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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Linearity of Lorentz Transformations from Principle of Relativity

Many derivations of the Lorentz transformations assume they must be linear maps on $\mathbb R^4$, where we identify the components of $\mathbb R^4$ with orthogonal coordinate systems associated to ...
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Considering below metric, find out $V_{r;θ;φ}$−$V_{r;φ;θ}$ for any arbitrary 4-vector $V^v$ , and how to interpret the result.? [closed]

Considering this spacetime metric, $$ds^2 = g_{\mu\nu} dx^\mu dx^\nu = \left(1 − \frac{r_g}{r}\right)c^2 dt^2 − \left(1 + \frac{r_g}{r}\right) dr^2 − r^2 dθ^2 − r^2 \mathrm{sin} ^2θ dφ^2$$ . Where $r{...
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How to compute volume of universe? then how to show that $k= 0$, $1$, and $-1$ corresponds flat , closed and open universe

Using the matric $$ds^2 = g_{\mu\nu} dx^\mu dx^\nu = c^2 dt^2 − a^2(t)(\left( \frac{1}{1-kr^2}\right) dr^2 − r^2 dθ^2 − r^2 \mathrm{sin} ^2θ dφ^2)$$ . where a(t) is scale fector . This is one of my ...
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How are spatial coordinate systems in physics defined?

Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
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Why does time seem to flow only in one direction? Does it have a dimension?If yes, then how will we express the dimension of time diagramatically? [duplicate]

The spacetime in relativity, follows the 3+1 formalism , I wonder whether time is a dimension or is it something else. I do not agree that we move in time. I think time is stationary. Probably , ...
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Kruskal coordinates from GR field equations

The "usual" way (as I've seen in most text books) of dealing with Schwarzschild spacetime is to start with Schwarzschild coordinates, then explore the nature of coordinate singularity at $r=...
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When we say that the universe is expanding, what is causing this?

I could understand an initial explosion imparting momentum to matter but where is the energy stored in space itself? How does empty space have momentum that causes this expansion?
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About the gravity field around a lightbeam [duplicate]

Imagine there is an infinitely long beam of light. It has impulse and energy. How it affects the spacetime surrounding it? Will masses be pulled towards it perpendiculary and pulled in the parallel ...
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What are the solutions of these time-travel thought experiments based on the known space-time? [closed]

(non-English questioner, sorry for any grammar issues, tried my best) WE HAVE TWO IDEAL TIME MACHINES: A modified Dragon capsule. We make a half-year time-travel; Case F: to the Future, and Case P: ...
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How does a static electric field behave in curved spacetime?

Imagine a simple capacitor of two parallel plates with a static electric field between them. This capacitor is oriented in a gravitational field such that the space between the plates is parallel to ...
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How does spacetime curvature "CREATE" gravity? [closed]

See, I am having a hard time understanding that how spacetime curvature works. Well, I am a beginner in astrophysics so kindly add full details in the answer and a figure too if possible. Also how ...
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Define absolutely NOTHING prior to the initial singularity before the inflation of space-time [duplicate]

British physicist Stephen Hawking stated "There was absolutely nothing before the Big Bang". Not only him Einstein and most of reputable scientists said that there was nothing before the ...
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How is it possible to have a quantum wave function used by quantum cosmology describing early stages of our Universe without time being considered?

In quantum cosmology a quantum wave function is used to describe the early stages of our Universe rather classical spacetime. However, the probability distribution does not depend on time. How is such ...
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Would I be able to tell if I was inside a piece of distorted space? Are objects distinct from spacetime?

If one could hypothetically stretch / squash / in some way distort a piece of space, an outside observer could tell by looking at the distorted object/space that it had changed because the difference ...
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If spacetime can expand faster than the speed of light, then can a black hole do that too?

I have read this question: Yes, the expansion of space itself is allowed to exceed the speed-of-light limit because the speed-of-light limit only applies to regions where special relativity – a ...
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What is the lower bound on the dimension of the LOCAL imbedding of a General relativistic Lorentzian manifold in a pseudo-Euclidean spacetime?

What is the lower bound on the dimension of the LOCAL imbedding of a General relativistic Lorentzian manifold in a pseudo-Euclidean spacetime? Imbedding is Isometric embedding to me. What about these ...
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Existence of time [duplicate]

what is time? is time only the change of position? Because we set a standard of 24 hrs and call it a day, but it is actually a change in position of the earth around its axis, similarly 365 days are ...
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Does vacuum spacetime have an inherent curvature?

I am a complete novice in physics beyond the high school level, so please excuse anything wrong in my question. So I have recently read that according to General Relativity, the presence of mass in ...
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Confusion interpreting the meaning of the different terms in Lorentz transformation while deriving time dilation

Let us have the familiar Lorentz transformations, given by : $$\Delta t_{s'}=\gamma\left(\Delta t_s-\frac{v\Delta x_s}{c^2}\right)$$ $$\Delta t_{s}=\gamma\left(\Delta t_{s'}+\frac{v\Delta x_{s'}}{c^2}\...
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Can one define a flow of spacetime?

One often reads things like, 'At the event horizon, the flow of spacetime exceeds the local speed of light.' But is this actually correct? Can you mathematically define some sort of spacetime flow ...
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Possible spin values in general $(p+q)$ dimensional spacetime

As far as I know, the reason particles can have only integer and half-integer values of spin, is because our $3+1$ dimensional spacetime transforms under the Lorentz group $SO^+(3,1)$, and the Lorentz ...
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Is it experimentally verifiable if we are a inside a white hole that never fully formed?

There are a lot of questions on this site about white holes, but none of them specifically answer my question. Most of these questions talk about observing white holes from outside, but do not talk ...
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If we find a star exploding 100 light years away, that means it happened 100 years before? [duplicate]

So can someone please help me with this? Can someone make the answer as simple as possible? So my question is if we see a star exploding like 100 light-years away, that means that star exploded 100 ...
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Is time intrinsically complex? Does it have an imaginary component? [duplicate]

In twin paradox, there is an unaccounted area in the unaccelerated frame of its Space-time diagram when one frame's simultaneity is being mapped to the other; ergo period motion of pendulum in one ...
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Clarification on the words timeslice and spaceslice

I just want some clarification what the words timeslice and spaceslice mean. In so many books and papers in higher-level physics the say something like "at a constant timeslice". Does this ...
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Is Universe expansion means that speed of time flow is increasing?

The massive objects compresses the space-time around themselves and it leads to slow down the time. If we are moving with speed that is close to speed of light, we are moving through much amount of ...
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Why would spacetime curvature cause gravity given that the value of gravitational time dilation is so small?

In this question, mpv provides the clearest explanation of the operation of gravity in his answer: The apple moving first only in the time direction (i.e. at rest in space) starts accelerating in ...
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How will the volume of a box change when it is moving?

Suppose, the length, breadth, & height of a box are all equal, it has the shape of a cube and volume $V$. Now, if the box travels at uniform speed $v \gt 0$, then the length $L_0$ will become $L$, ...
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Why does everyone say that the faster you move through space, the slower you move through time, when that's not the case?

Suppose, I'm on earth and my brother is moving away from earth at a constant speed, $v=0.8c$. Now, if 5 seconds $(t_0)$ pass for me, the amount of time that will pass for my brother according to me ...
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Gravitational waves on rigid bodies

I have a question on gravitational wave (GW) detection. I would assume that gravitational waves do not impact rigid bodies. I mean, GWs should be extremely weak with respect to electromagnetic forces ...
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Geodesically complete spacetime

By definition, a spacetime is geodesically complete if all inextendible curve are complete but is this equivalent to «if all geodesic of finite length has endpoints»? My situation is: I have a set of ...
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How do massive objects bend spacetime if space is just an empty being?

According to general relativity, space and time are interwoven to form the fabric and mesh of spacetime. But if space is an empty void thing and time is also not a physical substance or concept, then ...
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Does a uniform gravitational field exist? Is there any acceleration in a uniform gravity field?

This question arose in the Space Exploration forum, by non-physicists, so it likely sounds naïve. The question involved the plausibility of using a very strong gravitational field to accelerate an ...
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Does "correcting a clock for gravitational perturbations" mean calculating the sender rate and attributing the sender rate to the sender?

Experiments which are interpreted in terms of "gravitational red- or blueshift" generally involve a sender $S$ (or a sample $S$ of individual senders), and a receiver (sample) $R$, which ...
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When do we say that a given clock could be further corrected?

In a recent report on experiments with a sample of ultracold ${\rm {}^{87} Sr}$ atoms, T. Bothwell et al. (physics.atom-ph:2109.12238), the abstract ends and culminates in the following punchline: &...
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Euclidean space to Minkowski spacetime

Can you continuously deform (i.e., shrink, twist, stretch, etc. in any way without tearing) four-dimensional Euclidean space to make it four-dimensional Minkowski spacetime?
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Fourier transform of $\delta^3(\vec{x} - \vec{v} t) $

In "Classical Eletrodynamics" of Jackson, chapter 13.3, it is said that using the Fourier Transform: \begin{equation} F(\vec{x}, t)=\frac{1}{(2\pi)^2} \int d^3 k \int d\omega \hspace{0....
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A star is just born and starts travelling towards us at 99 percent speed of light. So how would an immortal observer observe the light from it?

An immortal observer is observing a new born star from billions of lightyears away travelling towards it at near the speed of light (99%). The star is a short living one and dies soon before reaching ...
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Is the speed of light the limit or just everything moves at this speed?

When I was a little kid, I was fascinated by the fact that we are not able to surpass the speed of light. I imagined a giant spaceship trying to catch a light beam like superman tries to catch flash. ...
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How does gravitational time dilation affect matter?

Einstein successfully melded together space and time into one entity called spacetime in his General relativity theory and gave us further insight into how matter affects spacetime. John Wheeler said “...
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A Question About the Surface of a Black Hole Singularity

In Kip Thorne's book, Black Holes and Time Warps, he states that the mass of the core of a star shrinks until quantum gravity takes over. And then discusses that at this distance, the singularity ...
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Scaling of null vectors

By definition any vector with $g_{\mu\nu}n^\mu n^\nu = 0$ is a null vector. For simplicity let's look at flat spacetime. Is there any physical difference between two null vectors like these two? \...
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Black holes with no space-time or no space-time only (metric)? [closed]

It is generally accepted that a black hole can be defined as a trapped surface or region of space-time where gravity is so intense that light can not escape. Another definition is that a black hole is ...
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Doubt regarding Space-time Grids [duplicate]

I had a doubt regarding space-time grids... I just don't understand, if the universe is three-dimensional (excluding the time dimension) why do we represent the universe as a single 2D fabric of grids ...
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Arguments for the dimension of space [duplicate]

I would like to collect arguments whose conclusion indicate that the dimension of space cannot be anything. For example, the existence of non-trivial knots implies that the dimension of space is $3$ (...
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Did gravity exist before the Big Bang?

Gravity is one of the biggest mysteries. It is the weakest of the 4 fundamental forces but we have no clue how it works. Einstein never was able to figure it out in his lifetime. There is evidence ...
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How can time slow down and speed up for a particle simaltaneously?

Suppose there's a kangaroo baby in its mother's pouch and there's a light bulb 300,000 km from them. If someone turns on the bulb, both kangaroos will agree that the light bulb takes 1 s to turn on ...
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The effect black holes have on light

We all know that light loses its energy when it is moving through expanding space and time. And sense a black hole can be summed up to a super compressed space time, shouldn't that mean that a photon ...
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Is electromagnetism caused by curved spacetime? [duplicate]

They talk about gravity being due to the curvature of spacetime. Does this also apply to electromagnetism, if so why and if not what's the difference?
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Why objects always have to move under gravity? [duplicate]

I saw the exact same question here but the answer is beyond my limited knowledge. Gravity is not a force as general relativity explained. then why an object always has to move along a geodesic? I mean ...

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