Spacetime Definition and 1000 Threads

Think "gravity waves", emitting from let's say a black hole. It's an uneducated hypothesis, but why not?

Please consider the following scenario: Assume we have an object (o) at rest with a mass = m. Hence, we can calculate by general relativity the gravitational force (g) on this mass. Now, assume we remain stationary, at the origin, and a velocity (v) is imparted to the mass along the...

(This problem was previously asked but poorly answered. Here is a link to the previous locked thread. https://www.physicsforums.com/showthread.php?t=202855) 1. State the problem, all variables and given/known data The star Alpha goes supernova. Ten years later and 100 ly away, as measured by...

Came across some interesting animations here...test particle orbiting a black hole: Orbits in strongly curved spacetime http://www.fourmilab.ch/gravitation/orbits/ The precession advance of Mercury [which helped confirm Einstein's theory] is described under ... The Gravitational...

what does this statement mean..?actually complete statement is-- " Einstein field equation is not very choosy about what kinds of states of matter or nongravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be...

Spacetime curvature observer and/or coordinate dependent? In another topic several people suggested that spacetime curvature is not absolute, it apparently depends on the observer and/or coordinate system. Apparently if someone goes fast (whatever that might mean in relativity) curvature is...

What proof or evidence -both theoretical or emperical - is there, that spacetime is quantized or continuous?

I have recently began to read about special relativity. I think I've got a decent grasp of how it works, but I have been confused on one point. Let's say you are in a spaceship going along at some constant velocity. If you fired a laser beam out into space you would see it moving at...

I am trying to understand the derivation of a solution of Einstein's field equations for a static, spherically symmetric spacetime (chapter 10 of Schutz's 'A first course in general relativity'). The derivation defines a static spacetime as one satisfying two conditions, one of which is that...

Is it possible to formulate a dynamical theory of spacetime geometry that isn't invariant under active diffeomorphisms? Or does requiring no invariance under active diffeomorphisms restore of gravity as a force? If yes, then it makes it difficult to disentangle the issue of active...

After reading some posts on PF, it seems that the 1st edition of Spacetime Physics by Wheeler and Taylor is considered to be the better one, having worked problems and solutions. I'm looking at a few used ones on Alibris and there's one from 1966 and a few from 1971. My question is is the one...

This has to do with the ADM formulation of GR. I am following MTW chapter 21 and Wald appendix E and chapter 10. On page 510 in MTW, they are talking about the covariant derivative on the hypersurface defined via the covariant derivative on the 4-manifold. They take the 4-D covariant...

Homework Statement Suppose on a spacetime diagram, an event happens at x=-4, t=5 and another event happens at x=0 and t=6. If there is a frame such that the two events happen simultaneously, what would the relative speed of that frame be? Homework Equations The Attempt at a...

I posted several questions on Galilean and Minkowskian spacetime on this forum lately, but I just don't seem to be able to get a real grip on things. I noticed that the core of my problems mostly arise from the definition of world lines. Therefore I tried formulating a definition of them in both...

In FRW universe, is space expanding or spacetime expanding? If the former... but I know that only spacetime can curve and expand. "Space" doesn't do that. Well?

I'm asking because some of you state that flat spacetime can't model black holes... meaning even between the Planck scale and event horizon, but yet atyy said spin-2 field in flat spacetime is equivalent to General Relativity for spacetime that is covered by harmonic coordinates which atyy...

I would like to perturb the wave-function of a localized charged particle with a potential that is close to a delta function in space and time. Do Maxwell's equations prevent such a potential in theory if not in practice? If so can I in a very loose sense think of the potential as giving the...

consider A and B particles synchronizing clocks. Immediately after that B flies off at high velocity at the same time A flashes light perpendicular to B's motion. It hits some target c. Now in A's frame the event happened after t_{a}=perpendicular distance/c. But in B's frame it happened after...

I'm trying to understand the causal structure of Minkowskian spacetime and I was wondering whether something can be said about the relation between the classification of events and curves. To clarify: for Minkowskian inner product \eta with signature (-+++), two events p and q can be timelike...

It is said that minkowksi spacetime is flat. How about galilean (Newtonian) spacetime, is it flat too? If not, what is it? It is also said that it is unknown whether there is geometry or spacetime inside Planck scale. If there is none. I can't imagine how the Planck scale without geometry can...

Hi, I have a question regarding the foliation of space-time by slices of constant "time". I know that such a foliation is possible given a globally hyperbolic manifold, and one can define a "time function" t, the level sets of which are 3-D Cauchy surfaces which foliate the spacetime. My...

Let me try to establish two things up front. First, is why I am making this post. And that is fairly straightforward: we have a pool of knowledge here that may provide clarification/refutation on some of the things covered below. Second, why do I even have a notion that the expansion is one of...

Does any of our quantum gravity theories like String Theory or Loop Quantum Gravity (what else?) answer "why" mass/stress/energy curve Spacetime? Or do they just describe it a priori? Note I'm not asking why mass/stress/energy curve Spacetime. I just want to know if there is a Quantum Gravity...

Hi, does flat spacetime + gravitons automatically lead to curved spacetime? In an old 2002 google thread sci.physics.research which is moderated...

Since it's been observed that mass causes the curvature of the spacetime continuum. I'm wondering how it curves the spacetime continuum at a distance. For example, a planet will curve the spacetime around it millions of miles away, yet all around the planet is the almost perfect vacuum of...

I've been reading up on the topic of gravitomagnetism, and how a gravitomagnetic field is created by a particle with mass moving through space the same way how an electromagnetic field is created by a particle with charge moving through space. Now I have been reading up on this topic, and...

Just a quick question on spacetime intervals in spacetime. Why is the spacetime interval between two events given by Δs^2 = -c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2, rather than c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2 (as if it were the distance between two points in four spatial dimensions)? Or more succinctly...

How viable is 8-dimensional Minkowski spacetime with the extra 4 dimensions in the imaginary plane. This is said to give mechanism for quantum entanglement because doing a Pythagorean calculations can make the distances 0. See: http://whyentanglement.com/ reviewed by Ken Renshaw Ken...

So this is problem 11.1 out of Jackson Electrodynamics: Two equivalent intertial frames K and K' are such that K' moves in the positive x direction with speed v as seen from K. The spatial coordinate axes in K' are parallel to those in K and the two origins are coincident at times t=t'=0. (a)...

The interval between two events ds^2 = -(cdt)^2 + x^2 + y^2 + z^2 is invariant in inertial frames. I was wondering, if this same interval still applies and is invariant in non-inertial frames?

Hello, Do current theories of cosmological expansion take into account the effects expanding space would have on a beam of light traveling through space? i.e. if an expanding medium of gas with constant pressure decreases the temperature/velocity of particles, would an expanding medium of...

Would the Higgs boson discovery support a 4-D spacetime model?

I am not so sure how to explain this. But when looking at sqrt( 1 - v^2/c^2 ) for time dilation. It seems to follow that you may be able to think about it as 1 = v^2 + t^2 if look at v as fraction of c, and t as the amount a clock will be dilated. Then you could think about it in your frame...

Hello PF, I have just been given an introduction to special relativity and its postulates. One of the consequences of special relativity of course is that space and time are entangled and that in order to assign a coordinate to an event, you must give it spatial (x, y ,z) and temporal...

As time is considered the 4th dimension can we say the 3-d world to be floating(advancing forward in time) in the 4D. If so is every inertial frame has is own velocity rate(moving in the time dimension) in the 4-D. When you have 3-D world if you want to bring 2 objects in contact you can bring...

I think I may have asked this question a few years ago, but I forget the responses. We know that gravity is the curvature of spacetime in the presence of mass and energy.. The curvature of spacetime was proved by experiment during a solar eclipse, whereby light from a star behind the sun was...

I am confused, how the motion of the planets we observing is circular? The motion of the every object in Spacetime is straight, but as we are watching it in 3D, it seems to be circular. What is the reason behind it? In simple words, how the straight motion of the objects in 4D(spacetime)...

It's fairly easily to visualize space bending as a result of the mass of an object, and that the bending of space is effectively gravity. But if mass always results in bending space (how else could it hold it in this universe?), is it possible that mass and the bending of space is precisely...

Is there any software or program which can plot spacetime diagrams which includes worldlines, hyperbolas, etc. given some inputs? If not. Why is there none when spacetime diagrams are very useful?

What's the present most popular consensus about non-locality and spacetime? Is it since the wave function is not something physical, there is nothing there in spacetime to be non-local about. So let's just extinguish the concept of physicality this means we just treat wave function and spacetime...

We know that we didn't go from Galilian Invariance to Lorentz Invariance by just adding length contraction and time dilation. We also added the speed limit of light as c. So Lorentz Spacetime is a completely new foundation than Galilian Spacetime. And Spacetime foliation as I understood it being...

Inside a black hole singularily, the center is pulling spacetime to it, but because the spacetime fabric inside and outside the event horizon are connected... it doesn't shear or break. But during a Big Crunch, the entire spacetime of the universe would be sucked back into the singularity and...

I have been studying up on special and general relativity lately :) But still a few things aren't clear to me (obviously) Is it energy and mass that curves it or only mass? Or putted otherway does a photon curve spacetime ?Edit: I think I figured it out, it's indeed energy that curves space and...

One can use the Principle of Extremal Aging to calculate the path of a freely moving body (in an inertial frame not subject to any forces) in spacetime, curved or flat. Why extremal? Why not just maximal? All the examples I know of involve maximum proper time for a freely moving body. For...

I try to get the gist of the Special and General theories of relativity for more than two years now. And I still don't understand if the geometrical explanation really explains or just describes what is physically going on when talking about all the relativistic effects (like gravitation, time...

Homework Statement Two friends with super-synchronized clocks. One goes on merry-go-round the other stands outside at the same point. The merry-go-round has a constant v of 45 m/s and takes 300s to go around. Find dt, ds, and dτ. Homework Equations v=dx/dt v=2πR/p using...

I (think I) understand that: 1. With the Schwarzschild metric, the ratio of proper time to coordinate time decreases ("clock runs slower") with decreasing radial distance. (And ratio of proper distance to coordinate distance increases.) 2. The geodesic path followed by a freely falling...

In a thread a while back, Mentz114 posted a Painleve chart for FRW spacetime; here's the link to the post: https://www.physicsforums.com/showpost.php?p=2985307&postcount=60 He posted the metric in Cartesian coordinates, and I've derived a corresponding metric for polar coordinates. (I'm doing...

How come a "positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space"?

If I bend a paper, it doesn't change the things written on it. If gravity is bent space(time), we shouldn't be able to detect it. (e.g. things shouldn't be dragged by it) So why are we talking about bending space, if it's not the space itself that is bending? it's only our mental...