Space-time Definition and 406 Threads

Fact: Spacetime is a curved pseudo-Riemannian manifold with a metric of signature (-+++). Fact: A manifold is a set together with a topology that is locally homeomorphic to R^n. Question: In the case of space-time, what is the set, what is the topology and what is n?

Is it accurate to claim that space-time curvature in general relativity means a curvature of a space-time with a Minkowski pseudo-metric?

...on the gauge-invariance of classical electrodynamics ? I'm thinking of flat Minkowski space-time of SR in which a charged particle moves and generates an electromagnetic field described by the well-known Lie/nard - Wiechert potential. In this situation can we say all spacetime is...

When trying to visulaize curved space, in popular books and science documentaries we seem to always see the http://www.metaresearch.org/cosmology/images/rubber%20sheet%20analogy.jpg" [JPG] taken from a book I have, and although it may be a little harder to draw an analogy from it, I think it's a...

when we teach classical space time diagrams we measure on the vertical line the dependent space coordinate whereas on the horizontal axis we measure the independent time coordinate in accordance with what we learn say in analytic geometry. in special relativity we reverse the situation...

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ? If yes, since time stops at speed of light, then does meter stick disappear at speed of...

Sorry, but I just want to know where I can learn more about this idea. ie. Where matter is, space-time is not. (I know it's a bad way to state the idea because space-time isn't within another space of some kind.) What I'm trying to explain is the idea that elementary particles are "voids" of...

First of all I am not claiming that I have a new theory or something.What I am just saying is that I have another viewpoint of looking at the things which will follow.Before that,I request you all that if you read the post please leave a reply,may be a comment,a flaw that you find,some...

I have a question that has been bugging me since my Special relativity course... (uhm that would be two years now...) We all know that matter produces a gravitywell that bends light. That has been shown lots of times, in fact astrophysics would be a bit dull if that didn't happen... But how...

I had this thought today; If I have a cup of pure water I know that it is composed of hydrogen and oxygen atoms. But there is also the empty space between the individual molecules and between the individual atoms and between the atomic particles. This empty space must be no different to the...

under which circumstances do we say that something in special relativity is the conseqeunce of space-time geometry (Minkowski)?

"Why is our space-time 3+1 dimensional?" The question had been raised by Kant and Hegel for more than 100 years Could there be any possibility of "simple explanation" within the framework of Relativity or Quantum Theory:shy:

Hi guys, I had an idea on the formation of worm holes...I'm not sure if this holds up at all but here goes. The basic idea is based on an elastic band. If you stretch an elastic band beyond the elastic limit, cracks start to appear until eventually the band will break...Now, imagine that...

What is the minium velocity that a particle can have through space-time? What is the maximum velocity that a particle can have through space-time? Thanks!

If space-time looks like a piece of fabric (or an inflating balloon, in the inflation analogy) what is on the other side of the fabric? Or does space-time not look like a piece of fabric at all...? Like some scientists are suggesting that it is a fluid...?

I was wondering if in the GR model for gravity it is possible that space-time be naturally warped (by which i mean warping not caused by matter). In such a region would one experience gravity, even without any matter around?

How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions. One is given that the Riemann tensor is an (2,2) irreducible rep of GL(4, \mathbb{R}) and obeys Bianchi I R_{[\mu\nu|\rho]\lambda}=0 Been trying this problem for 3 days and...

Hi guys. Been thinking about this for quiet a while now and I just want to see if I can get any answers to it. A 3D object is able to see 1,2 and 3D object right? (Within a reason, not saying we can easily see an electron) And we know there has to be more than 3D (excluding time for...

Hi All, I would like to hear opinions about an explanation I gave some time ago to provide physical fundamentation to the concept of instantaneous velocity. I started showing a typical situation where one calculates average velocity between events separated in time by one second. Along the...

Electromagnetism being mediated by space-time rather than particles or waves is based on the validity of the Minkowski space-time metric. Energy held by a quantum object A at an event 1 can jump to a quantum object B at an event 2 provided the proper interval separating the two events has...

I only dabble in physics, so a layman's explanation would be appreciated. My question is, can space-time be quantized? I know that Plank's constant is often used for both length and time, so does it apply also to space-time? I ask this question because it appears to me that this concept can...

Let me start by saying that I’m a novice when it comes to various theories in Physics and what I write below are my attempts to visualize the concepts behind what I learned. It’s more or less for my enjoyment in trying to understand Nature. Many concepts I present may be borrowed from existing...

Anybody-- A friend of mine, whom I highly respect, made the following comment the other day: "If you travel in one direction fast enough, you'll eventually get back to where you started." This was so strange an 'idea' I didn't even know how to respond! After awhile I asked him how...

What equation do you use to find the curvature a body of mass creates? I know the answer for the suns mass is 1.75 arc-seconds. So if I took the g of the sun and divided it by the g of the Earth and divided 1.75 arc-seconds by the ratio of the g difference would I get the Earth's curvature...

The old 2D paper describing 3D curvature is a little lame because it uses gravity to describe gravity. You know, the little ball circling the 2D psuedo-black hole, well remove gravity and the ball would fly off the 2D paper, you can't use gravity to describe gravity. It would be like saying...

Is it true that nothing physical can move in space-time? As a layman in GR i really wondered whether anything physical can move in space-time because movement in space-time is self-referential and will contradict the basic definition of space and time. Also check out this...

In http://www.freewebs.com/mouldy-fart/Space,%20Time%20and%20SR.pdf paper the author wrote: t'=\sqrt{\frac{4h^2}{c^2-v^2}}=\frac{2h}{\sqrt{c^2-v^2}} t'=\frac{2h}{\sqrt{c^2}}\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} Why so? Also, isn't the relativistic beta considered just v/c, not as the...

I understand that the curvature is caused by the depression of a mass in the space-time surface. What I don't understand is what is causing this depression. For example, is it the bodie's resistance to the motion of the space-time surface? Or is it that the curvature is caused by the...

hi, In special theory of relativity time is considered as a fourth dimension of space-time, using speed of light.I am worried, why speed of light should be involved in a theory of space-time ? Space and time must exist in the absence of light also. So do not we need a theory of space-time in...

Can our universe be described with mass imbedded in space-time? Every point in space-time may or may not be occupied by an amount of matter-energy (is the way things are conventionally thought of); but, in knowing that the density of space-time can vary, what if matter-energy is also a...

our current universe has no curve to it, this means that parallel lines stay parallel to the extent of infinity. suppose there was a universe that had a negative curve to it... this cause parallel lines to eventually intersect... what i am not clear on is if these lines would not only join at...

alright i have an understanding that deja vu is a ripple in space-time because of maybe a star going super nova or whatever, is that a creditable claim?

what causes space-time to become distorted by traveling at light speed or close to it at a quantum level

I just heard that the cosmological constant is a coupling constant in some perturbative expansion of some QFT and can be interpreted as a mass? Is this true? Wouldn't that be interesting? That would mean that the GR effect of expansion may be responsible (or may be an equivalent expression for)...

Heres what i don't understand, a massive body in space causes the space around it to warp in accordance with its shape, fine i understand that. What i don't understand is why the massive body would warp the space beyond the close surface of it's body. Which, according to einstein it does and...

I've been reading all about time cones, and space-time, and those general ideas. i forget if i already posted about it a whil ago, but if i did, obivously i didn't quite get the right answer because i still don't understand it... but i was looking at a picture too in an astronomy book a while...

I have been reading about Loop Quantum Gravity and about Spin Foam, and I am stuck on a (probably stupid) idea. It seems that one of the underpinnings of these concepts is that space-time is quantized in discrete units at the Planck scale. If space-time is quantized and the universe is...

Can anyone explain 4D space-time in a simple form ? Some say the Hawking's expalanation is the simplest but I don't get it :biggrin:

if common theory states that gravity exists due to a warping of space-time, then that really doesn't leave any room for the graviton, right? or wrong?

Things would need to have 'mass' in order to have inertia and be defined somewhere in space-time? If 'charges' did not have mass where would they exist (relative to each other)? More mass = more inertia (harder to change position). Order the position of charges with mass to allow them to...

I am trying to understand how Space and time Relate with Gravity. In Physics class i saw a video showing planets Rolling around on a grid with the sun Making the deepest indentation and planets making smaller ones. Now I can but help thinking that this didnt give me the full picture .. Is it on...

Dark energy is space and its interaction with vacuum particles is space-time. Matter affects dark energy and vacuum particles to curve space-time. Anyone agree?

I was reading the lectures compiled in "Six not-so-easy pieces" by the great Feynman. He was trying to explain the curvature of space(and subsequently space-time) through varying temperatures on a hot plate. Much like the curve of a sphere. Anyways I'm going to assume most of your are familiar...

Hi all, I was wondering if anyone of you has read the book of Laurent Nottale Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity why is not his approach adopted ?- as apparently, he extended the principle of relativity to scales and thus proposes a unifying...

Since every particle from photon to proton delivers energy when it interacts, then doesn't this energy distort space-time by its energy?

[PLAIN]www.ras.org.uk/html/meetings/2001/010309.html[/URL] :confused: :rolleyes:

Hello all, I seem to be misunderstanding a concept; perhaps someone could point me in the right direction. My knowledge of physics is very basic so please have some sympathy. Thanks General relativity shows that gravity is caused by the presence of matter that curves space-time. But now I...

According to Einstein's theory of general relativity, gravity bends or warps space-time. this is because the gravitons, or gravity waves, contain no mass and therefore exert their force over large distances with infinite speed. in other words, light from a star that passes by a large body, like...

Did Einstein meant by space-time continuous that time is just another dimension, like the other 3? If so, why are we experiencing this one that differently? (Should this have gone in the phylosophy section?)

I have seen a derivation of the dependence of the speed of light inside a Schwarzschild space-time: c depends on the radial position (r), but a light ray which moves radially has a different dependence on r as a light ray which moves tangentially. My question is whether such an effect may be...