Confused about a part in The Elegant Universe

[Chemical_Penguin]

Confused about a part in "The Elegant Universe" ...

On page 208, second paragraph, 8th line down:

Greene says "For instance, if you sweep your hand in a large arc, you are moving not only through the three extended dimensions, but also through these curled up dimensions. Of course, because the curled up dimensions are so small, as you move your handyou circumnavigate them an enormous number of times, repeatedly returning to your starting point."

Ok, the problem I am having is this: Are we really constantly going through these extra dimensions? If this were true wouldn't we be able to detect small particles disapearing and re-appearing even if it's maybe only for an EXTREMELY SHORT amount of time?

And secondly, when you use the analogy of an ant on a long one-dimensional garden hose that actually has a curled up 2nd dimension, the ant is not required to go through this dimension constantly returning to his starting point when he travels about through the 'left-right' dimension. But what Greene is saying is that when I wave my hand around that the tiny strings that make up the particles that make up my hand are forcefully traveling in these curled-up dimensions and I just can't graspwhy I am required to move through these dimensions when the ant in line-land is not.

If anyone can shed some light on this for me I'd appreciate it, or if my description above isn't good enough, tell me that also. I really want to udnerstand this. Thanks.
-Eric

 

[Phi For All]

First of all, I haven't read the book. It's on my list to read but I'll probably get the video from the library before I get time for the book. I can only help (?) with the first part of your question

Ok, the problem I am having is this: Are we really constantly going through these extra dimensions? If this were true wouldn't we be able to detect small particles disapearing and re-appearing even if it's maybe only for an EXTREMELY SHORT amount of time?

To wrap my mind around something for which I have no reference, I picture the curled up higher dimensions as spatial points (not because they are particles, just because they are so small) which are everywhere, at every possible place in the universe, at all times. No matter where you move in 3D, there you are, you've got the higher dimensions right with you. And if you were here on Earth and I was a billion light years away, the higher dimensions would be with you and I simultaneously. If they were accessible for us to move through to get where we wanted to go, it would be like a stepping stone that moved with you and you could step on if you moved your foot just so.... Whether you were stepping from one mountain top to the next mountain top or stepping from your front door to a moon orbiting a planet of one of the stars in the M87 galaxy 50 million light years away, it would make no difference to the higher dimensions. As far as detecting particles from these dimensions, I doubt if the particles they possesses are in a fixed state. I stopped reading about quantum wave states when I started reading about higher dimensions (only so much time, you know). I hope this helps, Eric. I just keep trying to move the pieces of the puzzle a little closer together every day.

 

[selfAdjoint]

On page 208, second paragraph, 8th line down:

Greene says "For instance, if you sweep your hand in a large arc, you are moving not only through the three extended dimensions, but also through these curled up dimensions. Of course, because the curled up dimensions are so small, as you move your handyou circumnavigate them an enormous number of times, repeatedly returning to your starting point."

Ok, the problem I am having is this: Are we really constantly going through these extra dimensions? If this were true wouldn't we be able to detect small particles disapearing and re-appearing even if it's maybe only for an EXTREMELY SHORT amount of time?

And secondly, when you use the analogy of an ant on a long one-dimensional garden hose that actually has a curled up 2nd dimension, the ant is not required to go through this dimension constantly returning to his starting point when he travels about through the 'left-right' dimension. But what Greene is saying is that when I wave my hand around that the tiny strings that make up the particles that make up my hand are forcefully traveling in these curled-up dimensions and I just can't graspwhy I am required to move through these dimensions when the ant in line-land is not.

If anyone can shed some light on this for me I'd appreciate it, or if my description above isn't good enough, tell me that also. I really want to udnerstand this. Thanks.
-Eric

Yes, we are continually passing through these compacted dimensions, according to string physics. At every point of space the full set of extra dimensions is present, and in order to pass through our extended dimensions we have to pass through the compact ones too. Compare moving your finger across this text. At every point of the two dimensional text, the third dimension of space allows your finger to touch.

We don't see any physical effects from this because the compacted size is much much smaller than a proton or than the Compton wave length of an electron, so they can't interact directly with the compacted dimension.

You are right that Greene's hose analogy breaks down when thinking about this issue. Any analogy can only be pushed so far. The physics works consistently, even if the popularization fails.