Some questions about dimensions 5 - 11

[JakeA]

in M Theory. The concept seems like a bit of mathematical trickery to me. If you come up with enough variables, you can ultimately model any logical system without having much insight into the system's fundamentals. I'm not dissing the theory or anything. Basically I don't understand it well enough to say much about it one way or another.

But anyway, I have a few questions about these dimensions if anybody can help me out.

1. Are they observable in any form? For instance I can observe distances with a ruler and time passage with a clock. Is there any way to observe these dimensions?

2. I've heard it said that the dimensions are "small." What does that mean? Does it mean that variations in these dimensions don't have easily observable effects?

3. Are they "relative" like space and time, meaning that an absolute time or position value has no meaning. Same for these dimensions?

4. Related to question 2, is it possible that values in these dimensions could produce observable and important effects? For instance I've heard it theorized that the Large Hadron Collider could create states in upper dimensions that could lower the energy threshold for creating a black hole. Is that plausible?

Thanks for any help on this subject.

 

[Orbb]

Hi JakeA,

in M Theory. The concept seems like a bit of mathematical trickery to me. If you come up with enough variables, you can ultimately model any logical system without having much insight into the system's fundamentals. I'm not dissing the theory or anything. Basically I don't understand it well enough to say much about it one way or another.

First of all, the number of 11 dimensions ist not really an arbitrary invention in String/M Theory, but rather a necessity for Supersymmetry to work consistently with Special Relativity. Therefore, in a way, these Dimensions could be regarded a prediction of Superstring Theory.

But anyway, I have a few questions about these dimensions if anybody can help me out.

1. Are they observable in any form? For instance I can observe distances with a ruler and time passage with a clock. Is there any way to observe these dimensions?

The additonal dimensions are also spatial dimensions, like the 3 known to us from everyday life. Therefore, apart from compactification, they do not behave any different. So if you had a ruler small and precise enough (which doesn't seem possible in practice, if the additional dimensions are of Planckian size), you could in principle measure distances in dimensions 5-11 in the same fashion as in dimensions 1-3.

2. I've heard it said that the dimensions are "small." What does that mean? Does it mean that variations in these dimensions don't have easily observable effects?

It means that, assuming one additional dimension (say, 5) has the size a, then by traveling a distance a in x5-direction, you would end up where you started (Compare with traveling around the globe as a 2-dimensional surface).

3. Are they "relative" like space and time, meaning that an absolute time or position value has no meaning. Same for these dimensions?

yes, see above.

4. Related to question 2, is it possible that values in these dimensions could produce observable and important effects? For instance I've heard it theorized that the Large Hadron Collider could create states in upper dimensions that could lower the energy threshold for creating a black hole. Is that plausible?

If that wasn't the case, the additional dimensions would have no physical significance. There are theoretical models, in which the extra dimensions' size is large enough to be detected in the LHC (e.g. by the creation of black holes, which wouldn't be possible if the dimensions were of Planckian size), however small enough that we cannot detect them in our everyday lives.

These are the answers I would give; I hope I am not mistaken in what I said.

 

[JakeA]

The additonal dimensions are also spatial dimensions, like the 3 known to us from everyday life. Therefore, apart from compactification, they do not behave any different.

Orbb, thanks for your reply. It was very educational.

I'm fascinated by the above, though. Here's a couple of, I hope not too silly, questions.

If I shoot something like a beam of light or a ping pong ball in a horizontal direction, and set up some sort of mirror at a 45 degree angle, I can reflect the trajectory into a pure vertical direction. Can I reflect trajectories from 1 - 3 into 5 - 11 if I build the right mirror, at least in theory?

To me it's sort of a head ache inducing question because dimensions 1 - 3 are arbitrary in relation to each other, i.e which way is up, down, left or right, I guess unless you're in a gravitational field in which case up and down aren't arbitrary.

Also, is nominal speed calculated using speed in dimensions 5 - 11?

For instance in 3 space C² = sx² + sy² + sz². Would you also need to add s5² through s11²? Maybe the speed of light is a problematic example, but I'm also interested in relativistic issues, so I brought it up.

Thanks.

 

[BenTheMan]

Orbb, thanks for your reply. It was very educational.

I'm fascinated by the above, though. Here's a couple of, I hope not too silly, questions.

If I shoot something like a beam of light or a ping pong ball in a horizontal direction, and set up some sort of mirror at a 45 degree angle, I can reflect the trajectory into a pure vertical direction. Can I reflect trajectories from 1 - 3 into 5 - 11 if I build the right mirror, at least in theory?

This is an interesting question, but the answer is no. Imagine it like this: suppose you want to make a very precise engineering drawing, but all you have is a Sharpie (i.e. fat, black marker). You can't draw very detailed lines using a fat pen---this is why engineers like these tiny 0.1 mm mechanical pencils. The same is true for your light: if you want to probe the features of spacetime at 10^{-34} cm, you cannot possibly get the resolution you need with light with a wavelength of 10^{-8} cm. As you go to higher and higher energies, the wavelength of the light becomes shorter and shorter. THEN, you may be able to deflect the light into the compact dimensions---this would correspond to creating Kaluza-Klein excitations at a particle accelerator, or something.

To me it's sort of a head ache inducing question because dimensions 1 - 3 are arbitrary in relation to each other, i.e which way is up, down, left or right, I guess unless you're in a gravitational field in which case up and down aren't arbitrary.

In my mind, this is the deepest question in physics---why are there three spatial dimensions? I don't know of any arguments from string theory as to why this should be the case. You're right, there IS a difference between the three dimensions and the other 7. The question is, why are they different?

Also, is nominal speed calculated using speed in dimensions 5 - 11?

For instance in 3 space C² = sx² + sy² + sz². Would you also need to add s5² through s11²? Maybe the speed of light is a problematic example, but I'm also interested in relativistic issues, so I brought it up.

Thanks.

Hmmm. Only particles which CAN travel in extra dimensions can have speed in the extra dimensions. Then, yes, you'd have to add other terms.

 

[trifractal]

In my mind, this is the deepest question in physics---why are there three spatial dimensions? I don't know of any arguments from string theory as to why this should be the case. You're right, there IS a difference between the three dimensions and the other 7. The question is, why are they different?

The difference is in the size of the dimensions, as you've been saying. The first 3 dimensions are infinitely large from our perspective, so we experience the potential they represent equally everywhere we go. The Planck scale dimensions are infinitely small from our perspective, so we can't physically take part in them. The components of our consciousness may be small enough to travel these dimensions directly, however.

Time, the fourth dimension, is truly where our existence is centered. It is the boundary of the dimensions we can freely travel, and the last we can truly experience- time is the one dimensional growth of our existence.

Is it possible that the dimensions could progress ever larger, effecting a space greater than that effected by 3d space? Would negative spatial dimensions fit for these in physics equations?

 

[starkind]

The metric I usually see in the mathematics of physics is -,+,+,+, where time is the negative. Space and time are equivalent in GR. I suppose this means that time "goes in the opposite direction," which I think means time is collapsing where the other three dimensions expand.

Welcome to the boards.

 

[JakeA]

>>>You're right, there IS a difference between the three dimensions and the other 7. The question is, why are they different?<<<

I've been holding off replying to this concept for a while because I've been thinking about it. Not that I've had any great revelations, but here's what I think. "Size" to a certain extent is a perceptual bias that we have. A better way of looking at it is statistical or probabilistic as in relevance. In our universe there's a higher probability that spatial information from 3 dimensions will be relevant to us, or in a non-perceptual view the objects in the universe. But is anything really not perceptual when you get down to it?

You can almost predict that there will be at most 3 important spatial dimensions just looking at numbers, continuity requirements, and the sorting algorithms that would be necessary to make sense of their probability distributions.

 

[trifractal]

The metric I usually see in the mathematics of physics is -,+,+,+, where time is the negative. Space and time are equivalent in GR. I suppose this means that time "goes in the opposite direction," which I think means time is collapsing where the other three dimensions expand.

Welcome to the boards.

Thanks. Yeah, that makes sense, like time is the dimension that ultimately overcomes the expansion of the others. That gets me thinking, do the physics account for a 0th dimension, perhaps underlying and permeating the other dimensions?

 

[starkind]

Perhaps it is better not to think of a dimension as a kind of place, as one might imagine from fictions such as "The Creature from Dimension X". Maybe we should think of a dimension as a process, as part of the process of measurement, rather than as a separate universe which exists in more or fewer dimensions than does our own. Then a "0th dimension" would plainly mean that there is nothing to measure...not a very useful idea in determining the behavior of objects.

Similarly, the first dimension is not first in the sense of coming before the others. There is no counting order in the set of dimensions. We are free to start counting wherever we like. Is there a zero dimensional object? How would we know it exists, if there is no way to measure it?

The idea of dimension is perhaps best understood mathematically, in which case we may say a volume has three dimensions, a surface has two, and a line has one dimension. There is a zeroeth dimension in that sense, which is the point. A point has no size to be measured.

However that is math, not physics. In physics, objects are not free to be infinitely small. There is a least measure of timespace, called the Planck limit. Without that limit on the process of measurement, the theory blows up into infinite energies, contrary to measured values. I would advise you to start with checking out "the plank length" as a search term in Wiki. I have to run now but will come back here later today to see if this is a help to you.

 

[Chronos]

A dimension is a degree of freedom. Any physical entity exists in at least 3 degrees of spatial dimensions and any number of other qualitative dimensions. Starkind is, however, correct. In quantum physics, spacetime does have a limit. This is why there is no true 'singularity' in nature.

 

[trifractal]

Interesting, interesting. Do you think this video:
http://video.google.com/videoplay?docid=-97057222894136590
gives a good description of the potential represented by the various dimensions?

 

[starkind]

It is, as the apology at the end suggests, a provocative view. Certainly it is a good exercise for anyone interested in thinking about the meaning of dimension. However it is almost certainly an oversimplification.

I like the constructivist approach, starting from the most fundamental idea and working upwards. However we have no reason to believe that these constructions actually represent a kind of evolution of dimensionality, where one simple action (folding, in this interpretation) can be repeated on lower forms to bring about higher ones.

Langauge is a clue to the problem. Phrases like "in the tenth dimension" are probably misleading. Is a dimension, as suggested here, really a place you can travel through? I am not comfortable with any representation that includes the idea of magical transport. If one needs to talk about constructing the third dimension by folding a two dimensional object, through what space does the folding take place? Folding a two dimensional object requires a third dimension through which the folding can happen. Folding already presumes a third dimension, so it cannot be used in defining the third dimension without invoking a tautology.

This problem comes from the constructivist approach, not from any quality of dimension.
We can talk about drawing a line, the simplest geometric element, between universes, which line presumably runs through a dimension higher than that which either universe can display. But in what way is this process really the same as drawing a line on a two dimensional surface? The two dimensional line is made up of a series of related points. It has length but no width or depth. The points, by definition, have no internal structure. But the "line" between universes is made up of a series of related universes, each universe taking the place of a point in a two dimensional line. Obviously the universes do have depth, as well as width and height and duration, and they possesses internal structure. In what way is such a line "the same" as a two dimensional line? Are there infinite universes between any two universes, as there are infinite points between any two points on a line? Hence, the oversimplification.

I don't wish to take any credit away from the producers of this video. They have done an exemplary job of assembling a rational justification for the existence of higher dimensions. Rationalizations are hazardous, but what is gained without hazard?

I still am not satisfied. Why is time "fourth" and not third or second or first? How do you account for dimensions such a temperature, color, rate of change?

I suspect "objects" are not inherently limited to any number of dimensions. Objects do not possesses dimensions any more than dimensions possesses objects. Instead, we should ask how many dimensions we need to describe an object adequately to our purpose. What is a three dimensional object? It is an object which can be adequately described by three measurements, each measurement fixing a quantity to a dimension. To say an object is three dimensional is not to say it hasn't any more dimensions, but merely to say that three is all we need to describe it for our purposes.

I am studying advanced mathematics but by no means have I become a master. Still, I have seen enough to suspect that the usual idea of dimensions, as admirably expressed in the book "Flatland" and extended to higher dimensions in this video and in other presentations, is at best, incomplete.

Well, you did ask what I think. For what it is worth...

R

 

[Naty1]

I've heard it said that the dimensions are "small." What does that mean? Does it mean that variations in these dimensions don't have easily observable effects?

It also means that many physicsts [POSSIBLY haven't been imaginative enough to realize the extra dimensions might be LARGE. Compactified/rolled up dimensions have been the "standard" under study for the longest time; the ADD model posits why gravity might be so weak...extra large dimensions could dilute gravitational strength. These large extra dimensions are associated with branes, multidimensional strings. The more extra dimensions, the more gravityis diluted and the samller tghe extra dimensions might be.

Lisa Randall, Harvard, discusses the ADD model in chapter 19 of her book WARPED PASSAGES, 2005.

Experimental testing of the Casimir effect to detect possible weaking of gravity (relative to the inverse square law) and the related possibility of extra dimensions at sub millimeter scales have so far NOT produced any evidence of such large extra dimensions...you can read about the general theory at http://en.wikipedia.org/wiki/Casimir_effect

 

[JakeA]

The Casimir effect is interesting. As I mentioned before, I view distances as probabilities, not coordinates specifying "place" that we perceive in the classical world. Small distances, high probabilities that unexpected things will happen.

Something like the Planck length can obviously be viewed as a restatement of the uncertainty principle in that you're attempting to reach a probability of 1 by shortening distances.

 

[Naty1]

1. Are they observable in any form? For instance I can observe distances with a ruler and time passage with a clock. Is there any way to observe these dimensions?

Not so far. Nothing in string theory has been experimentally verified.


2. I've heard it said that the dimensions are "small." What does that mean? Does it mean that variations in these dimensions don't have easily observable effects?

Theoretically the small dimensions are reflected via the string vibrational patterns...geometry sets parameters for particles...so the effects may be observable but not yet so unambiguously related to additional smaller dimensions.

3. Are they "relative" like space and time, meaning that an absolute time or position value has no meaning. Same for these dimensions?

I don't think string theory has been sufficiently developed yet to create any obvious conflicts with relativity...so for the time being, "yes".

4. Related to question 2, is it possible that values in these dimensions could produce observable and important effects? For instance I've heard it theorized that the Large Hadron Collider could create states in upper dimensions that could lower the energy threshold for creating a black hole. Is that plausible?

Yes, per # 2.

You might also find this thread of interest:
https://www.physicsforums.com/showthread.php?t=297908