02-25-2011, 11:30 AM
I've been reading some of the writings of Michiu Kaku. Science is not my background so if I interpret anything wrong, feel free to correct it. As I understand it, there are theories which suggest that there may be other universes with greater dimensions than ours, albeit they may be very, very tiny. He also uses the form of a box to illustrate what something in a fourth dimension may look like, but I could not even remotely envision what he was trying to say. So my questions are as follows:
1. Can we exist in a four dimensional or higher world? What if we took an astronaut suit, would that help? If these dimensions are on the quantum level, would there be enough space to fit a person (one part of me says yes because it is an ENTIRE universe, another says no because it is so small).
2. Can anywone explain the four dimensional box in a different, more plain, way? (I realize this may be an oxymoron, i.e. trying to explain four dimensions plainly)
3. Could any type of life exist in a higher dimension? Would we be able to recognize it?
4. How would we get to a higher dimensional world? Worm hole? Black Hole?
5. If there are higher dimensions, could there be a solely a lower dimension universe (like the flatlanders that Michiu uses to describe two dimensions). If not, why not?
02-25-2011, 12:12 PM
You misunderstand. It's not that there are other worlds that have more dimensions: Our world is (at least according to these models) the one with more dimensions. These extra dimensions might be rolled up so tightly that we can't notice them, or they might have a significant size and just be inaccessible to us for more complicated reasons (or a mix of both, of course). If the latter, then there might be other three-dimensional spaces separated from us in the extra dimensions (sort of like pages in a book). These other spaces would probably be more or less like our own, but it's possible that some of what we consider fundamental physical constants might have different values in some of them (for instance, gravity might be stronger or weaker). It probably wouldn't be possible for us to travel bodily to these other spaces, but communication might be possible between them through various gravitational means.
02-25-2011, 12:14 PM
These other spaces would probably be more or less like our own, but it's possible that some of what we consider fundamental physical constants might have different values in some of them (for instance, gravity might be stronger or weaker).In these other spaces, would the planets be cubical in shape rather than spheres, and would people talk backwards?
02-25-2011, 05:40 PM
In these other spaces, would the planets be cubical in shape rather than spheres, and would people talk backwards?
Me no understand this question. :)
Life in a two-dimensional world has been explored mathematically by many writers. There are a lot of surprising similarities and the math makes most actions possible, but I'm not sure that what we know of as life could exist, just because we depend on 3-D protein foldings and the myriad of other aspects of not-flat life.
Four-dimensional worlds (i.e., four spatial dimensions, not 3 plus time as is relativity) sound great in science fiction, but have the distinct problem that orbits become unstable. I'm not even sure that atoms are possible under such a scenario.
Otherwise, as Chronos says, what these theories say about other dimensions is that our three familiar ones may actually be integrally part of more that we just don't see. There is no traveling to them. They're as much a part of reality as up or sideways.
The multiverse is something else, BTW. In fact, there are many totally different theories that unfortunately each happen to be referred to as the multiverse, even though they imply multitudes in totally different and unrelated ways. There can be multiple types of multiverses happening because they aren't connected. Best not to think about it.
Half Man Half Wit
02-26-2011, 02:18 AM
There's a difference between 'dimension' as used in a pulp sci-fi ('Attack from the fifth dimension!') as opposed to a scientific sense. In the former, the word is used roughly synonymous to 'world' or 'universe' -- these dimensions are some place you can travel to. In the latter, dimensions are a characteristic of a space -- roughly, they are more like directions you can travel in.
Take our world: you can travel forward (or backward), left (or right), or, with the right means of travel, up (or down), making for three (spatial) dimensions. On a sheet of paper, you can travel only up/down, or left/right, without leaving it -- it's two dimensional. A single line has only one direction to go in, on a point, there's no direction at all, so these 'spaces' have a dimension of one and zero, respectively.
This also means that you can specify each point in some space by 1) specifying a point of origin, and 2) specifying how far to go along each of the dimensions in order to get there. So, on a piece of paper, you might start at the lower left edge, and give the location of any point on the paper by first giving the distance you need to travel to the right, and then giving the distance you have to travel up in order to get to that point. These two numbers then identify any given point on the paper -- they give it a name, its coordinates. This is then another, equivalent, way of specifying dimension: the number of numbers needed to identify any point in a space is its dimension. On a line, you only need to specify how far to travel -- one number, one dimension. On a point, well, there is only one point, which is already identified -- no number, zero dimension. In everyday space, you need to specify how far to travel up/down, left/right, forwards/backwards -- three numbers, three dimensions; this is the same as when you have a rectangular package, and its measurements are given as its width, length, and height.
From this point, 'higher' dimension are not such a strange step: you could simply consider a 'space' in which you need four numbers to uniquely identify each point (technically, our space is such a space, however, the fourth number is a temporal, rather than a spatial, coordinate: if you wish to schedule a date, giving just the location won't suffice to specify the meeting point uniquely, you'll also have to give a time; however, for the moment, let's contend ourselves with spatial coordinates). As far as a 'direction to travel in', this fourth coordinate is rather hard to visualize -- it would be a direction 'at a right angle to' all of the ordinary directions of our three dimensional space, much as the direction forward/backward is at a right angle to the two directions on the paper plane. However, as much as this third direction does not 'fit into' the plane, the fourth direction does not 'fit into' familiar three dimensional space; and since our imagination is three dimensional -- by habit, if nothing else --, we can't readily form a picture of such a direction.
But mathematically, there is no obstacle! You can talk meaningfully about four, five, six... even infinitely many dimensions, and in fact, many mathematicians do this quite routinely.
The question then is, as for physics, which is supposed to describe the world we observe -- why would you want to do that? Well, it turns out, that some theories, in order to be consistent, need a higher number of dimensions -- like, for instance, string theory (though to what extent it describes the world we observe, if at all, is rather controversial). So, the theory, involving in most formulations no less than ten dimensions, is easily (more or less) written down -- but then, what to do with all the surplus dimensions? If the world 'actually' has more (spatial) dimensions than the three we observe -- why don't we see them? Seems like a hell of a thing to just never have noticed!
So one has to figure out a way to 'hide' these extra dimensions, and that's where compactification comes in. Basically, what you do is something analogous to taking your two-dimensional piece of paper, and roll it up into a cylinder, as tight as you can. Now, this is still the same two-dimensional piece of paper, but, from a distance, you might not easily notice the second dimension -- it might look quite like a line, like a one-dimensional space. You have, at least on sufficiently great distances, effectively gotten rid of the second dimension.
So that's, in a pinch, how you (hope to) extract our three dimensional world from higher dimensional string theory spaces -- we're just big enough such that we don't notice the extra dimensions! That said, they should, if we look hard enough, still have some observable effects -- we'd just need a magnifying glass big enough, which we've build, at least for relatively large extra dimensions, with the LHC at CERN. Unfortunately, all it's done so far is to report back that there's nothing to report (which of course is a very valuable result in itself), i.e. that if there are any extra dimensions, they must be smaller than a certain size, or else, we would have seen them by now.
02-26-2011, 01:00 PM
-- like, for instance, string theory (though to what extent it describes the world we observe, if at all, is rather controversial).No, the String Model perfectly describes the world we live in! The problem is just that it also describes googols of other completely different worlds that we don't live in.
Half Man Half Wit
02-27-2011, 05:09 AM
No, the String Model perfectly describes the world we live in! The problem is just that it also describes googols of other completely different worlds that we don't live in.
I appreciate what you're saying, but, IIRC, it's not been rigorously proven that among all of those possibilities, there actually is a compactification that gets the resulting physics right; there are some intersecting D-brane models that come close, and you might say that being this spoiled for choice, it's virtually inconceivable that one can't at least get arbitrarily good agreement with experiment, but as far as I know it's still at least theoretically possible that string theory ends up describing anything but our universe.
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