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Can someone who knows more physics than I tell me if the question is even meaningful? My naive assumption is that we'd have as many dimensions as there are distinct things (atoms, I suppose).

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Do I know more physics than you? Problynot. But he’s my attempt to explain how I understood the article: We experience a universe with 3 spatial dimensions, if we imagine an axis through space, there are two other axes orthogonal to the first axis and to each other, that an object can move on any of the axes independently, without moving in any of the others. We can’t add a fourth axis, there is no fourth line we can choose along which an object can move without also moving in at least one other dimension - or at least that is our experience. We also know from seeing 2d shadows of 3D objects, that a higher dimensional object can be projected into lower dimensions. We can twist an object and see changes in a shadow that make perfect sense if we know the shadow is a 2d projection of a rotating 3D object. There are features of our universe that make sense if we think about the universe as a 3D shadow of a higher dimension system. So what does that mean? Are higher dimensional models a nice math trick, or do the models work because they describe the true higher dimensional nature of the universe, that we experience as a lower dimensional projection. Ok time to pass the baton who can take this deeper.

Good answer, a 4th dimension and the shadow projection analogy is brilliantly exemplified by Carl Sagan in this popular video: https://www.youtube.com/watch?v=UnURElCzGc0

I think it's also the most important analogy, more than things like a 2D being meeting a 3D being. The goal of these physics models is to better explain the world. It's a hint that a model is better when it simplifies things (not that the model itself is necessarily simple).

Think of the crazy things astronomers drew to explain the paths of the planets in the sky with the Earth in the center and circular orbits. But what if the Sun is in the center and the orbits are ellipses? Things are way easier.

Same thing happens if you look at the projection of a cube. It looks like chaos. But if you are aware of a third dimension, it all makes a lot of sense.

I think it helps build an intuition of how higher dimensions can help us explain physics, if instead of a shadow, you think of projection as a cross-section, like the ones you see in brain scans, where you only see one "layer" of the brain at a time. Objects that are moved into the plane of the scanner (so they intersect the plane) will essentially "pop into existence" from the perspective of someone looking only at that cross-section - and then that cross-section morphs and changes shape as the object is moved so different parts of it intersect the scanner. What if the same thing is happening when elementary particles pop into existence and later annihilate, that we're seeing the cross-section of a higher-dimensional object as it intersects our 3 dimensions? What if matter and antimatter are like the outer edges of such a cross-section, appearing in a single point as the object touches our plane, moving apart as the bulk of the object passes through our plane, and then finally coming together in a single point before disappearing (annihilation), as the object stops intersecting our plane?

> There are features of our universe that make sense if we think about the universe as a 3D shadow of a higher dimension system.

Which one would this be?

fair call,

I was trying to make it clear that my comments were 'how is understood the article and vid' and not my Wolfram/Weinstein 'physics is wrong I'm going to fix it' manifesto.

So let me try improve that line:

<strike>There are features of our universe that make sense if we think about the</strike>

<i>Kaluza-Klein theory proposed that electromagnetism could be modelled using an additional closed fourth dimension. Kerner generalised this approach to model gravity, time, electromagnetism and the strong and week forces using a total of 11 dimensions. I have understood these models as describing our experience of the </I>universe as a 3D <strike>shadow</strike> <i>projection</i> of a higher dimension system.

Kaluza-Klein was the exact point at which I lost interest in pursuing university physics, so the sentence is marks the point at which the ship of my knowledge hits the rocks. I loved first year physics, but in my second year at university a tutor convinced that physicists now worked exclusively on string theory, which he explained beginning with Kaluza-Klein theory. What he described reminded me of Copernican epicycles, and I felt so little enthusiasm for it, and was deeply disappointed after having loved first year physics and it was the end of my imagining I might be a physicist. Much later I discovered he was suicidally depressed the dry bloodless descriptions he gave were him trying to hang on and keep himself together while describing a subject he had come to hate.

Thank you for answering.

You don't need to know more physics. If you see something (a particle fe) disappear, and reappear somewhere else then a possible explanation is that it got there via another dimension. So if you eliminate all other possible explanations, the only remaining one is that there must be more dimensions. However, since things appearing and disappearing does not happen on macroscopic scale, the dimensions must be small.

So this is how UFOs move!

In this context, the dimensions are the degrees of freedom that a particle can move in. I think it becomes meaningful when you consider the metric (ie. definition of distances) and the laws of nature inside that space, and if additional dimensions help in formulating more phenomena with a less complex system of equations.

-> Classically, there are 3 spatial dimensions (directions of movement) with Euclidean metric, and all the classical laws (Newton's laws, gravity, etc.). Quite successful, but breaking down in extreme cases (high energy, ie. velocity/mass/etc). +there is a whole range of seemingly unrelated laws necessary.

-> with relativity theory (both special and general), time becomes a 4th dimension, but it has a special status in the metric (opposed sign), making spacetime non-Euclidean. One effect of this is suddenly you don't need a law of gravity anymore. Things just follow geodesics in this space. It also explains some effects that could not be derived from classical gravity. Essentially explaining more phenomena with less "overhead", in exchange for more dimensions.

That is what is called by the name of degrees of freedom.

The dimensions of space-time are to the degrees of freedom as the basis vectors of a coordinate system are to the homogeneous matrix. Or something like that.

That implies there ARE distinct things, doesn't it?

'Distinct in some context', I guess. Eg: a person could take a photograph of clouds in the sky and come up with list of rules to categorize them into a number of discrete clouds.

Don't take my comment too seriously, although it is based on serious speculation and thought.

I only wanted to refer on the one hand to the philosophical or at least linguistic problem, what a 'thing' is and the possibility of the unification to one field of the, up to now still multiform, thing in the quantum field theory we call Universe.

Just a mind game.

Or not...

;-)

What is meant in the article is that one needs currently 11 coordinates in a mathematical space which is supposed to be a mapping of our physical reality to describe a point in it.

Not at all serious but... maybe all electrons have the same mass, charge, etc. because there is only one electron, bouncing backwards and forwards through time. As it passes backwards we see it as the anti-electron (positron). When they meet they annihilate from our perspective, but that's just the electron being reflected and becoming a positron heading backwards.

To be clear this is all not at all consistent with observations - just a fun(?) thought experiment.

https://en.m.wikipedia.org/wiki/One-electron_universe

Out of interest, what observations is this not consistent with?

The argument against is summarized in the Wikipedia article.

Basically it is this:

We measure electrons in different places all the time.

Due to the speed of light it can't instantly move from A to B, so for this to actually be one electron it would have to travel back in time to be at some place at the right time.

However, an electron traveling back in time would appear as a positron, so if that what was going on we should be seeing a fairly equal number of positrons as we do electrons, as the one electron rushes around to appear as an electron where it needs to.

Except we don't, electrons outnumber positrons by a huge margin.

> However, an electron traveling back in time would appear as a positron, so if that what was going on we should be seeing a fairly equal number of positrons as we do electrons, as the one electron rushes around to appear as an electron where it needs to.

What about this part of the article though...?

  "According to Feynman he raised this issue with Wheeler, who speculated that the missing positrons might be hidden within protons."

As noted, the discussion between Wheeler and Feynman was in 1940, long before the development of the Standard Model[1].

In the Standard Model there is a sea of virtual particles in the nucleus, but they're virtual and hence not real in the sense that the positron in the One Electron model would have to be. At least that's my understanding.

Also, electrons can travel over large distances, CRT monitors do that all the time for example. So I'm not entirely sure how Wheeler imagined hiding the positrons in the nucleus would solve the whole positron problem.

[1]: https://en.wikipedia.org/wiki/Quark#History

The imbalace in observed particles could come from the fact that we move in the same (time) direction as electrons but the opposite (time) direction of positrons, couldn't it?

are you saying: what if dimensions are not discrete, but fields.?

Ah, no no no.

Oh, God, what have I done!?

What I wanted to indicate was firstly, as a physical speculation the possibility of a universal field in the sense of the quantum field theory, which shows additional dimensionality with breaking of its symmetry in hierarchical levels and thus there is in a certain sense only one thing, the universal field.

Secondly, the question when something is considered as an independent 'thing', which is a philosophical question.

Third, the question of the interpretation of the relation of mathematical apparatus and reality.

What does the dimensionality of the mathematical model mean? A scientific-theoretical question.

And the gluons of this all are just linguistics and semantics.

;-)))

Perhaps what you mean is the dimensionality of hilbert space

> Can someone who knows more physics than I tell me if the question is even meaningful?

Any new physical property could potentially be exploited to improve some existing idea. The discovery of the electromagnetic force eventually gave way to WiFi and 5G. The discovery of the quantum realm for example has yielded the concept of quantum computing. If we can discover high dimensions, we can eventually interact with them and use them.

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