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Author Topic: What are the Dimensions of Matter?  (Read 4587 times)

Offline namaan

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What are the Dimensions of Matter?
« on: 07/07/2011 17:35:44 »
So my question had something to do with why we have a 3D experience when matter is 4D...but then I remembered someone somewhere said that matter isn't 4D :(

So instead of my original question, I think this needs asking first: if matter needs 4 coordinates to be defined in spacetime, isn't it by definition, 4-dimensional? I get the feeling that I'm not asking the right question...


 

Offline JP

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What are the Dimensions of Matter?
« Reply #1 on: 07/07/2011 17:45:35 »
The number of dimensions is basically how many numbers you need to tell me to describe where something is.  Let's say you have a balloon floating in mid-air, you need to tell me three numbers: two numbers to specify where it is on the earth's surface and a third to tell me how high it is off the ground, so it's somewhere in three dimensional space.

If the balloon is moving, you can also tell me when it arrives at different points, in which case you need to tell me it's position (3 numbers) and the time it arrives there (1 number).  That's 4 dimensions.

We have a 4D experience, actually, since we move around in 3 dimensions of space, but also move forward through time.  If we were having only a 3D experience in space with no time, we'd never be able to move anywhere.  We do obviously experience time differently than space, so not all dimensions are created equal.
 

Offline namaan

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What are the Dimensions of Matter?
« Reply #2 on: 11/07/2011 04:38:35 »
Right, ok, but here's the problem I'm having in conceptualizing time as the 4th dimension and including the idea of the three spacial dimensions "moving forward" through the dimension of time. Given that the three spacial dimensions are curved across the 4th dimension, namely time, and we are moving forward through time, then consider this: near a massive body, spacetime is curved more than say in deep space, such that (depending on how you orient the direction of time's arrow) future time will "arrive" at a point near a massive body before/after a point in deep space.

In other words, let's imagine the rubber sheet analogy of 2d space that is curved across the 3rd dimension of time. In this analogy, you may either think of time as something flowing across a non-moving rubber sheet, or as the rubber sheet moving across the 3rd dimension of time. Either way, if this sheet is curved through the 3rd time dimension, then the same future will "arrive" at different points in spacetime.

What do you think, am I thinking this right?
 

Offline JP

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What are the Dimensions of Matter?
« Reply #3 on: 11/07/2011 21:57:04 »
Think about a 2D case of space-time.  You have a particle that can only move left or right along a line and it can move through time.  Space-time is 2D.  To describe this space-time, you need a 2D rubber sheet.  If you curve this space-time it doesn't "curve into" time, but it curves up or down out of the plane into a higher dimension in our 3D space.  To a particle confined to this sheet, that higher dimension is meaningless--it only knows about it's position and motion on the sheet.  If we had people living entirely on the sheet and asked them to come up with laws of physics, they would describe these laws entirely in terms of the space-time of the sheet, which could be done by saying they live in a 2D space-time which is curved. 

In general relativity, you model space-time as a manifold (the rubber sheet).  A 2D space-time would therefore be a 2D sheet, and when it bends you can visualize it bending into a 3rd dimension  A 4D space-time is a 4D "sheet."  We can't visualize this at all, nor can we visualize how it looks when bending into a "5th" dimension.  That's one of the reasons why visualizing GR is so hard.
 

Offline namaan

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What are the Dimensions of Matter?
« Reply #4 on: 12/07/2011 16:36:16 »
Sorry but either you totally lost me or I'm understanding there are 5 dimensions in GR? For example...

Quote
You have a particle that can only move left or right along a line and it can move through time.

So that's one dimension of space...the second dimension being our 4th dimension, namely time.

Quote
To describe this space-time, you need a 2D rubber sheet.  If you curve this space-time it doesn't "curve into" time, but it curves up or down out of the plane into a higher dimension in our 3D space.

This is where you've lost me. I thought it was space only that curves into time making spacetime, but it's actually that both space and time together curve into a higher dimension? I mean if space in this analogy is 1D, with 2D being spacetime, you're saying there needs to be a 3rd dimension to into which spacetime curves?

That's analogous to our 4D spacetime curving into a 5th dimension no? I'm not disagreeing, I frankly don't know enough to agree or disagree :(
 

Offline imatfaal

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What are the Dimensions of Matter?
« Reply #5 on: 12/07/2011 16:43:58 »
Namaan - it is 4-d space time which is curved.  Spatial dimensions do not curve by movement through the time dimension.  In the rubber sheet analogy - you are correct the sheet represents one spatial and one temporal dimension, this 2d spacetime is distorted into a third. within that 2d world you can only realise that your spacetime is curved - you cannot investigate that extra dimension; and similarly we can realised/theorise that our 4d spacetime is curved but not investigate the extra dimension.
 

Offline namaan

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What are the Dimensions of Matter?
« Reply #6 on: 12/07/2011 18:44:42 »
That makes sense actually, understanding time dilation is a lot easier now ;)
 

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What are the Dimensions of Matter?
« Reply #6 on: 12/07/2011 18:44:42 »

 

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