|Subject: The pure quantum world
Date: Tue, 26 Jul 2005 15:51:45 +0300
From: Dimi Chakalov <firstname.lastname@example.org>
To: "N.P. Klaas Landsman" <email@example.com>
CC: Catarina Carvalho <firstname.lastname@example.org>,
Tanmoy Bhattacharya <email@example.com>,
Salman Habib <firstname.lastname@example.org>,
Kurt Jacobs <email@example.com>,
Manoj Thulasidas <firstname.lastname@example.org>,
Norbert Straumann <email@example.com>,
Roland Omnes <firstname.lastname@example.org>,
"José Pereira" <email@example.com>,
Robert M Wald <firstname.lastname@example.org>,
Petr Hajicek <email@example.com>,
Domenico Giulini <firstname.lastname@example.org>
Dear Professor Landsman,
I'm reading your "Between classical and quantum" [Ref. 1] with immense pleasure. It is just a joy. Thank you!
You stated [Ref. 1, p. 76] that "neither decoherence nor consistent histories can stand on their own in explaining the appearance of the classical world." You also stated (quote from the abstract) that "classicality results from the elimination of certain states and observables from quantum theory".
May I ask you and your colleagues for help with elucidating the following issues.
Firstly, I can't understand why people believe that have denounced Hepp's solution to the measurement problem [Ref. 1, p. 65]. I think it is the only *exact solution*, and the fact that it requires an infinite apparatus and infinite time (as read by your wristwatch) should give us a hint to the pure quantum world. We just don't know its Hamiltonian time-evolution.
Secondly, if we look at the Wigner function [Ref.
2] of an unobserved quantum particle [Ref. 3], it
is not at all clear to me why should the Wigner function *even begin to
localize* in the intact quantum world. It can stay delocalized *forever*,
i.e., for an infinite time, as read by your wristwatch. You stressed that
it "may not be regarded as a probability distribution because it is not
necessarily positive definite" [Ref. 1, p. 43], and "its
total mass is not necessarily
Let's keep these "unattainable", as R. Feynman put it [Ref. 4], features of the pure quantum world, and switch to the clash of QM with the strong equivalence principle [Ref. 5]: a *real* observer cannot be a point in 3-D space but a 3-dimensional domain. We need two ideal observers to detect gravitation [Ibid.], but this "non-local" feature of gravity will inevitably probe the "unattainable" quantum world as well.
If all the above is true, we need quantum gravity to understand
Please see my efforts to introduce the notion of 'quantum-gravitational potential reality', NB argument on p. 12 from
Some possible implications can be read at
A penny for your thoughts! I'll keep them strictly private.
[Ref. 1] N.P. Landsman, Between classical
and quantum, quant-ph/0506082 v2,
100 pages, to appear in Elsevier's *Handbook of the Philosophy
[Ref. 2] Dietrich Leibfried, Tilman Pfau,
and Christopher Monroe, Shadows and mirrors: Reconstructing quantum states
of atom motion, Physics Today 51(4), 22-28 (1998).
[Ref. 3] Tanmoy Bhattacharya, Salman Habib,
and Kurt Jacobs, The Emergence of Classical Dynamics in a Quantum World,
Alamos Science, Number 27, 2002, pp. 110-125,
p. 115: "And these equations for the centroid are identical
[Ref. 5] R. Aldrovandi, P.B. Barros, and
J.G. Pereira, The Equivalence Principle Revisited, gr-qc/0212034 v1,
"An ideal observer immersed in a gravitational
field can choose a
"The apparent simplicity has one merit: it reduces the whole question to giving clear meanings to the three expressions in italics.
"The key notion is that of ideal observer,(8) which is
a time-like curve, a world-line. Such a curve represents locally, in well-chosen
coordinates, a point-like object in 3-space evolving in the timelike 4-th
direction. To represent an extended object -- in particular, a real observer
-- a bunch of world-lines is necessary, one line for each of its points
in 3-space. A real observer can know whether (s)he is accelerated or not
by making experiments with extended objects like accelerometers and gyroscopes.
The gravitational field (that is, the Riemann curvature) will be given
away by the deviations of the world-lines. We shall see why and how the
Principle holds only for ideal -- point-like in 3-space -- observers.
"What has been called "principle of equivalence" in most
recent discussions is a mathematical property, the vanishing of the Levi-Civita
(or Christoffel) connection at a point or along a curve. Reduced to that
aspect, however, the Principle would not be a distinctive character of
gravitation. The aptitude to vanish at a point or along a curve by a convenient
choice of "gauge" is a general attribute of connections, shared by gauge
potentials. The meaning and specificity of the Principle is, consequently,
involved with the question of why and how gravitation differs from the
other fundamental interactions.
"An ideal observer in a gravitational field is locally equivalent to an ideal observer in the absence of gravitation, while an ideal observer in a gauge field will always feel its presence. At least two ideal observers are needed to detect gravitation, but only one is enough to detect an electromagnetic field. In this sense gauge fields are local, and gravitation is not.
"Concerning the Quantum Mechanics of a system immersed
in a gravitational background, an ideal observer -- a point in 3-space
Subject: Inaccessible parameters in
the Strong EP?
I wonder if you can reconcile QM and GR by applying your 'inaccessible parameters' [Ref. 1] to the Strong Equivalence Principle,
I like your inaccessible/hidden quantum ontology [Ref. 2]. It is conceptually very close to the 'atemporal handshake' of John Cramer, isn't it? See ref.  in
Please convey my best regards to Prof. Aharonov.
I'm glad to see that the good old U.S. Navy is supporting your project, ONR grant N00014-00-0383 [Ref. 1], and wish you best of luck.
[Ref. 1] Yakir Aharonov and Eyal Y. Gruss, Two-time interpretation of quantum mechanics, quant-ph/0507269 v1.
"It must be emphasized that the states in the final boundary
condition, which we have taken to be specific in the examples, are generally
unknown prior to the completion of the measurement. Classically, a priori
knowledge of the future is of course an acausal state of affairs.
"Therefore, like in hidden variables theories, the parameters
determining the measurement outcome are inaccessible.
Still, like in
[Ref. 2] Yakir Aharonov and Lev Vaidman, The Two-State Vector Formalism of Quantum Mechanics, quant-ph/0105101 v1.
Yakir Aharonov: "Even at present, before the "future"
measurements, the backward evolving quantum state (or its complex conjugate
evolving forward in time) exists! It exists in the same way as the quantum
state evolving from the past exists. This state corresponds to particular
outcomes of all measurements in the future."
v1: It takes two to tango
RE: WAP_1: “What we can expect to observe must be restricted
by the conditions necessary for our presence.”
I agree that WAP_1 is logically consistent and can yield testable predictions (Fred Hoyle), "since “we” can only observe the properties of worlds that allow our presence", as you put it (hep-th/0508006 v1, p. 4). On the other hand, WAP_2 is sheer parapsychology IMHO.
I'm curious whether you'd agree that your WAP_1 just implies
In other words, 'it takes two to tango', the universe and your brain.
As to WAP_2, it cannot be constrained to a finite ensemble of universes, hence we have to play with an infinite "set" of possible universes, which is a dangerous game, of course. But if we follow the math only, an infinite multiverse requires, among many other things, an infinite number of meetings with Aliens, all of which with unit probability. That's parapsychology IMHO, and I hope Ken Olum (gr-qc/0303070 v2) and Bob Wald (gr-qc/0507094 v1) can elaborate.
Now, if you agree with the subject line, why not model the universe as a human brain? We might be able to explain how did bananas (dynamic dark energy) get into physics (Rob Caldwell), since the universe would "think" with its "dark" stuff,
See also the story in the context of GW astronomy,
May I ask you and your colleagues for comments and suggestions. Will keep them private.
Thank you for your email from Wed, 27 Jul 2005 08:03:46 +0200 (CEST).
> First, I do not understand the logic that leads from
I believe have specifically asked you to deliver facts.
Please see my
Please refrain from talking à la 'magister dixit'.
> Second, each of the three conclusions seems to be wrong.
I also asked you to be professional. Before jumping into any conclusion, please support your statements by elaborating on the following issues.
1. You do not even try to explain how you would measure
You have also completely ignored the problem exposed by John Stachel; see ref. 37 on p. 27 from paper.doc , which I sent you by email two days ago, upon your request. If you've lost my paper, you can download it from
Are you implying that you can measure a genuine non-local phenomenon, such as GW energy, simply by comparing two of its local values pertaining to two 'ideal observers'?
2. You talk about "orientation of the point pair with
respect to the
You have not even tried to comment on my arguments against
the very notion of 'propagation direction of GWs'; see Sec. 2.2. There
is no background spacetime (cf. p. 11) to help you define 'propagation
As to the so-called "polarization of the wave": what is your interpretation of the vertical axis along which you define "the dimensionless number h "? Please see Fig. 2 and read my arguments on p. 9.
> II. There is no question that we are able to measure,
at least in
Not until you explain how you would measure a genuine
It is not about 'improving sensitivity' but about the
What is UNIQUE in the non-local nature of GW energy, in your opinion?
> This ability is independent
of 1. our precise
Nothing is simple with the gravitational "field". I personally
> Please let me know if I have satisfied your conditions.
Thank you for your interest in my opinion on your feedback.
In general, I'm afraid you're
making a serious logical error: you
In order to prove that "each of the three conclusions
seems to be
But you totally ignored all my arguments, and pronounced
To sum up, I cannot accept your statements until you correct your logical error by examining my objections. Should you find something "nebulous", please reply professionally, by explaining what you were not able to understand.
Should you decide to reply professionally, please be assured that I will keep your professional feedback strictly private and confidential.
With kind regards,
P.S. Do you know LSC White Paper from 11 September 1999,
Here's an excerpt:
"At the sensitivities of LIGO I it is plausible, but not
Six years later, and after consuming nearly $500,000,000, they failed. These are the facts. Let's get real, okay?
Note: The non-locality of GW energy is exhibited in the local dependence of the pseudo-tensor on the choice of coordinate system [Ref. 6]. According to my files, references on this issue start from 1922. If you want to measure GW energy locally, as with LIGO, AIGO, TAMA, GEO600, or VIRGO, you will have to replace the pseudo-tensor in Einstein's GR with something new, and totally unknown, but then you'll most likely run against Einstein's GR. Alternatively, you can just try to define 'non-local measurements' in Einstein's GR, and reconcile them with the Strong EP [Ref. 5].
I have no idea what Petr Hajicek
had in mind to make him optimistic. Once I hear from him, I will elaborate.
If he replies professionally, however, I'll keep his feedback private,
and wait for the announcement of his discovery on CNN Breaking News.
"By definition, Tuv(Matter) describes all the local energy, so any energy due to the [Weyl tensor] must be nonlocal in character. The existence of nonlocal energy is also manifest in the fact that the local conservation law
Tuv^v = 0
is a covariant curved space equation.
One cannot just integrate Tuv(Matter) over a 3-space to obtain a conserved
total energy-momentum. The total energy-momentum of a system must, therefore,
involve nonlocal contributions due, perhaps, to the presence of Weyl tensor
or to nonlocal interactions (e.g. Newton's potential energy) between the
Tuv's at different points (...). The nonlocality of the gravity energy
was then exhibited in the local dependence of the pseudo-tensor on the
choice of coordinate system."
Re: Are Gravitational Waves Directly Observable?
On Thu, 28 Jul 2005 10:22:57 +0100
(BST), Leonid Grishchuk wrote:
In your first email from Tue, 26 Jul 2005 16:33:18 +0100 (BST), you offered (in Russian) to drop the description of GWs in purely geometric terms, and switch to the well-known presentation of the gravitational field as some variable field "in the sense in which we examine electromagnetic waves as variable electromagnetic fields" (translation mine - D.C.).
This reminds me of an old joke: a Japanese tourist in London asks a Scottish guy for directions, and he replies: 'Well, if I was you, I wouldn't start from here!'
To be specific, please see
> Thank you for the exchange of messages.
The pleasure was mine.
Subject: Re: GW
I cannot accept your proposed framework for discussion, because it completely ignores the most important issue in Einstein's GR: the UNIQUE non-local nature of the gravitational field, and the use of the so-called pseudo-tensors,
I do not want to provide "another framework", such as Brans-Dicke, nor would I switch to "some alternative model representations", which will 'sweep the garbage under the rug'. There are dozens of alternative presentations of the gravitational field (Rosen, Yilmaz, Born-Infeld, Logunov, etc.), which I don't want to explore either.
Why? Because all this is about Einstein and his unfinished task, as explained on p. 15 from my paper.
Please see also my NB point on p. 12. I'm sure you have a model of GW, which "possesses a well-defined direction of motion and polarization", but I'm afraid it deals only with 4 per cent of the stuff in the universe. The rest is a "dark" secret.
With kindest regards,
On Thu, 28 Jul 2005 08:36:55 +0200
(CEST), Petr Hajicek wrote:
Subject: Re: GW
> We must, therefore, use mathematics
to cope with this complexity, or
Great! Please explain what is UNIQUE in the non-local nature of GW energy, as I asked before.
You wrote: "The mass points may be equipped with some signal sending lamps, and this signal might be collected by some observer at another timelike geodesics given with respect of the coordinates. Now, we can calculate and discuss in a non-nebulous way, what the observer will get."
It's very nebulous, since I don't see anything non-local here, so please use math.
Subject: Re: GW
Thank you for your prompt reply. I very much hesitate to comment on it.
On Thu, 28 Jul 2005 17:15:37 +0200
(CEST), Petr Hajicek wrote:
Subject: Re: GW
> You should atack head on! The points
are all right in their heart and,
I said that I very much hesitate to comment on your ideas. It's a bit like that: I want to fix a car, and I do know that I need a wrench, while you're offering me a hammer. Everything in my paper.doc from July 25, 2005 (hereafter 'paper') is aimed at quantum gravity: "I want to know His thoughts; the rest are details" [paper, p. 15].
You say: "(T)he notion of energy is not needed for the calculation of how the GW acts on material systems and how the result of the action can be measured. This calculation can be performed by exclusive use of local formulae."
But I'm interested in the very nature of the non-local GW energy, because in the Hamiltonian formulation of GR there is no *unique* presentation of energy due to the absence of preferred time [paper, ref. 27], and all we can do is to solve the puzzle in some highly artificial, in my opinion, cases, such as asymptotically flat spacetimes [paper, p. 6; cf. also ref. 11, Ch. 3.12].
Thus, my task is to understand the *unique* presentation of energy, and the *unique* presentation of an intrinsic time interval associated to any timelike displacement [paper, ref. 23], in the absence of preferred time [paper, ref. 22].
Two immediate problems follow. Firstly, the meaning of the phrase 'in some other way' in the quote below, from R. Penrose [paper, p. 6]:
"The energy-momentum of empty space is zero, so the gravitational wave energy has to be measured in some other way that is not locally attributable to an energy 'density'. Gravitational energy is a genuinely non-local quantity."
The second problem is that the energy-momentum of empty space is NOT zero [paper, ref. 17]. All I can suggest is the 'shoal of fish' metaphor [paper, p. 14], and the notion of 'atemporal potential reality' [paper, p. 12].
This is my 'wrench'. Again, my goal is quantum gravity, and everything in my paper is just a tool to get closer to this ultimate goal. I don't want to use your 'hammer', since it kills from the outset the very possibility to reach the goal.
You can refute my tool by offering an alternative explanation of 'atemporal potential reality' [paper, cf. NB on p. 12].
Please attack head on!
Subject: Re: GW
Thank you for your email from Thu, 4 Aug 2005 08:27:11 +0200 (CEST).
I asked you to 'put your cards on
the table' by stating the conditions under which your model of GWs will
be disproved, namely, the conditions
> O.K. Dimi, we have now to start
a serious business. What about your
Thank you very much.
Now, I vaguely remember reading about this "exact plane wave" in MTW, will have to check it out in the library. I understand that this "exact plane wave" is your first model, which you've used to build your method of two particles and one observer.
Regarding the latter, you've explained it to me on Thu, 28 Jul 2005 08:36:55 +0200 (CEST):
"In theoretical physics, one assumes
first some theory, for example general relativity. If one is going to study
some phenomenon, GW, say, one constructs a model of the wave, the apparatus
and the observer within this theory. Within general relativity, it
be a spacetime with some coordinates, a metric field with respect to these
coordinates that represents the GW, and two mass points, say, timelike
geodesics with respect to the coordinates, that represent the detector.
The mass points may be equipped with some signal sending lamps, and this
signal might be collected by some observer at another timelike geodesics
given with respect of the coordinates. Now, we can calculate and discuss
in a non-nebulous way, what the observer will get. We can also discuss
in which sense my model of GW possesses a well-defined direction of motion
Then you elaborated, on Thu, 28 Jul 2005 17:15:37 +0200 (CEST):
"The non-locality of energy in general relativity is a large issue. The only unique result known is the uniqueness of the total energy in the asymptotically flat spacetimes. It is well-defined and calculable from the form of the asymptotic field.
"The notion of energy has in general to do with time symmetry. In the asymptotically flat region, we have the asymptotic time symmetry. If there is no time symmetry, there is no unique definition of energy. Hence, I claim: there is NO unique and useful concept of energy, rather that claim: the energy is unique and non-local.
"In agreement with that, for the
GW, there is no exact unique result. There are some approximate formulae
that use averaging over volumes with radii larger than the wave length
etc. I claim: the notion of energy is
"There is indeed nothing non local here: the GW is described as a metric field that is well-defined locally at any point, the only non-locality being that that field is defined at any point of the spacetime. Its action on the mass points, light signals of the lamps and the observer is described by a local differential equation (geodesic equation). The time of arrival of the signals at the observer and their directions with respect to a frame of the observer are also calculated in terms of local formulae. All this can be performed in terms of equations and there is no hint of any kind of non locality. You can do these calculation yourself if you need it (I can help you in 2006). It can be done for a general metric, in this way including any model of GW."
On the next day, Fri, 29 Jul 2005 08:20:15 +0200 (CEST), you added:
"I admit that some of my points have been formulated in a hurry and may contain small unprecisenesses or incompleteness. You should attack head on! The points are all right in their heart and, in fact, very well known."
Finally, on Wed, 3 Aug 2005 17:33:46 +0200 (CEST), you rejected my claim that there must be some non-locality in the measuring process of GWs:
"However, as my model shows, there is no such non-locality. I have written to you about this already. In fact, not much mathematics was necessary to see it."
Before going to the library to check out that "exact plane wave" in [Misner-Thorne-Wheeler, p. 957], may I say the following:
1. Please notice that the non-locality in the measuring process of GWs stems from the Equivalence Principle (R. Aldrovandi, P.B. Barros, and J.G. Pereira, The Equivalence Principle Revisited, gr-qc/0212034 v1):
"An ideal observer in a gravitational field is locally equivalent to an ideal observer in the absence of gravitation, while an ideal observer in a gauge field will always feel its presence. At least two ideal observers are needed to detect gravitation, but only one is enough to detect an electromagnetic field. In this sense gauge fields are local, and gravitation is not."
The fact that you use energy pseudo-tensors, which can be *locally* set to zero (as noted by D. Hilbert to A. Einstein well before November 15, 1915), also reveals the genuine non-local nature of GW energy; more from H. Weyl and R. Penrose, if needed.
However, many people, you included, seek some strictly *local* model of GW energy, perhaps because laser interferometers cannot perform any non-local measurements with (at least) two ideal observers/measurements; please see p. 5 in
I believe my argument on p. 5 is quite conspicuous.
Summary on (1): I cannot understand your logic. The way I see it, by confining yourself to a strictly local model, you're throwing the baby with the bath water. I was expecting that you will try to do better than Misner-Thorne-Wheeler's book published in 1973.
2. To the
best of my (very limited, I confess) knowledge, local considerations of
GW energy are very murky, to say the least. Please see
Summary on (2): I very much hope to learn from you on two generic (and vicious) ambiguities in Einstein's GR. In the singularity theorems, the so-called singularity is defined as the existence of a causal geodesic that is non-extendible and non-complete, hence it has ceased to be a causal geodesic.
Here I recall an old joke. Please
look at the drawing below. What do you see?
This is, obviously, an elephant walking on a rope, only it has just fallen off.
Your colleagues use math, but the "logic" is the same.
The second ambiguity shows up in efforts to extend the solutions to Einstein's field equations on large-scale spacetime domains, e.g., at "null infinity" [Ref. 2]. You again lose your elephant, don't you?
That's all for now. I'll go to the library by the end of this week, to see if the elephant is still in that "exact plane wave". I won't be able to reply by the end of this month, however, since I'll be leaving for London soon and will come back on August 29th.
References and notes
[Ref. 1] Hans-Jürgen
Schmidt, Lectures on Mathematical Cosmology, gr-qc/0407095
v1, p. 35, Sec. 4.2, "Why do all the curvature invariants
"The energy of the gravitational field, especially of gravitational waves, within General Relativity was subject of controversies from the very beginning, see Einstein . Global considerations - e.g. by considering the far-field of asymptotically flat spacetimes - soon led to satisfactory answers. Local considerations became fruitful if a system of reference is prescribed e.g. by choosing a timelike vector field. If, however, no system of reference is preferred then it is not a priori clear whether one can constructively distinguish flat spacetime from a gravitational wave. This is connected with the generally known fact, that for a pp-wave, see e.g. Stephani  especially section 15.3. and  all curvature invariants vanish, cf. Hawking and Ellis  and Jordan et al. , but on the other hand: in the absence of matter or reference systems - only curvature invariants are locally constructively measurable."
 Ehlers, J., Kundt, W.: 1962,
in: Witten, E., ed., Gravitation, an
 Hawking, S., Ellis, G.: 1973,
The large scale structure of
 Jordan, P., Ehlers, J., Kundt,
W.: 1960, Abh. Akad. Wiss. Mainz,
 Stephani, H.: 1982, General
Relativity, Cambridge University
Note: See the example of mass-energy
conservation law defined at *null
Subject: Re: GW
> Instead, I have claimed that this
energy is not well defined, and that
If you detect it, GW energy will be *localized* and perfectly defined, so I'll make some 'reverse engineering' of your model, and then we will jointly decide who will upgrade what.
> 2) My first model is valid independently
of its age because it is a valid
I'm sure it's valid, but it may be inapplicable, 'non sequitor' (pardon my French). Will see.
> 3) My measuring process is at any
point local in character. But the
This is certainly the most mysterious point in your model, since I have no idea how one could theoretically distinguish between (i) a sum of local processes yields a local process, and (ii) a sum of local processes yields a non-local process. Will see, again.
Subject: Re: GW
I'll be out of touch next week, then will leave for London, so please notice that I can write you again after I come back to Sofia on August 29th.
> finally, we arrived at the crucial
point: You deny that a GW can be
Jain! I deny that GWs can be described by the *current presentation* of the metric field. On the other hand, I stressed, starting from the first sentence in my abstract, that GWs do exist, and have suggested two (novel?) ideas regarding the presentation of *the correct* metric field: the 'shoal of fish' metaphor and the notion of 'quantum-gravitational atemporal potential reality' or briefly 'potential reality'. See p. 14 and NB on p. 12 in
> Hence, your GW is very different
from GW of
Yup. This is as it should be, since I try to introduce the missing 96 per cent "dark" stuff of the universe from the outset. I believe the reasons are agonizingly clear (paper.doc, p. 14). See also my explanation of 'relational reality' at
> Now, I am really curious, what you think a GW is.
Please follow the links above, and come back with specific questions. If you don't understand something, it will be entirely my fault.
The "uncle" here is Einstein. He very much hesitated to introduce the principle of general covariance, since it "takes away from space and time the last remnant of physical objectivity" [Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik 49 (1916) 769-822]. See also the excerpt from his letter to Schrödinger below.
I already asked Chris for his professional opinion on 'potential reality' (paper.doc, p. 12), and hope to hear from him by Christmas. But if you ask him about his opinion on this crucial issue, I suppose he will reply to you sooner.
Let me add some final words about your and Chris' persistent refusal to comment on my proposals.
If I was a professor in theoretical physics in some leading European university, I wouldn't really care about what people in Borneo, Bulgaria, or Botswana have to say about GR and quantum gravity. They just don't belong to my world. However, since I *respect* my own field of research, I would not ignore any *challenge* from these people.
If we were talking about our hobbies, say, if you were collecting bottle labels while I was interested in paper napkins, then I could understand your attitude toward my proposals.
I ask you and Chris to upgrade your attitude.
As to your model, I suggest you get in touch with Chris and Dr. van Elst.
With friendly regards,
Du bist (neben Laue) unter den zeitgenössischen Physikern der einzige, der sieht, dass man um die Setzung der Wirklichkeit nicht herumkommen kann - wenn man nur ehrlich ist. Die meisten sehen gar nicht, was sie für ein gewagtes Spiel mit der Wirklichkeit treiben.
Except for Laue, you are the only one who realizes that you cannot avoid accepting reality if you are honest. Most of the others don't even see what kind of a dangerous game they play with reality.
Albert Einstein to Erwin Schrödinger, 1950
(E. Schrödinger, M. Planck,
A. Einstein, H.A. Lorentz: Briefe zur Wellenmechanik (hrsg. K. Przibram),
Springer Verlag, Wien, 1976)
Note: Going back to "uncle" Einstein, let me again explain the crucial notion of 'potential reality': I claim that 'elements of physical reality' with definite but potential values exist irrespective of whether or not they are actually observed. In the context of QM, the potential reality has being exposed by Ernst Specker half a century ago [Ref. 1]: it is counterfactual, deterministic & unpredictable, and UNspeakable. In the context of Einstein's GR, the potential reality has being exposed in the hole argument: the "points" occurring in the base sets of differentiable manifolds, which we use to model spacetime, belong to the realm of potential reality as well: see the red Z axis here. Thus, the class of 'potential events' is undenumerable [Ref. 1], and the potential reality is a genuine non-Archimedean reality. It can accommodate the non-unitary unfolding of 'the unknown unknown' along the cosmological time arrow, right from the start at the ultimate potential reality [John 1:1]. If you decide to model the universe as a human brain, all jigsaw pieces fit effortlessly.
Do you, my dear reader, wish to join
the company of uncles Einstein, Schrödinger, and von Laue?
[Ref. 1] K. Svozil, Quantum logic: A brief outline, quant-ph/9902042 v2.
"In the late 50’s, Ernst Specker was considering the question of whether it might be possible to consistently define elements of physical reality "globally" which can merely be measured "locally" (50). Specker mentions the scholastic speculation of the so-called "infuturabilities"; that is, the question of whether the omniscience (comprehensive knowledge) of God extends to events which would have occurred if something had happened which did not happen (cf. (50, p. 243) and (51, p. 179)). Today, the scholastic term "infuturability" would be called "counterfactual."
"Let us be more specific. Here, the meaning of the terms local and global will be understood as follows. In quantum mechanics, every single orthonormal basis of a Hilbert space corresponds to locally comeasurable elements of physical reality. The (undenumerable) class of all orthonormal basis of a Hilbert space corresponds to a global description of the conceivable observables -- Schrödinger’s catalogue of expectation values (52). It is quite reasonable to ask whether one could (re)construct the global description from its single, local, parts, whether the pieces could be used to consistently define the whole. A metaphor of this motive is the quantum jigsaw puzzle depicted in Figure 6. In this jigsaw puzzle, all legs should be translated to the origin. Every single piece of the jigsaw puzzle consists of mutually orthogonal rays. It has exactly one "privileged" leg, which is singled out by coloring it differently from the other (mutual) orthogonal legs (or, alternatively, assigning to it the probability measure one, corresponding to certainty). The pieces should be arranged such that one and the same leg occurring in two or more pieces should have the same color (probability measure) for every piece.
"As it turns out, for Hilbert spaces
of dimension greater than two, the jigsaw puzzle is unsolvable. That is,
every attempt to arrange the pieces consistently into a whole is doomed
to fail. One characteristic of this failure is that legs (corresponding
to elementary propositions) appear differently colored, depending on the
particular tripod they are in! More explicitly: there may exist two tripods
(embedded in a larger tripod set) with one common leg, such that this leg
appears red in one tripod and green in the other one. Since every tripod
is associated with a system of mutually compatible observables, this could
be interpreted as an indication that the truth or falsity of a proposition
(and hence the element of physical reality) associated with it depends
on the context of measurement (53; 54) ; i.e., whether it is measured along
with first or second frame of mutually compatible observables. It is in
this sense that the nonexistence of two-valued probability measures is
a formalization of the concept of context dependence or contextuality."