Bohmian mechanics for instrumentalists and quantum measurement

[microsansfil]

TL;DR Summary

is there a relationship between the concept of perceptible and quantum mechanics measurement?

Hi,

I'm reading Demystifier's article about an interpretation of quantum mechanics. One concept that seems important for this interpretation is that of what is perceptible by us human beings compared to what is not (non-perceptible).

Demystifier says: A perception by a naked eye is direct, a perception by an electron microscope is indirect.

if we take the example of the vision, the image we perceive is not directly the "territory". Perception is a part of the larger visual system and is mediated by a complex process.

We need also theory to interpret what we perceive at the macroscopic level.

https://www.researchgate.net/publication/252483827_Light_Vision_Color

The eye is not a camera. Johannes Kepler (1571–1630), who gave an exact geometrical explanation of the image in a camera obscura, was aware that a retinal image could not justify the existence of a visual image.

The interpretation of the latter image is not determined solely by the optics; one also has to take into account neural factors, previous experience, expectations, memory and additional information from other senses. Blind people who are older when they are given the opportunity to see have difficulty in attaching meaning to optical images.

Can this concept of "perceptible" be a help to better understand what measurement in quantum mechanics is?

/Patrick

 

[microsansfil]

in first-order logic False ===> False / True is valid. This can be interpreted from a false assumption one can demonstrate (valid reasoning) all or its opposite.

/Patrick

 

[Demystifier]

Summary: is there a relationship between the concept of perceptible and quantum mechanics measurement?

In the paper I argued that there is, but I would certainly like to see what the others think.

 

[microsansfil]

Hi,

1/ "All perceptibles can be reduced to macroscopic positions" : the assumption is strong.

For example for the color vision there is the principle of Univariance which states that the effect of every photon that is absorbed is the same, independent of the wavelength or energy content of the photon (i.e : For each receptor, the same response can be obtained by all wavelengths (or frequencies) in the spectrum by merely changing the intensity of the light. A consequence of the univariance principle is that light of one wavelength and intensity can be interchanged with light of another wavelength and intensity without this resulting in any change (modulation) of the receptor’s response. ). Thus this interaction will be reduced to same macroscopic position because it concerns the same receptor’ ?

2/ To choose a representation, is to choose an orthonormal base in the space of the states E. You have chosen the representation in position {|r>}. However, a base can be discrete or continuous and therefore have very different mathematical properties. Even if the choice of a base is arbitrary, can we express all quantum mechanics in the base {|r>} ?

/Patrick

 

[vanhees71]

In non-relativistic QT of a single particle a common complete basis is $|\vec{x},\sigma_z \rangle$, where $\vec{x} \in \mathrm{R}^3$ denote the position eigenvalues and $\sigma_z \in \{-s,-s+1,\ldots,s-1,s \}$ the $z$-component of its spin. Using this basis leads to the wave-mechanical form of non-relativistic QT a la Schrödinger.

The many-body Hilbert space with a fixed number of $N$ particles are given as (anti-)symmetrized $N$-fold products of $\mathcal{H}$ with itself (for bosons (fermions)).

This cannot be applied to photons of course, for which you necessarily need QFT of a Fock space since there's no proper position observable for a proper photon and photon-number is not conserved. There's no non-relativsitic limit for photons since massless particles don't make the slightest sense in non-relativistic physics:

E. In¨on¨u, E. P. Wigner, Representations of the Galilei group,
Il Nuovo Cimento 9 (1952) 705.
http://dx.doi.org/10.1007/BF02782239

I can't say anything about physiological optics since I don't know much about it. Interestingly enough recently there was some finding hinting at the possibility that the human eye + brain is sensitive enough to "register" single photons.

 

[microsansfil]

and $\sigma_z \in \{-s,-s+1,\ldots,s-1,s \}$ the $z$-component of its spin. Using this basis leads to the wave-mechanical form of non-relativistic QT a la Schrödinger.

The Bohmian mechanics for instrumentalists, brings him back to a representation of a position to take in account that what we observe from, for example, a Stern-Gerlach apparatus.

/Patrick

 

[vanhees71]

Of course, the Stern-Gerlach experiment is the paradigmatic example for the statement that finally all measurements can be traced back to position measurements since it measures/determines the spin component by using a magnet to entangle (almost perfectly) position and spin component.

I'd not be so bold to claim this assumption about measurement are effectively always position measurments, but it's not so easy to find a counter example...

 

[microsansfil]

I'd not be so bold to claim this assumption about measurement are effectively always position measurments, but it's not so easy to find a counter example...

it is a fundamental question which, it seems to me, shows that the human subject cannot be removed as easily as one might think.

/Patrick

 

[vanhees71]

What have position measurements or other measurements to do with the human subject? Of course at the very end the aim of a measurement is that a human being takes notice of the outcome, but the measurement itself is pretty much automized nowadays, and many experimentalists look at the outcome by evaluating data on some computer storage.

 

[microsansfil]

Position derives from the senses by which human beings perceive "nature". We can imagine abstract observables like the spin, but at the very end, what we observe derives from our human being senses.

Another example is cloud chamber to observe particle.

That's how I understand the concept of "perceptible" defined in the article of Demystifier.

It does not mean that "nature" is only reduced to our senses.

/Patrick

 

[Demystifier]

Interestingly enough recently there was some finding hinting at the possibility that the human eye + brain is sensitive enough to "register" single photons.

Yes, but a human perceives it as a flash which she cannot distinguish from a flash created by many photons. This means that the perceptible in this case is the flash and not the photon.

 

[Demystifier]

Thus this interaction will be reduced to same macroscopic position because it concerns the same receptor’ ?

Yes.

Even if the choice of a base is arbitrary, can we express all quantum mechanics in the base {|r>} ?

In nonrelativistic QM, yes (plus a basis for spin degrees of freedom, of course).

 

[Demystifier]

What have position measurements or other measurements to do with the human subject? ... and many experimentalists look at the outcome by evaluating data on some computer storage.

Experimentalists look at the screen, where they see some lines (that make digital letters and numbers) with well defined positions.

 

[Demystifier]

I'd not be so bold to claim this assumption about measurement are effectively always position measurments, but it's not so easy to find a counter example...

Let me also add that if one could find a counterexample, one could easily disprove Bohmian mechanics. Many people tried to disprove Bohmian mechanics by other arguments, but not by a counterexample to the rule that all measurements can be reduced to position measurements.

 

[microsansfil]

many experimentalists look at the outcome by evaluating data on some computer storage.

in the same way, we can notice that many outcomes are numbers, real numbers. Are numbers a physical property of "nature" that we can observe/read or rather an abstract conception imagined by us, human being?

/Patrick

 

[Demystifier]

in the same way, we can notice that many outcomes are numbers, real numbers. Are numbers a physical property of "nature" that we can observe/read or rather an abstract conception imagined by us, human being?

Numbers, especially real (noninteger) numbers, are a human construct. The outcomes are not numbers by themselves, unless we interpret them so. A needle pointing to the letter "2" is not the same thing as the number two.

 

[microsansfil]

Numbers, especially real (noninteger) numbers, are a human construct. The outcomes are not numbers by themselves, unless we interpret them so. A needle pointing to the letter "2" is not the same thing as the number two.

Yes, what I wanted to raise awareness about is that what is stored in a computer is not what is physically measured. We need an interpretation/model that can be formalized by computer.

/Patrick