Spacetime Definition and 1000 Threads

Since determining how many points there are in a given volume of continuous spacetime would require divisibility by infinity, is set theory's infinite sets the only way to model continuous spacetime? Thanks, Jake

This is probably a bad question, but can it be transformed away? Say Alice is on Earth and Bob is far away in outer space. Bob would think that Alice's clock is running slow. Alice would think Bob's clock is running fast. A third observer, say Carl, anywhere in spacetime would have to observe...

In the formula for the Unruh effect, temperature (of a photon gas mostly) is proportional to the acceleration of some classical observer. But how can that be? Temperature is a scalar, while acceleration is a vector. The cause of the effect obviously preferres one spatial direction, and Rindler...

I am working on a story where superheroes have started to appear. Their powers are all based on manipulation of spacetime and mass, and not on electromagnetism. One character is a speedster who can compress time. He can experience many seconds while everything around him experiences one...

In a recent thread, the question came up of whether the presence of gravitational time dilation implies spacetime curvature. My answer in that thread was no: This was based on the obvious counterexample of observers at rest in Rindler coordinates in flat Minkowski spacetime; two observers at...

I was watching a seminar on black holes and one of the participants threw out as an aside that spacetime could travel faster than the speed of light - so within spacetime nothing could travel faster than spacetime but spacetime itself however was not bound by this rule so it could move faster...

As I understand it, in the context of cosmological perturbation theory, one expands the metric tensor around a background metric (in this case Minkowski spacetime) as $$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$$ where ##h_{\mu\nu}## is a metric tensor and ##\kappa <<1##. My question is, how...

If Hubble's constant = 160,000 m/sec/million light years and c = 299,792,458 m/sec, then shouldn't any two points in the universe farther than about 1,873,000,000 light years apart be expanding away from each other faster than c? Since light from sources much farther than this has reached us...

The images have been taken from page no.74,75 and 76, special relativity , A.P.French,1968 I understood that A1' and C1' are not simultaneous in S -frame. But I don't understand the principle on whose basis it is claimed that A1' and C1' are simultaneous in S' -frame. Here, the simultaneity is...

I never got an answer to my original question Why can't an event where light from that event hasn't reached our present point in space and time, reach a past point in space and time in 4D space...

Can many worldlines occur in 4D spacetime where observers in each worldline think they're the "real" worldine? Is there a mechanism preventing many worldlines from occurring in 4D spacetime. Einstein said this in his book Relativity: Look at this scenario. Event A occurs outside of the light...

PLEASE BE ADVISED: I'm a complete ignorant with regards to the details of what I'm about to say and I've never looked at the mathematics of the subject, let alone understand it. So most of what I am about to say comes from pop science. Excuse me in advance if I sound stupid or rhetorical...

I am doing some mathematical exercises with 3D anti-de sitter face using the metric ds2=-(1+r2)dt2+(1+r2)-1+r2dφ2 I found the three geodesics from the Christoffel symbols, and they seem to look correct to me. d2t/dλ2+2(r+1/r)*(dt/dλ)(dr/dλ)=0...

if GR is correct about spacetime (expanding of space) then i think time travel in back (back to the past) is impossible... suppose before 2 billion years ago (from now) the total space (volume) of universe was "X" so, it's clear that the space (volume) of the present universe must be greater...

A spacetime can be foliated by spacelike hypersurfaces which are related by an isometry ##\partial_t##.1. Why is ##\partial_{t}## called an isometry of the spacetime? 2. How are the spacelike hypersurfaces related by the isometry ##\partial_{t}##?

I was wondering that consequence of curvature of spacetime caused by an entire galaxy! Can anyone suggest?

Einstein's general theory of relativity describes the stars distort spacetime fabric and it appears a black hole makes a hole in the spacetime fabric. It is evident that the size of a galaxy does not change due to gravity but in large scale the distance between two distant galaxies increases due...

According to the Einstein field equations, matter and energy both curve spacetime. I'm wondering how magnetic fields contribute to the curvature of spacetime. I have a few questions: 1. Does a magnetic field in a current-free region of a curved spacetime still satisfy Laplace's equation? Or is...

First of all, I would like to admit that my understanding of general relativity is limited, though this will hopefully be remedied this summer when I take a GR class. I think we have all seen a sci-fi movie where the characters are stuck in a space where they are trapped in a sort of "warp...

I thought this was an easy enough question but then I managed to obtain arguments both for and agaisnt it and confused myself. Is there a clear demonstrable answer to this question in relativistic field theory? Is spatial and temporal orientation a convention?

In an inertial coordinate system in two-dimensional Minkowski spacetime, the metric takes the form $$(ds)^{2} = - (dt)^{2} + (dx)^{2},$$ and in an accelerating coordinate system in two-dimensional Minkowski spacetime, the metric takes the form $$(ds)^{2} = - R^{2}(d\eta)^{2} + (dR)^{2}.$$ The...

I am a student currently taking both Multivariable Calculus and Differential Equations. Instead of a final exam my teacher assigned a final project for Multivariable, and I chose to do something with Spacetime/Black holes. Within the scope of <100 hours of work, is there anything I can do with...

The ADM formalism gives a definition for the energy (Hamiltonian) of a static, asymptotically flat spacetime. This energy can be equated to the mass of the matter (for example, a black hole) which resides in this spacetime...

I try to understand where the intrinsic spin symmetry of spacetime (ISSS) is established. I read articles but still do not understand how to put together all the information to make a clear picture of where ISSS comes from. Minkowski space - Lorentz group O(1,3) - Covering SO(1,3) with SL(2)c -...

Homework Statement Question attached My method was going to be: set ##r=R## and solve for ##n(R)## set ##r=2GM## and solve for ##n(2GM)## I was then going to integrate proper time ##s## over these values of ##r##: ##\int\limits^{n=cos^{-1}(\frac{4GM}{R}-1)}_{n=cos^{-1}(1)=0} s(n) dn ###...

It's well known that a single particle can exist in superposition, but what about the gravity of the particle? Is the gravity also in superposition? I suppose this makes it difficult to write a wavefunction, since we can't express it in terms of a field over a single spacetime. But what if we...

When the universe is expanding then why not we are expanding along with it

Specifically, what I am wondering is gravity considered to be a physical contraction of space? For instance the space between any two points A and B shrinks as gravity grows stronger. Is this the right concept?

I read somewhere here (but couldn't find the exact message) where it was mentioned the size of spacetime during the Big Bang is the same size as it is now. But the metric expands. However semantically even though the metric expands, spacetime doesn't expand. But spacetime should get bigger now...

If the world is really described by say Bohmian Mechanics or Objective Collapse. does it mean Spacetime is also objective or a substance in some way or absolutely no relationship between the quantum mechanism and spacetime? But then if no connection.. how can one have a wave function that is...

Forgetting for the moment about curved spacetime, does the relativistic QFT in use today by experimental physicists live in Euclidean spacetime or Minkowski spacetime. Thanks in advance.

Suppose we have a curved spacetime with metric g, how can we find out the path of light throughout that space?

Some motivation: It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but...

Hello! I'm having a hard time finding realistic black hole simulations, but I saw one recently (black hole size comparison on youtube) that showed the following 3 black holes (attached). I noticed that the larger the black hole, the smaller the "distortion zone" was relative to the radius of...

It seems that, in general, mathematicians prefer the (-,+,+,+) signature for the Minkowski spacetime metric while most physicists prefer the (+,-,-,-) signature. Is there any evidence that Nature actually prefers one over the other? As usual, thanks in advance.

I was watching one of the documentaries of Brian Greene (Beyond Cosmos). here at (12:00-12:10) he says.The skater spins respect to space. My question is How can space-time can be a referance frame itself ? Is it means we can just pick a coordinate and make it a referance frame ? (Sounds...

This question is regarding classical black holes. So inside the event horizon, spacetime behaves strangely. Space is now one dimensional and only in the forward direction(that is, into the singularity) and time of events is preceived as forward and backwards since light from a source comes...

Correct me if I am wrong and pls answer to my question .The 4th dimension is also known as SPACETIME.Does it mean that if we if are able to understand it and if we apply it,we can travel space and time?If Yes then, will we be able to construct TIME MACHINE and travel through time?and also...

I received a reply about the value of space time curvature. Evidently it is not zero but an almost unconceiveably small number. I was just wandering how this number was gotten.

It is my understanding that most cosmologists prefer to describe our universe in terms of space-time as opposed to simply time alone or space alone (or in discrete combination). Why is it then that when we observe a red shift in distant galaxies or stars, we describe this to a physical expansion...

In my simulation of the twin paradox, i used the Lorentz transformation formulas to map events from one inertial reference frame into another IRF. Reading through various threads here, i read that spacetime is curved and that space can be considered flat only for small distances. So my...

I was looking at null geodesics in Schwarzschild spacetime. Carroll's lecture notes cover them here: https://preposterousuniverse.com/wp-content/uploads/grnotes-seven.pdf He notes (and justifies) that orbits lie in a plane and chooses coordinates so it's the equatorial plane, then uses Killing...

In every video and educational movie that I've seen, it shows Einstein's vision of Spacetime on an XYZ graph with a fourth dimensional time, but my confusion arises because the videos then put this graph on a two dimensional plane of "Spacetime." My question concerns the visualization of this, I...

I hope I am posting this in the correct forum, I am trying to better understand space-time singularities. I can find easily the basic, and advanced information on what it is and the different theories. My main question is how do scientists study these space-time singularities? Thank you for...

Hey guys, What is the difference between spacetime, quantum field and aether? For a beginner, maybe these terms seems similar because these terms indicating "something" that which has no shape. But what are the differences exactly between these?

I'm interested in tetrad formalism for describing phenomenons near Kerr black hole. I've read some papers and I have a question about Localy Non-Rotating Frame (LNRF). In all papers is mentioned that most of astrophysically important cases are in equatorial plane (EP) and deals with EP only...

I would like to know about this: Is there a limit to how much spacetime can warp? If there isn't, can there be? If we imagined an isolated object in the universe, how much would it warp spacetime per 1 cubic meter if it had the mass of 1 kg. No other gravitational forces are acting on this...

Hi. Recently I was watching youtube about time and spacetime. And I have few questions about it. If I well understood no one knows what is the time. Here are no formulas to describe time. If it is true how we know if other watches measure time and not our perception on time which can be...

Hello! I have a question that has been bothering me since I first started learning about Special Relativity: Given only the Minskowskian metric and/OR the spacetime interval, how can one reach the conclusion that the speed of light is invariant for every observer and how can one conclude that it...

Does spacetime have potential energy, and does an object with more potential energy have more mass? (E=mc^2)