I Modern View of Quantum Phenomena

[RUTA]

No, they don't. They're not a group in 3+1 spacetime; they're not closed under composition. Only in 1+1 spacetime do Lorentz boosts by themselves form a group.

Now you're conflating transformation with group

I understand that your version of it says that. I just don't agree with your version. I don't think you can just ignore the fundamental difference between Galilean invariance and Lorentz invariance, or say that it's not part of the relativity principle.

It's not "my version," I'm following introductory physics textbooks like Knight above. Here is Serway & Jewett
Physics for Scientists and Engineers with Modern Physics, Cengage, Boston 10th ed., Section 38.3 (2019)

Here is Essential College Physics Vol II, A. Rex and R. Wolfson, Cognella Academic Publishing, USA, 2nd ed., p. 438 (2021)

Here is Sears & Zemansky's University Physics with Modern Physics, H. Young and R. Freedman
Pearson Education, USA, 15th ed., p. 1218 (2020)

Which means your claim that I quoted at the start of this post is false, as I said.

Spatial rotations about a specific point in a specific inertial frame are a group, yes. But you have to pick a frame--or, equivalently, you have to pick a particular spacelike hypersurface of constant time for the rotations to operate in. If you change frames in Minkowski spacetime, you change which set of transformations are "spatial rotations", because you change which spacelike hypersurfaces are surfaces of constant time. So I stand by my statement that in Minkowski spacetime you cannot invariantly separate spatial rotations and boosts.

Ibid

 

[PeterDonis]

Now you're conflating transformation with group

I'm saying that if the transformations don't form a group, IMO it's highly questionable, to say the least, to use them in any kind of foundational argument.

 

[PeterDonis]

It's not "my version,"

It's the version you're using in your foundational argument. The sources you cite aren't making that kind of argument; they're just declaring the principle by fiat, because they're introductory textbooks, not peer-reviewed papers making foundational arguments.

 

[RUTA]

I'm saying that if the transformations don't form a group, it's highly questionable, to say the least, to use them in any kind of foundational argument.

But you do have to add SO(3) to Lorentz boosts to get the Lorentz group. And you can clearly do a boost (generator K) or a spatial rotation (generator J for angular momentum) independently. That's what I'm talking about, independent functionality. So invariance with respect to SO(3) doesn't distinguish between G4 and M4.

 

[RUTA]

It's the version you're using in your foundational argument. The sources you cite aren't making that kind of argument; they're just declaring the principle by fiat, because they're introductory textbooks, not peer-reviewed papers making foundational arguments.

Here are peer-reviewed papers where we have published this idea:

“Answering Mermin’s Challenge with Conservation per No Preferred Reference Frame,” W.M. Stuckey, Michael Silberstein, Timothy McDevitt, and T.D. Le. Scientific Reports 10, 15771 (2020)

“Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s,” Michael Silberstein, W.M. Stuckey, and Timothy McDevitt. Entropy 23(1), 114 (2021).

“‘Mysteries’ of Modern Physics and the Fundamental Constants c, h, and G,” W.M. Stuckey, Timothy McDevitt and Michael Silberstein. Honorable Mention in the Gravity Research Foundation 2021 Awards for Essays on Gravitation, May 2021. Quanta 11(1), 5-14 (2022).

“No Preferred Reference Frame at the Foundation of Quantum Mechanics,” W.M. Stuckey, Timothy McDevitt, and Michael Silberstein. Entropy 24(1), 12 (2022).

“Unifying Special Relativity and Quantum Mechanics via Adynamical Global Constraints,” W.M. Stuckey and Michael Silberstein. Journal of Physics: Conference Series 2948, 012009 (2025).

We had three reviewers for our book "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" W.M. Stuckey, Michael Silberstein, and Timothy McDevitt. Oxford University Press, Oxford (2024). Markus Mueller was kind enough to review it for us and it was blurbed by Adlam, Brukner, Bub, and Wharton.

I've presented it to physicists and philosophers at:
2022 American Physical Society March Meeting (online), Foundations 2023 (Bristol), Physics and Reality (Helsinki, June 2024), Q 100: Examining Quantum Foundations 100 Years On (Chapman University, March 2025), Fundamental Problems in Quantum Physics 2025 (Trieste), Quantum Information and Probability: from Foundations to Engineering (Vaxjo, June 2025), at the Institute for Quantum Optics and Quantum Information (Vienna, April 2022), and at University Roma Tre (June 2025).

No referee, reviewer or audience member has disagreed with our use of the relativity principle as stated above. How much more refereed do you need?

 

[PeterDonis]

you do have to add SO(3) to Lorentz boosts to get the Lorentz group.

Yes.

And you can clearly do a boost (generator K) or a spatial rotation (generator J for angular momentum) independently.

Only once you've chosen a specific frame. As I've said, there is no invariant way to separate boosts and rotations. The K and J definitions are frame-dependent.

 

[PeterDonis]

No referee, reviewer or audience member has disagreed with our use of the relativity principle as stated above.

Your use, yes. That was my point. All those other referees, reviewers, and audience members didn't publish those papers and books. You (and your coauthors--but they're not posting here) did.

 

[RUTA]

Your use, yes. That was my point. All those other referees, reviewers, and audience members didn't publish those papers and books. You (and your coauthors--but they're not posting here) did.

And Norton's references and the four intro physics textbooks. It's not idiosyncratic and it has found widespread acceptance. That's my point.

 

[PeterDonis]

It's not idiosyncratic and it has found widespread acceptance.

As a principle declared by fiat. Again, all those other references aren't making the foundational argument that you and your coauthors are. That makes a difference.

 

[RUTA]

As a principle declared by fiat. Again, all those other references aren't making the foundational argument that you and your coauthors are. That makes a difference.

Assuming the relativity principle is fundamental (not derived from something else, but "declared by fiat" as the starting point of a theory) is not unique to us. Again Norton and those four textbook authors all think that about SR and I have other quotes from Rovelli, Mueller and others in the quantum reconstruction program saying they want to follow that for QM (as we did). Here is a quote from Lorentz:

It will be clear by what has been said that the impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the ``true'' times or the ``true'' lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, ... .

I cannot speak here of the many highly interesting applications which Einstein\index{Einstein, Albert} has made of this principle. His results concerning electromagnetic and optical phenomena agree in the main with those which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle.

 

[PeterDonis]

Assuming the relativity principle is fundamental

That's not the assumption I'm questioning. The assumption I'm questioning is that "the relativity principle" is the same for Galilean and Lorentzian invariance.

A principle that says "The laws of physics must be the same in all inertial reference frames", to me, depends on a definition of "inertial reference frames" that includes how you transform between them. If you don't know which transformation to use between inertial reference frames, you can't test the principle. And that means the principle with two different transformations is not the same principle.

 

[gentzen]

If you change frames in Minkowski spacetime, you change which set of transformations are "spatial rotations", because you change which spacelike hypersurfaces are surfaces of constant time. So I stand by my statement that in Minkowski spacetime you cannot invariantly separate spatial rotations and boosts.

I upvoted this, because I didn't realize it before.
This raised the question for me, what we actually measure in spin measurement, if rotations are not allowed.
In an actual measurement, we can "in principle" rotate the detector (or Stern Gerlach device) around the beam. This is only a 1-parameter group, so 2-parameters are still missing for general "spatial rotation". I think I have seen in the past how to get at least one more parameter, but maybe the details are not important at the moment.

But important for me is that it is not as trivial as simply rotating a detector in 3D space.

 

[RUTA]

That's not the assumption I'm questioning. The assumption I'm questioning is that "the relativity principle" is the same for Galilean and Lorentzian invariance.

A principle that says "The laws of physics must be the same in all inertial reference frames", to me, depends on a definition of "inertial reference frames" that includes how you transform between them. If you don't know which transformation to use between inertial reference frames, you can't test the principle. And that means the principle with two different transformations is not the same principle.

Norton studied the history of Einstein's work on SR (here and here are two websites) and it was difficult because unlike his later work, there isn't much material on Einstein pre-SR. Anyway, what you said is precisely what Einstein struggled with in coming up with SR. It's not the principle of relativity that changed from Newton to SR, but the kinematic assumptions leading to different transformations between inertial reference frames. Indeed he thought Maxwell's equations were incompatible with the relativity principle until he realized it was his tacit kinematic assumptions, not the relativity principle, that were wrong. Here is a quote from Einstein then Norton (from one of those Norton websites linked above):

"The difficulty to be overcome lay in the constancy of the velocity of light in a vacuum, which I first believed had to be given up. Only after years of [jahrelang] groping did I notice that the difficulty lay in the arbitrariness of basic kinematical concepts."

The key to the puzzle is the relativity of simultaneity. If Einstein gives up the absoluteness of simultaneity, then the principle of relativity and the constancy of the speed of light are compatible after all. The price paid for the compatibility is that we must allow that space and time behaves rather differently than Newton told us.

Here is also from Norton https://sites.pitt.edu/~jdnorton/papers/companion.pdf:

Einstein’s special theory of relativity is based on two postulates, stated by Einstein in the opening section of his 1905 paper. The first is the principle of relativity. It just asserts that the laws of physics hold equally in every inertial frame of reference. ...

Einstein’s second postulate, the light postulate, asserts that “light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.” ...

Einstein pointed out immediately that the two postulates were “apparently irreconcilable.” His point was obvious. ...

How could these conflicting considerations be reconciled? Einstein’s solution to this puzzle became the central conceptual innovation of special relativity. Einstein urged that we only think the two postulates are incompatible because of a false assumption we make tacitly about the simultaneity of events separated in space. If one inertially moving observer judges two events, separated in space, to be simultaneous, then we routinely assume that any other observer would agree. That is the false assumption. According to Einstein’s result of the relativity of simultaneity, observers in relative motion do not agree on the simultaneity of events spatially separated in the direction of their relative motion.

See what I'm saying? There aren't two different forms for the relativity principle, but you have to take into account the relationships between inertial reference frames to apply the one form properly. And that requires empirically investigation.

 

[RUTA]

I upvoted this, because I didn't realize it before.
This raised the question for me, what we actually measure in spin measurement, if rotations are not allowed.
In an actual measurement, we can "in principle" rotate the detector (or Stern Gerlach device) around the beam. This is only a 1-parameter group, so 2-parameters are still missing for general "spatial rotation". I think I have seen in the past how to get at least one more parameter, but maybe the details are not important at the moment.

But important for me is that it is not as trivial as simply rotating a detector in 3D space.

That's why you have three Pauli matrices. You can see how the Bell spin states are invariant wrt transformations generated by those matrices and what it means physically in the Methods section of this paper.

 

[PeterDonis]

See what I'm saying?

I see what you're saying. I just don't agree with it. I'll bow out at this point.

 

[Fra]

No, I'm not. I'm pointing out that "the relativity principle", as far as physics is concerned, is not one thing. Galilean invariance is not the same thing as Lorentz invariance.

I can symphatize with RUTA's logic here in that he tries to add several "constraints" he calls principles and see what they imply for the theory.

I always views the first postulated of SR as a special case of what I consider the even more general principle that says that the laws of physics should be the same; as seem by all observers (observer equivalence)

I think this principle is separate and stands on its own, regardless of how the set of all possible "observers" are generated in a particular theory.

The special cases are then because you only consider subclasses of observers. As we know in SR as well as GR, "observer", really means just observers that differ by spacetime transformations. And in SR, we consider inertial frames only.

The postulate that there must exists a max limit to signal propagtion, that all observers agree upon, I definitely see as a separate postulate as well. But of course when ADDING them, it changes the spacetime structure. But as constructing constraints, I see them as separate, I think this is what RUTA suggests and emhpasize as identifying principal constraints is his main focus?

So for me, the principle of observer equivalence is the more genereal version of "relativity principle", which tends to apply only to spacetime frames; but an observer undeniably consists of more than a spacetime index (internal structure). But this is where already things start to reveal itself, as the only reasonable way I ever understood spin1/2 is precisely as an "internal transformation" - not external. So surely they constraints may start to conflict or interfere at some point.

/Fredrik

 

[gentzen]

That's why you have three Pauli matrices. You can see how the Bell spin states are invariant wrt transformations generated by those matrices and what it means physically in the Methods section of this paper.

I read that method section now. Obviously, you didn‘t understand my remark, or what I would like to measure. This makes me wonder whether you actually understood what PeterDonis said.

Let me try to make the connection clear: if the measurement device can only be rotated around the beam, then the direction of the beam can also be used to restrict the allowed movements of the measurement device: It is only allowed to move parallel to the beam. This now allows us to define the 1-parameter group of rotations that has invariant meaning in this scenario, and provides a connection to the Lorentz group.

But the remaining 2-parameters for the full 3-parameter rotation group apparently don‘t have such a nice invariant connection to the Lorentz group.

 

[RUTA]

I can symphatize with RUTA's logic here in that he tries to add several "constraints" he calls principles and see what they imply for the theory.

The postulate that there must exists a max limit to signal propagtion, that all observers agree upon, I definitely see as a separate postulate as well. But of course when ADDING them, it changes the spacetime structure. But as constructing constraints, I see them as separate, I think this is what RUTA suggests and emhpasize as identifying principal constraints is his main focus?

/Fredrik

Sorry, I didn't make the context clear. What we did in the papers and book I referenced above is part of the quantum reconstruction program involving many other researchers beginning in 1996 as part of the "second quantum revolution." Let me share some quotes so you don't get the impression that we are the ones who came up with this idea.

Rovelli 1996:

Quantum mechanics will cease to look puzzling only when we will be able to derive the formalism of the theory from a set of simple physical assertions (‘postulates’, ‘principles’) about the world. Therefore, we should not try to append a reasonable interpretation to the quantum mechanics formalism, but rather to derive the formalism from a set of experimentally motivated postulates. … The reasons for exploring such a strategy are illuminated by an obvious historical precedent: special relativity. ... Special relativity is a well understood physical theory, appropriately credited to Einstein’s 1905 celebrated paper. The formal content of special relativity, however, is coded into the Lorentz transformations, written by Lorentz, not by Einstein, and before 1905. So, what was Einstein’s contribution? It was to understand the physical meaning of the Lorentz transformations.

Zeilinger (1999):

Physics in the 20th century is signified by the invention of the theories of special and general relativity and of quantum theory. Of these, both the special and the general theory of relativity are based on firm foundational principles, while quantum mechanics lacks such a principle to this day. By such a principle, I do not mean an axiomatic formalization of the mathematical foundations of quantum mechanics, but a foundational conceptual principle. In the case of the special theory, it is the Principle of Relativity, ... . In the case of the theory of general relativity, we have the Principle of Equivalence ... . Both foundational principles are very simple and intuitively clear. ... I submit that it is because of the very existence of these fundamental principles and their general acceptance in the physics community that, at present, we do not have a significant debate on the interpretation of the theories of relativity. Indeed, the implications of relativity theory for our basic notions of space and time are broadly accepted.

Fuchs (2016):

Associated with each system [in quantum mechanics] is a complex vector space. Vectors, tensor products, all of these things. Compare that to one of our other great physical theories, special relativity. One could make the statement of it in terms of some very crisp and clear physical principles: The speed of light is constant in all inertial frames, and the laws of physics are the same in all inertial frames. And it struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak -- something that didn’t look to have much physical content at all, in a way that anyone could identify with some kind of physical principle -- if we couldn’t turn that into something like this, then the debate would go on forever and ever. And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements.

Hardy (2013):

The standard axioms of QT are rather ad hoc. Where does this structure come from? Can we write down natural axioms, principles, laws, or postulates from which can derive this structure? Compare with the Lorentz transformations and Einstein’s two postulates for special relativity. Or compare with Kepler’s Laws and Newton’s Laws. The standard axioms of quantum theory look rather ad hoc like the Lorentz transformations or Kepler’s laws. Can we find a natural set of postulates for quantum theory that are akin to Einstein’s or Newton’s laws?The real motivation for finding deeper postulates for quantum theory is that it may help us go beyond quantum theory to a theory of quantum gravity (just as Einstein’s work helped him go beyond special relativity to his theory of General Relativity).

Grinbaum (2017):

If, despite Einstein's wish, no constructive theory has materialized as a replacement of special relativity, it is not impossible to imagine that our intuitive desire to `fill the box' with physical systems for the purposes of better explaining physics is as illusory. The device-independent approach might stay as a legitimate way of doing physics, without any need to `fill the box,' much in the same sense as principle-based special relativity has not been surpassed by any constructive theory.

Mueller (website):

Can quantum theory be derived from simple principles, in a similar way as the Lorentz transformations can be derived from the relativity principle and the constancy of the speed of light? The exciting answer is ‘yes!'

Berghofer (2024):

The cornerstones of the quantum reconstruction program (QRP) have been independently formulated by Carlo Rovelli (1996) and Anton Zeilinger (1999). In both works, it is explicitly argued that quantum mechanics needs to be based on a set of simple physical principles. Both suggest concrete information-theoretic principles that could play such a role. And both mention special relativity as a role model in this regard: a physical theory that has counter-intuitive consequences but is widely accepted since it conceptually rests on clear physical principles. ... The success of and booming interest in quantum information theory convinced more and more researchers that the notion of information is crucial for understanding the foundations of quantum mechanics. In the year 2000, Christopher Fuchs and Gilles Brassard co-organized a conference with the programmatic title “Quantum Foundations in the Light of Quantum Information.” Fuchs’ paper of the same name has been highly influential, summarizing the methodology of this project as follows: “to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears to be better calibrated for a direct assault than quantum information theory” (Fuchs 2001).

I could post more such quotes, but hopefully this is enough to show that our work is contributing to a much larger effort.

 

[Fra]

I could post more such quotes, but hopefully this is enough to show that our work is contributing to a much larger effort.

I absolutely got that! But thanks for the nice array ot quotes! I just wrote RUTA's logic to express that I share the distinction of different principles you tried to make.

/Fredrik

 

[selfsimilar]

Here is an open access paper that serves as a 17-page summary.

So in what sense this tells us where the electron was before measurement, among other properties.

 

[RUTA]

So in what sense this tells us where the electron was before measurement, among other properties.

We have 30+ pages in Chapter 9 of the book on this, so what I write here is very superficial. The self-consistently shared information between interacting bodily objects establishes what we know as the "classical context" and that establishes the properties of the quanta of the interactions. So, when an electron is a quantum (as opposed to a track in a particle detector, say) it is not interacting with the bodily objects in the experimental set-up and has no worldline in spacetime (or it would be a bodily object, not a quantum). That the quantum is an electron in the spacetime context in this particular experiment is established by the source from previous spacetime contexts (so you can say, "I have a source of electrons for this experiment"). All that means the electron was emitted by the source and absorbed by the detector in the spacetime context of bodily objects for the experiment. There is no "hidden reality" for the electron between source and detector otherwise.

 

[selfsimilar]

There is no "hidden reality" for the electron between source and detector otherwise.

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

 

[bhobba]

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

You miss the point of why I started this thread.

Particles are not fundamental; they emerge from fields. For fields, the question is meaningless.

While not directly related to the position question, another point was that QFT is more or less inevitable once certain general assumptions, such as Lorentz Covariance, are accepted. Moreover, our current theories are effective - not fundamental. This has implications for the reality question of the fields and, hence, even particles. It may be like basic QM. We know it is just an approximation to QFT, and is incorrect. As yet, we do not know the situation with QFT.

The interpretation question has shifted. I still adhere to the statistical interpretation of ordinary QM, but like thermodynamics, we know it is not fundamental. For QFT, my interpretation is that it is inevitable, given Wienberg's Folk Theorem.

Thanks
Bill

 

[renormalize]

Moreover, our current theories are effective - not fundamental.

1) Can you elucidate the criteria by which a fundamental theory is distinguished from an effective one?
2) Can you cite examples of known fundamental theories?
Thanks.

 

[PeterDonis]

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

An effective theory is one that is admitted to not be fundamental. Or, if you insist on a definition that doesn't use either of those two words, an effective theory is admitted to not provide a complete explanation of the phenomena it covers, but to have some aspects that need to be put into the theory to make it work but which the theory can't explain. For example, the particle masses and coupling constants in the Standard Model of particle physics. The term "effective theory" is used because of the belief that an explanation of those aspects will require some deeper theory to which the current effective theory is an approximation.

2) Can you cite examples of known fundamental theories?

I'm not aware of any. All of our best current physical theories are effective theories.

 

[bhobba]

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

Your name here, renormalize, holds the key, as I think you probably know.

In QFT, early on, there was a deep problem. We kept getting infinity. Okay - we examine the math and see that improper integrals lead to the problem, i.e., an integral to infinity gives infinity. You can get a finite answer by not using infinity, but rather a large number called a cutoff. The trouble is what large number, and what does it mean? The trick of renormalisation is that you can manipulate the equations with a cutoff, so the cutoff is not explicitly part of the equations. Dyson showed that the infinities are still there - but they have been 'swept' under the rug, so to speak. It's the kicker in the joke; if you look under a QF theorist's rug, you find all these infinities swept under it. The advantage of doing this, however, is that these terms (ie those that blow up to infinity) can actually be measured and their values used. That those values depend on the chosen cutoff is all part of the so-called renormalisation group, where measured values change depending on the cutoff. The theory is not fundamental; we need to introduce this cutoff. It is believed that this 'trick' is effective up to approximately the Planck scale. Regardless, it is a trick because it is not fundamental - what is happening above the cutoff, we currently do not know, although research is ongoing, of course. To make matters worse, even this 'trick' has its own problems - look up the Landau pole.

Of course, this fits nicely with Wienberg's Folk Theorem - we only know the 'large distance' theory - if we want the theory at smaller distances at our current level of knowledge, blank out - all we know is regardless of what it is, at distances we can access (currently), it is no surprise it is a QFT.

Thanks
Bill

 

[selfsimilar]

You miss the point of why I started this thread.

The post was really intended for RUTA saying that his system does not seem to add too much to understand the conceptual problems of QM.

 

[RUTA]

The post was really intended for RUTA saying that his system does not seem to add too much to understand the conceptual problems of QM.

Again, I'm presenting our particular completion of the quantum reconstruction program (QRP), so this is not an idiosyncratic approach to resolving the conceptual problems of QM. There is a vast literature on the QRP and we have published several papers, blogs, and a book on our particular completion thereof, which deflates the 'big' and 'small' measurement problems and shows how the "big three" characteristics of QM (randomness, superposition, and entanglement per Brian Greene) follow from the observer-independence of h, as required by the relativity principle and Planck's radiation law, in exact analogy with SR per Rovelli's challenge. Accordingly, QM is complete as possible and there is no need for "spooky actions at a distance" or retrocausality or superdeterminism or the violation of intersubjective agreement or infinitely many realities. All this strikes me as significant progress in resolving the conceptual problems of QM, but I'm biased of course :-)

 

[gentzen]

I guess I don't understand what you're talking about then. The rotation is always in the plane perpendicular to the beam but the beam direction is arbitrary. The Pauli matrices allow you to specify that rotation plane in any direction relative to your Cartesian coordinates. This is all in accord with homogeneous spacetime per the Lorentz group.

If I have two entangled particles in "two beams" with known fixed direction, then I want to measure their spin, not the spin of two other particles corresponding to different "two beams" with different known fixed directions.

I could try to bent a given beam with some combination of electric and magnetic fields. That would probably also affect the spin in some "in principle predictable" way. And this part would exhibit a complex relation to special relativity. How sensitive the spin would react to minute details of the electric and magnetic fields and the particle momentum is also an interesting question (which probably also has a known answer).

 

[RUTA]

If I have two entangled particles in "two beams" with known fixed direction, then I want to measure their spin, not the spin of two other particles corresponding to different "two beams" with different known fixed directions.

I could try to bent a given beam with some combination of electric and magnetic fields. That would probably also affect the spin in some "in principle predictable" way. And this part would exhibit a complex relation to special relativity. How sensitive the spin would react to minute details of the electric and magnetic fields and the particle momentum is also an interesting question (which probably also has a known answer).

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.