Spacetime Definition and 1000 Threads

Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units? Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR? If so, What...

Einstein showed (via general relativity) that spacetime is curved by mass, mass moves in relation to this curvature, and that gravitation arises as secondary effect. Why then are we looking for quantum gravity as some sort of mass<->mass interaction? Aren't the fundamental interactions better...

I was reading this paper (*Green's functions for gravitational waves in FRW spacetimes:* [https://arxiv.org/abs/gr-qc/9309025](https://arxiv.org/abs/gr-qc/9309025)) and I had a specific question about one statement in the paper that I would like to ask: At page 6, the author says that...

This is a very basic question, and I am not sure I have the answer. A photon goes from point A to point B, only 1 meter distance apart from each other. A spacetime diagram would show a line connecting points A and B at a 45 degree angle. This can be a right triangle with equal sides, with...

By following article a magnetic field can produce a least a minimum distortion in spacetime. If we have a inertia disk spinning 50% inside of a strong closed magnetic field may we suppose that we will create an unbalanced in the angular disc moment producing a propulsion without mass variation...

Hi, there. I am currently reading the paper, Gravitational Faraday rotation induced by a Kerr black hole (https://doi.org/10.1103/PhysRevD.38.472). After Eq. (2.4), it reads that The paper does not provide the derivation of the equations and no related reference is listed. Also, ##k^i## is not...

With one spatial dimension ## x ##, the spacetime interval between two events ## A ## and ## B ## is ## \Delta s= \sqrt{(ct_{B}-ct_{A})^{2}-(x_{B}-x_{A})^{2}} ## I have a technical question: on the plane of the graph (x,y=ct), the ordinary distance between 2 points ## A ## and ## B ## is ##...

I was reading a paper by J.M.C Montanus which was published in <low quality journal reference removed> in which he claims under AEST the new gravitational dynamics and electrodynamics are reformulated in close correspondence with classical physics, and subsequently leads to the correct...

I created a model of spacetime based on an extension I added to the principle of relativity. I then derived the coordinate transformations which preserve the speed of light in all frames, which are different from the Lorentz transformation. I worked out the formulae for energy and momentum, and...

In describing the spacetime around a massive, spherical object, one would use the Schwarzschild Metric. What metric would instead be used to describe the spacetime around multiple massive bodies? Say, for example, you want to calculate the Gravitational Time Dilation experienced by a rocket ship...

Are there any kind of observed and experimentally verified processes or mechanisms where photon emission occurs and which are directly cause by spacetime expansion in some way?

What is the mathematical definition of spacetime here?

Sean Carroll has an article (https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/) where he explains that matter can gain energy from spacetime expansion. At the end of the article, he says: In general relativity spacetime can give energy to matter, or absorb it from...

Greetings. I registered to this forum because of a particular issue regarding Gravity. I'm no astrophysicist or mathematician, i searched to find an answer, but the terminology and equations are a little much for me. I feel the best direct way is to ask people with the right expertise. It is...

While not having a professional physics background I was still interested in knowing more about special and general relativity. Therefore I was trying to find out where the space time interval was coming from in relation to the speed of light. Of course this is the first point to start I...

About a year ago, I heard Leonard Susskind discussing how entangled black holes could create spacetime. As I was listening to Prof. Susskind describe the mechanisms for creating entangled black holes, and how these black holes might create their own spacetime, it occurred to me that if we were...

Suppose you have the following situation: We have a spacetime that is asymptotically flat. At some position A which is in the region that is approximately flat, an observer sends out a photon (for simplicity, as I presume that any calculations involved here become easier if we consider a...

Here is a simple scenario where Object A and Object B cross past each other on an x-axis (for simplicity sake, let's just assume that they somehow passed each other on one spatial dimension). As they cross past each other, a photon gets released in the positive direction, and then gets absorbed...

0:00 What is spacetime? 20:20 Kinematics, basic definitions 35:18 Motion of test particles 41:18 Frequency shift of light 1:10:19 Simultaneity

Hi, The quote below has been taken from this article, https://math.ucr.edu/home/baez/einstein/node2.html, which I came across. The quote doesn't make any sense to me, especially the part in boldface. Could you please help me with it?

This topic has been discussed in the past on this forum, however there is one point that seems to be unclear. One example of the setup is the following: The universe is at a stage where all the matter is concentrated in a single black hole, except two spacecraft s A and B that orbit it far...

In the meantime: What is your answer to the question: Why Is Minkowski Spacetime Non-Euclidean?

I cannot find the paper that is referenced here https://www.nist.gov/publications/why-minkowski-spacetime-non-euclidean Why Is Minkowski Spacetime Non-Euclidean? Author(s) J M. Cronkhite I have looked here https://aapt.scitation.org/action/doSearch?SeriesKey=ajp&AllField=Cronkhite&ConceptID=...

I have read that non-inertial frames are those, where time is not orthogonal on space. Does it just mean that the speed of light is not isotropic there or does it mean anything else? How can I picture more easily this concept (for space orthogonality I just imagine perpendicularity of one axis...

I have some questions about the space of the rectangle shown in the spacetime diagram. The red and blue lines are world lines of objects at rest with each other. 1) Does the rectangle have an area? (if no please go to question 3) 2) Is the rectangle a 2d Euclidean space? (if no please go to...

On my diagram, a person is traveling in a spaceship to the right in red, which is displayed as a Minkowski diagram . At the origin (0,0) the person traveling travels by a stationary person. And the 2 blue lines are the worldlines of two blue stationary rocks. But when I try to figure out what...

We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?

I understand the mechanism of defining the curvature of a 2D manifold via triangle. But I don't understand how this works in 3D. Meanwhile, Lawrence Krauss mentioned in his book A Universe from Nothing it does. How does this work in 3D?

This is my first post so I apologize if i am in error anywhere. I recently had a thought that I have had trouble confirming. Based on the following assumptions. 1.) As you accelerate an object near the speed of light it’s mass increases exponentially. 2.) Mass warps space time. 3.) Spacetime...

Is time travel possible in Newtonian curved spacetime?

Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...

I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...

Hi, although there is a lot of discussion here in PF, I'd like to ask for a clarification about the definition of 'spatial x direction' in the context of flat or curved spacetime. Consider a set of free-falling gyroscopes (zero proper acceleration) passing through an event A with different...

Gamma is a Minkowski spacetime diagram generator. I probably started this project in August and have been working on it almost full-time since. It will be a free, open-source application. The program can draw all the usual things: axes, grids events, and worldlines, etc. It's easy to create...

i do not know if the question about entangled particles has found mainstream answers; Suppose that pairs of maximally entangled particles are shared by Bob and Alice in a time independant gravitational field. Bob measures the spin in the direction of far fixed stars. There is a direction in...

Hi, reading Carrol chapter 5 (More Geometry), he claims that a maximal symmetric space such as Minkowski spacetime has got ##4(4+1)/2 = 10## indipendent Killing Vector Fields (KVFs). Indeed we can just count the isometries of such spacetime in terms of translations (4) and rotations (6). By...

Hi, I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space. To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the...

I recently had a discussion with my brother, about what it means to "move through time". His opinion is, that physicists cannot take this literally. His opinion is, that time is just an expression for change that takes place at different rates for different observers depending on their speed...

I'm not sure how to approach this question. So I start off with the fact the path taken is space-like, $$ds^2>0$$ Input the Schwarzschild metric, $$−(1−\frac{2GM}{r})dt^2+(1−\frac{2GM}{r})^{−1}dr^2>0$$ Where I assume the mass doesn't move in angular direction. How should I continue?

Hi, my daughter saw my MTW copy on the desk and she asked me about the picture with the apple in front. To introduce her to the idea of gravitation as curved spacetime I answered like this: Consider you (A) and a your friend (B) at two different spots on a garden each with a firecracker. Take...

I’m planning to write a 2D Minkowsky spacetime diagram generator tool. At this point, I am looking for help reviewing the specification. I am not looking for help with the implemenation. To be clear, I’ve written a complete specification, but it would be a waste if it was missing features that...

There are some traps for the unwary in spacetime diagrams. I'll note a few; does anyone have more? Let me use my favorite actors, Bob and Alice. Bob is the stationary observer; Alice is the moving one. Both are in inertial frames (or however one prefers to phrase it). We look at Alice's...

I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity. https://i.stack.imgur.com/JgBDJ.jpg Before this image Rovelli writes: "It's not...

For a observer on Earth, a rocket takes Mike from Earth to Pluto with a speed of 0.82 c for 33.72 yr. Find the space-time interval for the two events such as Mike leaving the Earth and reaching Pluto considering Pluto is at rest relative to Earth for the observer on Earth. I confess that i am...

Hi. My question is described in the summary. I'm seeking some advice. The Reissner-Nordstrom solution for charged spherical bodies seems to indicate that electrostatic fields will be a source of gravitation. I've not seen anything similar for magnetic fields but I can't imagine how it could be...

Let us denote the events in spacetime before the trip has started by subscript 1 and those after the trip is over by subscript 2. So before the trip has begun, the coordinates in spacetime for A and B are ##A = (t_{A_1},x,y,z)## and ##B = (t_{B_1},x,y,z) = (t_{A_1},x,y,z)##. After the trip is...

Robert Lawrence Kuhn: It seems that special relativity suggests time is like gravity and electromagnetism, not built into the absolute fabric of reality like logic and causation. David J Gross: Yes, time is dynamical. The phenomena are dynamical and are labeled by what we call time. Including...

As per the summary I don't understand why physicists talk as if gravitons are inevitable, when gravity is just curved spacetime? Why would curved spacetime have a particle?

In a paper written by Jonathan Schaffer entitled Spacetime the one substance (https://philpapers.org/rec/SCHSTO-7) which I have not read but which I found as a reference in a book by philosopher Philip Goff, Goff suggests that matter is actually created by a curvature in spacetime rather than...

Greetings! I have misplaced my copy of Spacetime Physics by Wheeler (1966 ed/red cover) and wanted to read it again. Was wondering if there is a major difference between the earlier blue hardback?