The Certainty of Quantum Set Theory

[james.goetz]

Here's my brief two-paragraph summary of quantum set theory (QST):

Birkhoff and von Neumann [11] introduced quantum logic in response to logical problems with the Copenhagen interpretation. Takeuti [8] formed the quantum logic into an introduction of QST. Eventually, Ozawa took the lead to develop QST into a feasible interpretation of quantum mechanics (QM) that coheres with the classical law of noncontradiction, predicate logic, and experimental physics [9, 10, 12, 13]. For example, QST defines quantum states with certainty instead of classical uncertainty.

In short, QST begins with a prior probability distribution of observables for a particular quantum state. This distribution looks similar to a corresponding Copenhagen probability distribution of observables for the quantum state, but QST assigns predicate logic to each observable in the prior set for the quantum state. For example, the existence of each observable in a particular quantum state is true or false. This results in a set of existing observables that completely defines the quantum state despite classically non-commuting observables such as momentum and position. Additionally, QST can define entangled states because it is a state-dependent theory instead of a particle-dependent theory. Furthermore, QST preserves the Copenhagen probability distribution for wave function collapse that results in probabilistic causality during the transition from one quantum state to the next. For instance, wave function collapse is the only element of uncertainty in QST.

References
8. Takeuti, G.: Quantum set theory. In: Beltrametti, E.G., van Fraassen, B.C. (eds.) Current Issues in Quantum Logic, pp. 303–322. Plenum, New York (1981)
9. Ozawa, M. Quantum reality and measurement: A quantum logical approach. Found. Phys. 41, 592–607 (2011)
10. Ozawa, M. Quantum set theory extending the standard probabilistic interpretation of quantum theory. New Generat. Comput. 34, 125–152 (2016)
11. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)
12. Sulyok, G., Sponar, S., Demirel, B., Buscemi, F., Hall, M.J.W., Ozawa, M., Hasegawa, Y.: Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements. Phys. Rev. Lett. 115, 030401 (2015)
13. Demirel, B., Sponar, S., Sulyok, G., Ozawa, M., Hasegawa, Y.: Experimental test of residual error-disturbance uncertainty relations for mixed spin-1/2 states. Phys. Rev. Lett. 117, 140402 (2016)

[thray]

Here's my brief two-paragraph summary of quantum set theory (QST):

Birkhoff and von Neumann [11] introduced quantum logic in response to logical problems with the Copenhagen interpretation. Takeuti [8] formed the quantum logic into an introduction of QST. Eventually, Ozawa took the lead to develop QST into a feasible interpretation of quantum mechanics (QM) that coheres with the classical law of noncontradiction, predicate logic, and experimental physics [9, 10, 12, 13]. For example, QST defines quantum states with certainty instead of classical uncertainty.

In short, QST begins with a prior probability distribution of observables for a particular quantum state. This distribution looks similar to a corresponding Copenhagen probability distribution of observables for the quantum state, but QST assigns predicate logic to each observable in the prior set for the quantum state. For example, the existence of each observable in a particular quantum state is true or false. This results in a set of existing observables that completely defines the quantum state despite classically non-commuting observables such as momentum and position. Additionally, QST can define entangled states because it is a state-dependent theory instead of a particle-dependent theory. Furthermore, QST preserves the Copenhagen probability distribution for wave function collapse that results in probabilistic causality during the transition from one quantum state to the next. For instance, wave function collapse is the only element of uncertainty in QST.

References
8. Takeuti, G.: Quantum set theory. In: Beltrametti, E.G., van Fraassen, B.C. (eds.) Current Issues in Quantum Logic, pp. 303–322. Plenum, New York (1981)
9. Ozawa, M. Quantum reality and measurement: A quantum logical approach. Found. Phys. 41, 592–607 (2011)
10. Ozawa, M. Quantum set theory extending the standard probabilistic interpretation of quantum theory. New Generat. Comput. 34, 125–152 (2016)
11. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)
12. Sulyok, G., Sponar, S., Demirel, B., Buscemi, F., Hall, M.J.W., Ozawa, M., Hasegawa, Y.: Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements. Phys. Rev. Lett. 115, 030401 (2015)
13. Demirel, B., Sponar, S., Sulyok, G., Ozawa, M., Hasegawa, Y.: Experimental test of residual error-disturbance uncertainty relations for mixed spin-1/2 states. Phys. Rev. Lett. 117, 140402 (2016)

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

[Joy Christian]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

***

[thray]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

***

Yep. Further though, were the function reduced to classical probability, the function is complete (all of its coordinate points are internally connected, or simply connected in topological terms) -- it cannot be the product of collapse.

A multiply-connected space of branching probabilities as the author suggests, works only up to uncertainty, and leaves no backward trace.

So necessitating another fiction, quantum entanglement. (I learned that from you.)

[james.goetz]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

Hi Thay, Not at all. Every quantum state endures a Planck time. QST is about defining the each quantum state that endures for a Planck time.

[james.goetz]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

***

Hi Joy, You're correct that nobody has detected wave function collapse. But if there is no wave function collapse, then there is the undetected MWI.

[Joy Christian]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

***

Hi Joy, You're correct that nobody has detected wave function collapse. But if there is no wave function collapse, then there is the undetected MWI.

That is just replacing one tiny fiction with another humongous fiction that no one has ever, or will ever see. Wave function has nothing to do with what is real.

***

[james.goetz]

Don't you think your last statement (" ... wave function collapse is the only element of uncertainty in QST") negates your argument?

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

Hi Joy, You're correct that nobody has detected wave function collapse. But if there is no wave function collapse, then there is the undetected MWI.

That is just replacing one tiny fiction with another humongous fiction that no one has ever, or will ever see. Wave function has nothing to do with what is real.

Interesting.

Do you have an overall QM interpretation?

And do you think that QST could work without wave function collapse?

[Joy Christian]

What "wave function collapse"? Has anyone seen it? There is no such thing. It is a fiction, made up to cover up the blatant flaw in the orthodox quantum theory.

Hi Joy, You're correct that nobody has detected wave function collapse. But if there is no wave function collapse, then there is the undetected MWI.

That is just replacing one tiny fiction with another humongous fiction that no one has ever, or will ever see. Wave function has nothing to do with what is real.

Interesting.

Do you have an overall QM interpretation?

And do you think that QST could work without wave function collapse?

I subscribe to Einstein's point of view: (1) Quantum theory is incomplete. (2) Bell's theorem is wrong. (3) Local-realistic view of the world is the only sensible view.

You will find some of my papers here: http://einstein-physics.org/research-programs/.

***

[james.goetz]

Hi Joy, You're correct that nobody has detected wave function collapse. But if there is no wave function collapse, then there is the undetected MWI.

That is just replacing one tiny fiction with another humongous fiction that no one has ever, or will ever see. Wave function has nothing to do with what is real.

Interesting.

Do you have an overall QM interpretation?

And do you think that QST could work without wave function collapse?

I subscribe to Einstein's point of view: (1) Quantum theory is incomplete. (2) Bell's theorem is wrong. (3) Local-realistic view of the world is the only sensible view.

You will find some of my papers here: http://einstein-physics.org/research-programs/.

Thank you.

I understand when you say that there is no detection of wave function collapses. On the other hand, there is no detection of a wave function enduring longer than 1 Planck time. Since the is no scientific evidence of a wave function enduring longer than 1 Planck time, then this suggests that a wave function never endures longer than 1 Planck time.

[minkwe]

On the other hand, there is no detection of a wave function enduring longer than 1 Planck time. Since the is no scientific evidence of a wave function enduring longer than 1 Planck time, then this suggests that a wave function never endures longer than 1 Planck time.

Do you know what a "wave function" is?

[james.goetz]

On the other hand, there is no detection of a wave function enduring longer than 1 Planck time. Since the is no scientific evidence of a wave function enduring longer than 1 Planck time, then this suggests that a wave function never endures longer than 1 Planck time.

Do you know what a "wave function" is?

A wave function describes the properties of a quantum state.

[thray]

And what are those properties?

[james.goetz]

And what are those properties?

I am an analytic philosopher with limited background in the known details about the properties of quantum states. I also understand that there is no consensus for a QM interpretation. For example, advocates of QST propose that the position and momentum of a quantum state can be simultaneously measured despite the proposal of the Copenhagen interpretation.

[Joy Christian]

And what are those properties?

I am an analytic philosopher with limited background in the known details about the properties of quantum states. I also understand that there is no consensus for a QM interpretation. For example, advocates of QST propose that the position and momentum of a quantum state can be simultaneously measured despite the proposal of the Copenhagen interpretation.

In that case you will immediately understand our point when I say that wave function is an epistemic object. It only represents a compendium of our knowledge of the physical system, not the properties of the system itself. In other words, it does not have any ontological significance. Admittedly this is a minority view these days, especially after the dogmatic acceptance of Bell's theorem by the physics community. However, some of us in this forum believe that Bell's theorem is simply wrong, and as a corollary Einstein's statistical interpretation of quantum mechanics and his epistemic view of the wave function become viable. Consequently there cannot be any such thing as "wave function collapse" on which you are relying, because what is collapsing is just the state of our knowledge of the system, not the system itself.

***

[thray]

Joy,

Like!

[james.goetz]

And what are those properties?

I am an analytic philosopher with limited background in the known details about the properties of quantum states. I also understand that there is no consensus for a QM interpretation. For example, advocates of QST propose that the position and momentum of a quantum state can be simultaneously measured despite the proposal of the Copenhagen interpretation.

In that case you will immediately understand our point when I say that wave function is an epistemic object. It only represents a compendium of our knowledge of the physical system, not the properties of the system itself. In other words, it does not have any ontological significance. Admittedly this is a minority view these days, especially after the dogmatic acceptance of Bell's theorem by the physics community. However, some of us in this forum believe that Bell's theorem is simply wrong, and as a corollary Einstein's statistical interpretation of quantum mechanics and his epistemic view of the wave function become viable. Consequently there cannot be any such thing as "wave function collapse" on which you are relying, because what is collapsing is just the state of our knowledge of the system, not the system itself.

Thank you.

I first want to clarify that I am not trying to defend QST because I don't have enough background in physics to do that. But I want to make sure that I have a clear summary of it. For example, this is a subsection of a thought experiment that I am revising. Below is a revision of the two paragraph summary without using the term "wave function collapse." Does this look any clearer?

Birkhoff and von Neumann [11] introduced quantum logic in response to logical problems with the Copenhagen interpretation. Takeuti [8] formed the quantum logic into an introduction of QST. Eventually, Ozawa took the lead to develop QST into a feasible interpretation of quantum mechanics (QM) that coheres with the classical law of noncontradiction, predicate logic, and experimental physics [9, 10, 12, 13]. For example, QST defines quantum states with certainty instead of classical uncertainty.

In short, QST begins with a prior probability distribution of observables for a particular quantum state. This distribution looks similar to a corresponding Copenhagen probability distribution of observables for the quantum state, but QST assigns predicate logic to each observable in the prior set for the quantum state. For example, the existence of each observable in a particular quantum state is true or false. This results in a set of existing observables that completely defines the quantum state despite classically non-commuting observables such as momentum and position. Additionally, QST can define entangled states because it is a state-dependent theory instead of a particle-dependent theory. Furthermore, QST preserves two points of the Copenhagen interpretation. First, each quantum state endures for 1 Planck time. Second, there is a probability distribution for the probabilistic causality during the transition from one quantum state to the next. For instance, the transition from one quantum state to the next is the only element of uncertainty in QST.

References
8. Takeuti, G.: Quantum set theory. In: Beltrametti, E.G., van Fraassen, B.C. (eds.) Current Issues in Quantum Logic, pp. 303–322. Plenum, New York (1981)

9. Ozawa, M. Quantum reality and measurement: A quantum logical approach. Found. Phys. 41, 592–607 (2011)

10. Ozawa, M. Quantum set theory extending the standard probabilistic interpretation of quantum theory. New Generat. Comput. 34, 125–152 (2016)

11. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)

12. Sulyok, G., Sponar, S., Demirel, B., Buscemi, F., Hall, M.J.W., Ozawa, M., Hasegawa, Y.: Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements. Phys. Rev. Lett. 115, 030401 (2015)

13. Demirel, B., Sponar, S., Sulyok, G., Ozawa, M., Hasegawa, Y.: Experimental test of residual error-disturbance uncertainty relations for mixed spin-1/2 states. Phys. Rev. Lett. 117, 140402 (2016)

[thray]

You should consider beginning, "If the Copenhagen interpretation of quantum mechanics is true ..." not at all an uncontroversial subject.

[james.goetz]

You should consider beginning, "If the Copenhagen interpretation of quantum mechanics is true ..." not at all an uncontroversial subject.

Yes, but that is implicit in that paragraph and overkill would not help my paper

[minkwe]

On the other hand, there is no detection of a wave function enduring longer than 1 Planck time. Since the is no scientific evidence of a wave function enduring longer than 1 Planck time, then this suggests that a wave function never endures longer than 1 Planck time.

Do you know what a "wave function" is?

A wave function describes the properties of a quantum state.

Just to add to the excellent responses you've already gotten from Joy and Tom -- I hope now you understand why it makes absolutely no sense to say

"... there is no detection of a wave function enduring longer than 1 Planck time."