Spacetime Definition and 1000 Threads

Is it correct to say that two arbitrary charged particles in space have a spacetime separation of zero? And if so, is this the explanation for how the electrostatic force between them acts instantaneously across any 3 dimensional distance. (By "instantaneously" I mean that the force would...

If the fabric of the universe is made of both space and time, and curving spacetime affects time, then I'm guessing it also affects space. I'm aware that an object shortens in length as it approaches the speed of light. But in the case of gravity, is space relative like time? Does an object on...

I want to produce some realistic figures showing the spatial trajectories of test particles in a Schwarzschild spacetime. For instance, I'd like to start a massive test particle at aponegricon (how often do you get to use that word!?) in an orbit that Kepler and Newton would have predicted to be...

Does the mass of a spinning object twist space time? If so is this why all natural satellites orbit in the same direction as the spin of the said object?

Solutions to the Klein-Gordon equation can be interpreted as spin-0 particles of mass m and charge +1, 0, -1? See here. I think same can be said for solutions to the Dirac equation in 1+1 dimensional space-time, solutions can be interpreted as spin-0 particles of mass m and charge +1, 0, -1...

Einstein's static universe obeys ##\rho = 2\lambda##. So, attractive and repelling gravity cancel each other. I'm curious about the spacetime in this universe. Because the scale factor is constant, it seems that neighboring co-moving test particles don't show relative acceleration, thus no...

My question is related to M. Alcubierres paper on the warp drive within general relativity. I was wondering about the realizability of this, setting the three energy conditions aside for the moment. Assuming the highest energy density known to me as an energy source, namely something like...

Supersymmetry interachanges bosons and fermions and can make bosons transform into fermions and vice versa... is there equivalent in quantum gravity where spacetime and matter can transform to each other and spacetime can become matter and matter can become spacetime.. isn't something akin to...

spacetime is classical and continuous.. so when quantum system form superposition or entanglement, how is time treated esp in qft? how does spacetime keep track of the particles of fields? or how does the fields or particles able to jump in spacetime.. how is this handle in qm or qft?

The trampoline analogy tries to explain gravity in terms of space time curvature the orbit of objects around a massive object can be understood, but what about centre of gravity of the massive object, the images of trampoline is generally shown as seen from top where the massive object is making...

Is the movement of a mass affected by its curvature in spacetime? For instance will a forward moving planet diverges from its original straight line path due to the curvature of spacetime cause by it?

http://en.wikipedia.org/wiki/Kaluza–Klein_theory ##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche) http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments) Also, a lot (if not all...

How do u use quantum field theory to explain why mass warped spacetime? Is it something like spacetime is like a field and mass can only interact with it. The presence of mass excites the field (spacetime) producing graviton which distort spacetime. Is it something like that? If not can some1...

Is it something like that involves gravitons? Like mass producing gravitons that warp spacetime? All is it something like qft whereby spacetime is just a field and only those with mass can interact with it, resulting in warped in spacetime which is equivalent to excitation of fields in quantum...

According to Special Relativity, the same event could have a different time duration and a different space extension for different observers, depending on their frame of reference. Relativity subsequently introduced the the notions of Spacetime as a continuum ( as opposed to the classical...

I'm still very early on in my reading, so forgive me if this question isn't coherent. In the "historical introduction" section of the 1920 University of Calcutta translation of the original papers of Einstein and Minkowski available via the MIT online archive, mention is made of the fact that...

I was trying to make a problem simpler by working in 1+1 spacetime, and I realized that it's far from obvious that quantum physics would even work in this case. Any non-spin related phenomenon could still work (e.g. quantum scalar fields, schrodinger equation) but in less than 2 spatial...

Is it true that as you go higher in energy, from 1 eV to GeV to 10 TeV, you can probe smaller spacetime region. Since the LHC has only probed up to the 4 TeV or so, it means they have probed the corresponding tiny region of spacetime.. meaning it is still possible spacetime becomes discrete at...

First of all, I'm having a difficulty in defining what a static spacetime is. Does it presume that the objects with mass in the system are just sitting around and doing nothing, with no motion, relative to our frame, so there can be no motion and change in curvature of spacetime through time...

when do you call a spacetime dynamical...when metric is time dependent or it depends on space ??...

This may seem an odd question but it will clear something up for me. Are "The spacetime interval is invariant." and the "The spacetime metric is a tensor." exactly equivalent statements? Does one imply more or less information than the other? Thanks!

Apparently we still need spinors for the Dirac equation in 1+1 dimensional space-time. Do spinors still do "funky" weird stuff in 1+1 dimensional space-time? Thanks for any help!

I have some questions regarding Newtonian spacetime; reference is MTW chap. 12. MTW translate the Lagrange e.o.m. for Newtonian mechanics (with a potential phi derived from a mass density rho via Poisson eq.) into a geodesic equation in 4-dim. spacetime. They explicitly construct the...

Is there an attribute of spacetime that determines the curvature that will be caused by a specific mass thus resulting to the corresponding gravity? In other words: can there be "harder" or "softer" regions of spacetime where the same mass will bend spacetime less or more thus resulting to less...

What is the velocity of a person's blood flow relative to the earth?

below the speed of light we experience one axis if time and three of space. So at the speed of light the space and time unify and we get 4 isotropic axes of spacetime. 4 identical dimensions. is this correct?

A ball thrown up comes down again because the ball follows the curvature of spacetime. So is it possible that the ball comes down and before hitting the surface, goes up again due to curvature of the spacetime,which now point upward.

Homework Statement I'm not in grad school but I've been trying to teach myself some GR and I asked a professor what problems he thought would be good to study. He mentioned this one. I'd ask him for help, but he's out of town this week. I've also attached a picture to this problem. (It seems...

I'm trying to understand the concepts of physics, but there's one thing I don't fully get... If there is some matter with a spatial and temporal coordinate, let's say coordinate X, is the matter "in" that time and place, or "is" the matter that time and place? In other words, does space-time...

Is space-time flat and if the answer is yes then how can objects orbit vertically and diagonally(since gravity is the warping of space-time)? Or does it exist from all sides?

Hi all, I was wondering if anybody else here thinks the concept of space-time dilation/concentration (curvature) is a little bit funny, not in the sense of it having an effect on the neighbouring particles, but in the sense of actually stretching or contracting, as though it itself had certain...

During the first second of the Big Bang a mind boggling amount happened. So much so that we need to measure it in plank time to appreciate all the stages that occur. And in that 'bang' spacetime was created. My question is this. As space dilated would time not dilate? Meaning. If I were able to...

Why do we say spacetime is moving and not space is moving in time dimension. And how is spacetime one. Also, there is only space, where changes(event) occur, and the rate of changes is describe with term time. That is, time is just a term and not actually a dimension like space(3 dimension).

The question that ponders upon the thought if the speed of light really is constant is a fairly common question. However, I was wondering about something and MAYBE this can provide some backup to the theory that the speed of light isn't constant, please point out any mistakes I make in stating...

Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space. The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal representation of the universe: "Neither does the theory of relativity, Bohr argued, provide us...

In special relativity a sphere in the rest frame for some observer looks like an ellipsoid for an observer with a relative velocity. Can we use the same reasoning for the Schwarzschild spacetime? Namely that a spherically symmetric spacetime produced by a spherical mass look ellipsoidal for an...

When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...

Observers that pass each other with a relative speed close to the speed of light will observe length contraction and time dilation at the other observer. In a spacetime diagram, this would be represented by two worldlines making an angle, right? Some textbooks suggest that some of the length...

Hi! I'm a student reading a book given to me by my teacher about relativity and spacetime. It says that the separation between events in spacetime is measured in "intervals," and I can understand that part. What I don't understand is why you subtract the squares of the distance in space instead...

How does one get time dilation, length contraction, and E=mc^2 from the spacetime metric? Suppose all that you are given is x12 + x22 + x32 - c2t2 = s2 How do you derive time dilation, length contraction, and E=mc^2 from this? What is the most direct way to do this?

It is unclear to me (1) what precisely diffeomorphism means and (2) what happens when all matter is removed from the spacetime. Sean Carrol says that: "the theory is free of "prior geometry" and there is no preferred coordinate system for spacetime." http://arxiv.org/pdf/gr-qc/9712019v1.pdf page...

We all know the concept of the universe expanding. Would it be possible that the universe is not expanding at all, but the spacetime between objects is increasing? My question comes from the idea that spacetime is changed due to the presence of gravitational objects and the idea that gravity is...

http://arxiv.org/pdf/1405.3492v1.pdf The birth of spacetime atoms as the passage of time The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new...

Can one say that every general curved spacetime, locally is maximally symmetric? I know that one can say that every general curved spacetime is locally flat (and therefore maximally symmetric with R=0), but I'm talking about a very high curvature spacetime, where still we can consider nonzero...

I was drawing a spacetime diagram to relate Doppler shift effect but i stuck at a point which i can't understand This is what I'm trying to draw An object with mirror is moving away from me with a velocity of 50% speed of light When each second passes in my clock i send light pulses at that...

In the equation ds2=dx2+dy2+dz2-c2*dt2 the units on the RHS are units of distance squared. But it would seem that units for a spacetime metric should somehow be in units which incorporate both space and time units. Undoubtedly this is an elementary question, but one has to start somewhere...

I have a metric g on spacetime and a spatial metric ##\gamma## such that the components of g can be written in matrix form as $$ g_ {\alpha, \beta} = \begin{pmatrix} g_{00} & g_{0 j} \\ g_{i 0} & \gamma_{ij} \end{pmatrix} $$ where ##i,j = 1,2,3## and ##\alpha = 0,1,2,3##. Now I want to find a...

This has bothered me for some time. In the ADM formulation, we foliate spacetime into 3+1 dimensions by creating 3 dimensional hypersurfaces via ##T = constant## along the worldline of some observer whose proper time is ##T##. This allows us to write dynamical equations for the evolution of some...

Homework Statement At time t = 0, a spaceship leaves Cape Canaveral (x = 0) at speed 2/3c, heading directly upwards (+x direction) toward a satellite in orbit. The satellite is located a distance 2 AU (see footnote2 if you forget what that is) above the earth’s surface. When the ship...