Why are the mathematical models of particle physics so complicated?

Why are the mathematical models of particle physics so complicated?

In order to calculate the motion of a single particle we have to take into account a literal infinity of contributions of virtual particles and field interactions etc. How can there be so much stuff happening down there?

Could it turn out that this picture is mostly a mathematical fiction? It reminds me of the epicycles of the geocentric model of the solar system. When the sun was put in the centre the equations became much simpler and more closely modeled the actual physics. Could a similar thing happen in particle physics too?

Because shoehorning particles for everything is retarded

>Could it turn out that this picture is mostly a mathematical fiction?
All models are "mathematical fiction", more or less by definition

Could it? Yeah. Is it? I dunno, that'd be a breakthrough if someone found that our model is seriously flawed.

OK, but you know what I'm getting at. The mathematics of heliocentric model is much closer to the actual physics than in the geocentric model.

So it's all epicycles then?

>It reminds me of the epicycles of the geocentric model of the solar system. When the sun was put in the centre the equations became much simpler and more closely modeled the actual physics

No, the heliocentric model still had epicycles up the ass. It's Kepler that got rid of them.

Alright, but you know what I'm getting at.

particles don't behave like celestial bodies, the premises of the question are flawed.

But neither are correct.

Not sure if troll..

Yes, it is possible that the apparent complexity is merely an illusion.

Novel mathematical models may be able to dramatically reduce the degree of perceived complexity surrounding this issue, as well as many others.

A basic example of this would be to generate an image of white noise using a quantum random number generator, which would leave you with a highly complex image that would require awareness of thousands of bits to describe it, say 128 x 128 = 16,384 bits.

Now, you could also produce a white noise image of the same size, by utilising the binary digits of the square root of two (i.e. 1.414213562… = 1.0100001010000110…).

Let’s say that this binary pattern can be generated by a computer program that is 100 bits long, then you would only need to be aware of 100 bits in order to describe a pattern of 16,383 bits, therefore reducing the apparent complexity significantly.

Furthermore, if we were to focus on a small section of such a pattern, then we would find it to be relatively easy to describe, for example a section of 9 bits would require one bit to describe each

However, as soon as we begin moving outwards things become more complex, for example a square cut out from the middle of the image would require far more information to describe it, and since it has been separated from the whole, it can no longer be described simply by √2.

In this situation the whole is less complex than its parts.

In fact, this example shows us that the whole can contain less information the some of its parts, and in some cases even one of its parts.

Yes, brilliant. This is this the kind of thing I'm getting at. It could that when we see the big picture it will turn out to be much simpler than the fragments we have now.

Precisely!

The problem with this model is that a complete description of the image would require knowledge of the computer that the code was being run on, which is likely to be much more difficult to describe than the bits it masks

It's an analogy of how apparent complexity can be described relatively simply.

It’s not a hypothesis supposing that the universe is a simple code running on a computer.

However, some hypotheses state that the universe is an analogue simulation running on a ‘naturally occurring ‘quantum computer (based on the structure of quantum field theory being mathematically equivalent to a spatially distributed quantum computer).

Calculating an exact expression for the path integral of a system is practically impossible in most cases, so we take the systems we can solve and do perturbation theory. The terms in the Lagrangian/Hamiltonian which are not in the solveable problem are then expanded in terms of Feynman diagrams. So we trade the impossibly difficult problem of finding eigenstates for our system for the relatively easy but complicated problem of calculating Feynman diagrams up to the accuracy we want. How much "stuff" happens depends entirely on what basis you take for your Hilbert space (where the basis elements are your "particles"), and in particle physics the basis is that of free fields.

This.

As an example, quantum field theory relies on operator-valued fields on R4 obeying certain Lorentz-invariant partial differential equations and commutation relationships

Of course, the mathematical structure isomorphic to our world has not been discovered, that is if it exists at all.

Are you looking for statistical mechanics?

>Why are the mathematical models of particle physics so complicated?

They're really not. Computing the results is the complicated part.

>In order to calculate the motion of a single particle we have to take into account a literal infinity of contributions of virtual particles and field interactions etc. How can there be so much stuff happening down there?

Because they're fields, not particles. Fields which are coupled to many other fields. The "motion of a particle" is not what we set out to calculate. It's the probability of an event happening if the system starts a certain way.

>Could it turn out that this picture is mostly a mathematical fiction?

That picture is at least 3/4ths mathematical fiction. It is clever though.

>that fermat's last theorem counterexample

Complicated in what sense? Sorry but this post strikes me as written by someone who actually has no idea what the mathematics behind the Standard Model is, but probably checked out the wiki page and saw lots of Roman and Greek letters and symbols he's never seen before.

>How can there be so much stuff happening down there?

There are something on the order of [math]10^{20}[/math] atoms in a grain of sand. That is an unfathomably large number for a barely visible volume of mass. Then decompose that into the fact that one atom has on average 260 elementary particles (quarks and electrons), and you can see that there are all these quanta, way more than a human I think will ever be able to faithfully imagine, interacting through 17 fields. So yes, there is a lot happening down there. Mathematically, it's not complicated to represent, really; it's just impossible to compute.

Literally everything pushes on every other thing, so yeah each particle modifies each other particle, which in turn modifies another particle, and that's generally why particles move

What the fuck are you on about? All of particle physics can be described by one general mathematical framework while epicycles only explains one single physical phenomenon.
Is this how stupid the usual freshman is?