Thread: Question on higher dimensions and gravity

Hi,

I read on this page:

Why exacly 11 dimensions? [Archive] - Physics Forums

that there are 11 dimensions because:

"A one dimensional matrix that describes EM. A two dimensional matrix that describes the weak force. A three dimensional matrix that describes the strong force. Now you are a theorist, and you see that gravity is described by a four dimensional matrix. So the logical thing to do is to lump all of these matrices together and get a 10 dimensional matrix. And you argue that the extra six dimensions that describe all of the forces are just tiny little dimensions so 1+2+3+4 = 10."

It goes on to say that:

"You have all of the forces in your 10 dimension matrix, but you don't have any matter..... Hmm.... it turns out that you can try to fix this problem by adding one more dimension which turns a force into matter and matter into forces. So this is where you get 11."

Here are my questions:

1. How accurate is this post? I could only find its information in one place.
2. How come we stop at a 4 dimensional matrix? If the forces were unified at the big bang, and they broke off from each other to get where we are today, couldn't they break off from each other even more, forming a need for an extra 5 dimensions?
3. I understand that gravitons are to gravitational waves as photons are to light waves. I also understand that Einsteins equations show that gravity is the curvature of space. However, when you think of "space" you are usually thinking of directions. Space isn't anything. "Space" is just directions. Einstein can show how gravity is the change of directions as two objects move in four dimensions, but is the actual reason gravity happens because of gravitons and gravitational waves, not the curvature of spacetime? For example, if the post I quoted above was correct, EM has photons that change an object's direction in one dimensional space, W and Z bosons change an object's direction in two dimensional space, gluons change an object's direction in three dimensional space, and gravitons simply change an object's direction in four dimensional space. That is why we have experimentally proven gravitational time dilation.

If anyone could answer any of these questions, that would be great!

Thanks,
Guymillion

Not there "are" 11 dimensions, but one hypothesis, unsupported by any actual evidence so far, suggests that 11 dimensions is one possible solution to some mathematical speculation.

Originally Posted by guymillion

1. How accurate is this post? I could only find its information in one place.

It sounds like nonsense to me. But I am no expert. I have seen a simple explanation of why 10 (or 11) dimensions but I would never be able to find it again.

3. I understand that gravitons are to gravitational waves as photons are to light waves. I also understand that Einsteins equations show that gravity is the curvature of space.

I don't think these two views are compatible. We don't yet have a quantum theory of gravity.

However, when you think of "space" you are usually thinking of directions. Space isn't anything. "Space" is just directions.

Correct. GR describes how these "directions" (dimensions) get curved by the presence os mass (or energy). Which then causes a change in the way matter move. Which we then perceive as gravity.

Einstein can show how gravity is the change of directions as two objects move in four dimensions, but is the actual reason gravity happens because of gravitons and gravitational waves, not the curvature of spacetime?

It is not clear if "curvature of spacetime" is "real" or just a useful mathematical description. If a future theory manages to include gravitons, it will have to be equivalent to this at some level.

If anyone could answer any of these questions, that would be great!

Hopefully, someone who knows what they are talking about will be along soon!

Thanks! That helped me a lot!

Originally Posted by guymillion

see that gravity is described by a four dimensional matrix

It isn't. Under General Relativity, which is our currently accepted theory of gravity, the description of gravity is contained in the metric tensor, which is ( in simplified terms ) a 2-dimensional matrix.

An interesting conversation but I'm not sure there is any consensus on the description of the forces in terms of matrices. But I don't know the math so I can't say definitively. Didn't someone named Kaluza write a paper showing that if there are really four spatial dimensions then when you expand Einstein's equations of general relativity to four dimensions that you have not only Einsteins original relativity equations but an extra set that are actually Maxwell's equations for describing the electromagnetic force? Kaluza did no research on string theory did he?

Originally Posted by Markus Hanke

Originally Posted by guymillion

see that gravity is described by a four dimensional matrix

It isn't. Under General Relativity, which is our currently accepted theory of gravity, the description of gravity is contained in the metric tensor, which is ( in simplified terms ) a 2-dimensional matrix.

Doesn't one simple variant of string theory incorporate gravity and predict the graviton? (though failing in other key points?)

Originally Posted by ballyhoo

An interesting conversation but I'm not sure there is any consensus on the description of the forces in terms of matrices. But I don't know the math so I can't say definitively. Didn't someone named Kaluza write a paper showing that if there are really four spatial dimensions then when you expand Einstein's equations of general relativity to four dimensions that you have not only Einsteins original relativity equations but an extra set that are actually Maxwell's equations for describing the electromagnetic force? Kaluza did no research on string theory did he?

That is correct, but the mathematical description of such a 5-dimensional space is still just a tensor of rank two, i.e. a 2-dimensional matrix.

Originally Posted by ballyhoo

Originally Posted by Markus Hanke

Originally Posted by guymillion

see that gravity is described by a four dimensional matrix

It isn't. Under General Relativity, which is our currently accepted theory of gravity, the description of gravity is contained in the metric tensor, which is ( in simplified terms ) a 2-dimensional matrix.

Doesn't one simple variant of string theory incorporate gravity and predict the graviton? (though failing in other key points?)

The ground state / simplest state of excitation of a closed string corresponds to what we describe as the "graviton", so in that sense all String models naturally incorporate gravity. Furthermore, it turns out that the maths of the string dynamics are only self-consistent in a curved space-time background; doing the maths automatically leads to the field equations of General Relativity. This way, at least in principle, the descriptions of both quantum mechanics and general relativity are both unified in the String models.
Note that what I said above is highly simplified, the actual maths behind these things are pretty complex.

Originally Posted by Markus Hanke

Originally Posted by ballyhoo

An interesting conversation but I'm not sure there is any consensus on the description of the forces in terms of matrices. But I don't know the math so I can't say definitively. Didn't someone named Kaluza write a paper showing that if there are really four spatial dimensions then when you expand Einstein's equations of general relativity to four dimensions that you have not only Einsteins original relativity equations but an extra set that are actually Maxwell's equations for describing the electromagnetic force? Kaluza did no research on string theory did he?

That is correct, but the mathematical description of such a 5-dimensional space is still just a tensor of rank two, i.e. a 2-dimensional matrix.

So, what does that mean exactly? That only two pieces of information (which vary according to particular regions?) combined (by multiplication?) describe five new pieces of information?

Originally Posted by ballyhoo

So, what does that mean exactly? That only two pieces of information (which vary according to particular regions?) combined (by multiplication?) describe five new pieces of information?

No, it means that this would be a matrix with five rows and five columns ( 5x5 ) in the 5-dimensional case, instead of a 4x4 matrix in the 4-dimensional case. However, the rank ( = dimension ) of the matrix is two in both cases. It is just the number of rows and columns that differs.

okay =) I know at least enough math to understand that.