How can you describe the observing system mathematically?

[Gurde]

hi,
It(my question) might sound funny to you guys but I've been reading a book on modern physics. (The Wu Li Masters by Zukav, i know, to physicist this seems a kind of crap but yeah...) I was understanding everything till I came at 'observables'. Zukav says that the information of the observing system can be 'mathematicalized' to observables so you can put them in the Schrödinger equation. Now my question is: how can you describe the observing system mathematically? (it is a non math book... )

I'd like to know...
greets

 

[inha]

First of all: Stop reading that book. Seriously, throw it away.

QM doesn't deal with the measurement devices but the results of the measurement. Momentum measurer mark I isn't an observable but momentum is.

As for the poll I voted yo. I can't say that I understand QM because I still have a lot to learn.

 

[quetzalcoatl9]

for those that votes "yes" that they understand QM - i think you are full of crap.

i know people who have been studying QM all their lives, and they will be the first to admit that they don't fully understand it - just that is is reasonable and works.

 

[Gurde]

First of all: Stop reading that book. Seriously, throw it away.

QM doesn't deal with the measurement devices but the results of the measurement. Momentum measurer mark I isn't an observable but momentum is.

As for the poll I voted yo. I can't say that I understand QM because I still have a lot to learn.

ok i'll throw it away it only costed 1.5€ 2ndhand
You have a point: this kind of books are almost allways written by poeple who say:
last year i got interested by quantum physics, so i wrote a book about it ==>impossible



but then what about the observables?

well i know quantum physics a bit: I've been studying only the work of Planck and bohr. For the rest i have te learn a bit more math i guess, but i have to be patient.

 

[Gurde]

btw, i have been reading some other books like
that one from Murray Gell Man (and i think he knows what he is talking about)

in that book he also talks about QM, but not about observables...

 

[MalleusScientiarum]

I would say it depends on your definition of "understands". Ultimately, if you mean "I know exactly why this works" then nobody understands physics. Since this is clearly not a functional definition, I'm going on the "can use this theory to make calculations and predictions and the like" as the definition.

 

[quetzalcoatl9]

I would say it depends on your definition of "understands". Ultimately, if you mean "I know exactly why this works" then nobody understands physics. Since this is clearly not a functional definition, I'm going on the "can use this theory to make calculations and predictions and the like" as the definition.

in that case my computer, while running QM molecular dynamics, understands QM as well.

QM, unlike classical mechanics, does not lend itself well to your definition, since a great deal of understanding is being able to answer questions like "what does this mean?" this is not always clear in QM, since it can come down to interpretations.

 

[Maxos]

Observables are described with self-adjoint (I don't know the right english word, but I mean L=L*) hendomorphisms of an infinite-dimensioned complex space, and the possible values are their eigenvalues.

Pure states of a QM-system are vectors of the space whose norm is = 1.

 

[MalleusScientiarum]

Okay, quetzalcoatl, explain to me why the principle of least action works, without it being subject to interpretation.

 

[quetzalcoatl9]

Okay, quetzalcoatl, explain to me why the principle of least action works, without it being subject to interpretation.

you are talking about a concept that was developed way back by Euler..it is not a strictly QM concept, in fact I would consider it to transcend both classical and QM. i don't see your point.

if you are referring to the feynman path formulation, then i still don't see your point, since this is just one formulation - in others words, you have a choice in using it or not, depending upon interpretation.

but i will play along...explain to me why the principle of Heisenberg uncertainty works, without it being subject to interpretation.

 

[reilly]

Observables are what we observe, and, thus, permeate all of science. from a scientist's perspective, quantitative observables are to be preferred. So physicists look at observables like length, time, speed, mass and force, and so on. And, it turns out that many important, useful and profound mathematical relationships exist among (numerical) observers -- Newton's Laws, Maxwells equations, Schrödinger's Eq. -- tricky indeed. Among other things, physicists search for these relationships, use them, and constantly test them. So any freshman physics book will introduce you to observables, what they are and how to describe and use them.

Quantum theory uses a rather abstract formulation of observables, Hilbert Spaces, operators, and all that stuff. But, control engineering and electrical engineering use concepts of states and observables generically similar to that of QM, particularly when probability and noise are involved, like with Kalman filters. So, the basic technique that solves story-book algebra problems , translation of words into math, then turn the crank to get the answer, has reached high levels of sophistication and abstraction in much of modern science.
Regards,
Reilly Atkinson

 

[IAN STINE]

Not only do I not understand QP, I do not understand my answer, nor do I understand your question. Are you speaking in an absolute or a relative frame of reference? Wait. Could you repeat the question? At least a very small amount of it?

 

[masudr]

you are talking about a concept that was developed way back by Euler..it is not a strictly QM concept, in fact I would consider it to transcend both classical and QM. i don't see your point.

if you are referring to the feynman path formulation, then i still don't see your point, since this is just one formulation - in others words, you have a choice in using it or not, depending upon interpretation.

but i will play along...explain to me why the principle of Heisenberg uncertainty works, without it being subject to interpretation.

Malleus was challenging you to explain classical physics which is basically the variational principle $\delta S = 0$ where $S=\int L dt$, or even better explain classical field theory where $S=\frac{1}{c}\int L d^4x$, since you say you understand classical mechanics but not QM.

 

[MalleusScientiarum]

The point was that at some point we look at the state of physics and go "We have no idea why these assumptions work, but somehow they do." Ultimately, if a theory models something accurately, then we should be satisfied with the result until we can start looking into trimming up the assumptions we made on the previous theory.

The least action principle works because hey, it works. Quantum mechanics works because hey, it works. We can't run around thinking that we can't understand quantum mechanics because it's all "weird" and "counterintuitive" (as if those words had any meaning with regards to daily experiences at the subatomic scale) while one of the most fundamental ideas of classical physics is an ad hoc assumption as much as the Schrödinger equation or rules for canonical quantization are.

 

[Jimmy Snyder]

Niels Bohr said: If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet.

The wave-particle duality alone profoundly shocks me, let alone the weirder ideas. So Bohr leaves open the possibility that I understand it. However, I doubt that I understand it as well as someone who has passed a college course in it, and I'm pretty sure I don't understand it in the way that Bohr means.

 

[metacristi]

One can grasp after some efforts the standard mathematical formalism but what really counts is it's interpretation. And here we have lot of problems for it is difficult (if not impossible) to fully reconcile the 'quantum world' with the commonsense valid at the macro level and especially to indicate a clear 'winner' upon the actual standards of rationality. Currently there are more valid interpretations of QM in spite of the fact that the official propaganda presents only copenhagenism and further developments (especially the consistent/decoherent histories) as the only reasonable paths.

Indeed some of them do contradict a part of the assumptions of theories valid at macro level (for example GR) but this is not a real problem, coherentism is not necessarily a sign of truth. Some (such as the pilot wave solution of Bohm where quantum entities are really particles guided by a distinct real wave) are very close to the classical view but again this is not a final problem in spite of the current widespread belief and propaganda that the quantum world is very far from commonsense.

What unite all of them is the fact that they are all 'built around' the standard formalism, the only one which makes testable predictions, at least currently. This means that there is true underdetermination at quantum level which brought about the real problem, we cannot make a clear difference between these interpretations. So even if some programes seem currently to edge slightly ahead in some rather minor respects (for example because using some of their assumptions QFT handle better spin, assure currently a greater degree of unification etc) it cannot be argued that this will ever be the case, that they will continue to be progressive in the future and the first choice program. This is why some scientists advocate the positivistic stance 'shut up and calculate', some of them even deem all existing intepretations as being 'metaphysical'.

Finally, no matter the position (in the light of current knowledge at least) I think Feynman's made the best description of the actual state of affairs 'I think I can safely say that nobody understands quantum mechanics.' (of course this does not mean we cannot define a fallible 'standard of knowledge'-today in my view this is held by the program 'refining' copenhagenism-even in the absence of sufficient reasons to make a clear difference but what counts is that currently we cannot make a clear difference, with sufficient reasons, between the existing interpretations).

 

[MalleusScientiarum]

Quoting Niels Bohr, who developed the very beginnings of quantum mechanics and did not see the full fruition of his ideas, seems like a silly thing to do. The fact is that it will only shock you if you are stuck in the idea that particles are these localized dots that interact with each other in determined ways. The universe has no reason to act that way at the atomic scale, and in fact if everything were classical we would have some interesting problems on the subatomic scale. I understand that we observe these experimental events, and have a solid formalism that predicts and duplicates results. As far as I can tell that is the best that anyone can hope to truly understand physics, and everything else is just philosophers misquoting physical results for their own purposes.

 

[masudr]

Who cares what Niels Bohr said about HIM understanding QM? The question is, "Do YOU think you understand [QM]?"

So he was a smart guy. Why shouldn't you be too?