I Modern View of Quantum Phenomena

[gentzen]

But you're just changing the direction of the beam, you're still going to make your SG spin measurement in the plane perpendicular to that beam. I don't see what this accomplishes physically.

It measures the spin of the particle in some specific direction, as it was initially before the bending of the beam.

(I am still a bit confused about the number of parameters. An arbitrary direction in 3D space would still only be two continuous parameters. Maybe I should try to look up the posts where that topic popped up last time.)

 

[RUTA]

It measures the spin of the particle in some specific direction, as it was initially before the bending of the beam.

(I am still a bit confused about the number of parameters. An arbitrary direction in 3D space would still only be two continuous parameters. Maybe I should try to look up the posts where that topic popped up last time.)

Suppose you start with the state $|\psi\rangle=|z+\rangle$, then you make a SG measurement along $\hat{b}$ making an angle of $\theta$ with respect to $\hat{z}$. It doesn't matter what coordinates you use for the $\hat{b}\hat{z}$ plane, your distribution of $\pm 1$ outcomes (in units of $\frac{\hbar}{2}$) is given by P(+1) = $\cos^2{\frac{\theta}{2}}$ and P(-1) = $\sin^2{\frac{\theta}{2}}$ so that the average is $\cos{\theta}$, i.e., what you would expect per simple Newtonian mechanics if the spin angular momentum vector for the quantum state $|\psi\rangle=|z+\rangle$ is $+1\hat{z}$. And since that direction is arbitrary, I'm not sure how you expect these results would change if you somehow changed the direction of the beam.

 

[gentzen]

Suppose you start with the state $|\psi\rangle=|z+\rangle$, then you make a SG measurement along $\hat{b}$ making an angle of $\theta$ with respect to $\hat{z}$.

Suppose you start with the state $|\psi_{\alpha,\beta}\rangle=\alpha |z+\rangle+\beta|z-\rangle$. Then there is a measurement that will always give +1, and never -1. I want to realize that measurement. When you measure the state $|\psi\rangle=|z+\rangle$ with that measurement, you will get P(+1)=$|\alpha|^2$ and P(-1)=$|\beta|^2$.

 

[RUTA]

Suppose you start with the state $|\psi_{\alpha,\beta}\rangle=\alpha |z+\rangle+\beta|z-\rangle$. Then there is a measurement that will always give +1, and never -1. I want to realize that measurement. When you measure the state $|\psi\rangle=|z+\rangle$ with that measurement, you will get P(+1)=$|\alpha|^2$ and P(-1)=$|\beta|^2$.

I would have to know what the phases $\alpha$ and $\beta$ mean physically. For example, in the double-slit qubit where you are illuminating the slits equally and in phase your state is $|\psi\rangle = \frac{1}{\sqrt{2}} \left( |S1\rangle + |S2\rangle \right)$ (S1 = slit 1, S2 = slit 2). So, when you do a "which-slit" or "position" measurement (you put your detector screen right up against the slits, say) half the time you get an outcome behind S1 and half the time you get an outcome behind S2. When you do an "interference" or "momentum" measurement (you put your detector screen far from the slits relative to the slit separation) every outcome lands in a constructive interference band. If you add a $\pi$ phase plate behind S2, the state is now $|\psi\rangle = \frac{1}{\sqrt{2}} \left( |S1\rangle - |S2\rangle \right)$ and the "position" measurement outcomes are the same, but the previous "momentum" measurement outcomes change where the bright bands are now dark and the dark bands are now bright.

 

[RUTA]

Suppose you start with the state $|\psi_{\alpha,\beta}\rangle=\alpha |z+\rangle+\beta|z-\rangle$. Then there is a measurement that will always give +1, and never -1. I want to realize that measurement. When you measure the state $|\psi\rangle=|z+\rangle$ with that measurement, you will get P(+1)=$|\alpha|^2$ and P(-1)=$|\beta|^2$.

You got me wondering how to show that no matter what orientation I choose for $\hat{b}$ in the xy plane, when $\hat{b}$ makes an angle $\theta$ with $\hat{z}$ the distribution of outcomes will be P(+1) = $\cos^2{\frac{\theta}{2}}$ and P(-1) = $\sin^2{\frac{\theta}{2}}$ averaging to $\cos{\theta}$. Let me start with $|\psi\rangle = \cos{\frac{\theta}{2}}|z+\rangle + \sin{\frac{\theta}{2}}|z-\rangle$ for $\hat{b}$ in the xz plane, which gives me P(+1) = 1 when I measure in the $\hat{b}$ direction, i.e., $|\psi\rangle = |b+\rangle$ (use Eq 17 in the Answering Mermin's Challenge paper to get $\sigma_b$ then show $\sigma_b |\psi\rangle = |\psi\rangle$). Now I rotate this state about the z axis by $\alpha$ to get $|\psi\rangle = e^{i \alpha/2} \cos{\frac{\theta}{2}}|z+\rangle + e^{-i \alpha/2}\sin{\frac{\theta}{2}}|z-\rangle$ (see Eq 24 in the Answering Mermin's Challenge paper), which does give those probabilities for any $\alpha$. To get a bit of a feel for this, let $\theta = 90^{\circ}$ (again, we're in the xz plane), then $|\psi\rangle = \frac{1}{\sqrt{2}}|z+\rangle + \frac{1}{\sqrt{2}}|z-\rangle = |x+\rangle$, which you can see from $\sigma_x |\psi\rangle = |\psi\rangle$. Now let $\alpha = 270^{\circ}$ and you get $|\psi\rangle = (-1 + i)\frac{1}{2}|z+\rangle + (-1 - i)\frac{1}{2}|z-\rangle = |y+\rangle$, which you can see from $\sigma_y |\psi\rangle = |\psi\rangle$.

 

[Fra]

1) Can you elucidate the criteria by which a fundamental theory is distinguished from an effective one?

Conceptually I think of it so that, when a "fundamental theory" is indistiniguishable from an "effective one" is a contextual question itself and and this is a statement about the capacity of when the physical context itself interactionwise decouples from the details. This itself then also implese the the original notion of "fundemental theory" is likely an armchair fiction itself.

The difference to me however, is how you chose to interpret all this from the perspective of trying to unify all interactions. You can view this effective theory as pragmatic only, or like I would like to do, sugges that the decoupling of certain details between interaction systems really is a deep insight into the nature of causality.

Ie the insight should IMO not just be that from a practical perspective, we as humans are unable to tell effective theory from fundamental theory, but rather than each subsystem of the universe (say subatomic agents) are unable to couple and interact beyond a certain complexlity limit. And this must somehow be related to HOW parts of the universe interact, and it must serve the purpose of a natural regulator, likely related to complexity/mass/energy or something similar, that would put an upper bound on their decoding capacity of detail. But how this all works, in the evolutionary picture is what remain to understand to me. This has conceptual meaning beyond mathematical regulatory trickery, but the picture is still not finished.

/Fredrik

 

[Homocistene]

This is not, strictly speaking, a discussion of interpretations per se.

We often see discussions based on QM as it was understood during the early days and the famous Einstein-Bohr debates. The problem with this is that things in QM have advanced tremendously since then, and the 'weirdness' that puzzles those attempting to understand QM has changed.

I recently came across a synopsis of these advances, allowing those interested in interpretational issues to understand the modern view.

https://rreece.github.io/talks/pdf/2017-09-24-RReece-Fields-before-particles.pdf

It is advanced, but I tagged it as an I-level. Beginners may not understand the details, but they should get a sense of the modern perspective.

It also provides background to my current view, based on Wienberg's Folk Theorem, that QM is the EFT that any theory will look like at large enough distances. It is very mathematically sophisticated, but after years of thinking about interpretations, I have come to believe there is no 'simple' way to understand QM. It is, by its very nature, very advanced mathematically.

The real 'mystery' is why QM is based on operators, and complex space ones at that. I have posted a heuristic view of why, but it is just that a heuristic. That said - is it a mystery? What was it Newton said - hypotheses non fingo (Latin for "I frame no hypotheses", or "I contrive no hypotheses"). Is QM any different?

Thanks
Bill

There exists no deep explanation about anything in the material world(space, matter, time, biology, life...). And as it turns out, the material world is very much not fundamental but secondary("emergent"). Whatever it emerges from, holds the final, deep and complete explanation that these discussions seek. Physics, as the science of the material world, cannot explain everything. The hope is to one day describe it in a unified theory but understanding will always be lacking. Due to the peculiar nature of the physical world

 

[bhobba]

There exists no deep explanation about anything in the material world(space, matter, time, biology, life...).

Those who have studied Weinberg's three-volume Quantum Theory of Fields would likely disagree.

Yes, there is much we do not know, but we certainly know some profound and surprising things, for example, that everything, as far as we can tell today, is a Quantum Field.

Thanks
Bill

 

[gentzen]

(I am still a bit confused about the number of parameters. An arbitrary direction in 3D space would still only be two continuous parameters. Maybe I should try to look up the posts where that topic popped up last time.)

I guess I found it, but I didn't write anything about how to get from one parameter to two, or that I am still confused about where I lost the third parameter. (What I found interesting about reading that discussion again was that I focused maybe a little too much on observation, just like Heisenberg, implicitly dismissing preparation and contextuality, and that the topic of what is wrong with Heisenberg's position later came up in that discussion.) That discussion was about silver atoms, which is useful, because those are uncharged, hence we can apply any constant homogeneous magnetic field without worrying that it would bent the beam.

Now I studied https://en.wikipedia.org/wiki/Elliptical_polarization until I understood where the third parameter disappears: The "missing" third parameter is simply the global phase! And if I would have used the four Stokes parameters instead, then the two "irrelevant" parameters are the total intensity and the degree of polarization, i.e. also in this case I end up with only two relevant/interesting parameters.

I would have to know what the phases $\alpha$ and $\beta$ mean physically.

With my focus on observation (like Heisenberg), the physical meaning would be defined by how I measure them. I cannot measure the global phase, hence that "third parameter" has no physical meaning.
The other two parameters can be measured as follows: If I send the beam of silver atoms through a constant magnetic field, the spin axis will rotate (with a speed depending on ...) around the direction of the magnetic field. So if the beam propagates in y-direction, I could for example first put a magnetic field in z-direction and control how long the silver atoms are there, and then do a Stern-Gerlach measurement in an arbitrary direction.

The other focus (unlike Heisenberg) to give physical meaning would be to describe a preparation procedure. I could use a Stern-Gerlach device to prepare the silver atoms in spin-up state, and then apply constant magnetic fields in z-direction for a given time, and then in x-direction for second given time.

---

What I was missing in the "old discussion" with vanhees71 was both where I lost the "third parameter", and the connection to special relativity, which explains why the "second parameter" feels so counter-intuitive. (The "first parameter" being simply the rotation angle of the Stern-Gerlach device around the beam.)

 

[RUTA]

I guess I found it, but I didn't write anything about how to get from one parameter to two, or that I am still confused about where I lost the third parameter. (What I found interesting about reading that discussion again was that I focused maybe a little too much on observation, just like Heisenberg, implicitly dismissing preparation and contextuality, and that the topic of what is wrong with Heisenberg's position later came up in that discussion.) That discussion was about silver atoms, which is useful, because those are uncharged, hence we can apply any constant homogeneous magnetic field without worrying that it would bent the beam.

Now I studied https://en.wikipedia.org/wiki/Elliptical_polarization until I understood where the third parameter disappears: The "missing" third parameter is simply the global phase! And if I would have used the four Stokes parameters instead, then the two "irrelevant" parameters are the total intensity and the degree of polarization, i.e. also in this case I end up with only two relevant/interesting parameters.


With my focus on observation (like Heisenberg), the physical meaning would be defined by how I measure them. I cannot measure the global phase, hence that "third parameter" has no physical meaning.
The other two parameters can be measured as follows: If I send the beam of silver atoms through a constant magnetic field, the spin axis will rotate (with a speed depending on ...) around the direction of the magnetic field. So if the beam propagates in y-direction, I could for example first put a magnetic field in z-direction and control how long the silver atoms are there, and then do a Stern-Gerlach measurement in an arbitrary direction.

The other focus (unlike Heisenberg) to give physical meaning would be to describe a preparation procedure. I could use a Stern-Gerlach device to prepare the silver atoms in spin-up state, and then apply constant magnetic fields in z-direction for a given time, and then in x-direction for second given time.

---

What I was missing in the "old discussion" with vanhees71 was both where I lost the "third parameter", and the connection to special relativity, which explains why the "second parameter" feels so counter-intuitive. (The "first parameter" being simply the rotation angle of the Stern-Gerlach device around the beam.)

I’m in the hospital. Had appendectomy last night. Can’t respond properly now.

Update: I'm home now and I see the post does not require my response. Thnx for your patience :-)

 

[RUTA]

sorry, I meant like the position of the electron in Hydrogen atom, for example.

Design a measurement, model it with QM to get a predicted distribution of outcomes, then conduct the experiment. The end result must be a distribution of quanta in a spatiotemporal context of bodily objects. According to this view of reality, quanta are not 'hidden' bodily objects.