Spacetime Definition and 1000 Threads

Suppose we use fractional derivatives (https://en.m.wikipedia.org/wiki/Fractional_calculus) in GR, hence we have a local group symmetry ##SO(3-\epsilon,1+\epsilon)## does any reference exist about an equation for ##\epsilon## ?, since it could depend on coordinates too.

My project for obtaining my master's degree in computer science involved ray tracing in Schwarzschild spacetime in order to render images of black holes. These light rays had to be computed numerically using the geodesic equation. However, I ran into a problem. The geodesic equation is given as...

Look at the paper in the link below: https://link.springer.com/content/pdf/10.1007%2Fs10701-016-0026-7.pdf It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed...

Some physicists, like Nima, Ed. Witten, Gross, and others have said/suggested that space-time is doomed, or emergent from something more fundamental. What ideas would replace space-time? Something similar to a perfect material? A fluid? Geometry? Quantum field theory of some sort? Entanglement...

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Schwarzschild Spacetime Continue reading the Original Blog Post.

In a recent thread, the following was posted regarding the "no hair" theorem for black holes: In the arxiv paper linked to, it says the following (p. 2, after Theorem 1.1): "Hawking has shown that in addition to the original, stationary, Killing field, which has to be tangent to the event...

I assume this forum to be the appropriate one, since the real problem is about covariance rather than electromagnetism. In electrodynamics in a curved background, the relation ##F^{\mu \nu} = A^{\mu , \nu} - A^{\mu , \nu}## stays in terms of ordinary derivatives. So, in particular ##F_{,\mu...

The geodesic for 2-D, 3-D are straight lines. For a 4-D spacetime (x1,x2,x3,t) what would be it's geodesic.?? The tangent vector components are ##V^0=\frac{∂t}{∂λ} , V^i=\frac{∂x^i}{∂λ},i=1,2,3## & ##(\nabla_V V)^\mu=(V^\nu \nabla_\nu V)^\mu=0,(\nu,\mu=0,1,2,3)##

Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.

Hi, I've written a script-based spacetime diagram generator. I have no idea if it has any value for anyone besides myself—you may have access to better tools than I do. When I looked for spacetime generators, I only found some very limited web tools and one downloadable program that wasn't much...

Published in the peer reviewed Journal of Applied Mathematics and Physics is the intriguing paper with the following abstract: https://file.scirp.org/Html/11-1721242_88041.htm "Entanglement and the tunnel effect phenomena have been repeatedly observed and are generically accepted under...

Though it is hard not to believe in the spacetime curvature that cause planets to follow curved path arround massive objects, I wander how come these paths are eliptical, the object change velocity when moving arround the massive object and what is more obeys the Keppler laws. If there is not...

Can anyone recommend me good books on the topics of Spacetime Hypersurfaces and Foliations of Space Time?

In reviewing one of Einstein's thought experiments, the accelerating elevator in space, and the resulting bending of light passing through the elevator, Einstein's predicted that light will bend in gravity. Now Einstein's original prediction was off by a factor of 2 because he hadn't yet...

I'm wondering if the galactic rotation curves could be attributed to a deviation of the metric of spacetime from the ideal Schwarzschild metric. The Schwarzschild-metric is a well tested good approximation for the regions near the central mass - but at the outer space, far away from the...

I am under the impression, there is no unique solutions to Einstein's field equations for a cosmological constant, or for higher dimensional spacetimes. Has anybody got a counter example for a solution including the cosmo constant to show there are multiple solutions, for example, i know of the...

I imagine Earths gravity well as a vibrating bubble, vibrating because all the other planets disturb it , then the galaxy as a seething mass of bubbles, then gravitational y bound galaxies as conjoined bubbles, I know this may be wrong but I can not imagine any thin else. What does 4D space...

As per my intro post, I don’t consider myself to have any science background beyond high school education. In a philosophy thread about time on City-Data Forum, where most of the entries are just general unscientific musings, I saw the following post: “Time is a distance in spacetime: v =x/t...

I've tried to find the answer to this but I can't I know what we experience as gravity is the bending of space by the mass of the Earth. But, a gyroscope is able to defy the Earths bending of space. Does a gyroscope on a small scale bend space perpendicular to the Earths bending and that's why...

Hi, There is a point that, in my opinion, is not quite emphasized in the context of general relativity. It is the notion of spacetime coordinate systems that from the very foundation of general relativity are assumed to be all on the same footing. Nevertheless I believe each of them has to be...

Hi everyone! Sorry for the bad English! I do understand (or at least I guess I do) that there's no universal clock and time in other worldlines may be dilated in relation to my worldline. What I don't get is why the spacetime must be a "finished" block and not an " open ended towards the...

Basic level thread here. If gravity "bends" the spacetime continuum, do a strong permanent magnet bend spacetime too? I'm no physicist, I'm layman, and I just don't know how this "bending" of spacetime works when a Jumbo jet is in free fall from 10 thousand meters high, pulled by Earth's...

Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space? $$ 1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...

I am revisiting the invariant interval spacetime issue , as explained in the book Spacetime Physics by E.F. Taylor and A. Wheeler. The explanation is clear and the invariant interval is correct, based on the data given and this is the whole point I am making, as explained below. In a...

Tldr: relative to what are we traveling through spacetime at the speed of light. It must be relative to something not moving through space nor time, which doesn't exist. (And possibly light, not sure though because light doesn't experience traveling through time) I understand we are talking...

I have a very quick question about the maximally extended Schwarzschild spacetime. I know you can't reach regions III and IV from I and II, and vice versa. But can you see in? If I'm in region I and I look down, the null paths reaching me originated in the white hole singularity. Likewise in...

Vacuum or dark energy have energy densities. (Markus, a science advisor at Physics Forums in 2003, estimated that dark energy has an energy density of about 0.5 Joule per cubic km.) I assume that the structure of space-time has an energy density, that it was measured and that it can be...

Hi. Would it be possible (at least in principle) to use the spacetime perturbance caused by the energy-momentum of a photon (or any other particle) to figure out which way it took in a double slit experiment? Can this question even be answered in today's attempts at quantum gravity?

<Moderator's note: Several threads merged and moved to cosmology.> So I’m wondering about gravity. I was under the impression that gravity was created due to the curvature of 4d spacetime and whatnot. Can someone explain to me what gravitons are in relation to that? Are the gravitons making...

Is it possible for two plains of parallel spacetime to exist separated by some sort of void? One being antimatter and one being matter with the void bringing neutral territory. Like a piece of paper between two big magnets.

Last night I was pleasantly surprised to discover that, given a particle trajectory x^2 - c^2t^2 = a^2 when viewed through a Lorentz transformation x' = \gamma (x-vt) t' = \gamma (t - vx/c^2) produces exactly the same shape x'^2 - c^2t'^2 = a^2 . I suppose this is equivalent to the...

In GR Mass is said to curve spacetime which is the explanation for Gravity versus Newtonian physics where it is explained as all matter attracts each other. My question is how does curved spacetime cause objects traveling at different velocities to follow different paths? If gravity was only due...

A long time ago, someone told me that Einstein thought spacetime is "smooth and continuous." Quantum mechanics is a proven fact. Quantum mechanics exists in spacetime, though. So can we at least conclude that spacetime is not continuous, and instead discrete? ...quanta of space and time...

Hello, can anyone show me if this integral can be evaluated? ##\frac{1}{a_0^2}\int_\Sigma\frac{dy'dz'}{\bigg(y'^2+z'^2+\tfrac{1}{(2a_0)^2}\bigg)^2}##

Hello, I have difficulty in evaluating this integral. Can anyone assists? $\frac{1}{a_0^2}\int_\Sigma\frac{dy'dz'}{\bigg(y'^2+z'^2+\tfrac{1}{(2a_0)^2}\bigg)^2}$

According to Minkowski, spacetime for non-accelerated systems is a four dimensional continuum which has four axes (three space, one time) set mutually at right angles to each other. The velocity of a body moving in a straight line will be the resultant of the component velocities along the...

I have read that the velocity of a body through spacetime is equal to 'c'. Can I therefore draw a spacetime velocity diagram (triangle) with sides: "v" velocity through space...

I have seen the equations relating energy, momentum, pressure/stress to the metric tensor and the curvature of spacetime, as I’m sure most people have. But what is the mechanism? I’ve read an interpretation in Quora (horrid source, I know) where energy and stress are basically “pushing” space...

It's been a couple of years since I've posted here, and am trying to get back into learning SR. I wanted to start with a general question: You often hear the phrase "we are moving through time". I've also seen space-time described many times as like a block. Another way I've seen it described is...

This is a refinement of a previous thread (here). I hope I am following correct protocol. Homework Statement I am studying Spacetime and Geometry : An Introduction to General Relativity by Sean M Carroll and have a question about commutators of vector fields. A vector field on a manifold can...

Homework Statement I am studying Spacetime and Geometry : An Introduction to General Relativity by Sean M Carroll and have a question about commutators of vector fields. A vector field on a manifold can be thought of as differential operator which transforms smooth functions to smooth functions...

So the gravitational field has energy and momentum, and so you can never have a spacetime with an energy stress tensor set to 0. Is this like a constant then? that you can calculate for a portion of spacetime with no "stress energy tensor"?

...why do people like Stephen Hawking talk about things/events "before" the Big Bang? If time (as part of spacetime) was created with this event, it also marks the point in time that had no "before", doesn't it?

Are there any theories in physics that allow for a time component of the various vector quantities besides the x,y,z components? For example the velocity of a particle to have a time component ##v_t## besides the x,y,z components ##v_x,v_y,v_z##

Some models of gravity, inspired by the main theme of spacetime fabric of Classical GR, treat the metric of the manifold and the connection as independent entities. I want to study this theory further but I am unable to find any paper on this, on ariXiv atleast. I will be very thankful if...

If the Milky Way's halo is displaced supersolid dark matter, and the state of displacement of the supersolid dark matter is referred to geometrically as curved space-time, then is the Milky Way's halo the physical manifestation of curved space-time?

These two ideas seem to be categorically opposed. The concept of an event as a point in spacetime seems to not square with uncertainty and the concept of quantum intrinsic randomness seems to not square with unchanging spacetime... Assuming it is unnecessary to explain further why this is a...

If a black hole that is feeding is actually ingesting the spacetime around it (and hence whatever may lie in that spacetime including light) what does it do when it is not ingesting but nonetheless has very strong gravitational attraction? Does it sit there dragging empty spacetime into it? If...

If I understand spacetime correctly, if you max out the "space" component (travel as fast as possible), you will travel at the speed of light (speed of causality) and time will stop (or nearly stop) advancing for you.. but what if stopped completely? so you stayed stationary in the exact x y z...