Showing posts with label Quantum Theory. Show all posts
Showing posts with label Quantum Theory. Show all posts

Monday, September 23, 2024

Is consciousness grounded in matter or the other way around?

 Is consciousness grounded in matter or the other way around?

 

We will ask physics about physicalism, zombies, and consciousness.
This video is an as-simple-as-I-could explanation of this article https://philsci-archive.pitt.edu/23108/.
We will use a bit of physics and math, but I'll introduce these smoothly, to make the trip easy and interesting. You can verify each step of the proof, and if you can find an error, please let me know. Many of the implications of this result remain open to be discussed later. 


Abstract of the article

If the mind of a sentient being would be reducible to its structure, any system with identical structure should be equally sentient. Based on the structural symmetries of Physics, I prove that this thesis has two unexpected consequences:

1) There would be an inflation of minds, living in apparently different worlds.
2) The content of these minds would be independent of the properties of the external world. That is, these minds would be unable to know anything about the world.

Since this contradicts empirical observations, structure alone is insufficient for sentient experience.

This excludes the purely physicalistic approaches to physics and consciousness. For physics to be as we know it, all physical properties have to be grounded in something sentiential.



Saturday, April 16, 2022

An underrated gem: WAY beyond conservation laws


I think the article Wigner-Araki-Yanase theorem beyond conservation laws by Mikko Tukiainen is an underrated gem (if we compare its content to the number of citations).


Here's why I think so.

First, I think the Wigner-Araki-Yanase theorem is underrated. It started with a paper by Wigner (here is an English translation.), who showed that you can't have an accurate ideal spin measurement which is also repeatable. By "repeatable" it's understood that, whatever result you get, by repeating the measurement you'll get the same result. In other words, accuracy requires that the measurement disturbs the system, so the spin is no longer what you measured it to be. You can avoid this by being satisfied with a less accurate result. Wigner also showed that repeatability can be obtained and the error can be made as small as wanted, if the measuring device is large enough so that the apparatus has large uncertainty for the conserved quantities.

Araki and Yanase generalized his result, and added some interesting observations, in particular that this limitation applies to the measurement device as well.

Wigner was brilliant enough to know how to give a more general proof, but he wanted the idea to be understood easily. He used the conservation of angular momentum along an axis to deduce the limitation of accuracy of spin measurement along an orthogonal axis. He only uses a conservation law, but all conservation laws contribute. He had to give a simple proof, without making too many assumptions about the evolution equation. So he probably thought, spin measurement is a simple example, and also entails the existence of other spin operators that are conserved by unitary evolution and don't commute with it.

While all conservation laws contribute limitations, on the one hand this is an expression of the symmetries, and on the other hand, in fact, they don't do anything. The limitation is in the transformation of the total state from the state before measurement into the state after the pre-measurement, that is, just before we invoke the collapse postulate (the collapse itself breaks the conservation laws). During pre-measurement the evolution is unitary, because collapse is invoked at the end. The evolution itself constraints the possible results of the measurement. Conservation laws were originally used as indications that we can use to find such limitations. A general proof in terms of general unitary transformations is very difficult, but you can look at a conserved quantity and deduce enough to know that the accuracy is limited if we want repeatability. So the conservation law was used to give a simple, although less general, proof. And to make it simpler, the conserved quantity had to be additive.
 
But these are just assumptions Wigner made to prove the result, and this made me initially think that there is nothing special or metaphysical about conservation laws in this context, despite Wigner's other very important realizations about the role of symmetry. But there is a very important lesson about symmetries (which, as we know from Emmy Noether, are the reason behind the conservation laws), as elucidated by the works of Ozawa, Loveridge, Busch, Miyadera and others.

Conservation laws are often used to deduce things without solving equations. But they don't constrain, they express the constraints of the system, since these constraints restrict the symmetries, and therefore the conservation laws. On the other hand, the symmetries of the system really capture an important aspect of the constraints, as explained in this wonderful article by Loveridge, Busch, and Miyadera.

The reason why I consider Mikko Tukiainen's paper important is that it seems to indicate another deeper aspect, that seems to go beyond that. He not only it gave a more general proof, but in that proof, conservation laws play no role (you can read it for free here). He used instead the idea of quantum incompatibility, which is a way to understand the major features of quantum mechanics that distinguish it from classical mechanics (although the most useful examples are still given by conservation laws). This is neat, complements the idea based on symmetry, and it's in some sense more general.

Both the symmetries and quantum incompatibility go deep, but maybe there is a deeper reason than both of these - the full range of such limitations of measurements is still unknown. And maybe there is no general characterization of this. But anyway, I think there's more to be learned about this.

Since both the WAY papers together have together a relatively small number of citations (hundreds), I consider them underrated too. This is another mystery to me.

Saturday, March 28, 2020

The negative way to sentience (comments welcome!)

I wrote an essay about sentience and its relations to physics. For the moment, I  keep it on ResearchGate, and I am welcoming comments.

The negative way to sentience (comments welcome!)


Abstract. While the materialist paradigm is credited for the incredible success of science in describing the world, to some scientists and philosophers there seems to be something about subjective experience that is left out, in an apparently irreconcilable way. I show that indeed a scientific description of reality faces a serious limitation, which explains this position. On the other hand, to remain in the realm of science, I explore the problem of sentient experience in an indirect way, through its possible physical correlates. This can only be done in a negative way, which consists in the falsification of various hypotheses and the derivation of no-go results. The general approach I use here is based on simple mathematical proofs about dynamical systems, which I then particularize to several types of physical theories and interpretations of quantum mechanics. Despite choosing this scientifically-prudent approach, it turns out that various possibilities to consider sentience as fundamental make empirical predictions, ranging from some that can only be verified on a subjective basis to some about the physical correlates of sentience, which are independently falsifiable by objective means.


Sunday, October 27, 2019

Representation of the wave function on the three-dimensional space

My last paper

Representation of the wave function on the three-dimensional space

One of the major concerns of Schrödinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the 3N-dimensional configuration space, rather than on the three-dimensional (3D) physical space. This gives the impression that quantum mechanics cannot have a 3D space or space-time ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wave function as a physical entity, in particular, the many-worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory. Here, a representation of the many-particle states is given, as multilayered fields defined on the three-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wave functions as defined on the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the nonexplicit and informal intuition of many working quantum physicists, who, by considering the wave function sometimes to be defined on the configuration space and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schrödinger cats just like the usual one. But, it may help various interpretations to solve these problems, through inclusion of the wave function as (part of) their primitive ontology. In appendices, it is shown how the multilayered field representation can be extended to quantum field theory.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.042115

Friday, October 20, 2017

A debate inside another one

Tim Maudlin debated Gerard 't Hooft about his cellular automaton interpretation of quantum mechanics in a series of Facebook posts, the fourth one being here https://www.facebook.com/tim.maudlin/posts/10155699914028398. Somewhere in the forest of comments I was engaged in a sort of sub-debate, with Tim, Hans, and others. Sabine was there too. The discussion was completely surrealistic, Tim and Hans completely misunderstood my point. This started by me intervening with a theoretical counterexample to a claim that all so called superdeterministic theories (in particular 't Hooft's) are not falsifiable, and of course it led to different topics. It is not known, but not a secret that the wavefunction collapse leads to violations of conservation laws, and that it is possible at least in principle to remove the collapse while remaining with a single world. But removing the collapse can be seen as superdeterministic (although I wouldn't call it like this, because it is based on spacetime, not on initial conditions), and I even proposed a principle to explain this, and experiments to test it. I paste here most of this *debate*, because there are some parts I am interested to keep. I skipped some parts in which I was not involved.