A 1-dimensional object can’t exist because if you multiply its length times its width, which is zero, and times its depth, which is 0, you get a volume of 0. An object with 0 volume is a non-existent object, just like a car with 0 gallons of gas does not have gas. Yet once you count to three dimensions, objects apparently exist despite (presumably) having no 4th-dimensional depth. It would seem more coherent or consistent, or at least simpler, metaphysically, to assume that objects we see have length, width, depth, and some amount of 4th-D depth to exist at all, lest their 4-D volumes be 0, hence making them not exist. Yet this same principle must then be re-applied to include 5th-D depth, 6th-D depth, 7th-D depth, and so on and on, ad infinitum. And that’s just what I’m arguing for: an infinite number of spatial dimensions.
And string theory posits just that. The common conception is that string theory holds for 10, 11 or 26 dimensions, but Paul Davies said in Superstrings: A theory of Everything? that that’s only for purposes of a simplified approximation, that string theory holds for an infinite number of dimensions.
The depth of these extra spatial dimensions is very small, or else reality wouldn’t behave as it does such that our reality appears 3-dimensional. But how would you possibly constrain a spatial dimension? In string theory, this is done by way of the extra dimensions being “curled up.” By analogy, imagine a one-dimensional world, only instead of existing on a line, it actually exists within the perimeter of a very thin tube. Because the tube is so microscopically thin compared to the macroscopic scale of its one-dimensional physical life, the effects of the second dimension aren’t noticed except through the experiments and models of their physics. In string theory, all the dimensions above the third are tightly curled in an analogous but higher-dimensional manner.
I’m still ambivalent about string theory though. It’s very complex and constantly growing, and yet it makes almost no predictions (I’ve only heard of one, and we don’t have the technology to test it yet). This pretty much makes it unfalsifiable and seemingly an ivory-tower endeavor. Not only that, but the strings it reduces things to are unintuitive, unobservable, as small as as small gets, and apparently made out of nothing but math. And I think that for a “thing” to ultimately lead to a sensory experience, it must have some substance to it, as in a property, that is somehow commensurate with that experience. Math is all just numerical values and abstract relationships between them. It’s like measurements of real things without the real things/substances being measured. For reality, experience and qualia to occur, you need actual substances.
Using math is great for modeling and predicting physical reality, but reducing the universe to mathematics is going too far. It lacks substance so it couldn’t give rise to reality/experience, and mathematics is purely abstract (see also https://philosophy.inhahe.com/2019/09/21/why-mathematical-platonism-is-silly), so it can’t be the basis of anything extant. Abstractions are strictly derivative of extant substances/phenomena/whatever.
Moreover, string theory is said to be not one theory, but a set of numerous possible theories, that figuring out which one is correct would take more computing power than we remotely have in this age. It seems not very coincidental, to me, that the theory poised to be the first Theory Of Everything is actually a statement that “one of a large subset of all possible theories is correct.” In what dimensions this set extrudes or does not extrude into the set of all possible or feasible theories is a subject worthy of notice, and beyond my knowledge of physics.
That leads me to another thought, though. In much the same way that any possible series of points on a graph can also be traced by a sufficiently complex polynomial equation, I wonder if there’s a possible universal formula in which every possible physics theory, or every possible TOE, is expressed as a series of parameters to that formula. That would be a beautiful generalization and simplification for the search for the ultimate physical theory.
When I say “possible theories,” of course I mean mathematically constructible theories. But I think that the real theory of everything—the only one possible, or at least the only one actually satisfying—might not be mathematical at all. It could be, for example, something more like a new-age principle. Perhaps that could capture the more living, less mechanical aspects of cause and effect that physicists don’t even dream of. Scientism supposes science to be all-reaching, while the things that physics can’t predict, particularly things within quantum mechanics, are thought of as “absolute randomness.” (Some interpretations of quantum mechanics are deterministic, but as long as they can’t actually predict any particular instances of the randomness in question, they’re just weak conjectures.)
And speaking of prediction, that’s the one thing all physics is based on. A physical theory is merely a mathematical relationship that’s validated by, and only by, prediction. Physics doesn’t actually purport to be doing anything other than creating useful models of phenomena. So physics isn’t necessarily an accurate representation of what’s going on metaphysically/”under the hood,” so to speak. That’s where interpretation comes in, and some theories have many interpretations. That space-time is curved is just one interpretation of the General Relativity, for example. We can’t even measure space as a thing-in-itself; how can we say that it’s curved? It’s just a mathematical convenience that we use.
Quantum mechanics has a few interpretations, such as Many Worlds theory, but on a deeper level perhaps it has none…Richard P. Feynman said, “It is safe to say that nobody understands quantum mechanics,” and also, “If you think you understand quantum mechanics, then you don’t understand quantum mechanics.” All QM has are equations that work in mind-blowingly counterintuitive ways, and they only predict things on a statistical level. This must be why Albert Einstein said, “if [quantum theory] is correct, it signifies the end of physics as a science.” Maybe we’re still waiting for the ricochet…
If the ultimate TOE is a mystical principle, it makes me wonder: how complex should the principle be? Surely, if not on a technical level then on an abstract level, it could accommodate both QM and GTR. They’re so foundational and all-encompassing that, even if physics merely makes useful models, the information of those two overarching theories should fit into our mystical TOE somewhere…but, a fundamental basis of physics is that you can predict/explain anything from the vantage point of “the view from nowhere,” that is, independently of any subject. This constrains physics to theories that are only ultimately work insofar as we live in an impersonal universe full of objective facts, which I don’t think is the case. Some questions arise:
- Should we incorporate physical theories, on the mathematical level, into our mystical TOE at all?
- If we do, how complex should the mathematical part of the TOE be?
- How would we integrate the mathematical parts of the TOE with the spiritual/mystical parts?
- How complex should the spiritual parts be?
- Would the mathematical part of the TOE necessarily be relegated to ”the view from nowhere”?
- What restrictions does the paradigm of causality impose on physics that mathematics and measurability themselves don’t? (I don’t remember why I asked this.)
In answering the first question, we should first ask (a) what it is in the universe that warrants a particular amount of complexity in an all-encompassing theory, and (b) what do we mean by all-encompassing, in that we don’t actually predict everything (for example, a practitioner of the ultimate TOE probably wouldn’t predict that a fly is about to land on their face)? Perhaps the amount of data we predict is commensurate with the amount of data we gather, for example, we can’t predict the weather presumably because we can’t measure the position and velocity of every air molecule, not counting the issue of computational limitations.
But if there is any amount of data we could gather by which to predict quantum randomness, we don’t know how much it is nor where to gather the data from. I don’t believe it’s the case that quantum randomness can be predicted with sufficient physical data, though. I also suspect that, since the so-called laws of the universe and its data are two aspects of the same whole, and it is only in human understanding that things are discretely divided, we’ll find more and more complexity to our “laws” as long as we’re looking for them. Hence physical law is unlimited in complexity, and probably ever-changing, just as the data they “operate on” is.
I say so-called laws because I don’t believe the universe behaves according to laws as such. Laws require energy to enforce, so the universe would constantly be drained of energy. Also, as I mentioned in ‘Notes on Freewill,’ if physical laws were restraining, constraining, or otherwise enactors of some sort, then you’d need further/more-meta laws to enforce or constrain those laws (because why else would they continue to consistently do what they do otherwise; and if they would just naturally continue to do as they do, then it’s equally plausible that the physical “laws” are just things naturally doing what they do rather than being laws as such), and further laws to enforce those laws, etc., to infinite regression.
By the way, I said that the ultimate TOE probably wouldn’t allow you to predict that a fly is about to land on your face, but perhaps if it were really the ultimate TOE then it would predict absolutely everything, or at least everything in one’s immediate environment. All theories ultimately describe the universe as we perceive it, even if that perception involves looking at measurements by scientific instruments. We do the best we can designing theories that try to explain things from arbitrary hypothetical perspectives that trivialize individual frames of reference, we draw an ultimately arbitrary line between the “rules” or “laws” of the universe and the “stuff” that the rules “act upon,”, and we then try to discover laws that work within those artificially constructed modalities, but it still comes down to explaining qualia in the end. So, perhaps if there were actually an ultimate TOE that perfectly encapsulated the essence of the workings of the universe, it would tell you exactly what you’ll see or hear at any given time.
As for the second question, there is beauty in mystical principles, while physical law, on the other hand, is a plethora of arbitrary constants relevant only to lifeless, labyrinthine, and ultimately unaccountable equations. Beauty is truth and truth is beauty, or so I’ve read, so spiritual/mystical maxims are likely more fundamental and universal than the laws of physics. See also https://philosophy.inhahe.com/2018/04/13/notes-on-science-scientism-mysticism-religion-logic-physicalism-skepticism-etc/#Reductionism.
Perhaps somewhere else in the universe, or in the multiverse, the gravitational constant is different, or there are more than three spatial dimensions, etc. Given that the variables are apparently set just right for physical life where we are, it must be that, unless this universe was specifically designed by God, the strong anthropic principle accounts for all of that. The strong anthropic principle requires the existence of many worlds/places with different physics varying in many dimensions. Thus a mystical-principle TOE might potentially tell you what is always so, while physical theories are a way of describing “where you are” currently in the all, or perhaps more accurately, what the nature of your current body is…
If, as the strong anthropic principle suggests, the universe is precisely that which is necessary to support your physical life as someone who would ask “what is the universe like?,” then the whole corpus of physics is fundamentally nothing more than a reflection of the nature of your own, current body. It’s actually a little more complex than that, because the question also depends on your current body living within what you would deem a universe and because it’s actually a question being asked, and answered by, the whole of humanity. And there are probably also other species living in the universe who are asking the same question, who are quite different anatomically, but whose bodies work on the same physical principles.
To the last question, I would point out that quantum mechanics apparently establishes correlations that uphold outside of causal time, as you might notice in Wheeler’s delayed choice quantum eraser experiment. It’s often said that the reason QM and GTR are incompatible is that they treat time differently. A theory that connects relativity with quantum mechanics is probably one that has a basis beyond time (such as the one in Julian Barbour’s books), or is at least one that’s not bound by the idea of prediction in causal time.