Expert: Courtney Seligman - 10/18/2011

Question
QUESTION: Hi Courtney. As an amateur cosmologist I come across much talk of multiverse, dimensions etc. It seems to me that anything we can detect/observe etc is by definition in, or part of 'our' universe. If these dimensions/ universes have no effect on our universe then they are irrelevant. So, are terms like multiverse/dimensions misleading? Or am I splitting hairs? I have wondered if dark energy is actually an effect from what we would term outside of our universe. But if this is the case can it be said to be outside of our universe!? Is this just a question of definition or a more fundamental point? Thanks for your time.

ANSWER: (Note added partway through answering your question: The start of this answer is about a definition of hidden dimensions which involves the space we actually live in. As discussed immediately below, those hidden dimensions may exist, and simply be too hard to observe for us to be directly aware of them; and if they do, they are part of the observable Universe, even though not as easily observable as the easily visible dimensions. There is, however, a different definition of other dimensions which may be more relevant to your question, and is discussed along with multiverses, following the dashed line.)

The question of multiple dimensions is part of some theories of why the fundamental forces of nature work the way they do. Those pursuing those theories feel that the math involved suggests that if there are "hidden" dimensions, it may explain some properties of the Universe that seem difficult to explain if there are only the three "known" dimensions of space, and of course the "dimension" of time. If I recall correctly, the most seemingly successful theories involve about ten or twelve dimensions.

However, although the extra dimensions are "hidden", it is not in the sense that they are unobservable. They are just so small that we can't see that they are there. It's like thinking of a "Flatland" universe consisting of a sheet of paper. There would be two "visible" dimensions -- length and width -- but if the sheet was sufficiently "paper-thin", so that you really couldn't go anywhere "in" the paper thickness without still being, as far as you could tell, in the same place as where you started, then the thickness would be "hidden". It would be there, but you couldn't tell that it was there, under normal circumstances. Similar, "hidden" dimensions are imagined to be far, far "thinner" than the smallest particles which exist in nature, so that an object at one point in "normal" space would occupy the entire volume of every corresponding point in the hidden dimensions. (There are variations of this idea in which the hidden dimensions do have "measurable" size, but are so tightly coiled around themselves, that their overall extent is still infinitesimal -- like wrapping a gossamer piece of the fibers used to make The Emperor's New Clothes round and round, so that even if miles long, they took up less "real" space than a mote of dust.)

In other words, hidden dimensions, if they exist, are part of every part of our Universe, and if we could figure out a way to observe them, would be instantly observable, everywhere. The only question is whether they do exist, and if so, how would you go about proving that? And so far, the answer to that is that they might or might not exist, and you just have to rely on the physicists and mathematicians involved in the work to declare that their models have succeeded in producing a satisfactory Theory of Everything.

My personal opinion of this idea is that it is conceivably correct, but I wouldn't want to waste any of my time seriously involved in the field, reading about it, or wondering whether I'll live long enough to find out if it is in any way possible. So although the above should be a reasonable summary of the idea, it may be "off" enough to raise the temperature of one of the people actually involved in such work. And although I'm dubious about the eventual success of the theory, I do think it is more likely to be correct than many other theories which are equally popular (however, to avoid boiling the blood of even more theoreticians, I'm deliberately omitting the names of those theories).

The point to be made about the theory of multiple dimensions is that whether it is correct or not, it is directly related to "our" Universe; and if it could be proven correct, the difficult involved in observing the hidden dimensions would not mean that they are not part of the observable Universe; just harder to observe, than the "visible" dimensions. (This is where it occurred to me that perhaps I ought to separate this possibly "real" part of the topic from the following, "unreal" parts, with a dashed line; and to add the note at the start.)
----------------------------------------------------------------------------------------------------

Now, on to multiverses which may exist in "other" dimensions, or not at all.

It is thought that our Universe most likely arose when an infinitesimally point in the space-time of some prior Universe suffered an infinitely large "glitch", and in the process, created the zero-size "point" of space-time now referred to as the Big Bang. As discussed at In the Beginning (see http://cseligman.com/text/prologue.htm), that zero-size infinitely energetic glitch would have created a whole new space-time, completely separate from the prior Universe, which became our Universe. It is thought that the rapid expansion of that point led to its soon becoming far too large for us to ever "see" most of it (thereby dividing our Universe into the part we can observe, the "observable" Universe, and the part we can't see, namely the rest of it). The existence of the part of the Universe beyond the Cosmic Horizon (set by the current age and expansion rate) is, in the opinion of almost all astronomers, and certainly all cosmologists, beyond dispute. In other words, anybody who gives any credence to the Big Bang theory feels sure that the Universe is much larger than what we can see of it; but that doesn't mean that if it is, the parts we can't see aren't there. In a sense, it's like looking at your local horizon. You know there is more Earth beyond that, and if you moved around a bit, you could easily prove that; it's just that in the Universe as a whole, you can't move around enough to make any difference, because the parts beyond your horizon are beyond your horizon because the space between you and your horizon is expanding at the speed of light, and you can't go that fast, so no matter how fast you head toward the horizon, it keeps getting further and further away.

In other words, the Universe beyond the observable Universe is presumably there, even though we can never hope to observe it. And in fact as time goes on, much of what is currently observable will become observable, because as distant parts of the currently observable Universe are carried away from us by its expansion, they will be carried away faster, and eventually everything now beyond about 100 million or so light years' distance will be going away from us faster than the speed of light, and although the distance we will be able to see at that time will be millions of times further than now, we will see nothing at all in it save for the objects that are not being carried away from us, at all. (Odd to think of the observable portion of the Universe shrinking toward us, even as it gets further away, and in some ways a little disturbing; but the time involved is millions of times the current age of the Universe, so it's not as though we'll ever notice any difference.)

So to start the ball rolling, in talking about other dimensions or multiverses, we are not talking about the parts of our own Universe which we can't see, just because they happen to be too far away, and the space between them and us expanding too fast, for their light to ever reach us. They are presumably just as much a part of the Universe as we are, just as the other side of the Earth would have been just as much a part of the Earth in ancient times, even if there was no way to tell it was there (the ancient Greeks, or Hellenes, knew that the Earth was round, and that there must be a large part of it so far away that no one had ever seen it; but they presumed that there were people and creatures there, just as there were in the regions they were aware of).

But I digress, and this is rambling on partly because I have to leave for work soon, and want to post an answer before leaving, so I'm hurrying a bit, and it's easier to just keep going than to go back and clarify things.

So, as far as multiverses in other dimensions are concerned. If a glitch in one point of space-time in a prior Universe could create our Universe (as is the favored theory), then why couldn't similar glitches in that or other prior space-times create other Universes. And if so, why couldn't you end up with, after a while, an infinity of Universes, each of which would be creating (in the same way) an infinity of other Universes, ad infinitum? That is what is generally referred to as the multiverse (although as always, when you can't actually observe what you're talking about, there are variations on the idea which are even more extreme; though it is hard to imagine how it could be more extreme, when you're dealing with an infinity of infinities).

Now, keep in mind that if the theory of our Universe's origin is correct, in the instant of its creation it created a whole new space-time, completely separate from the prior Universe, and from every other Universe that might have been created, as well. As far as some uber-world godlike view, each Universe in the multiverse would have zero size, and be completely separate from every other Universe. It would only be "inside" each Universe that you would have a rapidly increasing infinity of space, from which an infinity of new Universes could be created. So if the theory of our Universe's origin is correct, there must be an infinity of other Universes, none of which shares any part of the space-time of our Universe, or of any other Universe, so that none of them would ever be observable from any of the others.

In other words, whereas the part of our Universe that is beyond the Cosmic Horizon is truly part of our Universe, and only unobservable because of the Universal Expansion, every single other Universe in the Multiverse would never be observable from any other Universe, so admittedly, whether they exist is a matter of opinion. However, if the theory of the origin of our Universe is correct, then even though we can't observe any of the others, they must exist, just as much as ours does.

I suppose that something like this could be called meta-physics, meaning a part of physics which you can't actually prove. But the laws of physics that this is based on are presumably the same no matter where you are (although some versions of the theory suppose that the laws might be different in other Universes, in which case the theory might not be as self-consistent as it could be), and if so, then it is inevitable. It's sort of like saying that if balls fall here, they must fall elsewhere. So even if you can't see balls falling elsewhere, they probably do.

To summarize this section, although I believe that our Universe is the only part of the Multiverse that we can ever observe, or would ever be able to observe, even if you ignore the problems which prevent us from observing all of our own Universe, I'm in general agreement with the overall idea. I would disagree with those who think that it might be possible for one Universe to connect with another. Since the space-time in each one grows out of a point of zero-size, creating its own unique space-time, separate from any other space-time, I believe it to be impossible for any part of our Universe's space-time to ever intersect the space-time of any other Universe. If as they grew they were growing in some fixed-size super-space, and as they grew they ran out of room, it would be one thing. But since all the (rapidly increasing space) in our Universe is being created out of nothing, and as far as any other Universe ought to be able to tell, still takes up no more room than the single point of space-time in which it originated, there is no way for one Universe to ever be in any way connected with any other.
-------------------------------------------------------------------------------------------------

On to the final part of the question. What about "parallel" Universes which occupy other realities, which are supposedly a part of our own Universe, but completely separate from them.

There is a theory, based on quantum mechanics, that suggests that the Universe is not only growing in space-time, but within space-time, in a very odd way. Namely, that when something happens which could have two outcomes, there is no way to tell which outcome occurs until you make an observation of what happened. The idea is that before you do that, there are two possible "future Universes", one in which the outcome is one way, and one in which it is the other way. There is a subset of quantum mechanics which supposes that in such a case, there are actually two completely separate Universes, which occupied the same space-time before the event, but which occupy two different space-times afterwards, and that each of them is just as real as the other, and your observation doesn't tell you what happened, but which of the two Universes you happened to end up in. If you observe one result you are in one of the Universes, and if you observe the other result, you are in the other Universe. There is, of course, no way to tell if this is true, or to observe one Universe from the other. In this view, our Universe consists of an infinity of infinity of infinities (and you can keep going as long as you want with infinities), each of which differs from one of the others in only the most infinitesimal way. Whether this idea might be correct depends upon which quantum physicist you talk to. My general impression is that the overall feeling is that if something could happen, it will happen, and so such an infinity of parallel Universes might exist. However, unlike the Big Bang "if it can happen it will", in which the creation of a new Universe is extremely rare, the parallel Universe theory makes the creation of new Universes easier than blowing soap-bubbles.

Of course, as in the case of the Multiverse theory, the infinity (or infinities) of parallel Universes would be completely unobservable. Once the Universe splits into two Universes, there is no longer any connection between their future selves, and there is no way to access any part of the one from the other. As long as there is any difference between them, they will remain forever separate. As an example, suppose you had a pair production in empty space. Which way would the two particles (a particle and an anti-particle) go? In one "parallel" Universe the particle goes in one direction, and the anti-particle in the other. In the other "parallel" Universe the directions are reversed. Later on, of course, each particle may run into something else and be annihilated, and to a certain extent, the two Universes would be more similar than in-between. But the two annihilations would involve different particles in the "original" Universe, so there would be a subtle difference afterwards, in which one part of each Universe would have one less particle, and a different part would have one less anti-particle, and in that subtle way, they are still unique and separate.

As noted above, I don't know if this idea is real. It seems reasonable, but not as reasonable as the Big Bang, or even as reasonable as the Multiverse. And just as you could never observe any other Universe in the Multiverse, you could never observe any "parallel" Universe out of the infinity of parallel Universes (not that this prevents science fiction writers from bopping from one parallel Universe to another; and in fact, I wrote a short story based on that idea, myself. But that is where the "fiction" comes in, in "science" fiction.).
===================================================================

SO... where does that leave us?

(1) Hidden dimensions within our own Universe may exist. Or they may not. If they do, they are just as much a part of the Universe as the dimensions we can observe. Whether we will ever be able to tell, either mathematically or physically, whether they do is another matter. And so I find the idea interesting, but not interesting enough to spend any significant portion of my time. And whether you should waste any portion of your time worrying about it is up to you.

(2) The Multiverse almost certainly exists, but it is almost as certain that no part of it can be observed from any other part, so although theoretically almost as certain as the fact that things fall down instead of up, there is no conceivable observation that could prove that this is anything other than a magnificent idea.

(3) Parallel universes (and the supposed "extra" dimensions associated with them) may exist. If they do, you cannot move between them, but science fiction writers will insist on doing so, and TV programs and movies will use them as indiscriminately as tales of ghosts and werewolves. They are a gimmick used to provide a background for a pseudo-scientific story; but whether they are a useful gimmick depends upon how well the story is written. However, as noted above, it would be impossible to prove that they do exist, and there might be some disagreement as to whether they can exist, even among quantum physicists.

On a scale of 0 to 10, 10 being most likely, how likely is it that each of these can exist, or can be observed?

For hidden dimensions, I'd say the chance of their existing is about a 3 or 4 at best, but if they do exist, the chance of being able to prove their existence is more like an 8 or 9 (given the future technology required to do so; right now, the chance of being able to prove their existence is 0).

For the Multiverse, the chance of its existing is a 9 or 10. The chance of observing any other part of it is a 0.

For parallel Universes and "other" dimensions associated with them, the chance of their existing is somewhere between 0 and 10, but where is beyond my knowledge. If they exist, the chance of ever observing any of them is 0.

Given these odds, it's hard to say whether you want to think of any of these as having a "real" existence. But taken as a group of theories, they aren't necessarily as fanciful as wondering how many angels can dance on the head of a pin. The question is, fanciful or not, are they useful? I think the idea of the Multiverse is useful, though not as much so as portrayed in the media. The idea of parallel Universes is probably not as useful, but who can really say? And the idea of hidden dimensions, although perhaps a complete dead end, may at some point in the future prove to be an "astounding breakthrough" (to use future media-speak).

As noted above, time presses, and I've rambled on far too much, in an effort to squeeze in as much as possible in the time I had to answer this. I apologize for any typographical or grammatical errors, and if there is any part of this which muddied the waters more than it clarified them, just let me know and I'll be happy to try to do a better job when I have time.


---------- FOLLOW-UP ----------

QUESTION: First of all Courtney, thankyou very much for a thoughtful and thorough answer. Most of what you have written I have read (etc) about and understand fairly well (as much is reasonably possible anyway)! Its funny how such a simple question can illicit such an answer; an answer that i suspect could have gone a lot further!
I know I might be sounding a bit obtuse but I really dont mean to be. Would you agree with the following statement...a yes/no or maybe is fine....Anything that can be measured/ observed/ has an effect on etc in/on our universe is part of our universe. Here I am not talking about what theory might point to, but actual physical measurement.
This question stems from extensive reading of physics where multi dimensions etc etc are frequently mentioned but very respected scientists. I mentioned to a (perhaps not so respected!) scientist my pet theory of dark energy coming from 'our' universe's motion about a multiverse centre (for a simple way to put it). Forgetting if the theory stands up, I was told I was using un-provable meta-physics and thats not the scientific way. That just seems to be double-standards to me? I totally accept that many many people come up with ideas that dont fit with what we know and I cant just say 'prove me wrong. Im not saying we live in a cheese universe or dare I say it, God  moves planets or such-like mumbo jumbo. But I have found to have an idea put down on the basis I mention a multiverse very frustrating.
Also, if youd be so kind, one last question came to mind. I have read about possible other dimensions wrapped up so small we cant see them. I have heard that 10 or 12 seem most likely according to theory. My question is of numbering the dimensions. We are said to be in the 3rd dimension of spacetime. This would imply that the wrapped up dimensions are numbered 4 to 10 or 4 to 12. If these dimensions are wrapped up in ours, would it not be more accurate to view these dimensions  as dimensions between 2 and 9 or 2 and 11, and our dimension as the 10th or 12th? I know it seems common sense to think dimension (d)1 as pointlike, d2 line-like, d3 as volume (our universe). Rather than further dimensions being d4 d5 etc, is it not possible they are dimensions between d2 and d3 (say 2.1 2.2 etc etc) Given that we struggle visualising/ interpreting any other dimensions, and IF they are wrapped up so tiny IN our universe is this at least a possibility? Again, maybe I am asking a question that doesnt matter but I do tend to look at things a bit warped. Thats why I find your response so valuable. A book doesnt answer the questions that spring into my head!!! Thanks once again Courtney.

ANSWER: Yes, I would agree that if something can affect part of our Universe, then it should be considered part of our Universe. That doesn't necessarily mean it would be part of the "observable" Universe as normally defined, but it would be part of our Universe.

As an example, there is "brane" theory, being a shortened version of "membrane". In this theory, the Universe is thought of as being like a length of fabric, folded on itself in layers, so that very distant parts of the Universe (as measured along the length of the fabric) might be very close to us (as measured between the folds). It should be kept in mind that in this representation, all dimensions of our Universe that can be observed and are actually "part" of our Universe (whether 3, 4, 10 or 12) are "in" the fabric-like sheet, and any space between the "folds" is not part of our Universe, but just a way of visualizing things. It has been suggested that if such a theory were true, and the branes could slide around relative to each other, "collisions" or "near-misses" between different "layers" could produce shock waves in the regions near the "collisions", which could be used to explain certain things. The weakness of gravity relative to other forces has also been "explained" in this way, by supposing that the other forces are confined to the "fabric", but gravity can "leak" between the "layers" (this would also be a convenient but wrong way of explaining dark matter; it would just be regular matter in other branes).

Presuming brane theory were correct, then all of the folded fabric, no matter where it is located relative to us "in" the plane of the fabric, would be part of the Universe. The odd thing would be that unobservable parts of the Universe (the parts of the folded layers that are too far away to be directly observed) might be able to affect the observable parts of the Universe.

I find this idea interesting but repellant, in that it explains observable things with unobservable suppositions, and most particularly, it explains observable things which almost certainly have a more straightforward answer (even though we don't know what that answer is, yet) with a completely unprovable hypothesis. (And this is, in fact, one of the multitude of theories that I mentioned are floating around but which I preferred not to bring into the discussion because I didn't want to unnecessarily upset people who have spent their careers working on such nonsense. Although, even if it is nonsense, it wasn't necessarily useless to them, as the authors of such theories are far better known than I am, and undoubtedly take pride in both their work and the "position" it affords them.)

Of course, that would also suggest that if there were other Universes, which could be "close" to ours, so that they could somehow affect our Universe, then perhaps things here could be explained by things "there"; but as I explained in my original answer, if other Universes are created in the same way that ours was (or at least, the same way we think ours was), then each of their space-times is completely separate from all of the others, and even more so than each of the stars in our part of our galaxy are very well separated from all of the others (ignoring binary stars, which have nothing to do with such a discussion). For in the case of say, our Sun and the nearest known star, the Alpha Centauri system, there is a separation between them of about 25 million diameters. But even Universes created from a single prior Universe would be separated by an infinite number of diameters, since in the space-time frame of that Universe, each Universe would be only a single infinitely small point of space-time, and the distance between such points would involve more zeroes than I could write in this answer, even though I could add about 60 thousand of them, before reaching the AllExperts limit. So although there is probably an infinity of Universes, they cannot be "close", in any sense of the word; and there should be absolutely no possibility of them interacting with each other. It is for that reason that I stated that although the Multiverse theory is in some ways almost certainly correct, illustrations which show the individual Universes as having any size in comparison to the non-existent trans-dimensional "distance" between them, or in any way having any possible interaction, are more wrong than there are words to describe.

Finally, as for those 10 or 12 dimensions, that is what I was discussing in the first part of my answer. The idea is that you could have a large extent of "actual distance" in each dimension (perhaps even as large as in the three (or four, if you count time) "visible" dimensions, but that it is so tightly coiled around that the total distance, as measured "across" the coils, is far smaller than the smallest measurable distance (which would mean, a decimal point and then 40 plus zeroes). Since the other dimensions would be wrapped around themselves to the point of immeasurability (which may not be a word, but I think gives the idea), we can't be directly aware of them; but if it could somehow be proven that assuming they exist, then certain aspects of physics would become "natural and inevitable", instead of "that's just the way things are", then the theory would acquire an attractiveness that might make it universally accepted, whether correct or not.

As to how the other dimensions should be numbered, that would be completely arbitrary. It's like, how would you order width, length and height? Different people might put them in different orders. In fact, I remember when the building I work in was built, I was asked what size would I like to have the sink in the photography lab. I gave them the numbers in an order which seemed perfectly straightforward and logical to me, and was quite surprised to end up with a sink one foot wide, two feet from front to back, and three feet deep. There was nothing wrong with the order I used, but it wasn't the order the architect used, and no one thought to check whether the numbers might be right. I don't know how much it cost to make the thing, but it had to be the most expensive dwarven bathtub ever constructed.

So, in numbering the dimensions, any order could be used. However, the standard way is to treat the three visible dimensions as 1 2 and 3, in whatever order the author chooses; and then number the others from 4 onwards. I don't recall if any of the remaining ones had any special properties. They shouldn't have, any more than width is any different from length or height. The Universe goes equally far in all three directions, and if not for gravity, each direction is completely equivalent to any of the others. In fact, you can rotate the axes any way you want, and change their meaning, and they are still three "different" directions. The "umpteen" additional dimensions which might or might not exist would also all be exactly equivalent and more or less identical to each other, and for that matter, would presumably be identical to the "visible" ones, save for being coiled so tightly. So if you want to put them in some different order, I don't see why you can't. It just doesn't make any difference how they're numbered, unless you give each of them special, unique characteristics which do not exist for the ones we can observe, and probably do not exist for the ones we can't observe (presuming, of course, that those even exist).

I hope that helps, but again, if you have any further questions, feel free to ask away.



---------- FOLLOW-UP ----------

QUESTION: Thankyou again. I will remember the sink anecdote when ordering my bath!!
I also wonder if there are more straightforward explanations to as yet unknown phenomena. As a clue to my way of (opposite!) thinking, I have wondered if the discrepancy in the strength of the 4 forces was due to membranes focusing the 3 other forces, rather than gravity leaking out. Maybe this amounts to the same thing but it makes me realise whatever I read I wonder if it could be the opposite!!
I think I might not have been too clear with my dimensions question. I didnt mean numbering them for the sake of it but as to their natural progression. If you numbered (ordered) them you wouldnt logically put the dimension of volume (3d) in between that of 1d and 2d. Documentarys I have seen imply that the extra dimensions are 'above' that of our 3d or 4d spacetime. Given that our insight on extra dimensions is limited I just thought maybe these dimensions, if ordered by their physical properties may turn out to be more logically ordered below that of 3d or 4d spacetime. Wholly conjecture, but I just thought its a possibility...even if an irrelevant one!!

Answer
If by the xth dimension you are referring to a quantity encompassing the "space" occupied by all the dimensions, then the 4th dimension would be "above" the 3rd, the 3rd above the 2nd, and so on, just as a line is "larger" than a dot, an area is "larger" than a line, and a volume is "larger" than an area.

However, when physicists talk about so many dimensions, they are not talking about n-dimensional "volumes" which encompass all those volumes (although they could, for some purposes). They are talking about the DIRECTION of the axis which defines that dimension, as opposed to any other dimension. As an example, we can represent the position of an object in 3-dimensional space by three numbers: its x, y and z positions, relative to axes pointing in the x, y and z directions, starting from some point. You can rotate and move the axes and their origin, so that the numbers corresponding to a given object change; but in 3-dimensional space, you still need 3 numbers to specify its exact position (relative to the coordinate system).

In the same way, in an n-dimensional space, it would take n numbers to specify the position of an object. It wouldn't make any difference which way you turned the n axes which defined the coordinate system, so if, for instance, you rotated the axes until one of the axes pointed in a direction which originally defined another axis, then the "order" of the axes would be changed. It is in that sense that there is no ordering of the dimensions, save for whatever order we give them. But you are correct in that if space is N-dimensional, then an N-dimensional object would encompass more dimensions than an (N-1)-dimensional "surface", which would encompass more dimensions than an (N-2)-dimensional "surface", and so on. However... read the caveat below...

As already noted, I have considerable doubts as to whether using 10 or 12 or N-dimensional space to "solve" problems involving what we see in 3-dimensional space is of any real use. So although I have read enough about the subject to be able to discuss it as I have above, this is about as far as I can go, and if you need a more detailed answer you will need to contact someone who has more interest in the field, and a more detailed knowledge of its inner workings.

Btw, sorry about the delay in answering. Your question came in while I was getting ready to leave for work, and I just got home.