Curled Up / Small Dimensions In String Theory

[MistyMountain]

When string theorists say that higher dimensions are "too small" or "curled up," what do they mean?

Suppose, for instance, that the x dimension was curled up in three dimensions. Could someone draw a picture that?

If the x dimension was too tiny to be measured, what would this mean? Would we ever be able to get off the y-z plane?

Coudl someone draw or point me to a picture of 1) a curled dimension, or a 2) dimension too tiny to be ssen?

Thanks!

 

[rtharbaugh1]

Try this link:

http://en.wikipedia.org/wiki/Calabi-Yau_spaces

 

[DaveC426913]

I don't know if I can explain it easily.

Are you familiar with Flatland? A hypothetical universe that has only two dimensions? Knowing that will make it a lot easier to explain...

 

[MistyMountain]

Yes--Flatland was rather trivail--it only had two dimensions.

I have no problem envisioning up to five dimensions, and six dimensions on a good night, but then things get hazy aorund seven-ten.

If someone could plese draw the intersection of the eighth dimension with the ninth, this would help a lot.

I could then try to extrapolate the figure back to the seventh, and on through the tenth, and I will know the ten dimensions that String Theorists see.

I have heard it is beautiful. I will let you know when I get there. Thanks for assisting this traveler!

Thansks!

 

[DaveC426913]

?
I'm not sure if you're kidding or serious. You can envision these higher dimensions? Wasn't that the trouble you were facing in your original post?

I was humbly going to try to describe a *fourth* dimension all curled up.

 

[rtharbaugh1]

I have had some success (in my own mind) envisioning four dimensions, and have some ideas about five, six, seven, and eight, but have never managed to successfully convey my impressions to any other person, to the extent where anyone says they can see it that way, too. The language is very difficult, full of slippery definitions.

Mathematics has formalism to deal with higher numbers of dimensions, but I have not managed to make sense of that yet. I keep trying. The most common reaction from the learned is that humans cannot see in higher dimensions and most people think there is little reason to try.

My impressions have seemed beautiful to me, and seem to me to imply a higher morality as well, but these things are not factors that lead to success in today's culture. I have pursued them near to the edge of my own destruction, giving up friends, family, and social standing. I still think it is important, although I have little hope left of ever being able to communicate what I think I know.

Perhaps we could start by talking about four dimensions. The image looks like a long exposure in a still camera photograph of fast motion, where the moving figure blurrs and leaves a trace behind it where it has passed. Cartoonists and other artists use a similar effect to indicate rapid motion, so it is not a great stretch for most people to make the visual image. In my imagination, I can show myself a three dimensional object moving in this way, leaving a time trace.

Is this what you think of as a four dimensional image, Misty Mountain? Or can you express it in some other words?

Thanks,

Richard

 

[rtharbaugh1]

http://en.wikipedia.org/wiki/Holonomy

About halfway down this page, there is a table under the heading "Riemannian holonomy groups", Berger's list, which gives manifolds in higher numbers of dimensions. I have been studying holonomy groups for a while but still do not understand them. I put this here as food for thought.

R

 

[MistyMountain]

?
I'm not sure if you're kidding or serious. You can envision these higher dimensions? Wasn't that the trouble you were facing in your original post?
I was humbly going to try to describe a *fourth* dimension all curled up.

Hello Dave,

That would be great to hear about a "fourth" dimension all curled up.

Please do describe.

I think I can envision these things, but I am unsure.

I will try to draw a picture and post.

If anyone else could draw a picture, that'd be great!

Also, say if we had nine dimensions instead of ten dimensions, what parts of physics would not work according to String Theory?

Why do QM, GR, and SR (successful theories) only need four, but ST (unsuccsessful so far) need ten?

Why do we need ten?

What is the motivation?

Thanks!

 

[MistyMountain]

I have had some success (in my own mind) envisioning four dimensions, and have some ideas about five, six, seven, and eight, but have never managed to successfully convey my impressions to any other person, to the extent where anyone says they can see it that way, too. The language is very difficult, full of slippery definitions.
Mathematics has formalism to deal with higher numbers of dimensions, but I have not managed to make sense of that yet. I keep trying. The most common reaction from the learned is that humans cannot see in higher dimensions and most people think there is little reason to try.
My impressions have seemed beautiful to me, and seem to me to imply a higher morality as well, but these things are not factors that lead to success in today's culture. I have pursued them near to the edge of my own destruction, giving up friends, family, and social standing. I still think it is important, although I have little hope left of ever being able to communicate what I think I know.
Perhaps we could start by talking about four dimensions. The image looks like a long exposure in a still camera photograph of fast motion, where the moving figure blurrs and leaves a trace behind it where it has passed. Cartoonists and other artists use a similar effect to indicate rapid motion, so it is not a great stretch for most people to make the visual image. In my imagination, I can show myself a three dimensional object moving in this way, leaving a time trace.
Is this what you think of as a four dimensional image, Misty Mountain? Or can you express it in some other words?
Thanks,
Richard

Hello Richard,

I love trying to envision things in a physical manner, as that is what physics is all about.

It seems like you do too. :)

I think that when the math doesn't work and it makes no physical sense, then a theory is somewhat suspect. No?

Time is not a fourth dimensions so much as an emergent property of a fourth dimension that is fundamentally different from the three spatial dimensions.

The fourth dimension is fundamenatlly different, because of this metric:

x^2+y^2+z^2-c^2t^2=s^2

If we could only envision its "physical" reality for sure (sometimes I think I can), I feel we could anser the following questions:

Why is there a minus sign in the above metric?

Why is there a c in front of t?

Why does time's arrow point in the direction it points
in? Why entropy?

Why do photons appear as spherically-symmetric wavefronts
traveling with the velocity c?

Why does time stop at the speed of light?

Why is the speed of light constant in all frames?

What underlies all motion? What is the geometry of
motion that is missing in GR?

Why is time-reversal invariance violated?

I think a physical understanding of higher dimensions will give us satisfactory answers to these questions.

Perhaps ST have already answered them, but I have not yet seen it anywhere.

It all comes down to the physics of dimensions, when you think about it:

Why do moving bodies exhibit length contraction?

Why are mass and energy equivalent?

As physicists, we must always ask, "why" and "how"?

Asking "why" and "how" about gravity is how Einstein found out that dimensions warp and bend, that space-time curves and shifts!

Perhaps one of you will anser some of the above "how's" and "why's". :) Thanks!

And finally, what fundamental physical reality--what dimensional reality--gives us both the timeless, ageless photon--a concept of relativity--and quantum entanglement?

I'd love to hear how QM and SR and GR descend from the physics of dimensions

I think too often we get caught up in the math of diemsions, but it was Einstein, by always worrying about the *physics*, who furthered physics more than anyone else.

Thanks for your insights!

 

[Robine]

Calabi-Yau spaces (as suggested above) is a good place to visualize some space shape candidates. Currently the dimensions envisioned may be on the order of Planck length, billions and billions of times smaller than subatomic particles, far too small to be detected at present. So small,in fact, that most forces can't penetrate...except maybe gravity! Nobody knows. Brian Greene's FABRIC OF THE COSMOS provides good descriptions and concepts without string theory mathematics.

 

[rtharbaugh1]

Hello Richard,

I love trying to envision things in a physical manner, as that is what physics is all about.

It seems like you do too. :)

I think that when the math doesn't work and it makes no physical sense, then a theory is somewhat suspect. No?

Time is not a fourth dimensions so much as an emergent property of a fourth dimension that is fundamentally different from the three spatial dimensions.

The fourth dimension is fundamenatlly different, because of this metric:

x^2+y^2+z^2-c^2t^2=s^2

If we could only envision its "physical" reality for sure (sometimes I think I can), I feel we could anser the following questions:

Why is there a minus sign in the above metric?

Why is there a c in front of t?

Why does time's arrow point in the direction it points
in? Why entropy?

Why do photons appear as spherically-symmetric wavefronts
traveling with the velocity c?

Why does time stop at the speed of light?

Why is the speed of light constant in all frames?

What underlies all motion? What is the geometry of
motion that is missing in GR?

Why is time-reversal invariance violated?

I think a physical understanding of higher dimensions will give us satisfactory answers to these questions.

Perhaps ST have already answered them, but I have not yet seen it anywhere.

It all comes down to the physics of dimensions, when you think about it:

Why do moving bodies exhibit length contraction?

Why are mass and energy equivalent?

As physicists, we must always ask, "why" and "how"?

Asking "why" and "how" about gravity is how Einstein found out that dimensions warp and bend, that space-time curves and shifts!

Perhaps one of you will anser some of the above "how's" and "why's". :) Thanks!

And finally, what fundamental physical reality--what dimensional reality--gives us both the timeless, ageless photon--a concept of relativity--and quantum entanglement?

I'd love to hear how QM and SR and GR descend from the physics of dimensions

I think too often we get caught up in the math of diemsions, but it was Einstein, by always worrying about the *physics*, who furthered physics more than anyone else.

Thanks for your insights!

Hi MM

These are interesting questions. I would like to work on some of them here.

You said "Time is not a fourth dimensions so much as an emergent property of a fourth dimension that is fundamentally different from the three spatial dimensions."

This idea of a fundamental difference between space and time seems to violate the principle of space-time equivalence. I do agree that it is naive to think of time as a fourth dimension which can be simply added to the three spatial dimensions.

Can you or one of your avatars say something more about what you mean by time as an emergent property of a fourth dimension? I am afraid I don't get a very clear image from that.

You said:
"The fourth dimension is fundamenatlly different, because of this metric:

x^2+y^2+z^2-c^2t^2=s^2

If we could only envision its "physical" reality for sure (sometimes I think I can), I feel we could anser the following questions:

Why is there a minus sign in the above metric?"

Well, afaik, the metric you write is a four dimensional extension of the Pythagorean theorum. X, y, and z are clearly the three spatial dimensions we commonly deal with, and the phrase -c^2t^2 is the fourth. I see right off that c^2t^2 has dimensions of length squared, just as do x^2, y^2, and z^2. Why is it negative? I am pretty sure there is a common mathematical reason which I could find, if I could understand it. Instead I offer the following visual interpretation, subject to corrections.

Objects have duration in time as well as extension in space. Commonly we do not interpret objects as undergoing expansion in space as they progress through time. Time 'capacity' or 'density' must then increase in any object as it endures (I use the quotes because I do not have offhand a term as such for time). Since we do not wish to imply that objects expand as they experience time, the spatial contribution from the fourth dimensional translation has to be negated. This is just a thought, not something I am committed to. Corrections or explanations of the maths would be welcome here.

You ask "Why is there a c in front of t?" C is an absolute, the speed of light, which can be given the value in fundamental units as unity. It seems to be used here to introduce a time element into the equation, since the fourth dimension is taken to be temporal. I think we both have a problem with this assumption of time as a simply added fourth dimension, as discussed above. I hope for more clarification or direction from the PF mentors.

"Why does time's arrow point in the direction it points
in? Why entropy?"

The quick answer is 2nd law of thermodynamics. If I may rephrase your question, I should ask "Why do some processes seem irreversable?" Personally, I like the many 'times' interpretation of the Many Worlds Interpretation. Then the answer would be that some processes seem irreversible because the observer is "moving through" a spacetime structure which is in some cases not symmetrical. Suddenly it does not seem surprising that time's arrow points in a direction. We seem to be observers moving through a spacetime stucture. The spacetime structure seems to have many possible directions for movement. The direction of our motion is then opposite to the direction of the arrow of time. In this sense, the direction of our motion produces the seeming opposition (negative) direction of time.

We expand, is how I view it. So time and space seem to contract within us. We cannot logically accept that space is shrinking from view, so we take the proposition that time has a direction opposite to our expansion.

I would add that time does not have to be negative, but we have to negate time in order not to seem to be expanding. Again, I hope for corrections, especially ones that I have a chance to understand.

"Why do photons appear as spherically-symmetric wavefronts
traveling with the velocity c?"

You seem to have wave-particle duality in sight. Photons are the particle, and under some conditions of measurement they have a wave-like charachter. As for the velocity c, I would suggest, from a MTI, that c is a horizon. Photons, as particles, are then the substance of spacetime. It might be useful then to imagine the photons as stationary bits of spacetime, and our motion as appearing relitive to them. However like any horizon, you can never actually approach it. So the spacetime 'Substance' is not an absolute, only a necessity of observation. ST is not to be confused with an aether, just as the horizon of the Earth is not an actual place you can visit and grace with your chosen graphitti.

That is enough for now. I am getting tired and want to be my best on this forum. I would like to explore the idea of horizons with you, and how they apply to the rest of your questions. But I will break here and wait for comments.

Thanks,

Richard

 

[disturbed1]

my understanding of the elegant universe is that string theory identifies 11 dimensions in the unified m theory. m theory brought together the five flavors of string theory into one unified idea...6 tiny dimenisions which each have a unique shape are identified. these rapped up shapes provide the vibrations for stings from reacting with the 6 tiny multidimesional shapes... it includes the four dimensions of space time, and a higher dimension providing space outside our universe. 11 dimensions in all. Imagining dimensions can be difficult. they can be large and small..it appears that the three dimensions of space can be applied to these 6 new tiny dimensions in such a way to make them imaginable and have shape...these shapes are required to make the strings function. the 11th dimesion would be a higher area containing our universe and perhaps the multiverse. I'm nothing more than an uneducated geometrical philosopher looking at the vast universe. let's try and imagine the universe as a unit. imagine an invisible rubix cube or simply a see through box...it has lines enclosing the three spatial dimensions. add the x,y,z planes inside the box. I find it rather strange that this model has 11 lines...but I picture the outer perimeter of this universe not as 8 lines but as one plane or dimension. in other words turn your box into a sphere. now your left with four planes or dimensions known as space time. try imaging 3d objects inside or enclosing the sphere or box, this will lead to imagining the other 7 dimensions of the multiverse...always use x,y,z its not only the three dimensions of space but also a tool for measuring. Imagining the perimeter is tricky. existence is the question. where did time, information, and matter come from. information and matter seem inseperable. you can't have one without the other. try imaging a universe with these three units seperated...its seems unreal. can information exist without matter? can matter exist without information? can time exist without information? can information exist without time? can matter exist without time? can time exist without matter? these questions keep entering my mind lately...it appears as though dimensions will be unlocked in groups, with similar properties unique to each group. can anyone grow on this?