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Old Jul 9th 2018, 04:34 AM   #11
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Originally Posted by benit13 View Post
No. There's no distinction between mathematical dimensions and physical dimensions. Dimensions are just names for the orthogonal bases in coordinate systems.



They're not irrelevant. The object can still be described using the 3D Cartesian coordinate system you adopted.

There are physical phenomena that we can model using the laws of physics. Those laws of physics are framed using well known coordinate systems, like Cartesian, cylindrical and spherical polar coordinates, but there's nothing stopping you from defining your own coordinate systems and using those. For example, solid state physics makes use of reciprocal space, relativity can be framed using time as a dimension. Nuclear physicists sometimes use complex forms for things that are not complex, which can sort of be seen as a new 'dimension'.

Yes, most of nature can be described by using three spatial dimensions in your coordinate system, but that's not a fundamental property of the Universe. You could, for example, use a 1D or 2D system of coordinates if you want to describe a certain situation, which might be fine. However, there are other situations where one or two dimensions are not good enough. Similarly, some scientists find it easier to describe certain phenomena using many dimensions, but that doesn't mean that they are 'real'.



I'm not very good at relativity, but from what I understand, I think the answer is no. Einstein developed his theories by investigating the properties of objects as they approach the speed of light and never assumed or treated space as a material that can be warped and bent.
With respect, since you have written some very good posts here,

This question was posted at University level, in the General Relativity section.

Surely we should not offer the simplifications used in school?


The difficulty (which can by illustrated using an x, y frame) with cartesian systems is this.

Consider a point, (x, y).

This needs two pieces of information to specify it doesn't it, x and y ?

But waitup, does it?


Suppose I measure distance along some arbitrary curve to reach this point.

Then I only need one piece of information, not two, viz the distance.

The curve or line I measure along is a one dimensional manifold that we have embedded in our two dimensional x y frame.

But we don't need to if the one dimensional manifold is all there is.

And that is the concept behind General Relativity that is so difficult to get across, especially as we have a three or four dimensional (Space or Spacetime) manifold in play there.

Mathematically we can 'embed' our manifold in as many higher dimensions as we like and calculate as though they exist.

Mathematically it gets worse, because a Peano curve can reach every point in the plane (or even a solid cube) in this way, at the expense of the calculus, since we loose the concept of a neighborhood in doing this.
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Old Jul 9th 2018, 02:37 PM   #12
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Of course they are just one of many descriptive methods of an object with mass.

Believe Einstein thought time warps to maintain constant light speed.
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Old Jul 9th 2018, 03:49 PM   #13
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Originally Posted by lancew561 View Post
Believe Einstein thought time warps to maintain constant light speed.
Close, but not quite true. Einstein based his results for SR upon the Lorentz transformations in EM. Historically the Kinematical derivation for movement with a constant speed of light came later.

Oh, and as to the time warping, the SR definition of the time axis involves a complex number, not a warped space-time. Space-time as it is defined in SR is "flat."

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Old Jul 9th 2018, 06:41 PM   #14
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__________Yes__________

infinitely small flats are the time length variations (quantum again). Warping is just short for this.

If you solve the time dilation formula to c the speed of light it shows
that if you change velocity (I know relative) you must also change time in order to maintain a fixed speed of light. When he came up with this is another matter I believe. Einstein was taught by Lorentz and yes Einstein used his transforms in his equations with one major carry over that the speed of light again remains constant.
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Old Jul 15th 2018, 07:49 AM   #15
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Originally Posted by avito009 View Post
Well space has 3 dimensions: length, width and depth. But these are the dimensions of the object not of space. Space which exists without the matter does not have any dimensions then. Then how can these be dimensions of space as they appear to be dimensions of the object?
Space itself is said to have three dimensions because it takes exactly three numbers to designate a location in space. Your comments on length with etc are not relevant to the subject. Also note that it doesn't mean that it refers to three axes either. In cylindrical and spherical coordinates one or two coordinates refer to an angle and the other a distance. There is no need for something to be in that location for it to need coordinates to specify. Often it doesn't.
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Old Jul 15th 2018, 12:43 PM   #16
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Originally Posted by lancew561 View Post
infinitely small flats are the time length variations (quantum again). Warping is just short for this.

If you solve the time dilation formula to c the speed of light it shows
that if you change velocity (I know relative) you must also change time in order to maintain a fixed speed of light. When he came up with this is another matter I believe. Einstein was taught by Lorentz and yes Einstein used his transforms in his equations with one major carry over that the speed of light again remains constant.
Absolutely not. Its a misuse of the term "warp". Its either spacetime that's curved (aka "warped") or space that's curved. A one dimensional entity like time cannot be said to be warped. Even when you have (t, x) (i.e. two dimensions) it doesn't mean that time dilation is the same thing as being "warped." Many people make that mistake.
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Old Jul 15th 2018, 03:11 PM   #17
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Smile Space Time Dimensions

Hi,

I am weighing in on this thread because I think that part of avito009's point might be valid. Should 4d not be 5d. With one dimension of time, 3 dimensions of space and one dimension which is also infinite and which we could call possibility.

I do not want to comment on anything related to relativity or string theory here because that is not part of my point. (I really dont know anything about the 11 dimension predicted by string theory anyway)

It seems to me from a philosophical point of view we need a 5th dimension if the state of the universe is not predefined. Think of it this way, if a star is moving in one direction in time t at position x,y,z and it had or (did not) pick up a gravitational tug, at t2 it could be at x2,y2,z2 or it could be at x2',y2',z2' where the prime notation is a different possibility.

Whether the 5th dimension is an abstract construct or is real is another matter to decide. The mathematics and rules of it might need to be worked out, but it seems to me that this would offer a way out of the conundrum of time not having a preferred direction. (if only because the magnitude of the 5th dimension can never decrease)

I will leave it up to somebody with a lot more time and knowledge than what I have to tease out the details.
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Old Jul 16th 2018, 05:03 AM   #18
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Originally Posted by YellowPeril View Post
Hi,

I am weighing in on this thread because I think that part of avito009's point might be valid. Should 4d not be 5d.
His point is invalid due to a misunderstanding of what it means for a manifold to be warped. And no,4d should not be 5d. Spacetime consists of 3 spatial coordinates and one time coordinate. Anything else is not the spacetime of relativity.

To be precise he confuses time dilation and length contraction with the curvature in spacetime (which he calls "warp"). If he doesn't mean curvature when he uses the term warp then he's using the term warp wrong.
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Old Jul 21st 2018, 05:38 AM   #19
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Space Time Dimensions

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His point is invalid due to a misunderstanding of what it means for a manifold to be warped. And no,4d should not be 5dSpacetime consists of 3 spatial coordinates and one time coordinateAnything else is not the spacetime of relativity.

To be precise he confuses time dilation and length contraction with the curvature in spacetime (which he calls "warp"). If he doesn't mean curvature when he uses the term warp then he's using the term warp wrong
Fair enough I take your point. You can ignore my comments, I think I wrote that last post in a bit too much of a hurry and got carried away a little bit too much by my ideas which are actually just my opinion and not based on firm facts.
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Old Jul 21st 2018, 12:22 PM   #20
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Originally Posted by YellowPeril View Post
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His point is invalid due to a misunderstanding of what it means for a manifold to be warped. And no,4d should not be 5dSpacetime consists of 3 spatial coordinates and one time coordinateAnything else is not the spacetime of relativity.

To be precise he confuses time dilation and length contraction with the curvature in spacetime (which he calls "warp"). If he doesn't mean curvature when he uses the term warp then he's using the term warp wrong
Fair enough I take your point. You can ignore my comments, I think I wrote that last post in a bit too much of a hurry and got carried away a little bit too much by my ideas which are actually just my opinion and not based on firm facts.
No harm, no foul. It's always better to ask questions...that's how you learn things.

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