Spacetime Definition and 1000 Threads

Why can't distortions in spacetime be used to describe the fundamental forces other than gravity, i.e. the electromagnetic force, the strong nuclear force, and the weak force?

In this paper we have p18 an integral on space time M. The author takes a 3 dimensional space like Cauchy surface ##\Sigma## which separates M in two regions, the future and the past of ##\Sigma##. He gets so the sum of two integrals on these regions. He writes then let us integrate each of them...

I have read that as the universe expands that the "fabric" of spacetime expands. Does this mean that the metric basis for a given space is expanding? Also, does this mean the distances between the atoms in the lattice of matter is also increasing proportional to the expansion of the cosmos?

If gravitational lens can "focus" light, is it possible with gravitation, so that the resulting gravitation would be strangely unhomogenous? (If it is a dumb/noob question just tell we pls.)

Suppose we are in a Minkowskian space, away from all the source of gravity, and observe an accelerated frame from this frame. Acoording to Equivalence principle, we can consider the accelerated frame to be at rest and assume we have gravity in the accelerated frame. Thus, observer in the...

According to equivalence principle, gravity can be treated like acceleration "locally". Based on this principle we can treat a non-inertial frame at rest and explain the fictitious forces (of Newton's Laws) as gravity. From this we can prove that time elapses at different rates at different...

According to general relativity, time is a dimension, one of four dimensions that form 4D spacetime - a structure which is mathematically symmetrical and homogeneous. Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies...

The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...

Category of simple questions Obviously I am misunderstanding how an interval of space- time can be invariant under coordinate transformations. The following elementary (but obviously incorrect) calculation will illustrate my difficulty. Alice is leaving her two boyfriends, Bob and Charlie. Bob...

When Einstein wrote the special realvity he said that inertional acceleration and gravitational acceleration are the same, my question: Does it mean that any source of somthing that making body accelerate (force) is also curving the space-time? for example- spaceship that accelerating in empty...

I've been reading about the Dirac equation, and most authors eventually make some statement to the effect that the fact of spin and antiparticles falling out of the equation reflects a deep connection to the structure of spacetime. Is the implication that the math requires four particle states...

Hi guys, I was wondering if anybody could help me understand the concept of spacetime. My physics knowledge is quite limited but so far what I have gathered is: Spacetime is like a piece of paper (assuming it is 2d) but instead of width and length it has space on one axis and time on another...

Neil Turok, Director of the Perimeter Institute of Theoretical Physics in Ontario, Canada suggests scaling invariance is a fundamental property of nature, including spacetime. that nature does not recognize any kind of scale, including Planck scale. if true how would this affect the leading...

Per my layman's understanding, the apparent force of gravity, as explained by the general theory of relativity, is actually the result of rectilinear motion at uniform speed through warped spacetime. 1. If that's the case, what actually causes gravity for objects at rest with respect to the...

I have a problem with static/non-static spacetime. The problem is that the notion of spacetime includes time itself, so how can it change with time? Imagine an asteroid approaching the Earth-Moon system. The Earth-Moon system is a non-static spacetime, so presumably is giving off gravitational...

How does white holes curving the space-time manifold? (I prefer see picture of white hole influence in addition to the explanation).

I appreciate that this may be the 100th time this is asked but I am yet to see an answer which addresses the question head on. Given that reaching light speed creates both a length and time singularity; both length and time amount to zero for the propagating wave/photon. Why does that photon...

Hello, i try to find some opinions on these points a) If a brane action in a bulk is defined, in that case, that a brane is modelwise moving through a bulk, how is this ratio defined? Is this a regular "velocity" in that meaning, that space is being passed in a period of time? b) If a...

I want to calculate two things (This is not a homework question so I am posting here or actually I don't have homework like this) First question is finding universe volume using spacetime metric approach.The second thing is find a smallest volume of a spacetime metric (related to plank...

I would like to hear different examples of presenting the difference that general theory of relativity relates between a stretched piece of spacetime around a planet and a not stretched one far away from any kind of mass or energy distortions...these examples i would like to be written in a...

Do gravitational forces have to follow spacetime in the same way as light? Or does gravity act in a higher dimension? Thanks, T

I mean, I'm making a game, not making a gamer. I talked about making a gamer with my wife but she just grabs my head, analyzes, sees how big it is and says "nah, thanks". (this paragraph made sense because the topic title was "any gamers here?I am developing one") Anyway, the title of the game...

I'm wondering if time and light(entire spectrum) can only coexist simotanuously. When we look out into the cosmos and see stars they can be many light years away. Because it takes time for light to travel. That may have not been relevant. But what I'm saying is... Time is manipulated by the...

If mass curves spacetime in its vicinity, then consider the following case- Take a heavy hollow lead sphere which has 2 smaller lead balls placed in it. The Outer Sphere will curve spacetime around itself and thus will have its own gravity, but what about the 2 balls placed in it? The spacetime...

Why do we say gravity [GR] is a theory about ‘spacetime curvature’ and gravitational waves are ‘ripples’ but nobody uses such a description for electromagnetic fields? Don't EM waves 'ripple' spacetime? For example, one might imagine different types of spacetime curvature associated with each...

Hello, Cosmology for the layman says that there was a time t=0 when the universe was created out of infinitesimal length distance and before that nothing existed not even time. OK, but this rests on the assumption that there is always a manifold from which we cut off our space slices in the...

So, I'm still a bit new to the realm of physics but I was discussing theorized particles with my professor the other day and came to the conclusion, if gravitons do exist, could anti-gravitons be an explanation for why the universe is expanding? I was reading around and came across a similar...

I am not a physicist but felt compelled to create an account to pose a question/idea. Don't beat me up over this please... I was reading on Quantum Entanglement and how entangled particles seem to pass information between them at "faster than light" speeds. Now, given that entanglement is an...

planet Earth and the sun. in GR, gravity is not a force but simply a manifestation of spacetime curvature. the sun curves spacetime and the Earth is simply traveling through geodesic motion through curved spacetime. in string theory, the sun and Earth exchange virtual gravitons through a...

since a massless spin 2 field when perturbatively quantized gives rise to gravitons, which couple to everything and is identical to gravitation, is spacetime itself massless spin 2 field? do virtual graviton exchange also modify time and space?

I have been reading these notes: http://isites.harvard.edu/fs/docs/icb.topic455971.files/l10.pdf in which they claim that if two spacetime events are coincident in one frame of reference then they are coincident in all inertial frames of reference, thus spacetime events are absolute i.e. they...

Please forgive me if I am posting in the wrong forum. Also the board limits the length of the title. I wanted to ask about Effect of high intensity electric and magnetic fields on spacetime. To begin, 15 years ago this was published...

Hello, I'm sorry if this question sounds silly, but in QM the Momentum Operator is ##{\hat{p}}=-i{\hbar}{\nabla}## . In Relativistic QM in Flat Space, this operator can be written ##{\hat{P}_{\mu}}=-i{\hbar}{\partial}_{\mu}## . Would it be correct, then, to say that in curved spacetime the...

I've been working through Leonard Susskind's "The Theoretical Minimum" lecture series (which are a fantastic introduction to the topics covered by the way) and a couple of his comments confused me when he was covering the Kruskal-Szekeres metric/coordinates in General Relativity. The end of the...

Like spacetime , can sound be taken as a fifth dimension?

When spacetime is not bent the two objects, red ball and blue ball, will move strait up the y-axis as they move through time. (Space is x and time is y). Now I've made the assumption that either a) All things want to move the smallest possible distance to the next point in time or b) all...

I've a (perhaps somewhat stupid) question. Is there a good source, where one finds the plane-wave solutions (or what comes closest to it) for electrodynamics for the closed and open (non-flat) Friedmann-Lemaitre-Robertson-Walker metric. I try this myself for a while, because to my surprise I...

As far as I understand it, Einstein theorized that gravity was the result of the curvature of space created by the presence of mater/energy, but that idea seems like it does not meld well with the idea that gravity is the result of a specific force carrying particle, as with the other...

Purely theoretically, could it be possible to extract energy from spacetime's expansion? Like, say, imagine two celestial bodies far away enough so that they are not bound enough by gravity, they get farther away from each other due to spacetime expansion. We tie them to each other with a rope...

I see an example from book stated that a muon that are created at high altitudes can travel to the ground because of time dilation about its lifetime. In the view of muon, it travels shorter distance compared with the view of the Earth. Suppose there are two muons. In view of muon A, muon B is...

Hi all, Say two events happen in the same place according to one observer (1). They are separated in time by 3 years. According to another observer (2) that is moving relative to the first, the events are separated by 5 years. We can calculate, using the invariance of the spacetime interval...

Hi! Not sure if this is properly categorized,please correct me if it isn't. What if deja vu is just our brain misinterpreting 'reality' and exposing us to spacetime. Like skipping ahead in time(according to the definition of time in spacetime) but then it calibrates us back into the present...

Hi, So according to GR, energy bends spacetime, right? So that would include both light and mass. If I am understanding this right, light bends spacetime, and is also affected by the spacetime curvature. Could someone explain exactly what the spacetime curvature does to light (I mean like how...

In the Einstein Field Equations: Rμν - 1/2gμνR + Λgμν = 8πG/c^4 × Tμν, which tensor will describe the coordinates for the curvature of spacetime? The equations above describe the curvature of spacetime as it relates to mass and energy, but if I were to want to graph the curvature of spacetime...

The standard spatially flat FRW metric in Cartesian co-moving co-ordinates is given by: $$ds^2=dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ As far as I understand it the fact that the metric can be written in a form that is independent of ##x,y,z## implies that the Universe has the physical qualities of being...

Do we have Bose like and Fermi like particles (fields) in 1+1 dimensional spacetime, Fermi like particles (fields) that obey the Pauli Exclusion Principle? For what space dimensions does the Pauli Exclusion Principle operate? Thanks for any help!

Homework Statement The metric near Earth is ##ds^2 = -c^2 \left(1-\frac{2GM}{rc^2} \right)dt^2 + \left(1+\frac{2GM}{rc^2} \right)\left( dx^2+dy^2+dz^2\right)##. (a) Find all non-zero christoffel symbols for this metric. (b) Find satellite's period. (c) Why does ##R^i_{0j0} \simeq \partial_j...

could the bend be described mathematically? Not the vector the curvature.

Disclaimer: I am an aeronautical engineer with a background in fluids. My knowledge of cosmology only extends to articles and things I read before I go to sleep. So, here is my question: I have though about time travel, as many other people have. Currently we think it may not be possible, as it...

I'm currently reading Relativity: A Very Short Introduction. One part caught my attention: Does this mean that the future is already embedded in spacetime?