# How deep our experiments on non-determinism are?

Disclaimer: Sorry in advance, because I've probably misunderstood something from this introductory quantum physics lesson, or something else related to quantum physics or math. But, hey, I need to know what it is that I'm missing.

MIT 8.04 Quantum Physics I, Spring 2013 (2013) https://www.youtube.com/watch?v=lZ3bPUKo5zc

There's no need to watch the video unless I summarize very badly, hopefully the examples and induction will do the deal.

Letting aside how the quantum universe we live in is more concretely, we can conceive an abstract simpler universe in which we just have sources of particles, and two types of filters, namely Up/Down and Left/Right and then detectors were the particles end up so we can "see them". We can combine the filters any way we want for our experiments.

Here are some examples:

Depth 1:
Source--|UpDown|--Up----Detector: 50%
|--Down--Detector: 50%

Source--|LeftRight|--Left---Detector: 50%
|--Right--Detector: 50%

Depth 2:
Source--|LeftRight|--Left---|UpDown|--Up----Detector: 25%
|                |--Down--Detector: 25%
|--Right--|UpDown|--Up----Detector: 25%
|--Down--Detector: 25%

Depth 3:
Source--|UpDown|--Up----|UpDown|--Up----|UpDown|--Up----Detector: 50%
|               |               |--Down--Detector: 0%
|               |--Down--Detector: 0%
|--Down--Detector: 50%

Source--|LeftRight|--Left---|LeftRight|--Left---|LeftRight|--Left---Detector: 50%
|                   |                   |--Right--Detector: 0%
|                   |--Right--Detector: 0%
|--Right--Detector: 50%

Source--|LeftRight|--Left---|UpDown|--Up----|LeftRight|--Left---Detector: 12.5%
|                |                  |--Right--Detector: 12.5%
|                |--Down--|LeftRight|--Left---Detector: 12.5%
|                                   |--Right--Detector: 12.5%
|--Right--|UpDown|--Up----|LeftRight|--Left---Detector: 12.5%
|                  |--Right--Detector: 12.5%
|--Down--|LeftRight|--Left---Detector: 12.5%
|--Right--Detector: 12.5%

Depth 4:
Source--|LeftRight|--Left---|UpDown|--Up----|LeftRight|--Left---|UpDown|--Up----Detector: 6.25%
|                |                  |                |--Down--Detector: 6.25%
|                |                  |--Right--|UpDown|--Up----Detector: 6.25%
|                |                                   |--Down--Detector: 6.25%
|                |--Down--|LeftRight|--Left---|UpDown|--Up----Detector: 6.25%
|                                   |                |--Down--Detector: 6.25%
|                                   |--Right--|UpDown|--Up----Detector: 6.25%
|                                                    |--Down--Detector: 6.25%
|--Right--|UpDown|--Up----|LeftRight|--Left---|UpDown|--Up----Detector: 6.25%
|                  |                |--Down--Detector: 6.25%
|                  |--Right--|UpDown|--Up----Detector: 6.25%
|                                   |--Down--Detector: 6.25%
|--Down--|LeftRight|--Left---|UpDown|--Up----Detector: 6.25%
|                |--Down--Detector: 6.25%
|--Right--|UpDown|--Up----Detector: 6.25%
|--Down--Detector: 6.25%


As far as I understand, these abstractions could be implemented as real life experiments in many ways, with electrons, protons, photons and other particles, even molecules like carbon icosahedrons (whatever their chemical name is) and our physics expect the same results, because many people have probably tried with different particles and machinery, different distances, times, angles and nobody got anything different that could give us a clue.

Of course, I assume experimental physicists didn't stop at depth 4. So, after so much introduction, the first question is how deep they went? I expect a number absurdly big using mirrors and recursion or something.

But I also want to claim some things to see if I'm getting something wrong.

CLAIM 1: For any set of experiments like these in the examples, a deterministic model can be conceived that produces the same expected results as the non deterministic one.

CLAIM 2: For any such model, a superset of experiments could be designed so that the deterministic and the deterministic models gave non equivalent results.

So how can anybody claim that our universe is intrinsically non deterministic without having done infinitely "deep" experiments on non determinism? And also, again, how big was that number when they gave up on trying anything bigger if they ever did? I'm pretty sure I'm not the first one that a bigger number could demonstrably restore determinism if we just knew that number and designed an experiment knowing it.

Am I claiming anything wrong? It still feels like it, but I verified for myself. I mean, I only verified up to depth 20, but I convinced myself I can generalize to N depth. For more context, I have a little project proving my point, presumably I'm not revealing anything that was unknown to physicists and I'm just missing something. The project just doesn't allow N=infinite though, for I haven't figured out how to code infinite loops in rust yet. But to reiterate, real world experiments can't do that either, so I think I'm fine on that front.

https://github.com/jtimon/qcircuits

Here's the deterministic part that feels like "cheating":

https://github.com/jtimon/qcircuits/blob/master/src/hypotheses/det_bits.rs

Sorry, I hope the questions makes sense to somebody. If I'm missing something very obvious to some, I won't be embarrassed, I want to know what it is. Thanks in advance for the answers.

• You might find Bell's theorem relevant to what you're asking. Commented Mar 5, 2021 at 0:46
• yes, I have heard about it, and if ?I understood it correctly, it seems to imply that what I just did should be impossible, shouldn't it? Commented Mar 5, 2021 at 19:22
• @Timón Impossible for local interactions, There can be en.wikipedia.org/wiki/Quantum_nonlocality more variables that enter the theories than local ones. Commented Mar 6, 2021 at 5:58

A comment on

I'm pretty sure I'm not the first one that a bigger number could demonstrably restore determinism if we just knew that number and designed an experiment knowing it.

People are working on not deterministic theories. The problem is that experiments up to now have come to the conclusion that the underlying level of nature is quantum mechanical and have a standard model which encapsulates a myriad of data in elementary particle physics. Any deterministic theory will have to embed the data of the standard model.

Let me give you an example. Classical statistical mechanics of many particles, predicts the variables used in classical thermodynamics , while being based in a deterministic kinematic model.

G.'Hooft , a nobel prize winner, is working on such theories and has been contributing here on that , if you look at his profile here.

The bulk of experimental data which are fitted with non deterministic quantum mechanics are the problem in all deterministic theories.

• Thanks for answering, but the question is more generally how many levels of "filters" (which may vary with the experiment) have we experimented with? Why is that important? Because as I've shown, experiments that could be explained with a non deterministic model could be explained with a deterministic model as well. If after certain depth the experiment results were different, I don't think the other way around would work. Commented Mar 5, 2021 at 19:26
• The only "filters" that exist in the study of elementary interactions, is energy. The higher the energy in the interaction the more levels of the onion (molecules, atoms, nucleons/electrons, quarks) were uncovered and we are stuck with the standard model. All the projected experiments are trying to invalidate sections of the the existing model to find something new. Your filters are not applicable to the physics of the elementary particles. Commented Mar 6, 2021 at 5:41
• This "new" by going to higher energies of interaction. Commented Mar 6, 2021 at 5:49
• These filters are metaphors taken from a physics lesson from MIT, as explained in the OP. Did you watch that video? That may help you understand what I'm doing. He says these are metaphors for real experiments (I imagined, with electromagnets to separate moving particles by spin), did the teacher lie to me? Commented Jul 3, 2021 at 7:27
• I am just saying that elementary particles are studied by scattering experiments , they are not with a rising complexity of detectors but a rising energy. All new physics has come by increasing the energy of scattering, so determinism or quantum randomness has to be fitted to the exiting data. Commented Jul 3, 2021 at 7:39