# The universal quantum logic matrix

1. Jan 2, 2005

### Loren Booda

1. Could EPR spin statistics exhibiting violation of the Bell inequality be interpreted as refuting conservation of spin?

2. How are quantum truths in the microcosm configured to exceed classical ones there?

3. What type of logic, Boolean or non-Boolean, does a macroscopic observer itself experience while measuring quantum truth values?

4. Has universal physical logic changed between the quantum gravitation of the big bang and the macroscopically classical present?

2. Jan 2, 2005

### Caroline Thompson

I wonder if you are aware of the fact that there have never been any "loophole-free" violations of Bell inequalities? This means that the question of the correctness of this area of quantum theory -- the reality of "quantum entanglement" and the special logic required to derive it -- is currently an open question. See my web site or a wikipedia page I contributed last year:

Caroline
http://freespace.virgin.net/ch.thompson1/

3. Jan 2, 2005

### ppnl2

1. No. As a matter of fact it is the conservation of quantum spin that causes a violation of Bell's inequality. If we allow Quantum spin to be violated then we no longer have any way to say anything about the correlation between measurments.

I don't understand your other questions well enough to offer any help.

4. Jan 2, 2005

### Loren Booda

Let me try to redefine my questions #2-4:

2. Is quantum logic experienced on the microscopic level because it yields more truths there than classical logic does - a sort of logical correspondence principle?

3. We normally consider macroscopic observers to follow Boolean logic. How does such a classical observer perceive quantum, non-Boolean, events when measuring their properties?

4. Since the cosmos evolved from a predominantly quantum mechanical entity near the big bang to one more of classical logic today, has its overall logical system changed?

5. Jan 2, 2005

### Kea

logic

Hi Loren

Nice questions.

2. Is quantum logic experienced on the microscopic level because it yields more truths there than classical logic does - a sort of logical correspondence principle?

Are you sure this is how you want to phrase this question? Are you a microscopic observer? Anyway, never mind. It is a good observation to note that quantum logic involves more 'truth values' than classical (which of course has only two). This may be viewed as a consequence of the linearity of the lattice of subspaces of a Hilbert space. Whereas logical OR for sets is
simply union, in the linear case it must be the smallest subspace containing a and b. This destroys distributivity, and it is a simple fact of lattice theory that a quantum lattice can only be Boolean if it is distributive.

3. We normally consider macroscopic observers to follow Boolean logic. How does such a classical observer perceive quantum, non-Boolean, events when measuring their properties?

Tricky! I'd like to see someone answer this properly. Look at:

Topos Theoretical Reference Frames on the Category of Quantum Observables
Elias Zafiris
http://arxiv.org/abs/quant-ph/0202057

4. Since the cosmos evolved from a predominantly quantum mechanical entity near the big bang to one more of classical logic today, has its overall logical system changed?

Why are you imposing a classical spacetime on a question about quantum logic? I don't understand why people do this. Our best understanding of quantum logic fits into a unified framework (via category theory) and the classical (gravitationally speaking) limit is to be viewed as a restricted domain within this formalism. The classical limit is complex. So, no one can answer your question at present.

One of the founders of topos logic, F.W. Lawvere, has written a lot on things like the topos of evolving sets which one can think of as encompassing 'stages of knowledge'. F. Markopoulou of Perimeter has written papers on this topos in the context of causal sets.

By the way, I have said a little about these matters elsewhere on PF, where you might find some interesting references.

Regards Kea

6. Jan 2, 2005

### Wave's_Hand_Particle

Hi Loren, this is pretty obvious that the measurement from a Macro domain, on a Quantum domain is the problem to observer dependence.

Let me give you a bonafide example, if an effect of a quantum measurement, say (photon spin), reveals non-locality, then it really a measurement of relative scale to a Quantum scale, or from a vast observation frame to a minute unobservable scale that produces all the details of all paradox's.

Question: can a photon be measured at the first moment it leaves an atom?
Question: what is the farthest point a photon can be measured from leaving an atom without any interaction occuring?

In back to back photon emission experiments, like Aspects, photons are emitted from an atom, and travel away in opposite directions, the spin value of one can reveal the spin value of the other, even if the two photons are at either ends of the Universe. But, interestingly, if one photon happens to collide with a Blackhole, then this breaks one of the most fundemental of Quantum theories measurement foundations.

You can measure, from an hidden variable standpoint, common logic tells us that to do this, quantum theory has local effects, and non-local effects, and thus the wavefunction(measure) of the Universe should be a piece of cake?

7. Jan 2, 2005

### Loren Booda

Kea,

Can one thus correctly assert that quantum mechanics is overdetermined?

8. Jan 3, 2005

### Kea

What do you mean by overdetermined?

9. Jan 3, 2005

### Loren Booda

I suppose "overdetermined" means that Q. M. has redundant information ingrained in probability. I had heard the term applied to quantum mechanics before. Have you?

10. Jan 5, 2005

### Kea

It is not redundant. It is essential to the definition of quantum state.

11. Jan 5, 2005

### Loren Booda

Kea,

Then might quantum mechanics' probabilism provide more complete ("overdetermined") information than its classical correspondence, since the constant h tends toward zero in that latter limit?

12. Jan 5, 2005

### Kea

Lb

There are many long posts on PF which I believe answer what you're trying to get at, but I'm not sure because you are not explaining what you mean.

Anyway, the information referred to above is true statically. That is, in a sense there are more 'truth values' even before one considers the dynamics of a quantum system.

Now $\hbar$ only appears when considering dynamics, and
not of a single particle but of many particles. The fact that one
views $\hbar \rightarrow 0$ as a classical limit is a
simple device and does not say much, if anything, about how one
reads classical information in a quantum environment. ZapperZ has
been recommending some nice work (on PF) by the Decoherence crowd
on this subject, and I have recommended papers on the category
theoretic aspects of quantum information.

13. Jan 5, 2005

### Loren Booda

Kea,

Could you please offer some links for the recommended papers on decoherence and quantum information that you refer to?

14. Jan 6, 2005

### Kea

With pleasure.

A great website:

http://chaos.swarthmore.edu/comps/0306072.pdf

and papers:

Decoherence, einselection and the quantum origins of the classical
W.H. Zurek
http://hubcap.clemson.edu/~daw/D_PHYS455/RevModPhys.v75p715y03.pdf

A categorical semantics of quantum protocols
S. Abramsky and B.Coecke
http://users.ox.ac.uk/~mert1596/QUOXIC/talks/samson.pdf

A categorical quantum logic
S. Abramsky and R. Duncan
http://quasar.mathstat.uottawa.ca/~selinger/qpl2004/PDFS/02Abramsky-Duncan.pdf

Regards
Kea