# B Quantum and GR analogy?

1. Jul 26, 2016

### bluecap

I want to ask this in the Relativity forum but thought there are more quantum experts here. So most of you Bhobba, Neumeier, etc believe the world is really classical and all the quantum things are just for calculation purposes or aids. Can you take the analogy to General Relativity? Can we say that in GR, the world is still classical and the Einstein Equations are just for calculation purposes? But then matter really gravitate.. so it's not just classical thing? And if this is true and GR is anti-classical.. then it's not at all a stretch that QM is also not just about calculations or measurement theory in classical world? It would give stronger basis if GR is also like QM that matter really gravitate and is it not a clue?

2. Jul 26, 2016

### jambaugh

Something to keep in mind. Before you formulate a specific theory, as a language of description quantum mechanics incorporates classical mechanics as a special case so it is a more general language of expression. So if things are "really classical" then they are also "really quantum" in so far as being one or the other is a matter of the language of description. Now EPR/Bell inequality violation experiments would lend credence to the premise that nature is properly quantum in that a classical description is not sufficient for the better class of theories (better in their agreement with observation).

I'm not sure what your mental definition of "really quantum" or "really classical" is but keep this one point in mind. When you get beyond what is operationally meaningful, i.e. what can be translated to the laboratory or observatory actions, then either you're talking math or getting into philosophical issues which science properly does not address. In SR for example it is moot to argue whether there is an unobservable luminiferous aether. Whether there is or isn't is beyond scientific debate. What is meaningful scientifically is only what the theory predicts. The relativity of SR says you can ignore the question of this unobservable aether, or equivalently assume that it don't exist but that assumption is a matter of convention, not fact.

So consider the following question. How do you mean "really classical" or "really quantum" in an operational sense? How would you observe "really classical" or "really quantum" nature?

You should find, once you decide that point, that either there's a pretty straightforward answer to you question or the question is of the "how many angels can dance on the head of a pin" variety and unanswerable.

3. Jul 26, 2016

### bluecap

"really classical" in the quantum is the orthodox interpretation where majority of physicists follow, in that the wave function are just for measurement and statistical sense only, the world remains classical.

"really quantum" in the quantum is Bohmian Mechanics, Many Worlds, Objective Collapse, TI, etc.

I was asking if GR is like the orthodox qm or like Bohmian Mechanics, etc.

I've pondering this for days without resolution so hope you or anyone can give the case before the mentor locks this thread (and my question not answered). Thank you.

4. Jul 27, 2016

### jambaugh

That's not my understanding of the orthodox interpretation. Yes the wave-function is understood as describing our knowledge about the system, what you mean by "just for measurement and statistical sense only" I suppose. But the orthodox interpretation most definitely does not then follow with "the world remains classical". I believe this is a false inference you've made in misunderstanding in what sense the wave function is considered informational rather that representative. Possibly you misunderstood the point that the observers (being macroscopic recording mechanisms) are treated classically. This treatment goes hand in hand with the classical limit of quantum systems... as the systems get large and you look at aggregate variables those variables behave less and less as proper quantum variables and can be described classically.

The othodox a.k.a. Copenhagen interpretation is specifically agnostic about the underlying reality. It excises "reality" the way Einstein excised the aether in SR. We cannot know reality we can only see how things behave or act (the actuality) which is described by the wave function in their prediction of how likely given observations will occur. CI = Orthodox QM is positivististic about operational meaning. This is great departure from the prior classical theory which is built upon an ontological model (rather than the praxic=operational model of QM)

These are actually "more classical" (re)-interpretations of QM by trying to return to a classical ontological world picture.

The straight answer is Yes, (mostly) in that GR is a purely classical theory. You have (in the geometric model) a dynamic geometry determined by the distribution and currents of mass-energy in space-time. And particles follow their geodesic causal orbits as determined by this geometry. In a sense you simultaneously solve the equations for the flow of matter and the geometry which dictates and is dictated by that flow. All perfectly classical.

5. Jul 27, 2016

### bluecap

I'm mastering this paper shared by Bhobba over a hundred times. http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf
Here the The orthodox is not 'a.k.a. Copenhagen interpretation" as you said, the difference is thus (in the paper):

"The standard or orthodox interpretation is the only instrumentalist interpretation,
and therefore not really an interpretation at all: instead it merely
couples the mathematical theory to possible experimental settings. It includes
the measurement-collapse postulate (postulate 3 on page 6), but makes no attempt
at explaining its physical mechanism or what a measurement exactly is.

The Copenhagen interpretation, on the other hand, does propose the SciReal
view, by postulating that the classical is not to be derived from quantum theory,
but exists objectively, therefore recovering objective deniteness. As mentioned
before, this creates a problem of where this fundamental boundary between
the quantum world and classical realm is drawn."

Are you saying you don't agree with the paper shared by Bhobba (shared more than 150 times).
Here the orthodox interpretation follow with "the world remains classical". Ask Neumeier or even Vanhess, they will say there is
no mystery at all because quantum is just for computation, and the world remains classical.

If you can say you can agree with the paper. Is the GR like the orthodox or does it propose SciReal? This is my main question.

6. Jul 27, 2016

### jambaugh

I disgree on how the author you quoted characterizes CI. But if you wish replace where I use CI with "Instrumentalists", but let me point out it is THE interpretation of the formalism as it maps the mathematical formalism to what is observed or done in practice. That is an interpretation of the meaning of the mathematical constructs. The other "Interpretations" attempt to add to this an ontological model. That's their error.

As to what is and is not CI, most advocates of one of the ontological interpretations with whom I've chatted or who I've read misrepresents CI (as I interpret it) in that they focus on wave function collapse which they object to as a physical process and do not understand that the CI (as can be gleaned directly from the writings of Heisenberg and Bohr) does not interpret the wave-function as a representation of system state but rather a representation of information about how the system has or will behave. The paper you quoted b.t.w. has no citations referencing CI, and from where they constructed their definition of it. If you want to get the straight dope on CI start by reading Heisenberg's own description of it in "Physics and Philosophy, The Revolution in Modern Science".

I would disagree with the author in his characterization of the scientific realism of CI. He is confusing different orderings of "what is fundamental" and "what is derived". You must begin talking about QM from a classical language of the large scale because you must treat the recording devices and mechanisms in a laboratory classically. Our symbol structure is classical and cannot be other than classical because we must be semantically unambiguous with our mathematical structure and logic. That is the semantic foundation but it's an "outside-inward" direction with regard to what is happening in the natural world. Heisenberg directly speaks of expanding the system to include the observer within the quantum description. This implies that the classical description is an overlay on a more (physically) fundamental quantum world. What's more Heisenberg does this expanding to show the futility of trying to begin whole cloth with a quantum description.
You must (in CI) relate the quantum system description back to classical state based records of what happens in a lab/observatory.

I think you too may be making this confusion of orderings and it happens a lot when you transition from classic theory which though based on observation is typically taught by giving the object models first. In that object model the meaning of "fundamental" is the constituent atoms and their dynamics. One e.g. takes statistical mechanics as more fundamental than the thermodynamics it is used to explain. However before you can make observations of the constituent atoms to test the component assumptions of statistical mechanics, you must be able to build and calibrate a thermometer. In this sense, in terms of empirical primacy, the thermodynamic definition of temperature is more fundamental.

Note that such a reversal of primacy is what Einstein utilized to great effect in order to break out of the pre-relativistic mindset. Rather than giving some ontological formulation of time he said: "Time is what a clock clock reads." This allowed him to then ask about how different clocks might behave and how they might not necessarily agree. By putting the empirical clock as fundamental he was changing from the model to the science.

This is the problem again in QM. Too many people want to take the Hilbert space vectors (e.g. wave functions) as models of a reality. They are not, they are models of measurements. The dynamic evolution of them is a dynamic evolution of equivalent measurements under the equivalence relation of having the same (statistical) predictions on future observations. They ARE more fundamental then say classical atoms in this instrumental sense. And they each represent a specific classically described measuring device going "spling!" a certain way if-when it registers the system.

7. Jul 27, 2016

### atyy

In the orthodox interpretation, it is not sufficient to say that classical mechanics is a limit of quantum mechanics in order to say that the world is really quantum.

This is because the orthodox interpretation assumes the existence of the classical world in addition to deriving classical mechanics as a limit.

See for example, Landau and Lifshitz's or Weinberg's texts.

8. Jul 27, 2016

### bluecap

So you belong to the camp where wave functions are models of measurements (same camp as Balentine, Neumeier, Vanhees, Bhobba etc.).. but there is no theorem that would say the Bohmians, Many worlders, Objective Collapsers) misrepresent it by treating it as ontological. If there is a theorem.. all papers by them would be banned already and Wallace, Zurek out of job. I know you would say there is nothing to distinguish them. So at least say they are equivalent.. and so not really refuted.

But let's agree on the term "classical world". What I meant by classical world is tables and chairs made up of solid thing that is fixed. In Many worlds, the chair and tables split into many copies. These are not classical! In Bohmians, the chairs and tables have pilot waves attached to them. These are not classical. And so is objective collapse. Classical for me means Newtonian reality. Is this wrong concept? Isn't it Newtonian physics are also called Classical physics? And classical physics means bolts and nuts. So relativity is not supposed to be classical physics.. but relativistic physics... no?

9. Jul 27, 2016

### atyy

Much more fundamental to the viewpoint of Bohmian Mechanics is that reality exists, and that QM has a measurement problem. The reality of the wave function is not so important. The particular equations of BM are just one example of how the measurement problem may be solved. At the most fundamental level, Bohmians are not committed to the reality of the wave function. In fact, BM has two wave functions, and in a sense one wave function is real and one wave function is not real.

10. Jul 27, 2016

### jambaugh

Right. So by a classical world you mean
I said many do... no theorem just my observation (that many ascribe a "reality" to the wave function itself when describing CI and thus they (properly) take issue with the collapsing (physically real as they misrepresent it) wave function. Properly stated CI's collapsing wave function is a revision of representation of information given new observations. No FTL causality issues there. This is one of the issues advocates for alternative interpretations claim to address. But I believe you understand my position now.
You may be using "classical" in a peculiar way. A classical description is a description based on objects which have objective properties. e.g. particles as points with definite position (or possibly as spheres with a radius as well). This is in contradiction with the positivistic component of CI where, being operationally defined, a property is only meaningful when observed. To say a physical entity has a given property one is saying that said property is measured. In the absence of measurement such an empirically based property has no definite value. It is a semantic shift in the meaning of "property".

Note that by going from the ontological objective property description to this empirical property description one goes from an object base language to a process language (in the sense described by A.N. Whitehead).

So, Classical = Ontic (as in ontological) = Object = State Based Reality (what is)
and Quantum = Praxic (as in practical/pragmatic) = Process = Observation Based Actuality (what happens)

Now as I under stand the MW and Bohmian interpretations, (and not being an advocate of either I'm less familiar with them so correct me if I err)...

In Many Worlds the universe containing a classic chair in one state splits into many universes containing classical chairs in various possible states.

In Bohmian pilot wave interpretation there's a a classical chair composed of classical particles whose behavior is guided by a set of classically describable pilot waves (waves having a definite state = the wave function for the particle).

(classical in the sense I've described above.)

11. Jul 28, 2016

### Staff: Mentor

That's not what I believe.

I believe its the other way around. The world is quantum and classicality emerges as a sort of illusion.

GR is a theory that makes a specific claim about the world. That claim is no prior geometry. When expressed in the language of math gravity and the Einstein field equations more or less follow. The reason is the power of mathematics in expressing physical ideas. Unless you know it its very hard to appreciate it. But once you do its elegance and beauty is - well breathtaking.

I was formally trained in computing and applied math. That allowed me to read physics books and I was hooked.

The book that changed me was Landau - Mechanics:
https://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960
If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.

The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.

That is the message of modern physics - GR, QM - all have told us the same truth - symmetry is the key. Its deep, powerful and beautiful; and once you understand it almost magical.

As far as QM goes we can now present QM in a similar way thanks to Hardy:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

Last edited by a moderator: May 8, 2017
12. Jul 28, 2016

### Staff: Mentor

I quote that paper a lot - but that part is just the authors view.

Copenhagen does NOT say that. Let me repeat it again since the author stated it - Copenhagen does not say that. Copenhagen says QM is a theory about observations that appear in an assumed classical world. The author is falling into a logical trap, and since it was written by a philosopher he knows he should take greater care - but he isn't the only one - everyone does similar things - me included. The error is, even though Copenhagen assumes a classical world, it is not saying it cant explain that classical world - it simply leaves it up in the air .

In modern times great progress has been made in doing that, and that paper explains some of it, but a few issues remain. Suffice to say nowadays QM can explain the classical world.

Thanks
Bill

13. Jul 28, 2016

### bluecap

I just reviewed this book "Introducing Quantum Theory" by J.P. Mcevoy where it is mentioned "the existence of a state is given by the square of the normalized amplitude of the individual wave function (i.e. Psi^2). This was another new concept - the probability that a certain quantum state exists. No more exact answers, said Born. In atomic theory, all we get are probabilities"

So in Bohmian mechanics.. I read references where " Bohmian mechanics is
clearly a deterministic theory, and, as we have just explained, it does account for quantum
randomness as arising from averaging over ignorance given by j(q)j2."

In BM. Particles have path. So I understand BM is not about wave function but about what it is not. But then, what you mean BM has "In fact, BM has two wave functions, and in a sense one wave function is real and one wave function is not real". Is the pilot wave the wave function that is real or the one that is not (and what is the other)?

14. Jul 28, 2016

### atyy

In Bohmian mechanics, the wave function determines the probability distribution of initial positions. In some sense, probability is not real. So that wave function is not real.

In full Bohmian reality, there can be no probability at all, not even the distribution of initial positions. There is only completely deterministic dynamics.

However, Bohmian mechanics must be able to explain why there is the appearance of a distribution of initial positions (Valentini's work shows that de Broglie's version of the dynamics is more natural than Bohmian dynamics for this purpose, which is one reason the approach is often called de Broglie - Bohm).

15. Jul 29, 2016

### bluecap

Jambaugh stated that "the CI (as can be gleaned directly from the writings of Heisenberg and Bohr) does not interpret the wave-function as a representation of system state but rather a representation of information about how the system has or will behave." He will be online a day from now and I need answers right away. Is there anything in physics that has similar concept or procedure that is as complex (or lower in complexity) as the wave function being representation of information about how the system has or will behave? This can give stronger position to the CI if other concepts in physics are similar to it.

16. Jul 29, 2016

### Staff: Mentor

Exactly what the state is was elucidated by the mathematician Gleason:
https://en.wikipedia.org/wiki/Gleason's_theorem

Thanks
Bill

17. Jul 29, 2016

### bluecap

But you said early that "I believe its the other way around. The world is quantum and classicality emerges as a sort of illusion." But in Gleason stuff "Gleason's theorem therefore seems to hint that quantum theory represents a deep and fundamental departure from the classical way of looking at the world, and that this departure is logical, not interpretational, in nature.(wiki)": The bottomline line is that Gleasons is still classicality at the core. Or do you consider Gleason's logic as saying "The world is quantum and classicality emerges as a sort of illusion"?

18. Jul 29, 2016

### vanhees71

The point is that quantum theory is more comprehensive than classical theory, i.e., it correctly describes more phenomena than classical physics. On the other hand, you can derive classical behavior of macroscopic systems as a course-grained description of the underlying quantum behavior of the microscopic constituents. The most straight-forward example is the kinetic theory of gases, where you can derive the Boltzmann equation (classical) from the underlying Kadanoff-Baym equation (quantum) via the gradient expansion, i.e., you average out the short-ranged and short-time fluctuations being interested only in the slowly (in space and time) varying changes of the macroscopic ("bulk") quantities. For situations very close to equilibrium you can go further and derive the even more coarse-grained level of equations known as fluid dynamics (ideal and viscous).

19. Jul 29, 2016

### Staff: Mentor

Its a theorem. It reduces QM formally to just one axiom - see post 137:

'An observation/measurement with possible outcomes i = 1, 2, 3 ..... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.'

It got nothing to do with classicality.

Thanks
Bill

20. Jul 29, 2016

### bluecap

For illustration. How do you apply Gleason's theorem to a hydrogen atom with an electron and a nucleus. If the electron is not really a wave (or a probability wave), how can it be stable in the atom. Maybe we are back to pre-quantum Bohr's atom? And add Gleason's theorem and you don't have to go through the quantum period? Because Gleason's theorem is akin to quantum logic and an operational thing... you have a nucleus and electron.. and Gleason's theorem would produce any output without having to imagine the electron as a wave (akin to Matrix Mechanics)?

21. Jul 29, 2016

### stevendaryl

Staff Emeritus
Well, in Bohmian mechanics, the wave function plays two roles:

1. $|\psi|^2$ at time $t=0$ gives the probability distribution for the particle's initial position.
2. $\frac{-\hbar^2}{2m} \frac{\nabla^2 |\psi|}{|\psi|}$ is the "quantum potential".
The first role of the wave function is consistent with the idea that the wave function just reflects our ignorance of the exact location of the particle, but not the second. If the wave function affects the trajectory of a particle (through the quantum potential), then it seems that it must be real. (I mean, physical--not in the sense of real versus complex)

22. Jul 29, 2016

### Staff: Mentor

The same way as usual - you solve Schrodinger's equation.

Gleason changes nothing about QM except understanding what the state is. QM is based on two axioms:

Axiom 1
Associated with each measurement we can find a Hermitian operator O, called the observations observable such that the possible outcomes of the observation are its eigenvalues yi.

Axiiom 2 - called the Born Rule
Associated with any system is a positive operator of unit trace, P, called the state of the system, such that expected value of of the outcomes of the observation is Trace (PO).

What Gleason showed is, basically (technically you need non-contextuality without going into exactly what that is), axiom 2 follows from axiom 1.

The state is simply an aid in calculating probabilities. Of course different interpretations have more to say on it - but formally that's what it is.

Thanks
Bill

23. Jul 29, 2016

### vanhees71

Well, various interpretation say more about it, but from a purely physics/scientific point of view, there is nothing more to it. The point of Gleason's theorem seems to be that it shows a kind of uniqueness to the Born interpretation of the state, i.e., it's the only probability measure in the sense of quantum theory there is consistent with the rest of the postulates. What's however missing in bhobba's account of the axioms is the entire part on dynamics.

24. Jul 29, 2016

### Staff: Mentor

Indeed. The details however aren't really germane to this discussion. It is interesting to note that's where symmetry I mentioned before comes in.

My point was simply that the state isn't the primary thing so as to shed light on the query:
Formally its something the other principles of QM imply, rather than being fundamental itself.
In particular since its not fundamental then its purely a matter of interpretation if it is what an electron is, or isn't:

States describe the probabilistic behavior of observations on quantum objects. We have all sorts of interpretations of what they mean similar to the interpretations of probability itself, but they are just that - interpretations.

Strangely, and interestingly, many QM interpretations are simply about the meaning of probability:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

Last edited: Jul 29, 2016
25. Jul 29, 2016

### jambaugh

Certainly. Classical probability distributions are likewise representations of information about a system. Release one molecule of perfume in the center of a room and the probability density for the position of that molecule (heavy and distinct enough to be treated classically) will be a Gaussian (normal) distribution with time increasing its standard deviation. There is even an analogue to the Schrodinger's equation in the form of the diffusion equation (a.k.a. the heat equation.)

Wave function values are square roots of probability densities with the additional phase degree of freedom encoding relative dynamic and correlation information. That is the Born interpretation which identifies the meaning of the wave function. You might even call that the... Born Identity! (Sorry couldn't resist.)

The point here is that this is all the interpretation necessary to do the science. Further "interpretation" is either redundant or contradicts this interpretation. If it contradicts it isn't QM and if it is redundant then it is introducing additional unobservable entities (like doing SR with an aether "causing" clocks to slow and rods to deform) in the form of pilot waves or splitting parallel worlds and the entire hidden mechanics of cause and effect implicit in those additions.

There can be no additional predictions in such "interpretations". They are only designed to satisfy prejudices of specific adherents (the desire to "visualize" a state based object model within a theory, which if properly understood transcends such a world picture) or to address non-issues arising from misunderstanding of the orthodox Copenhagen interpretation which distinctly refuses to add to the above "Born Identity" (sorry couldn't help myself there either! :) That misunderstanding is that the collapsing wave function is not a collapsing physical entity but rather a collapsing conceptual entity and thus it's causally OK since the collapse happens in the mind... not caused by the mind, wholly within it! I decide to update my description based on new information, an observation.

There is a perfectly valid classical analogue to that as well. The value of your lottery ticket, and simultaneously the value of all other lottery tickets distributed throughout the country, will (within your mind) suddenly collapse from their expectation value to their prize value once you learn the results of the drawing. Or more "physical" if you observe that perfume molecule at some point in the room you will update (collapse) your probability density function to one centered at the observed location and starting with 0 deviation (delta function).

Let me finally caution that this is an analogy. The probabilities for quantum systems do not behave as measures over a state space. They don't add up correctly resulting in Bell type inequality violations. You can derive Bell's inequalities by noting that for measure m, the measure of a symmetric difference (xor) is a (pseudo? quasi) metric. It satisfies the triangle inequality: $m(A\sim B)+m(B\sim C) \le m(A \sim C)$ where $A\sim B = (A\cap B')\, \cup\, (A'\cap B)$. With some work you can transform Bell's inequality to this form of triangle inequality.

Bell inequalities reflect the assumption that probabilities form a measure on the set of states of reality. Their empirically observed violation points to the need to reject objective state based descriptions (unless you can keep all probabilities singular (1 or 0) by constructing such absurdities as infinitely splitting parallel worlds, or causally questionable pilot waves.)