Does quantum mechanics disprove the Principle of Sufficient Reason?

Question

Lets say a scientist were to perform the double slit experiment. He sends in one electron through the slits and then that he measures the random location on his measurement device after the wavefunction collapses. Now if one were to ask what was the specific cause/reason that electron was measured at that specific location, you would have to say there was none, at least with the Copenhagen interpretation. So then this goes against the Principle of Sufficient Reason since there is no reason for that the electron to be measured at that specific location.

The principle of sufficient reason being that everything must have a cause and/or a reason.

Answer 1

The philosopher Robert Nozick said it does. Only a weakened form of the PSR can survive.

Paraphrasing: if there is no reason for something, then there is at least a reason for there being no reason

The mathematician John Conway who wrote on quantum foundations also explicitly stated the original PSR contradicts quantum mechanics as such.

What QM actually is is still hotly contested. So there are many interpretations where the PSR would still hold. I don’t know of other cases of explicit denial of the PSR beyond above but I’m sure there are some. But limiting ourselves a bit, it is clear textbook QM and the original PSR conflict.

Answer 2

Arguably not, if you allow chance to be a cause, which Aristotle noted in his Metaphysics - over 2, 500 years ago (!) -that some philosophers argued for. This thread of thought has been forgotten since the success of Newtonian physics, which does not allow such causes, and is strictly deterministic.

Answer 3

I would say no.

First of all, the PSR needs to be formulated in a better way. What you describe it is the version that we normally would call the principle of causality, or what Schopenhauer classifies as the principle applied to the world of phenomena. One way to frame it is to say that everything that changes has a cause.

Now if one were to ask what was the specific cause/reason that electron was measured at that specific location, you would have to say there was none, at least with the Copenhagen interpretation.

Here you mean "cause" as existing in the mathematical model. What we can conclude only is that our mathematical model cannot say what is the cause, not that it does not exists. Some in the past, like Einstein, had argued that maybe with a better math we could determine the results. But even with the undeterministic way, the only conclusion we can have is that if there is a cause, it is not in the mathematical model (or in any mathematical model).

To give an example of that, one can take the Wolfgang Smith's interpretation given in his book The quantum enigma were the cause is what we could call substantial form in aristotelian terms. The substantial form is not something that can be described mathematically, so this is the reason why in his perspective, we have this limitation in our models.

So, the fact you cannot describe with equations or predict it, does not mean that it does not exists. This would need some additional axiom like only what is described mathematically exists in the physical world. But this is a bold claim and it oversteps the boundaries of physics.

Answer 4

The question doesn't specify a particular variant of the Principle of Sufficient Reason and I'm not going to go through all of the variants in the Stanford Encyclopedia of Philosophy PSR article.

Rather I'm going to describe how quantum physics explains the results of experiments.

Before getting on to the explanation the controversy I will briefly explain the interpretation of quantum theory. The equations that are used to make experimental predictions from quantum theory are not controversial. Nor is the fact that those equations accurately predict the results of experiments. But there is a controversy over how to understand that success partly because quantum theory seems to imply the existence of multiple versions of all the systems you see around you.

One set of theories is typified by the Copenhagen and statistical interpretations. These theories say that you're not allowed to ask what's happening in reality to bring about the experimental results. This doesn't make much sense since an experiment involves setting up a situation about which your theory makes a prediction and then seeing whether the prediction is fulfilled. But that situation is itself described by the theory so if you're not allowed to talk about what the theory implies about reality, then there is no standard by which to judge whether the experiment was set up correctly. Such a theory can't explain experimental results so it's not relevant.

The next set of interpretations change the equations of motion of quantum theory to match what people think reality should be like. In particular advocates of these interpretations want the systems they see around them to exist in only one version. These theories include spontaneous collapse theories

https://arxiv.org/abs/2310.14969

and pilot wave theory:

https://arxiv.org/abs/2408.05403

Since these theories change quantum theory the question isn't really about them and in any case they have an unsolved problem in that they can't currently reproduce the predictions of relativistic quantum theories, which are the vast bulk of all successful predictions of quantum theory:

https://arxiv.org/abs/2205.00568

There is an intepretation of quantum theory which doesn't modify the equations of motion but just tries to work out what they imply as one would for any other scientific theory: the Everett interpretation.

The equations of motion of classical physics describe some measurable quantity, such as the x position of a particle, in terms of a function that gives a number x(t). When you measure the x position at time t you get the result x(t).

In quantum theory the equations of motion are written in terms of Hermitian operators called observables. The possible results of a measurement of an observable are its eigenvalues. Quantum theory predicts the probability of each of the possible measurement results. In general what happens to the system depends on what happens to all of the possible values: quantum interference. For an example see Section 2 of

https://arxiv.org/abs/math/9911150

When information is copied out of a quantum system information is suppressed and this is called decoherence:

https://arxiv.org/abs/1911.06282

The objects you see around have information copied out of them on a much smaller scale of space and time than the scales over which they change significantly so the amount of interference they undergo on the scales of everyday life is negligible. As a result they are sorted into layers each of which acts approximately like the universe as described by classical physics:

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

This is often called the many worlds interpretation of quantum theory but it is just an implication of treating quantum theory the way you would treat any other scientific theory when working out its consequences.

Quantum probabilities are explained by symmetry properties of quantum states not by things happening randomly:

https://arxiv.org/abs/quant-ph/0405161

https://arxiv.org/abs/0906.2718

https://arxiv.org/pdf/1508.02048

If you ask why a specific event happened the answer is that it was one of the possible outcomes and there is an explanation of the physics of the system that will tell you what those outcomes are. This explanation also covers why an event has a given probability.

Answer 5

It is still philosophically conceivable that physics is deterministic in the classical sense as I have tried to outline in this provocative conversation with ChatGPT. It is very long but extremely precise developing slowly step by step.

Answer 6

You can prove the motion of matter is deterministic in the Newtonian sense. Consider the proposition denoted by the statement "tomorrow there will be a sea battle." Some days it's true, some days it's false, but on any given day it's not true and false simultaneously, therefore the future cannot be changed. And if the future cannot be changed then it isn't probabilistic. This is what is meant by saying "the motion of matter is deterministic." With that in your limited storehouse of mental knowledge, you can actually do quite a bit. First you can throw the Copenhagen interpretation of Quantum Mechanics in the garbage. Next you can dispense with the Born interpretation of the wavefunction which Schrodinger hated. The only thing left is to explain wave-particle duality in a manner that explains the double slit experiment, while not contradicting determinism. If you do that, then the path of a particle through the apparatus will obey the principle of sufficient reason, simply because the motion of any piece of matter is deterministic, in the Newtonian sense. So all you need to do is figure out what a particle really is, and the answer to that question must incorporate a wave characteristic, and also a particle characteristic. The particle characteristic to choose is localizability. A particle isn't spread out in space varying in amplitude over a continuum of x coordinates. It has a single center of mass x coordinate. It now seems to follow that no particle has a wave characteristic, but that is experimentally false, as proved by the double slit experiment, as well as the Davisson Germer experiment. There is only one answer possible, and it is this: The size of a particle oscillates, ranging from a point to some finite value. So if a single particle approaches two closely spaced slits, and it's size is small enough it passes through one slit behaving like a particle, but if the next photon (or electron) is sufficiently big, it passes through both slits simultaneously, and it is this effect that leads to a diffraction pattern forming on a distant screen when you fire a large number of the same kind of particle at two closely spaced slits.

Summary

If you understand the principle of sufficient reason as being true if the motion of matter is deterministic, and you know somehow that the motion of matter is deterministic, and you know what a particle really is, by knowing how something can have particle and wave characteristics, then you can see that quantum mechanics (the Schrodinger equation) doesn't contradict the principle of sufficient reason, rather the Born interpretation of the wavefunction contradicts it. Then you can ultimately hang your hat on determinism and classical Newtonian physics augmented by a different conception of 'particle' than that held by Newton or modern physicists. I got the idea for what a particle really is, from looking at circular waves in my dog's water bowl. Waves traveled from the center until they reached the edge of the bowl, and were reflected back to the center, where they vanished. The size of the bowl represents the maximum size of the particle, and hence the maximum amplitude of the wave or wavefunction as physicists call it nowadays. The time it takes for the wave to travel from the center to the edge and back to the center is the period T, and the frequency of the wave is given by f=1/T. So you model a particle as a spherical wave, that reflects at the radius of the particle. Using this model, the De Broglie wavelength of a particle satisfies nλ=2πr only if there is some tension along the circumference of the wave and it vibrates like a string of length 2πr. When the tension reaches its maximum allowable value, the wave reflects heading for the center. However, in De Broglie's model the radius is constant and the wavelength varies. In this model r varies, which suggests a second wavelength relationship, in addition to DeBroglie's. That relationship is found by postulating that the spherical wavefront jumps through space by a distance L each jump. It is this wavelength that is related to the frequency f that I previously used. This means there's another quantum number call it N. Thus, the spherical wavelength L satisfies NL=r, where r is the varying size of the particle. r eventually reaches the maximum value A (amplitude of the wave with period T and wavelength L) when the tension along the circumference of the wave reaches its maximum allowable value, at which point the spherical wavefront reflects, and the whole thing repeats in perpetuity for an indestructible particle.

From an AI article:

In quantum mechanics, the evolution operators are considered unitary, meaning that the time evolution of a quantum state is deterministic in the sense that given an initial state, the future state is completely determined, but the outcomes of measurements on that state can still be probabilistic due to the nature of quantum superposition; this is why quantum mechanics is often considered not fully deterministic despite having unitary evolution operators.

As I explained, the measurements of position aren't what's causing the diffraction pattern, it's the varying size of the particles passing through the slits that causes it. The motion of any single particle is deterministic, so outcomes of measurements on the future state of a particle aren't probabilistic in the least.

Answer 7

Sufficient reasoning is a subjective term based on (1) the depth of the subject being discussed, (2) the audience to which you're propositioning of reason is addressing & (3) the logical rationality of the proposition.

In other words, quantum mechanics requires reasoning of a quantum mechanical nature to be adequately expressed. It may not be understood (or even comprehensible) in terms of colloquialism but may very well hold true as far as the quantum realm is concerned.

So you must take into account the fact that we may not have discovered a way to accurately predict or reproduce the seemingly random placement of the collapsed particle. But in no way does that suggest that the answer doesn't exist somewhere off in the infinitude of multiverse.

At some point, an answer will manifest itself in order to reproduce the result of an experiment. Which is actually an indication the the answer is already in existence. It's only non-existent as far as this realm is concerned. It's a matter of finding proper alignment with the correct universe and merging with on another. Which, as it stands, is achieved through a great deal of focus and dedication on the part of the select individuals intelligent enough to tread that particular path.

Answer 8

Contrary to a popular misconception - maybe many people are not aware of - Quantum Mechanics (at least according to the classical interpretation, see e.g. Bell Inequality) IS deterministic, because its evolution operators are unitary.

What is unknown, however, is whether General Relativity is deterministic or not. See e.g. cosmic censorship in black holes.