I've always wondered why there has to be a discrete number of forces, rather than it being a spectrum describing types of interactions.
Many theoretical physicists believe these fundamental forces to be related and to become unified into a single force at very high energies on a minuscule scale, the Planck scale, but particle accelerators cannot produce the enormous energies required to experimentally probe this. Devising a common theoretical framework that would explain the relation between the forces in a single theory is perhaps the greatest goal of today's theoretical physicists. The weak and electromagnetic forces have already been unified with the electroweak theory of Sheldon Glashow, Abdus Salam, and Steven Weinberg for which they received the 1979 Nobel Prize in physics. Some physicists seek to unite the electroweak and strong fields within what is called a Grand Unified Theory (GUT). An even bigger challenge is to find a way to quantize the gravitational field, resulting in a theory of quantum gravity (QG) which would unite gravity in a common theoretical framework with the other three forces. Some theories, notably string theory, seek both QG and GUT within one framework, unifying all four fundamental interactions along with mass generation within a theory of everything (ToE).
split
[caveat - i'm not a physicist, but]
we know forces unify at higher temperatures/energies, and there is no limit to how high temperature can get (maybe? i guess temperature is the same as the mean velocity of the particles, so for particles with mass this cannot exceed c, right?) however the the high energy zone is inaccessible with current technology above a certain level.
but in the other direction, we hit a floor at zero kelvin. which we can access, and can therefore test. so we know that going right down to zero kelvin / electron-volts / joules / meteres per second does not split any of the known forces further. this is how we know that they are the fundamental forces, i think.
https://en.m.wikipedia.org/wiki/Gauge_boson
(there might be a graviton, too)
With a Grand Unification Theory, they might turn out to be one force with several aspects (eg electroweak force), but that's not really a continuum.
There are phenomena explained by the particle model, and there are phenomena that are not. This is true of all models, and it's a a strong claim that we could eventually land on a "correct" model at all.
To be fair, a "particle" as the term is used in quantum field theory doesn't refer to a billiard ball, it's a perturbation in a "field" and encapsulates behaviour which could be described as wave or particle or neither.
The utility of a model is what it describes.
In my view, we're sailing awfully close to metaphysical waters with phrases like that.
That scale is the point at which we might gain some level of confidence that we know what "really" is a particle (or its constitution), whether it is truly a point particle or if it is just convenient to assume that at the present time.
Of course, the scales involved are far beyond anything we have been able to probe. And this arguement relies fundamentally on the interaction between gravity and quantum mechanics, even though those theories are famously not compatable. So the 'theoretically' in theoretically impossible is doing a lot of work.
Essentially, each force does describe a type of interaction. So what does one-third of a type look like?
The same may be true of other seemingly different forces: https://en.wikipedia.org/wiki/Grand_Unified_Theory
Before, we thought there were two. Now we know there are one. We do not say "one and a half."
I'm not conversant enough with physics to do more with this article than say "wow, that's cool!" and let my mind run into all sorts of fun science-fictional speculation... but wow! Fractals are cool, and fractals in _physics_ are _very_ cool!
Of course that raises the question of "shouldn't A.5 then just be considered its own type?" at which point I suppose we'd have to refer to how these "types" are constructed, which seems more like a mathematical/computational (ontological?) question than a purely physics question. Then, I suppose, the question further resolves to: which assumption makes our equations easier to work with?
Please correct me if I'm entirely off-base.
However, this "theory" I proposed wasn't essentially about physics; it was ontological in nature, encroaching more on the field of CS's type theory as it applies to conceptions of physics.
Don’t worry though, you aren’t alone. There is a thriving community of people coming up with their own “theories” or proving how pi is exact equal to 3.125
Do _you_ have an actual point to make, or are you being mean for the sake of it? I would sincerely like to engage with you, if you're quite done accusing me of trying to trisect the angle.
However OP wasn't even asserting anything of a discovery or a revolution. He actually ended his post by asking a question: "Then, I suppose, the question further resolves to: which assumption makes our equations easier to work with?"
Any decent man would have explained to OP about how the best fitting generalizations/abstractions in mathematics and physics also fit the most specific cases. Instead we had a gatekeeper put OP down like a wild fox in a hen house. It's shit like that, that makes humanity stink of arrogance and petulance. It's people like that, that discourage positivity while dispersing platitudes. Their subscription to authority has no basis in merit, it is exactly like John Baez says: "Crackpot Index #9) List your credentials"
Out of curiosity, how does this differ from the criteria of choosing the assumption which makes the equations easier to work with?
I feel as if they are the same, though perhaps lacking a careful qualification on my part: "which assumption makes our equations easier to work with (without introducing incorrect solutions)?"
Given the choice of abstractions, assuming each abstraction is apt as the next and none of them is "more wrong" than any other, wouldn't the choice of abstraction come down to ease? (or aesthetics, possibly)
I'd love your take, and doubly so if I seem to be coming at this backwards.
For instance, Matrix mechanics is equivalent to the Shrodinger wave formulation, but it did not catch on for reasons listed here.
[1] https://en.wikipedia.org/wiki/Matrix_mechanics
Another system that did not catch on, is Nonstandard analysis, which uses infinitesimals. It is equivalent to the standard curriculum analysis that uses limits.
[2] https://en.wikipedia.org/wiki/Nonstandard_analysis
It's hard to pinpoint exactly why these systems weren't chosen. It's not just aesthetics or ease of use. It's a bit of arcane history too. Nonstandard analysis took a while to make rigorous. And by that time, standard analysis had already enveloped the "cult of science." Once standards are set, they rarely change if the current methods are "good enough." I've always sought intuition with everything, so I know about these alternative methods.
I find it sad that so many in academia resign themselves to symbol pushing without a real understanding, and then repeat the same misgivings on their pupils. If methods do exist to achieve better intuition, then we should promote them. Often, alternative yet equivalent formulations do provide that intuition.
HN is a bit of a cult of personality itself but ironically, about every month on the dot, a submission gets front paged - geometric / vector algebra or quaternions, and how they simplify and clarify the intuition behind 3D transformations.
Yet the same HN has curmudgeon gatekeepers that also pop up like clockwork in any science thread, just to make sure all lines of thought correlate to the rote symbol pushing they learned. They didn't gain intuition, so they must feel that it's either impossible to, or that no one else has the right to intuition either.
Anyhow... I hope I answered your inquiry.
I'll never stop working on artificial life and digital systems. The heart of information is at my dying core. :-)
https://home.sandiego.edu/~shulman/papers/sdg-pizza-seminar....
Here's one I find particularly fun, wherein you disregard law of excluded middle to use nilpotents!
I'm currently trying to digest "Geometric Algebra: An Object-Oriented Approach." It is a real pleasure to see you mention some of my pet favorites; thank you, thank you, a hundred times over friend! You've put a song in my heart today.
EDIT: I was so wrapped up in having met a fellow traveler that I forgot to leave an "in," should you wish to continue this thread.
I also find it a tragedy that my foray into the constructivist and sundry corners of math was relegated to self-study. Having approached a few professors on this topic, the general consensus seems to be "why waste your time?"
To what do you think the intuitive power of these equivalent-but-alternative foundations is owed? Personally, I think it has something of the basis that colors the division of the analytically- vs algebraically-minded; yet even the cause of this is a mystery!
(However, let me be careful here: I don't wish to give the impression of undue competence. I'm broadly-read, but woefully underskilled.)
I'm elated over having delighted and filled you with music. Your kind words have made me beam from ear to ear as well :-)
I think the intuitive power of these other formulations comes from the spatial/geometric imagery that these disciplines naturally provide. Another aspect is the conversion of unwieldy processes into simpler objects. Like nonstandard analysis replacing the limit process with the infinitesimal object.
The paradigm of replacing large processes with things that can be intuited might not be very profound if as programmers we bring up first class functions. A function is just an object anyhow! True but the human mind seems to be less efficient at composing functions than composing objects. So though it's all interchangable, we seem to work better when we are given mentally ergonomic foundations. Back to what you said in your previous posts, the ease of manipulation in these alternative theories, it probably lends a bit from this exchange of complicated processes for simpler things.
[1] https://en.wikipedia.org/wiki/Synthetic_differential_geometr...
Let's say I pick electromagnetic and gravity.
If I start using this 'electrogravity' 'half/mixed force' to describe the trajectory of charged objects I'm throwing, it seems like the correct response is not "shouldn't that be its own type?" but "you're just combining two forces for no reason". If you can look at a web of interactions and separate it into two completely independent mechanisms, then there's no fractional force.
And the scenario of throwing a charged ball fully fits "interaction that exhibits characteristics of both, is fully described by neither, yet exhibits no properties which can't be typified by some combination of the integer endpoints"
This is because the discrete energy levels don’t like to share the exact same energy levels as neighbors (Pauli exclusion principle).
For single atoms, the energy levels are exactly defined by the Schrödinger equation:)