http://www.straightdope.com/mailbag/mdimensions.html <- this article…
according to the superstring theory, m-theory, etc there are 10-11 dimensions…
I’m surprised that wasn’t mentioned. Also, it says
Sometimes they do insist on going backwards, in some elementary particle calculations. But I don’t know anything about that.
That’s a bit oversimplified. At least one quantum interpretation involves multiple universes.
The question that was asked, John, was:
HIghly speculative quantum interpretations aside, only one universe is known to exist.
Or perhaps I should say, at most one.
But we’re not talking about how many ‘universes’. We’re talking about how many ‘dimensions’ make up our known ‘universe’, right? Hence 4 is as speculative as any other answer and currently, (to my understanding) m-theory is the most favoured by many physicists and the ultimate goal for a lot of them are to unravel the m-theory equation.
The point is that there are NO real dimensions. The concept of “dimension” is a mathematical model that helps us understand the universe and the world. It’s a convenience, it’s not real. If you’re doing a project that requires that you map temperature, then you can use temperature as a “dimension” and the math all works just fine. It’s not like there are great huge axes somewhere, marked off with units, to define the x, y, and z directions.
I disagree CK, degrees of freedom are clearly a property of any physical system, you needen’t define the x[sub]1[/sub], x[sub]2[/sub], x[sub]3[/sub], …, x[sub]n[/sub] axes in order for there to be n degrees of freedom. Yes you can argue it’s a mathematical model, but you can also use the same arguments to say that 1 potato + 1 potato = 2 potatoes is just a matehmatical model.
Dimensions are not reference frames. Saying that there are no real dimensions would be like saying heat is not “real”
Which you can say if you want to.
Sigh.
How about a line, is a line “real” ? The answer is that a MATHEMATICAL line is NOT real, there is nothing real about a line that has no thickness and extends forever. It’s an abstract idea.
Of course, we can use the concept of line for lots of things, it’s a very handy model. But I defy you to draw a mathematical line for me, or a mathematical point. They don’t exist in the real world, they are concepts, constructs, that exist in a theoretic mathematical world… that happen to have very practical uses.
Similarly, the idea of dimensions is very a useful math-theoretic concept. Bu is our world three-dimensional? Well, it depends. Yes, that can be a useful model. But if I’m giving you driving instructions, I damn well better give you directions that coincide with the streets. Telling you that the way to get from your house to my house is to travel along the x-axis, then the y-axis, is not going to be very useful.
Another example: I can use the model of a two-dimensional plane to tell you how to drive around my neighborhood. But if I get a larger area, I need a different model. The surface of the earth can be modelled as a two-dimensional object curved through three-dimensional space, but again, that’s just a model that’s convenient. If I need to use a larger area, like the solar system, I probably need a three-dimensional model that curves through four-dimensional space.
There are situations where you might need to consider temperature (heat), or color, as an additional dimension.
In short, the concept of the universe being 3-dimensional is just saying that there is a mathematical model which is often useful in small local calculations.
Sure, It’s a valid argument, but going back to my earlier post imagine if jkim’s question had been: “I had one potato and someone gave me another potato, how many potatoes do have?”, you could apply exactly the same arguments or simlair arguments, e.g. the possible problems of modelling potatoes a discrete entities, etc. But in all probabilty you’d just answer “two.”, the point being that any description of something is at some level a model and I don’t see why this particular description needs to be singled out.
Infact these arguments are even weaker against this particular example as in all currently observed situations there are three spatial dimesions, this model has no observed flaws.
You have not defined what you mean by “real”.
How I define real:
Real is something you can detect with your senses(eg a house), or something with overwhelming evidence to support its existence(eg. an electron)
I dunno, I’m a mathematician, but I keep running into other people who have the same notion though
<< Infact these arguments are even weaker against this particular example as in all currently observed situations there are three spatial dimesions, this model has no observed flaws. >>
Sorry, but you’re wrong, and that’s my point. The three-dimensional model does NOT work in “all currently observed situations.” At the subatomic level, it’s highly inadequate to explain motion. At the galactic level, ditto.
And there are times when, even for a local situation, three dimensions are not needed or are inadequate for a model – like, traffic flow along a highway needs to take into account that the countryside is not path-connected (that is, the highway only connects certain points to other points, and traffic doesn’t go in a straight line across country.)
I too was a mathematician, RM, and my point is that the model of three-dimensions is extremely widely accepted, but it is not always the most useful model to use.
CK, I’m not sure what you mean, SMTs (string and M theories) excepted on both extremely large and extremely small scales three spatial dimensions are a feature of models. Yes, in general relativity space may no longer be Euclidian, but never the less it is still three dimensional. Quatum field theories also use three spatial dimensions.
There’s also the business about having to have an ODD number of dimensions. Somewhere I read it has been proven that it’s impossible for waves to propagate in any EVEN number of dimensions. Kinda hard to have a viable universe where waves can’t propagate (although this would improve the quality of TV)
That’s not counting time, as a dimension, right?
First, waves can propagate in all sorts of dimensions. Compression waves can propagate in one dimension. Transverse waves require at least two: one for the propagation direction and one for the oscillation direction.
Now C Dexter Haven appears to be a fairly rare bird; he is a mathematician who is not a platonist. Plato would hold that not only is a mathematical line real, it is more real than the merely “sensible”, which is what C Dexter calls real. (After all, the pythagorean theorem held, within the realm of Euclidean geometry, before mankind discovered it.) I’m also a rare bird, a physicist who is becoming a platonist. For whatever reason, physicists and mathematicians tend to differ as to the reality of mathematical constructs. Physicists tend to view math as a tool for modeling reality. Mathematicians tend to view mathematical truths as real things they discover.
Strictly speaking, C Dexter Haven appears not to believe that truth, justice, and the pythagorean theorem exist. He could, I suppose, argue that they exist in the sense that our brains adopt some physical state when we understand them. A platonist would then argue that no, that phsyical state is merely the state of our brains understanding the concepts, not the true concepts themselves. 2500 years of wrangling, and philosophers haven’t proven one or the other, so we can argue it is contentious.
Most physicists would still say dimensions are real. They thoroughly understand C Dexter Haven’s point - when solving for the motion of 10x23 particles, they might adopt 10x23 dimensions. There are some measures of “dimension” that are irrational. Fractal dimensions are not integers. However, the term “dimension” for the original question really refers to the number of degrees of freedom to solve the kinematics of a free particle.
Newtonian mechanics requires three spatial dimensions, with time as parameter for describing curves. Relativity says that you can adopt different frames of reference that mix time and space relative to other frames of dimension, so there are really four dimensions, one timelike and three spacelike. The leading theories at small dimensions require that there “really” be something like 10 or 11 dimensions.
Now, C Dexter Haven can argue that there is no more reality to this definition than any other. All physical theories incorporate mathematical models and are arguably no more than mathematical models. There is no resolving the issue, even with his definition of reality. I must move to sense everything not in my field of view. Do I sense the dimensions I move through to see other things?
I should have proofed that. Hopefully the fifth paragraph is still understandable.
I’m also curious what you’re referring to with this (assuming that by galactic you mean cosmological).