According to Einstein’s General theory of Relativity, the universe operates on four dimensional spacetime.
I can take an object and, with a ruler or tape measure, fairly accurately estimate it’s length, width, and depth.
If it is in motion, I can measure by stopwatch how long it takes to traverse some spot on it’s trajectory.
3 spatial and one temporal dimensions which I personally can detect with low-tech instrumentation.
A five-dimensional extension to 4-D GR called Kaluza-Klein theory exists, which can describe gravity PLUS electromagnetism.
(Acknowledgements to Chronos, who has stated several times in earlier threads of mine as to the interesting mathematical trick KK theory is, as it does not describe Quantum electrodynamics.)
Now, you can describe the universe with 11 dimensions (M-Theory), 26 dimensions, or even as many as 248 dimensions as per The Exceptionally Simple Theory of Everything (based on the E-8 Lie Group).
These higher dimensions are described as being “curled up” on the Planck Scale:
But do they actually exist?
I can understand the compelling logic of knowing a working theory won’t work if certain dimensions don’t exist.
But are there any physical examples of higher dimensional evidence?
Are these extra dimensions spatial, temporal, or something else? If they are something else, they are pretty easy to imagine - they are just additional characteristics of a point in space. If they are spatial, can they be rotated into our world, just as three dimensional objects can pass through a plane (as in the story Flatland)?
We don’t even know that 4 dimensions exist. The 3 spatial dimensions may be a hologram on a 2D surface.
That said, the question itself may not be sensible. The universe behaves as if it has 4 dimensions from our macroscopic scale. The number may be different at a different scale (like those tiny curled-up dimensions of string theory). It may be that other scales are completely opaque to experiment, and that multiple interpretations with different dimensions are all consistent with theory.
We don’t yet have any evidence of higher dimensions. It’s possible that very fine measurements of gravity could demonstrate them–if it gets stronger at very close range, for instance. But that hasn’t been done, and even if every experiment comes back negative, it doesn’t disprove extra dimensions.
Proposals for a spacetime with more than three spatial dimensions date back to the 1920s…
including Kaluza–Klein theories and later string theories as well as others. However, “constraints on extra-dimensional models arise from astrophysical and cosmological considerations, tabletop experiments exploring gravity at sub-mm distances, and collider experiments”, that is, a lot is ruled out and certainly nobody has a positive result concerning the existence of extra dimensions.
In addition, dimension is used in a mathematical sense that describes properties rather than a physical sense. In fact people familiar with general relativity will insist that just because 3D space can be described as curved doesn’t mean that there is a higher spatial dimension that it is curved in; the “curvature” is simply a built-in property of the 3D space.
These are not all equal. M-Theory is a highly speculative fundamental physical theory in which spacetime is indeed 11-dimensional, but the number 26 originates in bosonic string theory, which can’t describe matter particles (fermions), and hence, is not a candidate description of our universe. The 248 comes from the dimension of the Lie group E_8, which has no connection to the spatiotemporal dimension. (In comparison, the gauge group of the standard model of elementary particles, SU(3)\times SU(2)\times U(1), is 8+3+1=12-dimensional.)
As for the number of dimensions of the universe, we have as of yet no evidence for anything other than 4. Although, as @Dr.Strangelove notes, there is the added wrinkle that gravitational theories are conjectured to often be describable by non-gravitational theories in lower dimensions (by conformal—‘scale-invariant’—quantum field theories in flat space), but such descriptions are only known for universes with a negative cosmological constant, as opposed to the positive value that seems to characterize our universe. However, I’m not sure I would consider either description as ‘more real’ than the other in such a case: they would simply yield two equivalent descriptions of the same physics.
That’s putting it mildly. Theorists have so far been unsuccessful in narrowing down string theory to a version that describes our actual universe. In fact some people wonder if string theory is a theory of every possible logically consistent set of physical laws that a universe could have.
We don’t yet have any verifiable theory that unifies quantum mechanics and general relativity. String theory is a candidate for a “theory of everything”, but there are alternatives such as Loop Quantum Gravity and Causal Dynamical Triangulations.
None of these have yet made any experimental predictions or are even developed enough to reproduce existing physics. String theory gets the most attention but after several decades seems no closer to experiment than it had been at the beginning (that’s not to say no progress has been made–just that the destination seems to recede further into the distance as well).
But even if string theory is somehow borne out by experiment, it still doesn’t really mean that the extra dimensions truly exist. They might remain mathematical abstractions forever.
Though at some level this becomes a problem of pure philosophy. Imagine a world where it was impossible to view atoms directly. We’d still have indirect evidence for them via thermodynamics and other things. But if you can’t actually observe them, are they really there?
That’s what Einstein first became renowned as a physicist for: producing a mathematical analysis that showed that the observed Brownian motion of tiny particles exactly matched what you would observe if they really were being bombarded by tiny little BBs in thermal motion.
But that is the world we live in. Pretty well up until the atomic force microscope. And calling that direct observation is a stretch. By the time we had got to some form of direct observational evidence we had also mostly finished the Standard Model.
Galileo was one of the first to explicitly realise that direct observation wasn’t the touchstone of truth it had once been held to be. That was one of the key stepping stones to modern science.
The philosophy of science takes us down some interesting byways. The unreasonable effectiveness of mathematics is an unexpected one. Very hard to argue with, but also sometimes very hard to make sense of. Which does take us back to the OP.
If some grand unified theory demands multiple dimensions - what are we to make of it? Obviously experimental validation of predictions would be a start. Given none of such (or any) GUTs have had much success on that front is a good reason not to give the idea much time. But if one did? 4D spacetime gives us enough problems on a philosophical front. Does all of time already exist? Does that question actually make sense to ask? (How can time already exist, already is itself defined with time.) Does the past exist? Does the future exist? Is this compatible with free will? Who are you and what am I doing here?
Does some other multidimensional theory make any of these questions easier? (Probably not.)
Occam’s Razor would suggest that we might be best off holding off on worrying about any of this. Makes for lots of popular writing, and has made a few physicists some good coin, but not so much real science.
Years ago, I read an interesting piece in Sci-Am about sphere packing: the math of how tightly spheres could fit together. In 3 dimensions, the face-centered cubic is the densest, but up around 8 dimensions, gaps start to appear, calling for a different pattern, and when you get to 24 dimensions, your packing scheme has to change drastically.
So, who is going to be packing 24-dimensional spheres in a 24-dimensional box? A sphere has a specific mathematical definition, which is useful to study in multidimensional math. Mostly, it is about things like signal processing, and perhaps encryption.
A “dimension” is a linear scale upon which quantitative measurements or comparisons can be done. It is an abstraction that can be correlated to some degree to the real world. But an axis is a literal straight line, an unnatural thing. There are no straight lines in the real world (universe), so dimensional measurements are merely approxmations of what we observe.
In the realm of reality, four dimensions are mostly practical for describing location (you could add three more if you want to include motion, because nothing is ever not moving, anywhere). Additional dimensions would simply be scalar descriptions of a thing or place. Approximately.
It is not sufficient to rule out (or in) big, flat extra dimensions; you also have to consider the possibility of small and/or warped extra dimensions.
Well in usual (quantum) field theory the fields live in some fixed space-time.
Matt Parker, famed mathematician, wrote in his book Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More, that we’ve proved up to 11 dimensions exist, but we lack the ability to observe them.
Much like 2D beings can only observe height and width but not depth, we 3D beings can’t observe the 4th dimension. The closest we can come is seeing a 4D object’s “shadow,” assuming any 4D being would care to oblige. Furthermore, a 4D being can see all our dimensions simultaneously, much like 3D beings can see all of a 2D being’s dimensions simultaneously. A 2D being can only see height and width, and a neighboring 2D being would appear as a line.
Or at least seem to. The topology of spacetime at fermion scale is profoundly difficult to study.
I take the most extreme position: you cannot have a true vacuum because space has to have something in it. Space exists because there is stuff in it. In a weird way, matter and energy create space because it needs to have a place to be, otherwise there would be no space.
Thus, spacetime is not independent from its tennants, and it is shaped by them. If it looks flat to us, that is only because we are looking at it from the inside and do not have a way to see its shape.
In order for the concept of sphere packing to even make sense, you need more than just a set of variable parameters. You need some sort of metric on those parameters, so you can say how close one set of parameter values is to another set. And the specific solutions to the sphere-packing problem you mention depend not just on there being a metric, but on it being the same Euclidean, Pythagorean metric used in familiar 3-dimensional space (though of course generalized to other numbers of dimensions): With other metrics, the answer would be different.
The “extra dimensions” posited by string models (they’re not theories) are actually of this sort, a generalization of the dimensions we’re familiar with, at least on a small enough scale. They’re not just a list of variable parameters.
He might have posited that, and it might be true, but we’ve proven no such thing.
It should be noted that our description of the universe is not the universe. That is, a four-dimensional spacetime is a convenient tool to explain the universe, but that doesn’t mean the universe is a four-dimensional spacetime.
Exactly. The focus should always be on the usefulness of the model, rather what is.
For example, is gravitation due to spacetime being bent into a higher dimensional space? Or is it due a non-uniform metric internal to it? It’s silly to argue about what really causes gravitation when what actually matters is a more useful way to describe it.
Normal gravitation, on scales where people have been able to test it, is four-dimensional, but that does not tell you what “really” happens e.g. on quantum gravity scales.