Comments about the book "Foundation of Quantum Theory" by Klaas Landsman

This document contains comments about the book: "Foundation of Quantum Theory" by Klaas Landsman
This book is available as an e-book. To download the book select: https://link.springer.com/book/10.1007/978-3-319-51777-3
In the last paragraph I explain my own opinion.

Contents

Reflection

Introduction

page 5

Let us now review the philosophical motivation Bohr and Heisenberg gave for their mutual doctrine of classical concepts. First, Bohr (in his typical convoluted prose):
This prose is very interesting. The Q to ask is if Bohr today would write the same.
The elucidation of the paradoxes of atomic physics has disclosed the fact that the unavoidable interaction between the objects and the measuring instruments sets an absolute limit to the possibility of speaking of a behavior of atomic objects which is independent of the means of observation.
You cannot speak about an absolute limit. The issue is to what extend we can speak of the behavior of atomic objects independent of the means of observations.
The answer is you can not. There is always a certain dependency at both classical and quantum level.
As soon as we are dealing, however, with phenomena like individual atomic processes which, due to their very nature, are essentially determined by the interaction between the objects in question and the measuring instruments necessary for the definition of the experimental arrangement, we are, therefore, forced to examine more closely the question of what kind of knowledge can be obtained concerning the objects.
The problem is you can speak about individual atomic processes, but in reality it is not, it is more. The measurement process is part of it. This measurement process can influence this individual behavior, which you should try to minimize.
On the other hand, it is equally important to understand that just this circumstance implies that no result of an experiment concerning a phenomenon which, in principle, lies outside the range of classical physics can be interpreted as giving information about independent properties of the objects.
It should be emphasized that the measuring process is both an issue at classical and quantum level
Almost at the bottom of this page:
In classical physics science started from the belief—or should one say from the illusion?—that we could describe the world or at least parts of the world without any reference to ourselves.
That is correct at both classical and quantum level.
Its success has led to the general ideal of an objective description of the world.
This objective description of the world should not describe and human activities.

page 6

Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event.
I doubt that related to schrödingers'cat.
Natural science does not simply describe and explain nature; it is a part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning.’
This sentence is tricky. The issue is to what the evolution of the world is independent of ourselves. It is. Natural science is all what is involved to unravel the laws in action. That is what humans do, but the laws it self are independent of us.

page 7

A second argument in favour of the doctrine lies in the possibility of a peaceful outcome of the Bohr–Einstein debate, or at least of an important part of it; cf. Landsman (2006a), which was inspired by earlier work of Raggio (1981, 1988) and Bacciagaluppi (1993).
This debates toke place around 1930, which involved thought experiments.
This debate initially centered on Einstein’s attempts to debunk the Heisenberg uncertainty relations, and subsequently, following Einstein’s grudging acceptance of their validity, entered its most famous and influential phase, in which Einstein tried to prove that quantum mechanics, although admittedly correct, was incomplete.
The problem with this sentence is that first of all you must specify what Einstein means
One could argue that both antagonists eventually lost this part of the debate, since Einstein’s goal of a local realistic (quantum) physics was quashed by the famous work of Bell (1964), whereas against Bohr’s views, deterministic versions of quantum mechanics such as Bohmian mechanics and the Everett (i.e. Many Worlds) Interpretation turned out to be at least logical possibilities.
See Reflection 1. - General
The common ground referred to concerns the problem of objectification, which at first sight Bohr and Einstein approached in completely different ways:
That means there are differences between the two.
However
On a suitable mathematical interpretation, these conditions for the objectification of the system turn out to be equivalent! Namely, etc
What follows is a mathematical treatment of the subject including the remark "That there are no entangled states involved". The paragraph ends with the sentence:
Thus Bohr’s objectification criterion turns out to coincide with Einstein’s!
That means there is no issue? Or is this a wrong interpretation.

page 8

The doctrine of classical concepts implies in particular that the measuring apparatus is to be described classically; indeed, along with its coupling to the system undergoing measurement, it is its classical description which turns some device— which a priori is a quantum system like anything else—into a measuring apparatus.
This sentence requires a clear definition of what is meant with classical versus what is a quantum system.
Runs this definition parallel with the concepts macroscopic versus microscopic?
The issue that any experiment always includes classical (macroscopic) elements and sometimes quantum system (micros copic) elements, including the measuring apparatus.
The solution of the raised issue lies in the details of the actual experiment discussed.
In view of its importance for their interpretation of quantum mechanics, it is remarkable how little Bohr, Heisenberg, and their followers did to seriously address this problem of a dual description of at least part of the world, although they were clearly aware of this need:
If you want to discuss the world in total, most of it can be described classical at macroscopic level, Only a small part requires quantum mechanics or a description at microscopic level.
If you want to discuss an experiment using single photons this is completely the reverse.
Again it is important to know the details of the experiment being discussed.
Specific it is important what the function of the operator is.

page 9

If only the instruments are sufficiently heavy compared with the atomic objects under investigation, we can in particular neglect the requirement of the [uncertainty] relation as regards the control of the localization in space and time of the single pieces of the apparatus relative to each other. (Bohr, 1948, pp. 315–316).

page 14

Part II, entitled Between C0(X) and B(H), starts with a survey of some known results on the grey area between classical and quantum, such as Bell’s Theorem(s) and the so-called Free Will Theorem.
IMO everything related to "Free will" i.e. all human behavior belongs to classical mechanics.
Bell's Theorem, insofar as it describes experiments involving single photons or particles belongs to quantum mechanics.

1. Classical physics on a finite phase space

2. Quantum mechanics on a finite-dimensional Hilbert space

3. Classical physics on a general phase space

4. Quantum physics on a general Hilbert space

5. Symmetry in quantum mechanics

6. Classical models of quantum mechanics

page 192

item 3. point d
Conway and Kochen, on the other hand, resolve the contradiction their FWT (Free Will Theorem) established by inferring randomness of outcomes from freedom of settings.
Consider an experiment where the polarization angle of a photon is measured on both sides and where the operator can select on either side either the X or Y direction.
In such experiments if you observe one side, keeping the selection the same, the outcome is completely random. If both selections are in the same direction the individual outcomes are completely random, but in cases where each reaction creates two photons the angles can be correlated, implying that the two photons are entangled. The explanation of this correlation is inside the reaction that created the two photons. The details of the reaction (which can not be measured) can be called hidden parameters.
In case different directions are measured the outcomes are also completely random. In such cases correlation can not be demonstrated.
In anyway the actions of the operator have nothing to do with the outcome of the experiments, nor with the "Free Will" of the operator. What can influence the outcome is in sofar when you set the switch in the X direction the actual mechanical direction will be the same.

page 200

Determinism firstly means that there is a state space X with associated functions
What is such a function in practice ? Is Newton's Law such a function? I doubt this because the the trajectories of all the stars etc is influenced in principle by all other stars etc in the universe.

6.2 The Free Will Theorem

page 204

Noting various other notions of locality (such as Einstein locality in local quantum physics, which requires spacelike separated operators to commute, or Bell locality, discussed below), the above idea might be called Context locality, but we will simply refer to it as Locality. In our deterministic setting, a precise formulation is this:
  • Locality means etc
What follows is a mathematical treatment of what "Locality means"
This treatment is mathematical correct. The problem is what it physical mean.
See also what follows.
This finally brings us to (our reformulation of) the Free Will Theorem:
Theorem 6.13. Determinism, Freedom, Nature, and Locality are contradictory.
A major problem is what is the definition of Determinism, Freedom, Nature, and Locality
And maybe more important what means contradictory
What next follows is called proof
Maybe you can prove this theorem, but what does it physical mean?
Does that mean we humans have no Free Will ?
This Theorem introduces a much more basic question:
To what extend can the universe at microscopic level described mathematically, using the four above mentioned concepts
I'm inclined to reasonable doubt.

6.3 Philosophical intermezzo: Free will in the Free Will Theorem

page 205

This concept has two poles. One is the “will” itself, requiring a sense of agency, deliberation, and control. This pole seems to require some form of determinism.
The emphasis is on the word: Will
The other pole of free will is the adjective “free”, i.e., the ability to do otherwise, which at first sight requires indeterminism.
The emphasis is on the word Free
See Reflection 2. - Free Will
The problem of free will is that these poles seem contradictory. Many authors conflate free will with moral responsibility.
When Free Will is considered related to human behavior there is no contradiction.
The issue is strictly to make choices i.e. how to choose.
  • Compatibilism denies the contradiction, claiming that free will and determinism coexist. This position may be defended in many ways, among which one finds:
As soon as determinism comes into the picture you have to define what you mean.
Reconceptualizing “the ability to do otherwise” in a deterministic world.
The world is not deterministic nor indeterministic.
  • Incompatibilism accepts the contradiction, once again branching off into:
What follows is not clear because the concepts deterministic and indeterministic are not explained.

page 206

Although hard incompatibilism has our sympathy, our opening question concerning the notion of free will in the FWT drives us into the compatibilist direction, since determinism is among the assumptions shown to be contradictory by Theorem 6.13.
IMO don't use both concepts. Anyway I do not think it is sound physics to select a concept (if different concepts exist) in order to validate a Theorem and not the other concept which invalidates the same Theorem. See Page 204
Like other compatibilists before him (starting at least with G.E. Moore), Lewis attempts to make sense of the intuition that even in a deterministic world one in principle has the ability to act differently from the way one actually does, despite the fact that the latter was predetermined.
What is a deterministic world? This sentence is not clear. See Reflection 3. - Deterministic world

11. The measurement problem

11.1 The rise of orthodoxy

This placed measurement squarely outside quantum mechanics for the second time: the first time was in the insistence that the measurement device (“if it is to serve its purpose”) had to be described classically (cf. the Introduction), and now we also learn that the interaction between the quantum object undergoing measurement and the apparatus in question is “uncontrollable”, despite the fact that Bohr and Heisenberg regarded quantum mechanics as a complete theory: their argument was apparently that precisely the classical nature of the apparatus makes the interaction uncontrollable.
IMO it is wrong to make a distiction between quantum mechanics and classical mechanics. In each experiment they are both involved.
This in turn justified the classical description of the device, in that registration of a measurement result ought to be “objective”, so that reading it out by performing a measurement on the apparatus, so to speak, should not introduce any further disturbance and hence uncontrollability (or so the argument goes).
Any measurement in principle is a process which influences the process you want to measure. What you want is to minimize this influence.
Consistent with Bohr’s point, a more detailed conceptual analysis of the measurement process was given by Heisenberg (1958, pp. 46–47, 54–55), who consistently refers to the quantum state or wave-function as the “probability function”:
Immediate when you switch from a process or experiment which involves classical measurements to what is called the probability function (I expect at particle level) you enter into the field of (difficult) mathematics.
‘Therefore, the theoretical interpretation of an experiment requires three distinct steps:
  1. the translation of the initial experimental situation into a probability function;
  2. the following up of this function in the course of time;
  3. the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function.
In process control we use somithing similar. It is called Laplace transformations.
In mathematical notion it looks like: f(t) -1-> f(p) -2-> f1(p) -3-> f1(t)
Step 1 is what you can call a forward transformation. Step 3 is a backward transformation.
Step 2 is the actual process which only uses Laplace functions.
Laplace transformations make it simpler to split the process into smaller entities.

In reality the above 3 steps are very difficult to perform.
Specific step 2 is very tricky.

After [the] interaction [with the measuring device] has taken place, the probability function contains the objective element of tendency and the subjective element of incomplete knowledge, even if it has been a “pure case” before [i.e., it has become a mixture].
The sentence IMO is the same as my claim that any measurement influences (the parameters) of the process that you want to measure.
My interpretation is also that if you want to quantify this disturbance, is very difficult and depends about the characteristics of the measurement process (apparatus). See Reflection 4. - Complications related to measurement issues.

page 439

Yet the authors mainly repeat von Neumann’s analysis (confirming its lofty status):
‘The interaction with the apparatus does not put the object into a new pure state. Alone, it does not confer to the object a new wave function. On the contrary, it actually gives nothing but a statistical mixture: It leads to one mixture for the object and one mixture for the apparatus. For either system regarded individually there results uncertainty, incomplete knowledge. Yet nothing prevents our reducing this uncertainty by further observation.
Suppose you have one photon which is influenced at event A. The issue is that before event A you can call the state of the photon a pure state and the same for the state after event A. The problem is when event A is a measurement the result tells you something about the state before event A but 'nothing' about the state after the event. To call the state after the event a mixture is IMO not very helpfull.
Opponents of the Copenhagen Interpretation (the most prominent among whom were Einstein and Schrödinger) were well aware of this tension between formalism and ideology, which in the form of Schrödinger’s Cat even reached immortality (!):
The following text is interesting but not clear.
The psi-function of the entire system would express this in such a way that in it the living and the dead cat would be mixed or spread out on equal terms.
How can you describe something in a mathematical form when the meaning is not clear?.
The last sentence is particularly powerful, contrasting Schrödinger’s (as well as Einstein’s) view that physics should describe some sharply defined reality (of which quantum mechanics at best produces blurred pictures) with the Copenhagen view, according to which reality itself lacks focus (with quantum mechanics providing the best possible picture of it).
The object of physics is to predict the reality as accurate as possible. The problem is that observations (in the past) are not 100% accurate nor the laws are known (specific the parameters) with 100% accuracy. This results that the predictions (into the future) are not 100% accurate.
This is both at classical level and at particle level.
This contrast confirms our idea that Schrödinger’s Cat metaphor specifically draws attention to the problems that arise from the Copenhagen “duality postulate” that macroscopic systems (such as measurement devices and cats) admit both a classical and a quantum-mechanical description.
The major problem related to Schrödinger’s Cat is the half-life time of the radio active decay of the radioactive element involved.

11.2 The rise of modernity: Swiss approach and Decoherence

page 441

To explain the last point, we quote Leggett (though somewhat out of context):
‘Now, following Schrödinger, let us consider a thought experiment in which the quantummechanical description of the final state, as obtained by appropriate solution of the time dependent Schrödinger equation, contains simultaneously nonzero probability amplitudes for two or more states of the universe that are, by some reasonable criterion, macroscopically distinct (in Schrödingers example, this would be “cat alive” and “cat dead”).
How is it possible to calculate the solution of the Schrödinger equation in a thought experiment?

page 442

‘The measurement problem has been called “the reality problem” by Philip Pearle. This is a better name for it. We perceive objects in the world as being in definite states. A door is either open or shut, a given ball either is in a given box or it is not. The wave function, however, can have superpositions of these things, suggesting that the door can be simultaneously open and shut at the same time, and that the ball can be both in the box and not in the box at the same time.
Yes is can be said that a door is either open or not open and that a ball is either in-a-box or not in-a-box, but in general that is too simplistic. A car can be anywhere on a road from A to B.
It is possible in principle that the wave function supports the idea that an object can be in two states simultaneous. However what is the purpose of such a claim if that can not be tested in reality. What this implies is that the concept of "being in two states simultaneous" is not clear.
A related subject is: that the concept "the collapse of the wave function" is also not clear.
More technically, the measurement problem has come to be seen as a special case of the problem of explaining at least the appearance of the classical world from quantum theory.
Sentence is not clear.
If the measurement problem is seen from the Copenhagen perspective this is eminently reasonable, as both problems involve the dual description of either the apparatus or the world around us as both classical and quantum (and its possible failure).
Sentence is not clear.

11.3 Insolubility theorems

11.4 The Flea on Schrödinger’s Cat

12. Topos theory and quantum logic

The topos-theoretic approach to quantum mechanics (also known as quantum toposophy) has the same origin as the quantum logic programme initiated by Birkhoff and von Neumann, namely the feeling that classical logic is inappropriate for quantum theory and needs to be replaced by something else.
This sentence can only be understood is there exists a proper definition of what quantum theory is, specific when it should be applied.
For example, Schrödinger’s Cat serves as an “intuition pump” for this feeling (at least in the naive view—dispensed with in Chapter 11—that it is neither alive nor dead).
From a physical point of view the cat is either alive or dead.
From a human point of view we do not know what the actual state is before we look, but after we observe we know.
IMO there is no reason to introduce extra logic to explains what happens at elementary particle level.

Reflection 1. - General

The book "Foundation of Quantum Theory" (book 1) is a very impressif book. In some sense you can compare it with the book "Newton's Principia" (book 2) for the common Reader by S. Chandrasekbar. Both books are a mixture of readable text and methematics. Mathematics in the form of theorems to slowly quide you to a conclusion.
For the common Reader to read the text is a joy and adds knowledge to your mind. The mathematics is the cherry on the pudding.
However there is a great difference between the two books. Book 1 is about quantum mechanics and book 2 about classical mechanics. This is my interpretation. Book 2 is the opinion of one man: Isaac Newton. This makes the whole book very concise, balanced. The object of the book is also straight forward: The movement of the planets around the Sun. Book 1 is a mixture of the meaning of many people, each of which is often not clear and consistent.
See Page 7
In the discussed section the opinions of Einstein versus Bell and Bohr versus Everett are compared in some sense to reach some unification. The problem is there is no clear underlying subject which is discussed. It would have been much simpler if all these people discussed the same experiment and try to explain the outcome. Unfortunate that is not the case.
A typical case is Everett and the Many Worlds view. The problem the whole many worlds view is not clear and cannot be demonstrated. As a consequence one cannot claim that Bohr is wrong.

Reflection 2. - Free Will

In 6.3 Philosophical intermezzo: Free will in the Free Will Theorem the concept Free Will is discussed. In fact the concept is divided in two parts Free and Will as if they can be discussed separately. This is wrong. They are both part of the human brain or mind. In fact all people have a "Free Will" in principle. This becomes clear if you ask a person to select one ball out of a bag which are all numbered. He or she can select any ball he or she likes freely.
However that does mean that we can always do what ever we like, Infact there are many rules which control or guide our behaviour. For example if we drive a car, we have to follow the rules. If you are in a yail, your freedom is very limited.
What is important that in order to explain "Free will" the concepts determinism and indeterminism don't have to be used.

Reflection 3. - Deterministic World & Laws of Nature

A Deterministic World implies that the total evolution of the world can be described by laws. To be more specific by the laws of nature. There are two main problems involved.
  1. We don't know what these laws of nature are.
  2. We don't know what the actual state of the universe is at present, at all levels of detail.
The claim that the world is either deterministic or indeterministic or both does not make sense.
The only thing that makes sense is the claim that certain physical phenomena can be described (within a certain accuracy) by physical laws. A typical example is Newton's law. This law can be used to describe to decribe the movements of planets (within a certain accuracy) if they are spherical. In principle they can be used to describe the movement of any object. The problem is that than you have to know the shape and its internal structure and that is impossible.

Reflection 4. - Complications related to measurement issues.

In order to understand the universe or the details of any process, measurements are necessary, to know what has happened in the past, to unravel the laws that describe its behavior and to predict the future.
The problem of any measurement is that the measurement will disturb what you want to measure. This problem exists specific if you want to measure what happens at elementary particle level (atoms) and even smaller (quarks). What you measure, for example at elementary level, is only an average position. This measurement inturn will influence the direction of the particle measured, which will make it difficult to measure its speed.
However and that is important the fact that you cannot measure something does not mean that at any moment a specific atom, electron or photon does not have a specific position. With position I mean the center of the atom, electron or photon. The point I try to make is that incase you cannot measure something, does not mean that 'below the surface' there is not a deeper reality, which can be described (measured) if better tools were available.

The same can be said about the uncertainty principle which says something about the incapability of humans to perform accurate measurements but does not say anything about the underlying reality. There exists no uncertainty in the movement of electrons around its nucleus.

Related to quantum mechanics (elementary particle physics) there exist the opinion that a measurement here can have (instantaneous) influence of the state of something overthere. This is specific the case when entanglement is involved. In that case it is important to agree upon that entanglement (correlation) can only be established when 'the same experiment' is performed many times. Only when you have performed the experiement 1000 times you can claim that the particles are correlated, meaning that the state of one particle is A the state of the other particle is non_A. And vice versa.
The reason why instantaneous action can not be involved is because this would invalidate the rule that any measurement is a process which follows the common accepted laws of physics. One of these laws is that any physical influence propagates below the speed of light. The problem is that if we assume that there are measurements which influence others at a distance this would invalidate all measurements and all results related to the LHC. Maybe not all but than maybe some. If that is the case than which one? IMO none.

Reflection 5. - Schrödinger's Cat.

As part of the Schrödinger's Cat (Thought) experiment a cat is put in a box. Immediate when this is done, without doing anything else, you can ask the question: what is the (physical) state of the cat. The most logical answer will be: alive. This can easily be tested by opening the box. However accordingly to quantum mechanics the state of the cat is both alive and dead (simultaneous).
Next you switch a lever which is connected to the box and you ask the same question: What is the state of the cat. Again the most logical answer is: alive. According to quantum mechanics the state of the cat is both alive and dead (before you look in the box). Next you look inside the box and you see that the cat is dead. How come? The cat was healthy. This raises also an other question: Is quantum mechanics correct? Was the cat in the box alive and dead simultaneous.
If you want to answer you must know much more detail what happens inside the box when you change the position of the lever. In fact you must study the hidden parameters involved. Inside in the box there is a radio active element which decays in for example an alpha particle. Important is the half life of this decay process. To get some idea if you start with 120 atoms of a radioactive element and the half life is 1 minute then after 1 minute only 60 atoms will be left implying that on average after each second 1 alpha particle will be released. In the next minute that will be each 2 seconds, 4 seconds etc. This alpha particle will release a poison inside the box and the cat will be dead. To find the half-life you have to perform many experiments. You could also use this list: https://en.wikipedia.org/wiki/List_of_radioactive_isotopes_by_half-life. The importance of all this the more you know the better you can predict that if you look after 1 minute the cat is dead. This reasoning is based on two laws: that the amount of radioactive material used should be large and that the half-time should be small.
Does this mean that quantum theory is right. Yes if the two mentioned laws are subject of quantum mechanics.
Does that mean that Einstein is right. Yes insofar the hidden variables approach he supported means that you need the details of the processes involved to explain the outcome of a certain experiment.
Does this mean that in the schrödinger's cat experiment there is superposition involved? No. Based on the results of the experiment the answer is clearly no.

Reflection 6. - Quantum Mechanics versus Mathematics.

Is it possible to describe the quantum mechanical world by means of mathematics?
  1. First of all there exists no quantum world nor a mathematical world. There only exists one world or one universe which we can study at different levels of detail. The further away we observe, the longer ago happened what we observe and the less accurate.
  2. Generally speaking we can only perform mathematics at microscopic level (individual particles) in some specific cases, but in general the answer is no. It is very difficult to perform methmatics (make accurate prdeictions) based on individual experimenst.
    • What we can use the periodic table https://en.wikipedia.org/wiki/Periodic_table which gives the number of protons, neutrons and electronic in each atom. The rules are mathematical and there are no empty places (any more)
    • What also follows very strict rules is the behaviour of the electrons in shells and the ionization energy. See: https://en.wikipedia.org/wiki/Periodic_table#Electron_configuration
    • A different story is the https://en.wikipedia.org/wiki/Standard_Model
    • At quantum mechanical level the most interesting case is the Double-slit experiments (with waterwaves) and photons. See https://en.wikipedia.org/wiki/Double-slit_experiment
      What is important that the double slit experiment says something about the behavior of photons related to a single or a double slit (that photons can interfere) but can not be used to explain anything else.
      The last sentence of the document reads:
      Physicist David Deutsch argues in his book The Fabric of Reality that the double-slit experiment is evidence for the many-worlds interpretation.
      This is a typical a case where you want to explain something that is not clear (the results of the double-slit experiment) by something else (The many-worlds interpretation) which is also not clear.
  3. IMO most experiments at elementary particle level (specific the results of collisions or reactions) can not be described by mathematics. The best we can do is to draw a Feynmann diagram, which describe more or less which particles collide and what are the fragments, but the details are hidden.

Feedback

If you want to give a comment you can use the following form Comment form
Created: 10 April 2018

Go Back to Book and Article Review
Back to my home page Index