Spacetime Definition and 1000 Threads

Been reading laymen's books on general relativity and I'm in need some clarification! ... Line 1: The shortest path from a point 9.8 meters above the surface of the Earth to another point at the same location in space but 1 second later in time. Line 2: The shortest path from a point 9.8...

I've been meaning to ask this for some time, and now I've plucked up the courage! It is puzzling to me that many fundamental relationships in GR are explained in terms of euclidean space. Taking for example the geodesic deviation equation, it occurs to me that if defined in 3+1 spacetime there...

Hello, The following has been confusing my friends and I, I want to make sure I have this clear as it is fairly elementary. (note set c = 1) Ed is falling radially into a black hole, the Schwarzschild metric is: ds2 = (1-2μ/r) dt2 - (1- 2μ/r)-1 dr2 his proper time is dτ2 = (1-2μ/r) dt2 -...

Mathematically, ##T_{\mu_\nu} = 0## ##\Rightarrow~R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 0## Now multiply both sides by ##g_{\mu\nu}## with definition of ##R = g^{\mu\nu} R_{\mu\nu}## ##R - \frac{1}{2} R = 0## ##R = 0## Is that my imagination wrong? I thought 'empty space' might not...

I am intrigued to see what spacetime curvature is like in reality. Most images or ways to imagine it tend to look at spacetime as a fabric which it is not precisely. So how would be best to imagine it... Do any of the picture demonstrate this? What is the best way to imagine it?

All Bianchi type spacetimes have metrics that admits a 3-dimensional killing algebra. They are in general not isotropic. Bianchi type IX have a killing algebra that is isomorphic to SO(3), i.e. the rotation group. But what does it mean? If the fourdimensional spacetime is invariant under the...

Hi Bear with my possible ignorant. I am puzzled over this dilemma. If General Relativity states that gravity is the curvature of spacetime, that is, no spacetime no gravity, and the cause of curvature is matter (mass), it means that if no matter, there is no gravity. I understand that...

http://arxiv.org/abs/1404.1750 How many quanta are there in a quantum spacetime? Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen (Submitted on 7 Apr 2014) Following earlier insights by Livine and Terno, we develop a technique for describing quantum states of the...

I was wondering since it is usually foliated into 2-spheres and these are not themselves parallelizable(only the n-spheres S1, S3 and S7 are). I know the timelike Killing vector field is not global, but is the a global basis of vector fields in Schwarzschild spacetime? I mean a basis in a...

Looks like the new Cosmos TV series is about to start. We'd like to keep discussions about the series in a single thread, so feel free to post your thoughts and reactions and questions in this thread. I really enjoyed the original Cosmos TV series with Carl Sagan. It was a bit over-done at...

Are there any theories or thoughts that view spacetime as 'having' a coefficient of thermal expansion... analogous to the CTE of water? An inflection with density in regards to temperature?

I know that the spacetime in special relativity is not curved and that the axis can be transformed via the lorentz transformations. I was wondering if the curved spacetime in general relativity can be transformed in such a way, and if so, how?

Could spacetime itself be a field?

This is a very basic question, but I cannot get my head around the following: Any physical system should be invariant under changes of coordinates, because these are just a way of parametrizing the manifold/space in which my physical system is embedded. Now, let us consider a system that...

Hi, I'm just beginning to learn relativity, but I have a question about why gravity is so different from other forces of nature in GR. As a start, I read that Einstein tried to find a differential geometric representation of the physical universe which represents the Maxwell equations in a...

I'm writing a sci-fi story and I'd like to make it, at the very least, scientifically plausible (in the way that alcubirre warp drives are possible assuming we could get our hands on something with negative mass which, as far as we know, doesn't exist). The basic assumption for these questions...

Homework Statement Show that the S' axes, x' and ct', are nonorthogonal in a spacetime diagram. Assume that t = t' = 0 when x = x' = 0. (Hint: use the fact that the ct' axis is the world line of the origin of S' to show that the ct' axis is inclined with respect to the ct' axis. Next, note...

Are there any theories/papers/thoughts that view spacetime as being a condensate, basically a superfluid of spacetime, akin to the Higgs field? I see the pictures and equations that describe the inflation of the (observable) universe- the curvature of spacetime... and wonder if there might be a...

Spacetime 'loaf' according to "Fabric of the Cosmos" From what I learned watching Brian Greene's "Fabric of the Cosmos" episode on Nova, if you look at spacetime like a loaf of bread, then each 'slice' depends on your relative speed compared to another point in the loaf. This I have no problem...

I am just wondering - is space-time curvature in the presence of energy-momentum ( i.e. in interior solutions to the EFEs ) always pure Ricci in nature ? I had a discussion recently with someone who claimed that, but personally I would suspect that not to be the case in general, since I see no...

Hey everyone, for anyone who saw my thread in the chemistry section you know I'm changing my view point to that of the "there are no dumb questions", and with that I have a couple of things I've been curious about for a while regarding spacetime. First off, from reading and research I am...

In special relativity we have the invariant spacetime interval ds2 = dx2 - c2dt2. If we think about classical (non-relativistic) space and time as one spacetime in which the transformation between reference frames is given by the Galilean transformation, is there a corresponding spacetime...

In non-relativistic quantum mechanics, an important set of functions are the normalized square-integrable ones. Those are functions on \mathcal{R}^3 such that \int |\Psi(x,y,z)|^2 dx dy dz = 1 I'm just curious as to whether there is some analogous concept for curved spacetime. One...

Hi I have buyed the book Spacetime physics - Introduction to Special Relativity; Second Edition. It is a great book, although I am currently only at second chapter. There are exercises with solutions in this book. The problem is, there are solutions only to odd numbered exercises. Can I...

http://arxiv.org/abs/1309.0400v2 Time and probability: From classical mechanics to relativistic Bohmian mechanics H. Nikolic (Submitted on 2 Sep 2013 (v1), last revised 30 Sep 2013 (this version, v2)) Bohmian mechanics can be generalized to a relativistic theory without preferred foliation...

Well, I'm totally in a mess now

Does the curvature of spacetime have a unit?

"The" Classical Path, QM Path Integrals and Paths in Curved Spacetime Hey Guys! I've got an exciting question! It's been burning on my mind for years, but I think I can formulate it now. It's not so much a specific question, but rather a physical story which perhaps this thread can uncover...

I understand that the speed of light can be slowed down when it passes through different mediums. I also understand that general relativity describes how space time is cured and this curvature depends on the mass of local objects and that it can influence the direction of light. So my...

Here goes a conceptual question that has been bugging me: Consider the famous eclipse experiment that shows the Sun's gravitational lensing effect, allowing a star that would otherwise be obscured by the Sun to be visible from Earth. Say an observer wanted to travel to the star from Earth and...

In special relativity, length dilation is defined as follows: X' = X0√(1 - V2/c2), where X' is the apparent/dilated length and X0 is the "proper length" Therefore proper length: X0 = X'/√(1 - V2/c2), where c > V > -c I read a book on the spacetime approach to relativity using the...

i am trying to understand the relationship between the two on a local and global scale and how these two concepts are related to the Ricci scalar. Is it correct to say that as far as we know on a global scale, spacetime is flat so that the Ricci scalar is zero. If so, what can be said about...

Ansatz metric of the 4 dimensional spacetime: ds^2=a^2 g_{ij}dx^i dx^j + du^2 (1) where: Signature: - + + + Metric g_{ij} \equiv g_{ij} (x^i) describes 3 dimensional AdS spacetime i,j = 0,1,2 = 3 dimensional curved spacetime indices a(u)= warped factor u = x^D =...

I've been thinking about the geometry of spacetime itself, and it has really been mind-blowing in some way. If space and time are so alike that we can treat them in a way that objects have a temporal extension as well as a spatial one, my question will be about this fact. So let's suppose...

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space...

Hi there. I have a dump question for you guys. I really wonder about curvature of spacetime. I read that due to Omega_tot=1 the Universe is assumed to be flat. But on the other hand something like the curvature of the universe is mentioned... I also thought that the energy stress tensor...

Something is throwing me here. No matter how fast one is going, relatively speaking, one is in the same universe as everyone (and everything) else. We're all going through the same spacetime, albeit at different velocities. You're in the same universe as I am and we both see the same space...

Question: does the physical curvature of spacetime ever "move"? Something isn't adding up with Einstein's theory--or, more likely, I'm just not understanding it correctly! How can we say that the curvatures of spacetime created by the presence of stress-energy is giving us a continuum? When I...

Firstly, I’m not a mathematician. My understanding of Einstein’s theories comes from popular science books (Cox, Greene, Gardner) so this is at the level of the ‘block universe’ model (or Brian Greene’s loaf, if that’s more familiar) and spacemen flying around the universe. So, on the face of it...

I am not quite sure what field the study of spacetime and energy would apply, considering I'm looking at it from a very, very big-picture point of view. I have a few theories and have done some math in regard to these three fields, and some of my conclusions have been quite interesting. I desire...

Suppose we have a field that is represented at each point in space by an angle that is a function of time, θ(X,t). Can we make the following identification with the electromagnetic vector potential A_μ(X,t) of a moving point charge with velocity v_x, v_y, and v_z? θ(X,t) = A_0(X,t)...

i was just reading a article that said that if the higgs boson is proven for fact, then the concept of the mass effect (spacetime pressure and curvature) would be obsolete. Is this true? i spent so much time teaching my self about SR and GR.

Mass curves spacetime. The relative acceleration of nearby geodesics of free test particles indicates the sign of the spacetime curvature. Convergent geodesics mean positive, divergent negative curvature. But also the metric expansion of space curves spacetime. The geodesics may be convergent...

I'm getting older and dumber, it seems. In his book "The Fabric of the Cosmos", from page 49, Green points out some basic vector thinking. Given a fixed speed over the ground, as you head more West of North, your speed North decreases, whilst your speed West increases. He suggests that this...

Hi, I am wondering what everyone here thinks about some of the work that has gone into researching quantum mechanics without spacetime. I am only a third year physics student at college (having done classical mechanics, electromagnetism and quantum mechanics upto perturbation theory, special...

So Newton says that gravity is an attractive force and some people believe in gravitons to transmit that attractive force, but Einstein says the attraction is actually due to moving along the curvature of spacetime (caused by the bodies' mass). I'm not asking which is correct, but my question is...

I was studying the twin paradox (of Einstein special relativity) and everything was working well until I get to the traveler's spacetime diagram. First let me introduce the paradox for you to understand the diagram. Pam is the twin sister of Joe. Pam goes out Earth in 2007 in a spaceship...

Hi, This is my first post and first of all I would like to thank all the contributors to this forum for the amazing amount of information provided here. I’m not a physicist, but I like physics (although I have only a qualitative understanding of it) and I like to smash my brain on difficult and...

http://arxiv.org/abs/1204.3672 Gauge Theory of Gravity and Spacetime Friedrich W. Hehl (U Cologne and U of Missouri, Columbia) (Submitted on 17 Apr 2012) The advent of general relativity settled it once and for all that a theory of spacetime is inextricably linked to the theory of gravity...

Author: William Lewis Burke Title: Spacetime, Geometry, Cosmology Amazon Link: https://www.amazon.com/dp/0935702016/?tag=pfamazon01-20 Prerequisities: Level: