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Old Feb 6th 2011, 09:41 PM   #1
ohm
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spacetime

what i know is that space is three dimensional frame to locate position of an object and time is just added to it to make it more significant and make four dimensional.
What i don't undestand is
1) i m unable to imagine this fourdimensional concept ( as in three dimension three axes x,y,z can be taken such that each make an angle of 90 degree with each other, then at what place can i attach this another one to make it four dimension)
2) i have read that space is curve( somewhere not space, spactime is curved ). What is difference between these two things except dimensional concept.
3) if space is empty then how can an empty space be curved( whereas i have read somewhere that space is not empty)
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Old Feb 7th 2011, 11:51 AM   #2
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Originally Posted by ohm View Post
what i know is that space is three dimensional frame to locate position of an object and time is just added to it to make it more significant and make four dimensional.
What i don't undestand is
1) i m unable to imagine this fourdimensional concept ( as in three dimension three axes x,y,z can be taken such that each make an angle of 90 degree with each other, then at what place can i attach this another one to make it four dimension)
2) i have read that space is curve( somewhere not space, spactime is curved ). What is difference between these two things except dimensional concept.
3) if space is empty then how can an empty space be curved( whereas i have read somewhere that space is not empty)
1) Mostly you are on the right track. Ordinary 3-space (in the absence of masses; for that we need General Relativity) is Euclidean. That means the 3 space axes are "stuck together" at right angles. The time dimension is a bit trickier. (Lorentzian) space-time has what is called an "indefinite metric." That is to say space-time is not at all Euclidean. I'm not certain how to the time axis is "attached" to the 3-spaces axes, but I don't think it can even be visualized since it is 4 dimensional.

2) Due to the indefinite metric space-time is curved (non-Euclidean, or more precisely it is non-Riemannian.) Space, in Special Relativity, is flat: it is Euclidean. On the other hand, if there are masses present then a curvatiure is introduced to the space axes as well. (There is a whole "machinery" involved here. If you pick the right set of coordinate axes you can make a very small part of curved space Euclidean again. This is the basis for differential geometry and I'm not going to go into that right now.)

3) There are a number of ways to answer this question. First, empty space can be curved if there is a gravitational field present. But again we are talking about GR and differential geometry here. It depends. once again, on your coordinate axes. On the other hand, Quantum Physics says there is no such thing as an empty vacuum. This is due to virtual particles popping in and out of the vacuum, and is a topic that I am again not going to discuss here.

Please feel free to ask the questions I've put off if you like. The differential geometry bit I can do in this forum, but the vacuum question should be posted in the Quantum Mechanics forum.

-Dan
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Old Feb 10th 2011, 09:40 AM   #3
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sorry. There is some technical problem in my internet connection. That'r why i am not responding properly.
First of all i thanks for ur response.
1) u thought that it is not possible to visualise four dimensional spacetime. So i think it is useless to try to imagine this.
2) u have disscussed "indefinite metric" and differential geometry . What is this ?
3) i have seen a rubbel sheet model. Does it indicate empty space. If it is then how can empty(nothing) can be curved.
4) i have also seen light cone along with world line. How can straight worldline be path of movement of earth in four dimenssion.
Kindly response this.
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Last edited by ohm; Feb 10th 2011 at 09:43 AM.
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Old Feb 11th 2011, 09:06 AM   #4
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kindly response anyone.
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Old Feb 13th 2011, 09:06 PM   #5
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in GR which is curved "space" or "spacetime"?(pls don't mention dimensional concept to distinguish these two things as i am unable to imagine this four dimensional concept)
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Old Feb 14th 2011, 11:53 AM   #6
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Originally Posted by ohm View Post
sorry. There is some technical problem in my internet connection. That'r why i am not responding properly.
First of all i thanks for ur response.
1) u thought that it is not possible to visualise four dimensional spacetime. So i think it is useless to try to imagine this.
2) u have disscussed "indefinite metric" and differential geometry . What is this ?
3) i have seen a rubbel sheet model. Does it indicate empty space. If it is then how can empty(nothing) can be curved.
4) i have also seen light cone along with world line. How can straight worldline be path of movement of earth in four dimenssion.
Kindly response this.
1) I certainly can't visualize it, thought there are probably some topologists that claim to be able to. The best that an otherwise ordinary human could do is to be able to visualize three dimensional "sections" of the 4 dimensional object. Since I can barely manage three dimensional objects, four dimensions are hopelessly out of my league. 8]

2) A metric is, more or less, a way to measure "distances" in a given kind of topological space. For example, in Euclidean three dimensional space the metric is s^2 = x^2 + y^2 + z^2. In Minkowski (aka Lorentzian) space-time the metric is s^2 = x^2 + y^2 + z^2 - (ct)^2. (Some authors use the negative of this.) It is called "indefinite" because s^2 can be a negative number.

3) The rubber sheet model is nice, but really only gives a rough idea of what's going on. Still, like the Bohr model of the atom, it has its uses. The idea is that if we put a mass on a level rubber sheet, it will cause an indentation. This gives us an idea of what how gravity and curved space-time function. Any small ball rolled near the object in the center will no long roll in a straight line, but will have a curved path. This represents the effects of a gravitational field.

4) As I understand it the light cone shows what "events" (basically coordinates) that one can reach when starting out at a different event. It is represented by a cone marked off by straight lines (which represent the places that an object traveling at the speed of light can reach.) Any event outside the light cone cannot be reached.

-Dan
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