Spacetime Definition and 1000 Threads

Author: Sean M. Carroll Title: Spacetime and Geometry: An Introduction to General Relativity Amazon Link: https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20 Download Link: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html Prerequisities: Contents: Contents: 1...

Author: Edwin F. Taylor (Author), John Archibald Wheeler (Author) Title: Spacetime Physics Amazon Link: https://www.amazon.com/dp/0716723271/?tag=pfamazon01-20 Prerequisities: Contents:

I know that mass warps spacetime and that's basically the force of gravity (warped spacetime), but why does mass warp spacetime? Is it because mass implies energy and energy warps spacetime? If so, then why does energy warp spacetime?

I have done quite a bit of research regarding the subject of spacetime, but what I want to know is, what was the reasoning behind it? I understand the subject and agree with it, but I want to know how Einstein came about the idea.

In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?

The way I understood spacetime, we think of spacetime being its own entity, with which matter interacts, the way there is water in an aquarium wether there are fish or not inside it and the fish then interact with that medium. Couldnt it be possible, that rather than spacetime being its own...

I was wondering if someone wouldn't mind offering me an explanation as to the differences between a flat spacetime versus a conformally flat spacetime (if there even is a difference).

Homework Statement I am trying to derive the line element for this geometry. But I am not sure how to show that ds can't contain any crossterms of d\theta and d\phi Homework Equations ds must be invariant under reflections \theta \rightarrow \theta'=\pi - \theta and \phi...

Consider a mode of vacuum zero-point energy at a point in space. Its energy E is related to its frequency f by E = \frac{1}{2}h f. In terms of the mode oscillation period \Delta t the energy is given by E = \frac{1}{2}\frac{h}{\Delta t}. Now let's us imagine that \Delta t becomes smaller and...

Homework Statement A Spaceship is moving with speed ß=4/5. Its length at rest is 1sec. A light is turned on at the rear of the ship, reflected back from a mirror at the front. a.) How long does an observer at rest say it takes for the light to return to the rear of the ship (total round...

Hi, I have to write a spacetime line element for the shape of a cube of cosmological dimensions. This cube is expanding like this: i)With time, the cube becomes elongated along the z-axis, and the square x-y shape doesn't change. ii)The line element must be spatially homogeneus. (I don't...

While simultaneity conventions for inertial frames in flat spacetime (SR) are non-controversial, numerous questions, discussions, and debates in this forum indicate how confusing and controversial notions of simultaneity can be for more general cases. A couple of formal and true answers are...

Hi friends what are intrinsic properties of spacetime ? curvature & torsion ? or they are just properties of connections ? Since in teleparallel gravity we consider them as properties of connections. thank u

is spacetime not the same as space and time ?? please explain what's the difference between "spacetime" and, space and time ? i heard space has it's own properties and time has it's own properties but "spacetime" has completely different properties. Please explain. Thanks

Quantum mechanics in 1 + 1 dimensions is equivalent to qft in 0 + 1 dimensions. This is because the position x(t) of a particle can be replaced by a scalar field \phi(t) , and the momentum is replaced by the momentum conjugate of \phi(t) . Also, in the bosonic construction of heterotic...

The concept of spacetime ripping or breaking (down) is common in science fiction, but does it have any basis in real physics? Inside the singularity of a Black Hole, it seems that spacetime is stretched infinitely by gravity (conjecture, but a common belief, right?), but could it be possible...

So, I read an article yesterday about a potential design for a spacetime crystal. The idea behind a spacetime crystal/4-dimensional crystal is pretty interesting and I'm curious to know what others think about them/this...

Hi, this isn't really a homework problem... but I'm just wondering I see the time axis as c*t, now people say that its to scale the time axis so that the world line of light is 45 degrees. But if you were to multiply time by the speed of light, wouldn't you just get the units metres or...

Hello, Can anyone explain to me the next settence, found http://relativity.livingreviews.org/open?pubNo=lrr-2011-7&page=articlese16.html in section 1.4: "The causal structure of the Green’s functions is richer in curved spacetime: While in flat spacetime the retarded Green’s function...

Homework Statement Imagine that your boss is on the Earth-Pluto shuttle which travels at a constant velocity of 0.60 straight between Earth and Pluto a distance of 5.0 h in an inertial frame attached to the Sun. An hour into the flight (according to your boss’s watch) your boss sends a laser...

Hello: I would like to understand how to compute the shape operator (and eigenvalues etc) for a complex example like the Schwarzschild spacetime. It's easy for a submanifold in Euclidean space, but I don't know how to do it for the more advanced examples like the schwarzschild spacetime in...

"simplified" spacetime and Emc2 vs Quantum Theory I tried to post this in the textbook or homework section but it kept saying i was not allowed? So, to attempt to keep to the rules of the site i will ask my question but also try and start a discussion to try and keep things interesting. Ive...

I've wanted a visual aid to the curving of spacetime and I can't seem to find one. What I am thinking about would be a 2D simulation of a 3D grid, a matrix, made up of evenly spaced lines. Initially, it would simulate flat spacetime, composed of cubes with grid lines at all the...

I was wondering how spacetime could be relative and quantized. It doesn't make sense to me. I am especially interested in how this works in causal dynamical triangulation. I think it is a very interesting theory, and it sometimes doesn't get enough credit. But, I can't understand how at a tiny...

Hello, everybody. I have some doubts I hope you can answer: I have read that the n+1-dimensional Anti-de Sitter (from now on AdS_{n+1}) line element is given, in some coordinates, by: ds^{2}=\frac{r^{2}}{L^{2}}[-dt^{2}+\sum\limits_{i=1}^{n-1}(dx^{i})^{2}]+\frac{L^{2}}{r^{2}}dr^{2} This can be...

Homework Statement How does one actually solve the integral for the Wightman function for a massless quantum scalar field in 4D Minkowski spacetime? That is, what is the integration technique to go from: \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \int_c d^4k \, \frac{1}{(2 \pi...

What's being curved, when mass bends the "spacetime continuum?" Okay, I've read lots of books about Einstein's spacetime being curved by mass and all, but I've never read a really good hypothesis as to what, exactly, is being curved. You can't curved nothing (sounds like a double negative, but...

I understand that the Wilkinson Microwave Anisotropy Probe has made observations of the angular size of early fluctuations in the Cosmic microwave background. As the observed angular size is the same as the expected angular size it seems that light traveling to us from those early fluctuations...

I was wondering about this question when I was reading my new book The Universe in a Nutshell by Stephen Hawking and the images in the book depict space time as a linear fabric. I don't understand how this could be if the sun has a spherical gravitational pull, as we see at the very outermost...

i recall einstein idicating that there was no longer a reason to posit an aether after special relativity was published, but later wrote a short paper indicating that there was, in effect, an aether after all. ref -...

Internal symmetries of the SM -U(1), SU(2), SU(3)- are usually said to belong to abstract spaces unrelated to spacetime symmetries, have there been many attempts to relate internal symmetries to spacetime symmetries, and if so how far have they gotten?

Apologies if this is the wrong topic, but I think it's relevant under GR since it involves curved space time and I can't see it applying to Newtonian systems. I found an article about swimming in space by deforming one's body. This should not be possible according to my understanding of...

I'm studying the Milne Universe in two dimensions. The metric is similar to that of Rindler spacetime, but with time and space inverted. ds^{2}=-dt^{2}+t^{2}dx^{2} The Carter Penrose diagram of this spacetime would be the same of Rindler spacetime?

The (0,0) and (r,r) components are: g_{00}= -e^{2\phi},g_{rr}=e^{2\Lambda}. From the first component, combined with the fact that the dot product of the four velocity vector with itself is -1, one can find in the MCRF, U^0=e^{-\phi}. What does this mean? In the MCRF, the rate of the two clocks...

Since two observers with coinciding origins at t=t'=0 both measures a light wave to be moving at c they will both claim that r^2= (ct)^2 and thus that r^2-(ct)^2 = 0. Thus r'^2 - (ct)^2 = r^2 - (ct)^2 = 0 which is really just stating that 0=0 for events following the spherical wave off...

Hi there: I've learned that there's no such thing as gravity, just the curvature of spacetime that makes objects that are close to each other act like it existed. Does Higgs Bossom discovery tell us that there is a gravity force after all?

We talk about space time as a fabric. Does it have mass?

Hi all, I don't know much about physics other than what I've read about it and learned from an introductory astronomy course. I've been told to imagine spacetime like a rubber sheet that bends in when you drop something with mass on it, and I've seen diagrams of how this works. What I have...

I think that it is correct to say that everywhere, spacetime is expanding. Is it expanding within the radius of electrons within atoms? Are the radii getting larger over time? I believe it correct that the distance from the nucleus to an electron exceeds the diameter of either one by...

Homework Statement The spacetime interval between the origin in frame S and an event, A, is found to be r = 8 lightseconds. In frame S' moving in Standard orientation with respect to S at speed v = 0.5c event A is measured at a distance r' = 6 lightseconds from the origin. (a) What is...

So we often see visualizations of what the space time curvature of a black hole looks like, as in a funnel. http://www.astrosociety.org/pubs/mercury/9802/images/embedding.gif But are there any predictions or observations of space time curvature looking like a really steep mountain whose peak...

Hi, I was wondering if anyone could clarify something for me. I have been reading about the curvature of Spacetime and have come across a few things in articles in conjunction with de Sitter and Anti de Sitter spaces "Negative curvature corresponds to an attractive force" and "Positive...

There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation). Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?

Hello forum! I would like to begin by stating that I am no expert in general relativity, nor in physics or mathematics, although I have some basic understanding of calculus and linear algebra. So if you can keep the math simple, I would appreciate. Also, please correct me if I'm wrong. As...

This is several questions crammed together because they overlap in my mind. Thanks! Is the Higgs Field something that occupies the complete void of space, or is it thought to be a property of space itself? Was the Higgs Field caught up in the mass of the pre-big bang singularity, or would...

Somone in these forums linked to this and I finally got around to reading it and wanted to share the ideas: What do you think of the overall description...and last paragraph?? Why?? http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/ [Mostly quotes but I...

Howde all. With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang. Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies. Lets say now that...

well yeah i understand that in general theory of relativity is about bending of space time. but why does the bending of spacetime itself is not relative? i mean look at these photos, why does spacetime was bended that way? why not sidewards? why not on top? just want to know why. thanks :)

If gravity does not act directly on objects, rather it distorts nearby spacetime, objects falling towards a massive object are just following the geometry of the distorted spacetime. Why is light ray not-so-readily following this distorted spacetime? The "straight line" light ray travels should...

I am new to the topic of special relativity. Having read a bit of Feynman and googling for answers I am still a bit lost. While I have an aptitude for logic, it does not extend quickly into physics or maths. So quite likely I am barking up the wrong tree and about to demonstrate my ignorance but...