Probable or Causal (Deterministic) QM? That is the question.
anton vrba
I have followed the recent heated discussion with some amusement, wondering whether learned men truly have nothing better to do than to regurgitate matters that are already settled.
As we all know, Bell’s theorem and the CHSH experiments have convincingly ruled out local hidden variable theories, yet they do not exclude the possibility of a global or universal hidden variable. Rather than being drawn into senseless arguments, I would urge academics to focus their attention on the unresolved and fundamentally important question: Is quantum mechanics probabilistic or causal?
To that end, I would like to propose an experiment designed to address precisely this issue. As a retired electrical engineer, I lack the institutional connections necessary to carry out such an experiment, but many members of this group may have those resources at their disposal.
The proposed setup is inspired by the pioneering work of Ou and Mandel
(Phys. Rev. Lett. 61, 50–53, 1988), whose experiment used a Type-I SPDC crystal to produce signal and idler photons subsequently interfered at a beam splitter after a 90° rotation of the signal polarisation. Bell inequality violation was observed at station B, but not at the earlier station A (see schematic below).
The prevailing interpretation is that the beam splitter itself induces superposition, entangling the two photons and .
In contrast, I argue that entanglement originates during the down-conversion process, not at the beam splitter. This can be demonstrated through a simple variation of the experiment:
The signal and idler photons are each passed through quarter-wave plates oriented at ±pi/4, producing circularly polarised photon pairs and . Observation of a Bell-inequality violation in this configuration would support the de Broglie–Bohm causal interpretation and pilot-wave theories, thereby pointing to the existence of a global or universal hidden variable.
And what might such a hidden variable represent?
In my view, it reflects a universal conservation principle (in the Noetherian sense) — that the universe as a whole is nilpotent, a perfect balance of opposing quantities.
A natural question arises: Why is the Bell inequality not violated at station A?
At station A, the particle components of the photons are synchronised to a linear pilot wave, retaining their respective linear polarisations independently of one another. In contrast, at station B the pilot wave becomes circularly polarised — a superposition of and — enabling mutual interaction between the two photon (particle) states. This apparent “spooky action at a distance” is, in fact, the manifestation of a universal constraint ensuring that the cosmos remains nilpotent.
This idea has solid mathematical backing, and I am willing to discuss it with anyone interested in an alternative philosophy.
Kind regards,
Anton L. Vrba
Jan-Åke Larsson
Dear Anton,
In your second setup, if the state at A is not entangled, neither is the state at B.
Meaning: if there is be no violation at A for any combination of measurements, there cannot be a violation at B for any combination of measurements.
The reason is simple: the photons need to interact to create an entangled state.
Note that de-Broglie-Bohm and pilot-wave interpretations give predictions that are identical to the Copenhagen interpretation, or many-worlds or consistent histories. These cannot (yet?) be distinguished in experiment.
However, you are free to try. This setup will not do it.
Best
Jan-Åke
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Jan-Åke Larsson
Professor, Head of Department
|
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Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512 Please visit us at www.liu.se |
GeraldoAlexandreBarbosa
Richard Gill
 | |
GeraldoAlexandreBarbosa
X. Y. Zou, T. Grayson, L. J. Wang, and L. Mandel, Can an ‘‘empty’’ de Broglie pilot wave induce coherence?,
Phys. Rev. Lett. 68, 3667 – 22 June, 1992.
Abstract
According to the de Broglie pilot wave theory, a pilot wave which is empty of photons is still capable of physical effects like induced coherence. We have carried out an experiment to test this prediction. The experiment involves interference of photons produced by down-conversion in two nonlinear crystals and depends on the mutual coherence induced between the two signal beams by an idler. When the photon is removed from the idler by a beam splitter, it is found that the resulting ‘‘empty pilot wave’’ no longer induces coherence. This violates at least the Selleri-Croca version of the de Broglie pilot wave theory makes the physical reality of the corresponding pilot wave doubtful.
Jan-Åke Larsson
To know that a photon is removed from the idler, you need to perform a measurement. That measurement destroys the interference even in the pilot wave theory. That experiment does not show what they claim.
/Jan-Åke
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GeraldoAlexandreBarbosa
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anton vrba
Dear Anton,
In your second setup, if the state at A is not entangled, neither is the state at B.
Meaning: if there is be no violation at A for any combination of measurements, there cannot be a violation at B for any combination of measurements.
The reason is simple: the photons need to interact to create an entangled state.
Note that de-Broglie-Bohm and pilot-wave interpretations give predictions that are identical to the Copenhagen interpretation, or many-worlds or consistent histories. These cannot (yet?) be distinguished in experiment.
However, you are free to try. This setup will not do it.
Best
Jan-Åke
On 10/7/25 00:32, anton vrba wrote:
I have followed the recent heated discussion with some amusement, wondering whether learned men truly have nothing better to do than to regurgitate matters that are already settled.
As we all know, Bell’s theorem and the CHSH experiments have convincingly ruled out local hidden variable theories, yet they do not exclude the possibility of a global or universal hidden variable. Rather than being drawn into senseless arguments, I would urge academics to focus their attention on the unresolved and fundamentally important question: Is quantum mechanics probabilistic or causal?
To that end, I would like to propose an experiment designed to address precisely this issue. As a retired electrical engineer, I lack the institutional connections necessary to carry out such an experiment, but many members of this group may have those resources at their disposal.
The proposed setup is inspired by the pioneering work of Ou and Mandel
(Phys. Rev. Lett. 61, 50–53, 1988), whose experiment used a Type-I SPDC crystal to produce signal and idler photons subsequently interfered at a beam splitter after a 90° rotation of the signal polarisation. Bell inequality violation was observed at station B, but not at the earlier station A (see schematic below).
The prevailing interpretation is that the beam splitter itself induces superposition, entangling the two photons and .
In contrast, I argue that entanglement originates during the down-conversion process, not at the beam splitter. This can be demonstrated through a simple variation of the experiment:
The signal and idler photons are each passed through quarter-wave plates oriented at ±pi/4, producing circularly polarised photon pairs and . Observation of a Bell-inequality violation in this configuration would support the de Broglie–Bohm causal interpretation and pilot-wave theories , thereby pointing to the existence of a global or universal hidden variable.
And what might such a hidden variable represent?
In my view, it reflects a universal conservation principle (in the Noetherian sense) — that the universe as a whole is nilpotent, a perfect balance of opposing quantities.
A natural question arises: Why is the Bell inequality not violated at station A?
At station A, the particle components of the photons are synchronised to a linear pilot wave , retaining their respective linear polarisations independently of one another. In contrast, at station B the pilot wave becomes circularly polarised — a superposition of and — enabling mutual interaction between the two photon (particle) states. This apparent “spooky action at a distance” is, in fact, the manifestation of a universal constraint ensuring that the cosmos remains nilpotent.
This idea has solid mathematical backing, and I am willing to discuss it with anyone interested in an alternative philosophy.
Kind regards,
Anton L. Vrba
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Jan-Åke Larsson
Professor, Head of Department
Department of Electrical Engineering
SE-581 83 Linköping
Phone: +46 (0)13-28 14 68
Mobile: +46 (0)13-28 14 68
Visiting address: Campus Valla, House B, Entr 27, 3A:512
Please visit us at www.liu.se
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Jan-Åke Larsson
Dear Anton,
I am just stating what is needed for your setup to work, sorry if it sounded dismissive. It is not an "academic" point of view, I am trying to explain the physical situation to you, using deduction, meaning logical analysis. If "this" then "that".
A more thorough walk-through of the three experiments will follow here, I apologize in advance for the complexity but this is what is needed.
[Ou and Mandel, PRL 61:50 (1998)]
The first setup in your original email has a
(single) type I SPDC source that creates a |HH> photon-pair
state from a |V> coherent-state pump.
The photon-pair state is not entangled; it is separable.
The HWP changes the upper photon state so that the state is
|HV>.
This is still not entangled; it is
separable.
This is then put through the beamsplitter
and it creates a slightly more complicated state than the
entangled |HV>+|VH>, because it is also possible to have
two photons out at one port at B with opposite polarizations and
none out from the other, I'll write (HV)0 or 0(HV) when this
happens.
This could be written |HV>+|VH>-i|(HV)0>+i|0(HV)>
(equation (2) in their paper)
Ou and Mandel then postselect events generated from
|HV>+|VH> and ignore events generated by
|(HV)0>-|(VH)0>
This is allowed because it is a local postselection that is
invariant of the setting theta_i.
They in essence use the state |HV>+|VH>, which is the
desired entangled state.
This state can violate the Bell inequality.
The reason this works is a) it is a coherent process and b) at
either port, there is no way to know which photon is output of H
or V.
It is essential that the paths before the beamsplitter have
exactly the same lengths otherwise this won't work, if the
lengths are not the same the state is not entangled, if the
lengths are not stable the output will be noisy (in qm language:
mixed).
It is incredibly fragile.
[Vrba, proposal (2025)]
Your setup (the second one in your first email) has a (single)
type I SPDC source that creates a |HH> photon-pair state from
a |V> coherent-state pump.
The photon-pair state is not entangled; it is separable.
The two QWPs change the photon states so that the state is
|RL>.
This could be written |HH>+|VV>+i|VH>+i|HV>.
This photon-pair state is not entangled; it is separable.
There is no way to postselect the entangled state
|HH>+|VV> nor |VH>+|HV>.
The state cannot violate the Bell inequality.
[Kwiat et al, PRA 60:R773 (1999)]
The third setup uses the same logic as the first.
It has two type I SPDC sources, the first creates a |HH>
photon-pair state from a |V> coherent-state pump, and the
second creates a |VV> photon-pair state from a |H>
coherent-state pump.
However, I quote from the paper: "these two possible
down-conversion processes are coherent with one another, as long
as the emitted spatial modes for a given pair of photons are
indistinguishable for the two crystals"
In plain English, if the two cones coincide, there is no way to
know which crystal generated an output photon pair.
For the same reason as in the first case above, if a) the process is coherent and b) there is no way to
know which crystal generated the pair, the
output is the entangled state |HH>+|VV>
(There is actually a phase between the terms that depends on the
details of the crystal)
It is essential that the cones coincide otherwise this won't
work.
It is less fragile but still pretty hard to do.
All completely logical.
(Pilot waves would give the same predictions.)
Modern sources use the same basic idea but have several layers sandwiched and outputs in a different manner, I'll stop here.
Best
Jan-Åke
GeraldoAlexandreBarbosa
Although ideas like “the photons need to interact to
create an entangled state” are commonly stated, they are not correct. “Interaction”
between photons may happen within a medium or when the photon energies are such
that pair-creation is possible, like 
(hbar omega bigger or equal 2 rest mass times c square), otherwise there is no
interaction.
Entanglement occurs not by interaction but by path (and time) indistinguishability of photons.
As cited, "these two possible down-conversion processes
are coherent with one another, as long as the emitted spatial modes for a given
pair of photons are indistinguishable for the two crystals"
As Jan-Åke said: In plain English, if the two cones coincide, there is no way
to know which crystal generated an output photon pair.
These ideas have been experimentally demonstrated. See for example:
Control of visibility in the interference of signal photons by delays imposed on the idlers;
X. Y. Zou, T. Grayson, GA Barbosa, and L. Mandel; Phys. Rev. A 47, 2293 (1993).
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Jan-Åke Larsson
Perhaps I was unclear. Let me clarify:
To know that a photon is removed from the idler, you need to perform a measurement. That measurement destroys the interference also in standard quantum mechanics, even in the Copenhagen interpretation. That experiment does not show what they claim.
This directly contradicts their claim, and thus your claim that pilot waves were discarded by experiments around 1990 (Mandel).
Best
Jan-Åke
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anton vrba
The common understanding is indeed as you describe, and it is not new to me—it reflects Bohr’s Copenhagen interpretation. However, I find Kwiat’s statement curious:
“These two possible down-conversion processes are coherent with one another, as long as the emitted spatial modes for a given pair of photons are indistinguishable for the two crystals.”
On what physical basis can such coherence between two spatially separated SPDC crystals be asserted? Kwiat’s geometric explanation (Ref. [19]) appears to be an assumption introduced to fit the observed result, leading to the conclusion that “if the two cones coincide, there is no way to know which crystal generated an output photon pair.” From this, one infers a superposition state , which indeed matches what is measured.
But what is it that we are actually measuring? Both and are individually entangled photon pairs.
In my view, the arrangement of "two physically separated SPDC crystals" cannot themselves be the source of entanglement. The coherence must already be present in the pump laser beam, while the SPDC process itself is nilpotent, producing intrinsically entangled photon pairs.
The key question to ask is why the Bell inequality violation was observed by Ou and Mandel only after the beam splitter, and not before—and similarly in Kwiat’s 1999 configuration. The only plausible explanation, in my opinion, is that at the observation point there exist both and components, whereas at position (A) in [Vrba, Proposal (2025)] only a single component is present. By introducing quarter-wave plates to generate simultaneous and photon pairs, the observation point would then contain both and components—just as in the setups of Ou & Mandel and Kwiat (1999).
I will provide a mathematical justification in the next day or two to support both the proposed experiment and the above reasoning.
My intention is to sow a small seed of doubt and to propose an experiment capable of distinguishing between Bohr’s Copenhagen interpretation and a de Broglie–Bohm–type causal framework. Should the experiment confirm my prediction, it would require a fundamental re-evaluation of quantum mechanics.
Jan-Åke Larsson
Dear Anton,
You don't seem to understand what an entangled state is. In your setup, the observation point contains both H and V but in a separable combination, not an entangled one.
Jan-Åke Larsson
Thanks Geraldo, that is a better description. In this particular case I was referring to Anton's setup, and the fact that he would need to bring them to the same spacetime event (same place in space and time), to make them indistinguishable. Along the lines of the Ou-Mandel setup: "interaction" through a beamsplitter. Even then he would likely need to do similar postselection as them.
Best
Jan-Åke
Jan-Åke Larsson
And to be completely clear, the quotation marks on "interaction" is there because the processes for the two photons are independent. In this particular case, the photons are reflected or transmitted on an individual basis, they do not interact. What is important is that they become indistinguishable after the beamsplitter. This is how all interferometers work.
Best
Jan-Åke
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GeraldoAlexandreBarbosa
anton vrba
I do understand what an entangled state is! However, I must disagree with some of the commonly offered explanations.
Let us return to my Type-I SPDC experimental setup — but instead of measuring polarisation entanglement, consider frequency entanglement. For this purpose, I refer to Baek & Kim (2009) [Baek, S.-Y. and Kim, Y.-H. (2009) “Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion,” Physical Review A, 80, p. 33814.] and specifically to their Figure 2(d):
First, let us measure the detuning probabilities of either the idler or the signal independently. The detuning outcomes are distributed symmetrically — 50 % > 0 (denoted ) and 50 % < 0 (denoted ). However, once the idler’s detuning is measured, the signal’s detuning becomes instantly determined as its opposite — the familiar Bertlmann’s socks analogy.
Since we do not know in advance whether the detuning will be positive or negative, we can reproduce the standard quantum-mechanical argument that the system exists in a superposition of and . Only upon measurement does the detuning wavefunction “collapse”, yielding a definite outcome for both photons. Thus, we can write the correlated state as
Of course, one may argue — correctly — that this must be so because of Planck–Einstein energy equivalence and that Noether’s theorem requires
Indeed, Noether’s conservation law functions as a global hidden variable, universally constraining all observable outcomes. By the same reasoning, if the signal and idler frequencies emerge entangled through this conservation principle at the instant of down-conversion, then the photons’ polarisation degrees of freedom must likewise be governed by the same global—or universal—constraint. In such a framework, entanglement is not a manifestation of our ignorance or an artefact of measurement collapse, but a direct consequence of a nilpotent universe, in which all interactions preserve perfect balance. The conventional formulation of Bell states and wavefunction collapse, therefore, reflects our epistemic limitation rather than the underlying physical reality.
Jan-Åke, as the Head of Electrical Engineering, you possess the engineering instinct to question the foundations of quantum mechanics not merely from the established theoretical standpoint, but as an engineering exercise grounded in physical reasoning. When quantum mechanics was first formulated, neither SPDC processes nor results such as those of Baek and Kim were known. Our present technical capabilities now reveal phenomena that compel us to revisit and re-evaluate the assumptions once taken as fundamental. I believe we owe this critical re-examination to the next generation, to whom we entrust the challenges of tomorrow.
Mark Hadley
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Jan-Åke Larsson
Dear Anton,
First, as Mark says, it is not clear that this produces an entangled state.
Second, even if you do produce an entangled state to say something interesting you need to go beyond EPR. Please read
Bell, J. S. “EPR Correlations and EPW Distributions.” Annals of the New York Academy of Sciences 480, no. 1 (1986): 263–66. https://doi.org/10.1111/j.1749-6632.1986.tb12429.x .
You'll find it in Speakable and Unspeakable.
Best
Jan-Åke
Austin Fearnley
There will have to be a flip at some point in time when realism and non-realism flip definitions. Jan described QM as local and non-real but after acceptance of the Nobel prizes QM should eventually be described as local and real. After opposition fades away. Or maybe 'old-realism' becomes 'new-realism'.
I am interested in Anton's nilpotent idea. I do not know whether to think nilpotent is a law or if we seem to be only by chance living in such a state, and if that state is required for our existence. I think, sometimes, that we are living 'on the edge'. Maybe the only place to be. On the edge between say dS and AdS space. Maybe where times are running in opposite directions, as I think dS and AdS would have oppositely signed trivectors and I think the trivectors determine the time directions within the space.
As Mark knows, I am very anti superposition for fundamental particles. IMO it can occur in QM only because QM is a branch of statistics. But IMO superposition of fundamental particles is not describing ontology even in the new-reality I mentioned above. Having said that, in my preon model fundamental particles are not fundamental as they are composed of preons.
OTOH for me to to use superposition, my model using preons could maybe be taken to appear to be the superposition of two different spacetimes with two opposite time directions simultaneously. Perhaps we are on the edge of two different spaces. And maybe nilpotent is connected with this. Thermodynamics would give times arrow for the combined space but each space would have its own time arrow.
Jan-Åke Larsson
No, I said there are two alternatives
1. Along the lines of the Copenhagen interpretation: non-realist
(and signal-local)
2. Along the lines of Bohmian mechanics: realist and nonlocal
/JÅ
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