How Many Dimensions Are There?

Factual Questions
1

I don’t know if there is any exact answer to this question. But just exactly how many dimensions are there, altogether? I mean, is there any consensus on this?

Just to review for you what I already know. Most humans only perceive the the four dimensions of space-time: length, width, breadth, and time. The formula for a hypersphere is X[sup]2[/sup]+Y[sup]2[/sup]+Z[sup]2[/sup]+T[sup]2[/sup]=R[sup]2[/sup], where T is time, and R is the radius. [Edit: and for other dimensions, just add more letters, starting at W. For example, a fifth-dimension hypersphere would be X[sup]2[/sup]+Y[sup]2[/sup]+Z[sup]2[/sup]+T[sup]2[/sup]+W[sup]2[/sup]=R[sup]2[/sup], and so forth.] Our human brains are not wired the right way to perceive other dimension (I heard in high school once). And the remaining dimensions are tightly woven around the particles of atoms (I once hear on the Science Channel–whatever that even means).

That last one is a little weird. Because I wonder, what happens when an atom is torn apart, like during a nuclear explosion? Do the dimensions get torn apart with it? Maybe that is a good question for another time. Or maybe you could answer that too, if you want.

I don’t know if I have made my question clear. I know many different physics theories postulate a multitude of dimensions. I am wondering how many are actually known. Or probably at least, if that is clear.

And are there any maximum number? That also is a good question, I think.

Thank you in advance, to all who reply:)

:):):slight_smile:

2

Those extra, tiny dimensions are purely theoretical and are fudge-factors to make some physics equations work. They may or may not actually exist.

3

How many dimensions are there in what? Dimensions are a mathematical concept, not a physical one, and while the math behind physical processes often has some number of dimensions, it’s not always the same number, nor are they always the same dimensions.

As an example, many physical processes can be described in terms of dimensions that we might call length, width, and height, and possibly by another one we might call duration. So we might say that there are three, or maybe four, dimensions. According to string models, there might be more dimensions that work similarly to that, so there might be 11 of them, or 24, or whatever number those kids are saying nowadays. Alternately, a lot of physics problems are worked in six-dimensional phase space, which has three dimensions for position and three for velocity (or sometimes momentum).

But then, there are also physics problems whose dimensionality doesn’t look anything at all like that. One of my friends, for instance, was working on a project to reconstruct an image from incomplete information. How many dimensions does an image have? You might be tempted to say that it’s two-dimensional… but for his purposes, it was actually millions of dimensions, one for the value of each pixel. Each possible image that he could reconstruct corresponds to one point in that millions-of-dimensions space, and he was effectively searching that space for the point which best maximized the fit to his data and heuristics.

4

Oh, but to go back to the matter of spacetime dimensions, such as the four you described or the 11 or whatever of string models. We certainly don’t detect those extra dimensions directly. One possible reason for this might be that they’re wrapped up very tightly, but if this is the case, it’s generally expected that the scale on which they’re wrapped up is much, much smaller than atoms. By way of analogy, for instance, consider a drinking straw: If you look at it very closely, it’s a two-dimensional sheet of plastic, and if you want to specify a point on it, you’d need two coordinates. But if you zoom out, it’s a basically one-dimensional structure, and you’d only use one number to specify a point on it.

But there are also other models for the extra stringy dimensions, which don’t have them rolled up tightly, or possibly at all. And those models come up with other reasons why we can’t detect them. And we have no idea which, if any, of these models are correct.

5

You’re not a true collector, are you? Because, if you were, you would probably be running out of dimensions rather than specimens… :slight_smile:

6

That sounds like something people say and they must be talking more about our sensory ability for time-space dimensions or something. We certainly do perceive time right in our brains and can perceive that as a dimension even though not exactly as space-time, just how things change and move over time within our 3D perception. But that’s not through direct sensory input. However, within our ability to see there are color and brightness that add dimensions to our visual perception. Vision is not simply sensing of the spatial dimensions. We just don’t have the sensory organs for those other physical dimensions being discussed.

7

Since dimensions are mathematical, there is no limit to their number. See Infinite-dimensional vector function. Those functions are common in physics.

Also, Chronos didn’t say this specifically though his answer implies it, dimensions are not tightly woven around the particles of atoms. So they can’t be blown up.

We also know from math that everyday things work differently in higher spatial dimensions. Orbits are unstable in four dimensions. Knots cannot happen in more than six dimensions. Math is full of little goodies like this. That’s one big reason why string theories have to tuck the extra dimensions away in some mostly invisible fashion because everything we see has stable orbits and knots.

That makes the question of why humans can perceive only three spatial dimensions interesting. Are those really all that can ever be perceived? Maybe. Yet our ability to perceive them doesn’t mean more aren’t possible. We can’t perceive neutrinos though trillions of them pass through our bodies every second. What’s more interesting is that no instrumentation we’ve developed can even theoretically directly perceive more than three spatial dimensions no matter how many science fiction stories are built around them. We can look indirectly for evidence of more than three, however. String theory, e.g., states that multiple dimensions would produce effects that could be detectable. Whether these effects have been detected is disputed, but that’s a different issue.

Yours are hard questions to answer because they deal with a lot of tricky definitional issues at various scales and in multiple disciplines. Another way of saying that the universe does not conform to what humans think is common sense.

8

I once asked an owl, but the asshole bit into my universe when he passed 3.

9

What the dimensions are is up to the philosophers … when they decide, then mathematicians are ready for them …

10

Exactly. The ***last ***person you want to ask about dimensions is a physicist. Ask a carpenter, or a machinist. Or a practical engineer. Someone that measures and builds things. There are 3.

Dennis

11

The existence (or lack thereof) of physical extra dimensions is by definition a physical question, not a philosophical or mathematical one (I only need 4 dimensions to unravel any knot, by the way).

It is unfortunately true that dimensions that are really, really small are currently not detectable experimentally. We can still rule out some theories of large extra dimensions, not philosophically but experimentally as explained here, though, admittedly, each one of these searches depends on some assumptions, so it always possible we are hampered by a lack of imagination and it’s actually turtles all the way down.

12

If T were an ordinary spatial dimension, this would be correct. But if the time-like T dimension is measured with real numbers then a Minus Sign is usually substituted for the Plus:
X[sup]2[/sup] + Y[sup]2[/sup] + Z[sup]2[/sup]** - **T[sup]2[/sup]

I hope one of our mathematicians or physicists will comment. What is a “hypersphere in space-time” anyway?

13

That thingie with 11-or-whatever dimensions existing infinitesimally small on a sub-atomic level.

Assuming that hypothesis is true in some form, this is how explain, or rather present it to myself in VERY layman’s terms.

Let’s use a 2D world as in Abbot’s Flatland (which Sagan used beautifully as an analogy).

So there’s a world that lives on a sheet of a paper and creatures on it are geometrical shapes. They can’t see from “above”, they can’t see the interiors, they see only one side of other geometrical shapes, a thin line.

But wait a second. There’s no depth in 2D world. How thin is the line? Infinitesimally?

So, if 4th (or more) spatial dimension exists, we do actually “see” a tiny edge of it.

Our world is not really 3-dimensional. Rather 3.0001.

Silly, I know. But it helps me to comprehend, even if it’s probably totally wrong.

14

My thoughts exactly, after way too much reading on the subject.

15

This issue about the number of dimensions is intrinsically related to the very nature of reality.

When breaking away with mythology, ancient Greek philosophers tried to determine the ultimate ‘essence of things’.

Today’s knowledge seekers dismiss philosophy as inadequate and futile since science can provide us with everything there is to know, reliably speaking.

Mythological knowledge justifiably seems to be unreliable because it’s metaphorical, ambiguous and untestable. In contrast, scientific knowledge is supposed to be rigorous and clear – reliable.

What happens to rigor and clarity when one speculates about or postulates the existence of millions or an infinity of dimensions? What happens to the chances that one should reach the goal of effectively fighting ignorance?

In Howard Shwartz’s ‘Tree of Souls: The Mythology of Judaism’, God is said to have left his creation unfinished and challenged anyone claiming to be some kind of divinity to try and complete it. To this day, the unfinished corner of reality has been teeming with demons, winds, earthquakes and the like, none of whom has ever managed to produce something capable of completing God’s creation.

My point? Fighting ignorance doesn’t equate having everyone get a PhD in Physics and Astronomy. If people with scientific propensities and preoccupations find it hard to clearly and rigorously expound on how many dimensions one can really rely on, then science must have changed its methods and goals. There’s nothing wrong about that in principle except that scientists should admit it.

16

n.

17

Like I said, there are a great many physical situations for which that’s true. But that doesn’t change the fact that that friend of mine was working with a real, physical situation which really did have millions of dimensions.

It sounds like you’re saying that if reality is too complicated to easily understand, then we should pretend that it’s not so complicated, so we can understand our pretend world better. One might as well say that a star the size of our entire inner Solar System is too hard to understand, and that we ought therefore to declare that there are not, cannot be, any such stars.

18

I have another take on why this is totally wrong.

Scientists don’t play games of what if? They construct equations whose solutions make predictions about the real world that form models which can be tested. The many worlds interpretation of quantum mechanics does predict that an astoundingly huge number of new universes are being formed every instant because that emerged out of the mathematics. Recent studies have found evidence that Parallel universes could solve a big problem with black holes. Black hole descriptions will never be a part of philosophy. Only math and physics can handle them. With exquisite rigor and clarity.

It’s hard to come up with any better example of fighting ignorance than this. That we can sit here on Earth and solve deep questions about the universe is amazing. You can only disparage it if you deliberately cut yourself off from all understanding of the subject.

19

Depends on what you mean by ‘dimension’. Dimension is a number attached to a vector space, manifold, or similar object. If I’m working dealing with, say, a system that has 3 space coordinates, 1 time coordinate, and 1 temperature coordinate, that’s a 5-dimensional system.

So, you’re asking about the shape of the universe. Locally, it looks like a flat 3+1 dimensional space: 3 space coordinates plus 1 time coordinate. That may not hold globally, though; the surface of the earth is a 2-dimensional space (locally, you have latitude and longitude) embedded in a 3-dimensional space. And so on.

In the classical setting, the distances between objects in this space are given by ds^2 = dx^2 + dy^2 + dz^2; this is the standard straight-line distance between two points. The point is that in any inertial (i.e., non-accelerating) reference frame, that distance should remain the same. Except that doesn’t hold: we see (depending on what frame of reference you’re in) distances contract and time dilate at high velocities. The distance function we actually want to use is ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2, taking the time coordinate into account as well. In general relativity, the universe is no longer flat: energy (including massless particles) corresponds to local curvature in spacetime, in a precise and quantifiable way. We’ve verified both special and general relativity extensively in experiment.

So, on to more theoretical stuff. For various technical reasons, string theory appeared in the 1960s to be an attractive solution to certain problems in physics. (Attractive to mathematicians, at least. The physicists I know personally all seem to loathe string theory.) If you connect up string theory to the methodology of quantum field theory, you get some very nonphysical effects like tachyons except in certain dimensions. They happen to vanish in 26 dimensions, so problem solved: The universe has 26 dimensions. As for where those dimensions are, it doesn’t really matter; they’re significant only on a much smaller scale than we care about outside string theory. Think of the surface of a desk: If you’re doing your work on the horizontal top of the desk, it doesn’t matter whether it’s several meters deep or microscopically deep in the vertical direction. There are also other reasons why 26 dimensions is plausible in the theory, but they’re a bit technical to get into here. There are also other variants of string theory with different critical dimension (superstring theory has 10 dimensions, for example) and different ways of getting around the fact that we don’t see those extra dimensions, but it’s the same principle.

Of course, this is just a summary and should be taken with a grain of salt.

20

Yup. It’s not like scientists sit around all day and say, “Dude, what if there were, like, 26 dimensions?” When a scientist posits something like that, there’s a reason for stating it, experimental evidence and mathematical theory making it plausible, and a potential way of falsifiying it. Everyone is aware that the universe certainly looks (3+1)-dimensional; but just as relativity makes predictions about uncommon situations that nevertheless have been verified, the idea here is that other phenomena reduce the situation to the one we’re familiar with in most circumstances. These ideas are often wrong, but there’s a difference between having a plausible idea that’s not supported by experiment and just making up shit.