commanded by Alice and Bob are at rest next to each other in outer space. The clocks of the spaceships are synchronised; and when they are close by Alice can see Bob's clock ...
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Lectures on wormholes
I am currently writing a review as a thesis project and I must cover black holes and wormholes, static and stationary. For black holes I found this lecture where black holes are approached from a more ...
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Where does the negative signature case come from in the Pythagorean derivation of distances in spacetime?
I am reading Why does $E=mc^2$ (and why should we care?) by Brian Cox and Jeff Forshaw. I want to understand these three sentences
(from page 76/77):
Once we follow Occam and make these two ...
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Time dilation query 2 [duplicate]
The examples for the theory show that The clock run faster or slower and show time interval, not that the time itself does not differ in two frames one is in motion relative to other. Then, what is ...
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Time dilation query [closed]
In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an ...
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What exists in the world according to the special relativity? [closed]
Before I learned about special relativity, I thought that only one 3-dimensional state of the world exists. Then, like in game of chess, in one "turn" previous state is destroyed - and the ...
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Differences and similarities between $\mathbb{R}^4$, $\mathbb{R}^{1,3}$, $T_p\mathbb{R}^4$, and $T_p\mathbb{R}^{1,3}$
Consdier $\mathbb{R}^4$ with Cartesian coordinate and $\mathbb{R}^{1,3}$ with spacetime coordinates. Also consider their corresponding tangent spaces $T_p \mathbb{R}^4$ and $\mathbb{R}^{1,3}$, ...
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Are branes topological defects? How else could they be physical?
As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But ...
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Internal and external Einstein equation from warped spacetime metric
If I have a $D$ dimensional manifold, with Einstein equation
$$R_{MN} - \frac{1}{2}g_{MN}R = T_{MN}$$
and, as a solution, a warped metric, with d external dimension (denoted using greek indices $\...
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Geometrically Impossible Spacetime
A result in math says that $S^n$ carries a Lorentzian metric iff $n$ is odd.
Using it we can observe that a 2-sphere spacetime is impossible, a 3-sphere spacetime is geometrically possible, but again ...
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Energy and momenta of a field on a curved manifold
In a curved spacetime with metric $g$, let us have a complex scalar field $\Phi$. The stress energy momentum tensor of the field is defined as,
$$T_{ab} := \frac{-2}{\sqrt{-g}} \frac{\delta S_\Phi}{\...
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What symbol is used for 'proper distance'? [closed]
Proper time and proper space are generally defined as what an observer would measure in their own rest frame. If $\tau$ is a commonly used symbol for the proper time, what is the corresponding symbol ...
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Can we see the rest-energy of a mass as its kinetic energy in the $ct$-direction?
A mass $m$ at rest has an energy $E=mc^2$. Can we say this is its kinetic energy in the $ct$-direction?
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Could the universe be a topological defect in a higher space?
I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, ...
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Does special relativity imply that there's such a thing as absolute time, or base time?
If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as "absolute time" or &...
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Why is Spacetime described as flat even though we live in 3 dimensions of space?
I’ve always heard and seen diagrams that show spacetime as being “flat” or in 2 dimensions with curvature. How does this correspond to the 3 spacial dimensions that we perceive to exist in?
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Problem with deriving the Lorentz Contraction [duplicate]
I am trying to prove the contraction. I know there are several ways one can do it. The way I am trying to solve is said to be complicated and that there is an easier way to do so. Because I don't have ...
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What is difference between an infinitesimal displacement $dx$ and a basis one-form given by the gradient of a coordinate function?
In general relativity, we introduce the line element as $$ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}\tag{1}$$ which is used to get the length of a path and $dx$ is an infinitesimal displacement But for a ...
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Lorentz Transformations derivation
I was reading derivation of Lorentz transformation but I don't understand why the constant a here is equal to -c^2.
Full pdf: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
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Is it possible to conceive concepts like a coordinate system in a completely empty space?
I am very poor at English, so I used ChatGPT to translate my question.
My question is here (Is my idea right?):
Is it possible to conceive concepts like a coordinate system in a completely empty space?...
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