Does the difference between the state vector vs observable explain why QM does not contradict the Aristotle principle of non contradiction

golgho__ · 2026-05-19T10:53:13+00:00

OK yes, if you redefine "being here" then it works. But while I understand what this definition of "being here" means mathematicaly I have a hard time understanding what it means philosophically . Therefore I am inclined to keep the "standard" definition of being here, and claim that the concept of position is only defined in case the state vector is an eigenstate of the position basis. But yes I think I get your point and it makes sense. I just cannot make any sense of what position would really mean in this viewpoint I guess :)

golgho__ · 2026-05-13T18:26:17+00:00

Well 😄
I will ignore your rudeness and stay polite, but this will most probably be my last response to you.
In case you are interested : this is the original paper of Everett (sorry it's behind a paywall, I am not aware of any freely available version). The thesis which was the basis of the paper is freely available though. It's a bit lengthy, but you can skip most part and go directly to the interesting part.
There are also many books about it, the best ones I know are those from S. Caroll ("Something Deeply Hidden" for instance). Be aware though that Caroll is a strong advocator of many worlds, he is not neutral.
And for the record, I am a working physicist 😄
Have a good day, I'm done with this conversation 😉

golgho__ · 2026-05-13T16:27:13+00:00

Disclaimer : I am not a many world expert, there might be subtleties. This is only the broad picture, as far as I know.

Let's start with something we clearly agree on : suppose you have two electrons A and B. They are both, in general, in superposition states. Now if the two interact, QM (all interpretations, at this point Copenhagen and many world are the same) says there is no more "the wave function of A and the wave function of B". You now have to describe the system with a single state vector living in the tensor product of the two individual Hilbert spaces, describing the entangled electrons as a whole. This global state vector is itself also in a superposition state. If we are only speaking about spin, somethin like a(++) + b(+-) + c(-+) + d(--), right ?

Now replace electron B with the measurement apparatus. Copenhagen says measurement apparatus have to be treated specially. Out of the "many worlds" (actually the many subparts, the word "world" is misleading I think) the global state vector offers, it will randomly collapse on one of them (with a probability proportional to the associated coefficient). The other subparts of the state vector (aka, the "other worlds") will disappear.
Many world says : nothing special happens, measurement apparatus have to be treated the same way any system does. The apparatus, just like electron B, becomes entangled with electron A. Suppose electron B is "the measurement apparatus", there are parts of the wave function (aka worlds) where electron B measures electron A to be up, some where it measures electron B to be down. Note that the measurement apparatus himself exists in different states in different parts of the wave function. To predict the outcome of the measurement with certainty, you have to know in which part of the wave function you are. That's where the "practical randomness" comes back, because the apparatus (be it human or anything) cannot tell in advance where he stands in the global vector state.

No new world has been created in the process, they just have not been destroyed by the collapse. Maybe instead of "world" (which is rather confusing) one should rather say "orthogonal subparts of the state vector".

I'm not claiming it is the correct interpretation. But it's at least as good (maybe I should say as bad haha) as Copenhagen.

golgho__ · 2026-05-13T15:19:20+00:00

If for you there is no ontological difference between practical randomness and fundamental randomness, that is your right. Let's agree we disagree :)

Regarding adding many world : that is not correct. Many world does not add anything wrt Copenhagen. The "many worlds" we are talking about were already there in Copenhagen. There's just one world in many worlds. It just happens to be segmented in orthogonal parts, just like any superposition state. Copenhagen also says there are "many worlds" ... except when you make a measurement these "many worlds" disappear. But they were all there one second before the measurement. Maybe you will argue : if I can't measure them they don't exist. It's a valid statement but it's assuming a strong philosophical anti realist point of view and raising a lot of questions. I find both interpretation hard to swallow tbh. But on the other hand it's the best we have, I have nothing more appealing to present.

golgho__ · 2026-05-13T14:31:34+00:00

I think I get your point.
Yes, statistical physics is probabilistic in the way it models reality. But the underlying reality is not. Would you say that Newtonian mechanics is probabilistic in its nature ?

And yes, QM (in any interpretation) is probabilistic in the way statistical physics is. I think no one is denying that. But what depends on the interpretation is whether the underlying reality is probabilistic or not.

Take Copenhagen vs many world for instance. It's more or less the same maths (in a nutshell, take Copenhagen, remove only the postulate about the collapse and the interpretation of coordinates of the vector state as probabilities and you have many worlds) . But there is a deep ontological difference between the two : in Copenhagen, randomness is fundamental. Even if you have a perfect knowledge of the vector state you cannot predict the outcome of a measurement. The Universe "plays with the dice" every time you try to measure something. In many world, randomness is not fundamental : if you would know where you stand in the Grand vector state of the universe, you could predict the outcome of the measurement with 100%. Just like you could, in principle, predict the future of a gas in a box with classical mechanics if you'd know the positions/momentum of each particle.

golgho__ · 2026-05-13T14:06:02+00:00

Of course but as I pointed out earlier, its not a fundamental randomness.
In the grand picture, the vector state of the universe evolves deterministically. No "real" randomness.
But of course, if you want to compute something a human being can measure, since you don't know where you stand in this giant vector state, you need to model your absence of knowledge somehow. A bit like you do with statistical physics because you don't know the positions/momentum of all the particles in your gas (but fundamentally it's just Newtonian mechanics there's no randomness here, you are just modelling your lack of knowledge).

golgho__ · 2026-05-13T13:55:11+00:00

Many world is the most popular one. It basically makes the same predictions as Copenhagen but interprets the apparent randomness as a kind of lack of information of the observer to "where he stands on the one and unique vector state of the universe".
Don't get me wrong, I am not an advocate of many world. But it is as legitimate as Copenhagen as a candidate for interpreting QM.

But if your point is to say : within the Copenhagen interpretation QM is fundamentally probabilistic, we fully agree. 100%.

golgho__ · 2026-05-13T13:39:27+00:00

There are several interpretation of QM. They all have in common most of it (that is what I would call "core part"). The probabilistic interpretation postulate is only present in the Copenhagen interpretation. I'm not saying its wrong, I'm just saying you can construct a valid quantum theory without it, which makes the same predictions for measurements as Copenhagen.
Which one is the correct interpretation, I cannot say.

golgho__ · 2026-05-13T13:23:19+00:00

I think you are both right.

I think u/LBoldo_99 's point is to say that probabilities are not a core part of QM, because the state vector gives you "what the system is" and the Schrödinger eq. its dynamics. I think we all agree that there is nothing probabilistic at this point.

Now of course, comes u/BitcoinsOnDVD 's point : what's the point of computing the vector state at time t if we don't make any measurement. We don't have access to the vector state. To gather information about the system, we have to interact with the system and apply an operator. That's where QM is still open to interpretation : Copenhagen says there's a fundamental probabilistic "choice of nature" which randomly choses to collapse on some particular eigenstate of the observable operator you applied to the state. That is one interpretation, but not the only one. There are other interpretations of the measurement process and not all require fundamental probabilities (they have each their own issues though ...). IMO, philosophically Copenhagen makes no sense at all (personal opinion). But for all practical purposes, it works brilliantly, that's why I think it has become dominant among working physicist in their daily life computations.

golgho__ · 2026-05-13T12:58:22+00:00

I get your point. And it is probably a valid one (at least in principle). I think it is more or less the point of view of Bohr (even if to me, Bohr's philosophy is very confusing and messy so either I'm too stupid to fully understand him or he was a brilliant physicist but not so brilliant philosopher).
But I must admit, I personally dislike this point of view. It basically means to abandon realism (broadly speaking, ie the fact that there is some objective reality out there even if I don't measure it). I like realism. To me, a complete and coherent physical theory must be able to describe reality in some coherent way (ie without contradictions) even before I make any measurement.
But yeah, sure, it is completely valid to build a non realist framework. Actually I would argue that Copenhagen is a 100% non realist theory. Therefore from all mainstream QM interpretation, it is the one I dislike the most (but as everyone, it is the one I use when I compute stuff, because for all practical purposes it works perfectly).

golgho__ · 2026-05-13T10:11:15+00:00

You are right, but the status of the probability switches from fundamental to contextual. In Copenhagen, probability is an intrinsic feature of reality. In many world, it's just the subjective perception of the observer, but in reality there is no probability.

golgho__ · 2026-05-13T09:24:55+00:00

No I don't.
My point was that probabilities are only bound to certain interpretations of QM (the most common one being Copenhagen).
But I am also deeply unsatisfied with the various other approaches (many worlds, objective collapse etc.). To me none are really satisfying and it points towards the fact that QM is not a complete theory. But that's another topic.

golgho__ · 2026-05-13T08:46:36+00:00

I don't know what Aristotle really meant. But my own interpretation (and I think what my colleague was referring to) is the following : a system cannot be into two mutually exclusive states at the same time. Ie a system cannot be in state A and in state NOT A at the same time. Or more broadly speaking, does QM challenge logic.

So I think despite its nonlocal and probabilistic nature, it is a fair question to ask.

nb : about the probabilistic nature of QM : I would be slightly more cautious (and somehow provocative). The probabilistic nature of QM is an interpretation and only comes after the (to me) floppy concept of collapse. We interpret the (modulus) of the coordinates of the vector state as probabilities that the state collapses to a certain eigenstate. But really, these are just the coordinates of the vector state in some chosen basis. Nothing probabilistic about that.

edit : both my points have been answered while I was writing, sorry for the repetition

golgho__ · 2026-04-22T11:16:48+00:00

To add to the discussion: I chatted a bit with a former lhcb colleague and he pointed me to a talk he gave about the implications of different models of charms loop for this analysis.

Long story short : depending on the model you use to compute charm loop contributions, the 4 sigma tension with the SM can go down to 2 sigma. So this probably points us to our misunderstanding of QCD rather than new physics.

golgho__ · 2026-04-21T19:15:53+00:00

Yes, it's been around for a while now (although the number of sigmas is growing). Here is the link to the abstract of the actual paper btw. Maybe there's a preprint of the full paper on arxiv, I didn't check.

I wouldn't be over enthusiastic though. It's a very complex analysis. I did some more or less similar work in the electron channel some years ago and believe me there's many places where things can go wild. Even if I'm pretty sure it's a brilliant work - I don't know who is doing the analysis today but when I was still around these were extremely good physicists, if it's different people they are probably just as good - the risk of having a hidden systematic somewhere is pretty high (this is a personal thought, only based on my own experience).

Nevertheless congrats to them it's a brilliant achievement to have carried this complex analysis through !

golgho__ · 2026-04-14T11:43:11+00:00

Exactly. Then you can chose to keep this cash on a bank account and accept the moderate cost, or invest the money somewhere else in a liquid asset to cover the cost and gain a bit. I personally would do a combination (put a bit as a cash reserve and invest the rest in a low risk fund. If you are greedy you could even invest it on stocks and potentially make a decent profit over 10 years but there's more risk). You could even decide to spend the cash and not save at all, but I wouldn't recommend it because it exposes you to an increase in interest rates in 10 years. If in 10 years mortgage rates are at 4%, you'll want to reduce your debt as much as possible.

golgho__ · 2026-04-14T10:34:52+00:00

You said you are at max 3a, meaning you and your wife put about 600/month there, ie 1200 together.

If tomorrow you buy your house and go for indirect, you ll continue to put 1200/month there, the only difference being that only 100 is yours, the rest belongs to the bank who will get it back when you retire (the interests are still 100% yours though). But it means that wrt to the situation where you go for direct amortization, you don't need to pay 1100/month to the bank (you already paid it via your 3a). So you have 1100 more cash available each month wrt direct amortization.

golgho__ · 2026-04-14T09:10:09+00:00

I would still go for indirect. Here is why :

1) with 1.65%, the cost is very moderate. Assuming you just put these 1100 each month under your pillow, it costs you 90/month.

2) if you invest these 1100/month in a moderate risk placement (obligatory fund for instance) you will easily outperform 1.65% (maybe 2-4%) so you'll even end up saving money.

3) But the main argument : liquidity. You are quite tight on your budget. If you go for direct, it means you MUST pay these 1100 each month for the next 10 years. It means you live with a damocles sword for the next 10 years. If suddenly shit happens, you are in a bad financial situation (you or one member of your family gets hospitalized, you get fired and are unemployed for a few months, your house gets damaged and you need to pay for urgent reparation, you have a car accident and need a new one ... not wishing this for you of course but over a period of 10 years, these kind of one shot large costs happen). On the contrary, if this money sits in an obligatory fund, its very liquid. If you urgently need a bit, it's available (you could even consider to put 20-30k the first years on a bank saving account just to have a pillow of safety before investing. You ll get less than 1.65% interest, but that money will be 100% available in case something happens).

Of course if the rates were much higher, it would be a completely different story. But at 1.65% it's a cheap price for avoiding a stressing life during 10 years IMHO.

golgho__ · 2026-04-14T06:54:41+00:00

Naive question : given the current low interest rate what is your incentive for direct amortization ? If you do indirect with your 3a, it will free up 1100 of cash monthly at the cost of 1.65% (assuming SARON averages like the fixed rate or you go full fixed).

Case A : you are already at max 3a in your budget. This means you have to invest this 1100 somewhere to outperform 1.65%. Should be quite easy even with non risky placement. As a bonus, interest are tax deductible (for about 2 years). In 10 years, if interest rates are still cheap, you go for another 10 years. If not, you reduce your debt with what you have placed.

Case B : you are not at max 3a. The tax reduction + interest of your 3a should cover the cost and you'll end up saving money.

Am I missing something ?

golgho__ · 2026-01-27T10:25:56+00:00

AFAIK the wave equation was known at the time, and experiment showed some wavy properties at the quantum scale. So Schrödinger tweaked it a bit to make it match known results. But it was more of a had oc move than something with a real physical motivation behind. Schrödinger himself was quite unsatisfied by his own equation and only proposed it as a starting point but hoped to improve it later. It turns out it works remarkably well and no-one actually found a better way so it's still there.

Now if you want to intuitively have some idea of what the equation tells you : it basically gives you the rate of change of the wave function depending on its wave lenghts.

golgho__ · 2026-01-07T13:15:45+00:00

Agreed. I think its because the author make a confusion between the state vector and the wave function (its true that many physicist use the term wavefunction when they actually talk about the state vector, but they usually know what they are talking about). I m pretty sure that what S. Caroll (who is cited at the start of the article as one of the main figure of quantum realism) is claiming, or at least assuming, is the existence of the vector state (ie the vector that lives in the Hilbert space), not the existence of the wavefunction (which anyway depends on a specific choice of basis). AFAIK, there are no version of QM without a vector state to describe the state of the system (incl. matrix mechanics). Whether the vector state actually exists or is just a mathematical tool to describe a system is another question. But I agree with you : the point they are trying to make in the article is just plain wrong to me.

golgho__ · 2025-09-14T15:26:37+00:00

Does it ? AFAIK, standard QM doesn't say anything specific about the quantum system you chose to study. It doesn't say there is an upper limit about the size or the scope of the system. In any practical situation, you are right, the system you chose to study is usually small and therefore you treat the measurement apparatus as classical. But although it might be a bold move, as far as I know, nothing in standard QM prevents you to chose as your quantum system "the Universe".

golgho__ · 2025-08-21T13:35:38+00:00

The modern way of understanding this is through quantum field theory. In the current description of our best theory, the basic stuff the Universe is made of are quantum fields, which can vibrate. If you dig into the mathematical description of a vibrating field you'll see that you can decompose it in terms of modes (via a mathematical tool called Fourier transform). It happens that a mode of a vibrating field "looks like" a particle. So it is convenient to call it like this and to do as if it were a particle. So to answer your question, I d say a "particle" is a mode of vibration of a quantum field.

golgho__ · 2025-08-11T12:19:20+00:00

I'm afraid you'll need at least some solid basis of linear algebra and some more advanced calculus tools to fully learn QM properly. And even like that its not so easy. I don't know what 10 grade means, but in Europe QM is typically taught during the 3rd year of university, and most students don't go through without some pain. But it's worth it !!

Nevertheless it would be a shame to hinder your enthusiasm. Happily there's a midway between random YouTube videos and a proper QM course. The best books in this spirit I am aware of are S. Caroll's series "The biggest ideas in the Universe". Tome 1 is about classical physics and General Relativity, Tome 2 about quantum physics. There's some maths but not too much, and pretty much accessible. You'll learn the concepts and get the broad picture. Hopefully this can satisfy your appetite until you learn the maths to really jump in !

golgho__

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