High School Meaning of Wave Function Collapse

[bhobba]

It feels wrong to describe as having "no real relationship to the actual physical nature of things" a tool that, in the hands of an expert user, describes the physical nature of things with exquisite accuracy. It also feels wrong to use the term "blunt instrument" to describe something so subtle and precise that its error bars are like the wingspan of a good-sized beetle set alongside the continent of north america (roughly one part in $10^8$).

It feels to anyone that has actually studied the theory that way (including me), but if you haven't then its very hard to get across what's going on. We simply do not know why, as Wigner says, its like that. In talking to people who have not experienced it I think the best way for them to get a grip on it is its a description of reality - but a description is not the same as the reality it describes. If someone asked me what reality is, its what your theories say it is - but that is just an opinion - I can't prove it. But what I do know is when you study the theory you feel more and more - this is the reality. You may even get sucked into the rabbit hole of Penrose - I did for a while.

To the OP to see the issues in detail read Penrose - The Emperors New Mind and some of his other books.

Thanks
Bill

 

[Carpe Physicum]

Very interesting, especially the dartmouth article. I really like the analogy of map versus territory mentioned above. It's definitely a philosophical puzzle, to use the analogy, that the same map appears to be able to describe vastly different territories in some cases. In the article the author mentions that laws of heredity and physics are two territories that as of yet cannot be described with the same map. (Well he doesn't use the analogy but you get the point.)

So the mystery remains, why in the world would the same map be useful in describing physics and economics? Could it be that the maps are just blunt tools we clever humans force upon the data so to speak? On some other alien planet, their maps could be entirely different, maybe not even what we would call math. I'm reminded of Einstein saying he wanted to know god's thoughts. I kinda don't like that what I think I'm learning is that we (well the theoretical guys) are not figuring out god's thoughts, but only coming up with clever human tricks to handle human obtained data points, whether it's physics or economics. Nothing godlike about it. I truly don't like that idea.

 

[bhobba]

t's definitely a philosophical puzzle

And that is where its should be discussed - not here where by forum rules we do not discuss philosophy.

So please let's get back to the the threads purpose - wave function collapse. Quite a few answers have been given. Wave-function collapse, using the axioms of QM is a simple consequence of those axioms. We have had a discussion on precisely defining it - but regardless of the exact wording of it it's the change in a systems state from observing it. QM is about observations. The state allows us to calculate probabilities of the results of observations - and it naturally changes after the observation. Just like when you flip a coin you will get a head or tail - while flipping it's 50/50 what you will get - when it lands its one or the other. QM - same thing - but more sophisticated because of complex numbers are allowed.

Thanks
Bill

 

[Carpe Physicum]

And that is where its should be discussed - not here where by forum rules we do not discuss philosophy.

So please let's get back to the the threads purpose - wave function collapse. Quite a few answers have been given. Wave-function collapse, using the axioms of QM is a simple consequence of those axioms. We have had a discussion on precisely defining it - but regardless of the exact wording of it it's the change in a systems state from observing it. QM is about observations. The state allows us to calculate probabilities of the results of observations - and it naturally changes after the observation. Just like when you flip a coin you will get a head or tale - while flipping it's 50/50 what you will get - when it lands its one or the other. QM - same thing - but more sophisticated because of complex numbers are allowed.

Thanks
Bill

Understood. Would Physics Forums consider adding a dedicated Philosophy of Science sub forum? The problem I've run into is that general philosophy forums that include philosophy of science, at least the ones I've looked at, tend to devolve into silliness because there are few to none physics practitioners participating. Or if anyone knows of a good forum for it, please post a link.

 

[weirdoguy]

Would Physics Forums consider adding a dedicated Philosophy of Science sub forum?

There's not enough philosophy specialists here to maintain quality on such subforum.

 

[bhobba]

Understood. Would Physics Forums consider adding a dedicated Philosophy of Science sub forum? The problem I've run into is that general philosophy forums that include philosophy of science, at least the ones I've looked at, tend to devolve into silliness because there are few to none physics practitioners participating. Or if anyone knows of a good forum for it, please post a link.

We used to have one but it simply got out of hand. We deal with mainstream science here so it was shut down.

If you want to pursue these issues further a good place to start is Penrose and his books:
https://en.wikipedia.org/wiki/Roger_Penrose

I think, as far as it can be dealt with at the B level, collapse has been pretty much mined, but the thread will remain open for at least a while longer to see what other issues arise. As a group the mentors will make a decision on when it is appropriate to close it, but even after its closed you can always ask for it to be opened by contacting any mentor and it will most definitely be looked at.

Thanks
Bill

 

[bhobba]

There's not enough philosophy specialists here to maintain quality on such subforum.

That was the exact issue and why it got out of hand. I have just done a year long postgraduate philosophy 101, 102 course and enrolled in a graduate certificate on philosophy. I had to pull out because of issues of getting to the library to do research at the time - the certificate was via assignments you needed to research. It also had, unknown to me when I enrolled, a historical philosophical bias ie it was more towards discussing philosophy in a historical context. I was interested more in discussing it in a scientific context - history is not really my thing. I was offered admission to a Masters In Philosophy on what interested me, but that was 3 years part time and I still had the problem of getting to the library. That's solved now - but I am 63 and research is getting a bit beyond me these days although I do what I can.

Thanks
Bill

 

[jeremyfiennes]

When a layman like myself hears the term 'Wave function collapse' is brings to mind physical things. A wave of some sort physically getting smaller or shrinking. Obviously that's not what it is but it does sound like it. In reality, if I have it right it's just a fancy way of saying a measurement has been taken and whatever it was that was being measured has been found to have a value (or range of values). But it might as well be called 'measurement function resolution' or even 'monkeyguts'. And by using "loaded" terms (loaded with physical sounding meaning) confusion might accidently arise. This is similar to web programming with the awful term 'cookies'. We all know it's just a file. But you can imagine a discussion that takes the analogy too far, and wanders into things like, if I mix enough dough, and then add chocalate chips, I can create numerous cookies. And someone replies, well it depends on how you bake the cookies and the type of oven you use. Pretty soon you're talking about cooking itself, instead of file operations and data storage. And if you're not careful you come to conclusions about baking, i.e. about the analogy, and not file storage. Is there a possibility of something like that happening in discussing QM and wave function collapse? Discussions and conclusions are stated having to do with the math (the baking as it were) instead of the thing itself, the files or thing being measured.

I agree entirely. Another good one is "things existing in more than one place at a time", which in terms of everyday language is nonsensical. If a physical 'thing' is here, it cannot be there, and vice versa. What QM-ites mean is that if you make a measurement, you might find it here or you might find it there. But that is not the same. Why can't they say what they mean, rather than trying to confuse us with all this 'wierdness' gobbledigook which (according to them) only they are competent to understand?

 

[stevendaryl]

I agree entirely. Another good one is "things existing in more than one place at a time", which in terms of everyday language is nonsensical. If a physical 'thing' is here, it cannot be there, and vice versa. What QM-ites mean is that if you make a measurement, you might find it here or you might find it there. But that is not the same. Why can't they say what they mean, rather than trying to confuse us with all this 'wierdness' gobbledigook which (according to them) only they are competent to understand?

Nobody is trying to confuse anybody. There are aspects of what's going on that are just not very well understood.

 

[Carpe Physicum]

I think if you want to make your query one that can be answered you need to define precisely 'actual physical nature of things' AND have everybody, including philosophers agree. Good luck with that. In physics we take a simple view - we do not know or care about such things - the actual nature of things is what our theories describe but we do not worry about precisely defining that - we leave that to other disciplines - philosophy is usually what worries about that sort of thing but recently with Kuhn and his like others such as sociologists have got into the act.. And just like a map is not the territory, a mathematical description is not the actual nature of things - without saying what is even meant by that because you will likely get a lot of argument on it - but you will not get an argument on if the description (ie the theory) makes predictions in accord with experiment, everyday experience, observation etc.
Basically that's why pure math like linear algebra exists - for reasons we do not know the same mathematical ideas occur over and over again. We do not know why:
https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

And that it even crops up in non scientific areas such as Actuarial Science or Finance makes it even weirder.

But just my view - I am with Murray Gell-Mann:


But really nobody knows.

Thanks
Bill

Sorry just one more semi-philosophical post that's more directed to the mathies here. If the same math can be used in physics and other "human" areas, in what way could it be true that the math is elegant? I've always thought it was considered elegant because it only applied to the physical universe. Hence the universe is governed by elegant and permanent, emphasis on permanent (not temporary human areas) math. I remember being utterly disappointed to hear a friend who was heavy into advanced economics using some of the same complex math. But economics is merely temporary and human. So what's going on? Are economists just "faking it" so to speak?

 

[bhobba]

So what's going on?

Nobody knows.

Maybe its like Gell-Mann says the math describing various scales is approximately self similar - and a human construct like economics could be viewed as a very high level scale.

Or maybe mathematicians are not really that mad and its all Platonism

All joking aside it really is a mystery,

Thanks
Bill

 

[Carpe Physicum]

Nobody knows.

Maybe its like Gell-Mann says the math describing various scales is approximately self similar - and a human construct like economics could be viewed as a very high level scale.

Or maybe mathematicians are not really that mad and its all Platonism

All joking aside it really is a mystery,

Thanks
Bill

Einstein was and is an idol of mine, as is anyone who can think about the world in such abstract yet real terms. I'm going to go with option 2 Bill...Plato's forms were really his way of saying Tensor. ;)

 

[Fra]

I remember being utterly disappointed to hear a friend who was heavy into advanced economics using some of the same complex math. But economics is merely temporary and human. So what's going on? Are economists just "faking it" so to speak?

It is no conincidenceci think. Social and economical interactions and predictions have a lot of common abstractions to physical interactions. One major thing is that they all contain actions based on expectations. In physics we may ask what is real when its not measured, and which is more fundatemntal? Similarly I am economy the markets expected value of something vs the actual value. Path integrals are much like spreading risks.

Also an ever deeper lesson that i think most physicist does not appreciate, but lee smolin and roberto unger do, is the similarity and lessons to learn for physicists trying to explain origin of symmetries and laws, when looking at how social laws evolve. (See book: time reborn)

The result is initially depressing because it suggests that the unreasonable success of math in paritcle physics is because its limited to small subsystems.

/Fredrik

 

[zonde]

This is absolutely standard. And you really have all the information to perform the calculation yourself if it still isn't obvious to you. If you want to learn quantum mechanics, you should do these kind of exercises on your own. It's you who's doing the handwaving. I think none of your 2677 posts ever contained a calculation.

We perform the calculation for the state
$$\psi = h\otimes n\otimes n\otimes n$$
The interesting matrix entries of the $U_i$ are given by:
$$U_1 h\otimes n\otimes n\otimes n = h\otimes n\otimes n\otimes n$$
$$U_2 \frac 1 {\sqrt 2} (h+v)\otimes n\otimes n\otimes n = \frac 1 {\sqrt 2} (h+v)\otimes n\otimes n\otimes n \\ U_2 \frac 1 {\sqrt 2} (h-v)\otimes n\otimes n\otimes n = \frac 1 {\sqrt 2} (h-v)\otimes n\otimes a\otimes n$$
$$U_3 h\otimes n\otimes n\otimes n = h\otimes n\otimes n\otimes a \\ U_3 v\otimes n\otimes n\otimes n = v\otimes n\otimes n\otimes n \\ U_3 x\otimes n\otimes a\otimes n = x\otimes n\otimes a\otimes n$$
The remaining matrix entries are left as an exercise to the reader.
$$U_1 \psi = h\otimes n\otimes n\otimes n \\ U_2 U_1 \psi = \frac 1 2 (h+v)\otimes n\otimes n\otimes n + \frac 1 2 (h-v)\otimes n\otimes a\otimes n \\ U_3 U_2 U_1 \psi = \frac 1 2 h\otimes n\otimes n\otimes a + \frac 1 2 v\otimes n\otimes n\otimes n + \frac 1 2 (h-v)\otimes n\otimes a\otimes n$$
So $P(v\otimes n\otimes n\otimes n) = (\frac 1 2)^2 = \frac 1 4$ as expected and in accordance with Malus law $I=I_0\cos(0^\circ)^2\cos(45^\circ)^2\cos(45^\circ)^2=\frac 1 4 I_0$.

Ok, not to burden you with looking over all my 2677 posts I will do some exercise here.
So with 16 dimensions like that:

$\begin{matrix} H n_1 n_2 n_3\\ V n_1 n_2 n_3\\ H n_1 n_2 a_3\\ V n_1 n_2 a_3\\ H n_1 a_2 n_3\\ V n_1 a_2 n_3\\ H n_1 a_2 a_3\\ V n_1 a_2 a_3\\ H a_1 n_2 n_3\\ V a_1 n_2 n_3\\ H a_1 n_2 a_3\\ V a_1 n_2 a_3\\ H a_1 a_2 n_3\\ V a_1 a_2 n_3\\ H a_1 a_2 a_3\\ V a_1 a_2 a_3 \end{matrix}$

matrices appear to be like that:

$U_1=\begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$

$U_2=\begin{pmatrix} \frac{1}{2} & \frac{1}{2} & 0 & 0 & \frac{1}{2} & -\frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \frac{1}{2} & \frac{1}{2} & 0 & 0 & -\frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \frac{1}{2} & -\frac{1}{2} & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ -\frac{1}{2} & \frac{1}{2} & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$

$U_3=\begin{pmatrix}0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$

So with the state $\psi =\begin{pmatrix} 1\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0 \end{pmatrix}$ we should get $U_3 U_2 U_1\psi =\begin{pmatrix} 0\\ \frac{1}{2} \\ \frac{1}{2} \\0\\ \frac{1}{2} \\ -\frac{1}{2} \\0\\0\\0\\0\\0\\0\\0\\0\\0\\0 \end{pmatrix}$

That seems to agree with your calculation.

However I would question operational interpretation of say that dimension $H a_1 a_2 a_3$. As you say:

Neither the phonon modes in the absorbing polarizer nor the redirected beam in the polarizing beam splitter interact with the second polarizer. The situation is completely identical. The phonons are stuck in the first polarizer and end up as heat. You don't have to remove any of these modes from the description. Obviously, they are still physically there, so they must also remain in the model.

So the modes absorbed in first polarizer have to stay in the model, but for them to stay there they have to have some label from interaction with the second and third polarizer. And this labeling side effect seems rather artificial and detached from physical reality.

 

[AgentSmith]

Hugh Everett, who more or less invented the many-worlds hypotheses of QM, stated, or rather showed, that the wave function never collapses. He was roundly criticized at the time, ca. 1960-65, and left physics, but had his defenders, and has recently been sort of rehabilitated.

 

[rubi]

So the modes absorbed in first polarizer have to stay in the model, but for them to stay there they have to have some label from interaction with the second and third polarizer. And this labeling side effect seems rather artificial and detached from physical reality.

This makes no sense. The modes that are stuck in the first polarizer have no relation at all with the modes in the other polarizers. I don't know what you mean by "labeling side effect". There is nothing artificial in the model. It's absolute standard quantum physics and not at all detached from physical reality. We take tensor products of different systems and describe their interaction by unitary operators on the tensor product space. There's really nothing controversial about that.

 

[zonde]

This makes no sense. The modes that are stuck in the first polarizer have no relation at all with the modes in the other polarizers. I don't know what you mean by "labeling side effect". There is nothing artificial in the model. It's absolute standard quantum physics and not at all detached from physical reality. We take tensor products of different systems and describe their interaction by unitary operators on the tensor product space. There's really nothing controversial about that.

But the vector space has these dimensions associated with interaction history with polarizers. You are just adopting "n" as a sort of default state and "a" as a modified state. But "n" means that particular mode pointing in that direction has passed polarizer even if you take it as a default.
Or if it's not so then you have to give dual explanation for "n" dimension i.e. if vector points in "n" direction then associated mode either interacted with polarizer and passed it or it didn't interact with it at all.

 

[rubi]

But the vector space has these dimensions associated with interaction history with polarizers. You are just adopting "n" as a sort of default state and "a" as a modified state. But "n" means that particular mode pointing in that direction has passed polarizer even if you take it as a default.
Or if it's not so then you have to give dual explanation for "n" dimension i.e. if vector points in "n" direction then associated mode either interacted with polarizer and passed it or it didn't interact with it at all.

This is just a very basic model that allows you to effectively describe the transmission and absorption of photons due to the polarizers. The state just keeps track of which modes are present in the system. It has nothing to do with a history. Of course, you would normally start with a state containing only a photon, but that doesn't mean that this is somehow a "default state". As I said earlier, the model ignores all physical details and is just good enough to model the effect of the photon-phonon scattering on the polarization state of the photons due to the polarizer material, which is all you need here.

 

[zonde]

This is just a very basic model that allows you to effectively describe the transmission and absorption of photons due to the polarizers. The state just keeps track of which modes are present in the system.

But the model contains mode like $h \otimes a \otimes a \otimes a$. And it is meaningless.

 

[rubi]

But the model contains mode like $h \otimes a \otimes a \otimes a$. And it is meaningless.

How is it meaningless? It's a state that contains a phonon mode in each polarizer. This is the realistic situation, since in practice, no polarizer absorbs a mode completely. The idealized dynamics I gave cannot produce it from the $h\otimes n\otimes n\otimes n$ state, but you can easily include non-trivial absorption and transmission coefficients in the matrices and then photons will be partially absorbed in all polarizers, not just one of them. You can look at atyy's paper to see how it's done. (And by the way, this realistic situation can't be modeled by projections.)

 

[Carpe Physicum]

Sorry to post back in on what really is philosophy of science, but couldn't pass this up. Here's an article in advanced economics that illustrates a point I made earlier. https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/ I'm no mathematician, not even close, but this to me looks like an example of probability equations, including a reference to probability density. There's even pi in there. This looks suspiciously similar to equations I've seen in threads about QM. So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets? (There's nothing wrong with playing the stock market, but it's a tiny unimportant human activity compared to universal principles of elementary particles.) Seems to me one area of mathematical inquiry is, well, fooling itself. Or not. I don't know.

 

[Grinkle]

So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets?

That depends entirely on one's judgement-laden definition's of 'elegant' and 'similar' and 'in-any-way', does it not?

 

[Fra]

Sorry to post back in on what really is philosophy of science, but couldn't pass this up. Here's an article in advanced economics that illustrates a point I made earlier. https://www.physicsforums.com/insights/a-simplified-synthesis-of-financial-options-pricing/ I'm no mathematician, not even close, but this to me looks like an example of probability equations, including a reference to probability density. There's even pi in there. This looks suspiciously similar to equations I've seen in threads about QM. So how can we say the math is elegant in any way if similar math is used to discuss elementary particles and, ugg, calls and puts in stock markets? (There's nothing wrong with playing the stock market, but it's a tiny unimportant human activity compared to universal principles of elementary particles.) Seems to me one area of mathematical inquiry is, well, fooling itself. Or not. I don't know.

Don't underestimate the similarities between different complexity scales. The emergent rules of interaction on the market, as well as the population of players that survive, show striking conceptual similarities to emergent physical laws, and emergent population of elementary particles as you lower energy.

I think its a mistake often made by strong reductionists, to think that nothing important can be learned from studying complex system, such as economical systems. I think nothing could be more wrong. It may even be EASIER to learn from studying systems of intermediate complexity, than to probe deeper and deeper into matter.

Thus wether we find the mathematics to be similar it is not a coincidence. To find similar mathematics on these different scales are indeed beautiful.

I often think of particles as "players", their task is to gamble with their own integrity and try to survive. Those that survive populate the standard model, and their interaction rules would be stable in a "nash equilibrium" kind of sense.

Make sense?

/Fredrik

 

[Carpe Physicum]

Don't underestimate the similarities between different complexity scales. The emergent rules of interaction on the market, as well as the population of players that survive, show striking conceptual similarities to emergent physical laws, and emergent population of elementary particles as you lower energy.

I think its a mistake often made by strong reductionists, to think that nothing important can be learned from studying complex system, such as economical systems. I think nothing could be more wrong. It may even be EASIER to learn from studying systems of intermediate complexity, than to probe deeper and deeper into matter.

Thus wether we find the mathematics to be similar it is not a coincidence. To find similar mathematics on these different scales are indeed beautiful.

I often think of particles as "players", their task is to gamble with their own integrity and try to survive. Those that survive populate the standard model, and their interaction rules would be stable in a "nash equilibrium" kind of sense.

Make sense?

/Fredrik

Actually no. Human activity, being human, is temporary and negligible in the scheme of things. So to equate the mathematics describing trivial human activity and the grandness of the workings of the universe to me at least, and I admit I'm just a layman for whom Einstein and Bohr and in a different realm, Carl Sagan, are heros, is practically offensive. But maybe there's a way out. A friend on this forum pointed me to an interesting article that explained how confusion arises when epistemology and ontology in physics get mixed up. (I think he was saying that's one of the things the discussions about Einstein/Bohr debates bog down on.) The math of economics and experimental physics might be the math of epistemology. I.e. it's just a tool, not special in any grand sense, used to make sense of data, maybe even on a relatively deep level, and give clues to the underlying systems. And then there's another type of math used to address the ontology. Both are important of course so I don't mean to denigrate either - you need piano players and tuners both! OR is the current thinking that human activity, even macro activity such as playing the stock market, or raising chickens, or falling in love, really boils down to laws of nature discoverable by physicists? (And if that's the case, so be it.)

 

[Boing3000]

Actually no. Human activity, being human, is temporary and negligible in the scheme of things.

You need to use correct(useful) categorization. If an equation concern weasel and their "put" on food, would that make you "feel" better ?
The problem is about "scale" not of "personal taste". The "scheme of things" here being some agent driven by "force" to get some resource.

So to equate the mathematics describing trivial human activity and the grandness of the workings of the universe to me at least, and I admit I'm just a layman for whom Einstein and Bohr and in a different realm, Carl Sagan, are heros, is practically offensive.

What is offensive to me, is anthropocentrism, and to think that for some reason, a no-nonsense principle like "least action" (and beautiful, when expressed in math form) would not apply to human activity. Have you ever done some trekking ?

The math of economics and experimental physics might be the math of epistemology.

They definitively are. Ontological claims may be usefull to choose some direction for the "next step", but science is mostly concerned by epistemology (experimental verification).

I.e. it's just a tool, not special in any grand sense, used to make sense of data, maybe even on a relatively deep level, and give clues to the underlying systems.

It does, or it does not. "underlying" things are more treacherous that you think, and most definitely an excursion into the abyss (as Feynman beautifully explains)
Is the universe made "of field" or of little "strings" ? What if it does make any difference at all ? Even if the math turns out to have great deal of similarities ?

 

[richrf]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

The book traces the history of the foundational questions of Quantum Physics (which is what the OP addresses) as well as discussing in some depth the Bell Inequality Theorem and what it means in fairly layman's terms.

It is approaches the subject from many angles including the impact that philosophical positivism, political, and cultural biases had/has on quantum scientific research and how how alternative viewpoints that are explicitly and implicitly suppressed, specifically in the context of Bohmian Mechanics and Everett Many Worlds Interpretations.

The footnotes and bibliography are robust. Be forewarned, it does not put the scientific research culture in a very good light. In any case, it is very readable and once again raises the question, what is it precisely that we are talking about?

 

[jon4444]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

As someone also interested in the foundational questions, I found that book a disappointment. It did give interesting insight into research culture, but I felt it was rather weak on subject's like Bell's Inequality. (E.g., I had to go elsewhere to discover that experiments related to Bell's theorem involved a different type of entanglement than considered by Einstein, et. al. I still don't know if Bell's advances were due to him "discovering" this other form of entanglement or Einstein just missed the implications of entanglement with polariziation.)
Other major weakness was Becker's argument for why falsifiability shouldn't be a criteria for a scientific theory. After reading his book, I came away feeling more supporting of what I learned in school supporting Copenhagen Interpretation. Briefly, if there's no testable difference between explaining entanglement using retro-causality versus some form of non-locality, and over time differing explanations such as these haven't led anywhere constructive, then they have no explanatory power. What does "retro-causality" mean to us (who live in a world where we can't observe such a thing)--might as well resort to an explanation involving magical invisible unicorns.

 

[richrf]

As someone also interested in the foundational questions, I found that book a disappointment. It did give interesting insight into research culture, but I felt it was rather weak on subject's like Bell's Inequality. (E.g., I had to go elsewhere to discover that experiments related to Bell's theorem involved a different type of entanglement than considered by Einstein, et. al. I still don't know if Bell's advances were due to him "discovering" this other form of entanglement or Einstein just missed the implications of entanglement with polariziation.)
Other major weakness was Becker's argument for why falsifiability shouldn't be a criteria for a scientific theory. After reading his book, I came away feeling more supporting of what I learned in school supporting Copenhagen Interpretation. Briefly, if there's no testable difference between explaining entanglement using retro-causality versus some form of non-locality, and over time differing explanations such as these haven't led anywhere constructive, then they have no explanatory power. What does "retro-causality" mean to us (who live in a world where we can't observe such a thing)--might as well resort to an explanation involving magical invisible unicorns.

I may be incorrectly understanding your comment, but in regards to Bell's Theorem and polarization, I believe that the book described how it was papers written by Bohm that were the inspiration for Bell to use polarization as the backdrop for his theory to test non-locality. As the book explained, Einstein's primary objection to the completeness of Quantum Theory was that it undermined locality as demonstrated with EPR.

As for the Copenhagen Interpretation, Becker's main thrusts were that a) there was no such thing as there were serious disagreements among its advocates and b) the measurement problem is never addressed in any forthright manner, the problem being quite substantial and not peripheral to the interpretation as discussed in the book.

I found a good Youtube video of Becker at Google in which he summarizes his thoughts.

 

[Carpe Physicum]

For the OP, I thought I might bring to his/her attention a new book by Adam Becker, called "What Is Real?"

Just started reading the book. Looks good. It's good to know too that the issue is actually a real one, not one of these "gee you're just a stupid layman suckered in by silly shows on TV".

 

[richrf]

Just started reading the book. Looks good. It's good to know too that the issue is actually a real one, not one of these "gee you're just a stupid layman suckered in by silly shows on TV".

For those who are interested in what precisely is quantum, the issue is very real. What is great about the book is the meticulous manner in which Becker walks through the history and documents with great precision the sequence of events which are rarely discussed our written about. I always had my suspicions but Becker provides the documentation.

Also, Becker does a great job of underscoring the issue of non-locality beginning with EPR and Bell's inspired solution to the problem together with a brilliant exposition of the Bell Theorem. The book is one part history, one part philosophy, one part physics and one part political thriller. A great read and a keeper.