The problem is that we have to include the human brain. As stated lucidly by Asher Peres, "We work as if the world could be dissected into small independent pieces. This is an illusion, because, as Bell's theorem shows, the entire world is interdependent. But there is no other way of working. (...) One may speculate whether, in a complete description of the whole Universe, including our brains, determinism would be restored." [A. Peres, "Existence of "Free Will" as a Problem of Physics", Found. Phys. 16(6) 573 (1986), p. 580]. But what is the problem with the physics of brain? I call it 'the brain catastrophe'. There are many "catastrophes" in physics, which have never happened. Max Planck tried to explain why the so-called ultraviolet catastrophe has never happened, and a new, quantum physics was born. (Not surprisingly, his ideas were not embraced by the established physical community at that time.) There is another catastrophe, related to the vacuum energy density, which too has not happened. For example, if we take the vacuum energy density, cut-off at Planck scale, to be 10^{94} g cm^{-3}^{ } -- which is roughly 10^{123} times larger than the present observation! -- then the cosmic microwave background radiation would have cooled below 3K in the first 10^{-41} s after the (putative) Big Bang, and expansion rate (Hubble parameter) would be about a factor of 10^{61} larger than that observed today (E.W. Kolb and M.S. Turner. The Early Universe. Addison-Wesley, Menlo Park, CA, 1990). Obviously, the answer to the question of why this catastrophe has not happened is one of the greatest challenges we are facing today. Is there a similar "catastrophe" in the brain? A simple example, to get started, can be derived from well-established neurophysiological findings (Chris Nunn, A computational conundrum, Q-Mind Digest, 27 June 2000): an action potential can run with the speed of up to 250 miles per hour along any of 10,000 to 100,000 connections [John Parnavelas, The Human Brain: 100 Billion Connected Cells. In: From Brains to Consciousness? Ed. by Steven Rose, Penguin Books, London, 1999, pp. 18-32], and in many cortical synapses the probability for neurotransmitter release, at a pre-synaptic terminal, can be as low as 30 per cent. To be specific, think of the brain of a batter, in his default mode and in the case of his extremely fast reaction to the incoming ball, measured in thousandths of a second. Now, imagine a compilation of errors for "correct transmission" in all neural networks in his brain, and an immediate cascade or dominoes-like effect spreading over the whole brain. No, such disasters do not happen. They must happen though, if we consider the brain as a machine, but are somehow avoided by some unknown physics of life. Hence we have two alternative options: either to assume that some immaterial ghost or other mystical entity (e.g., Eccles' psychons) has taken control over our brains, or to seek new physics. I certainly choose the second option and suggest a special propensity-state of the brain, in the putative global-time mode of the Universe (called John-state). It is a physical entity and can act on matter, included the grey one, creating the unique faculty for 'action on itself' -- we think about our brain, with our brain, but the brain does not violate the relativistic causality (no superluminal causal influences in the local time, as read with a physical clock). As to the human mind, I conjecture that it is a mental reflection (qualia) from the John-state of its brain. It is a genuine non-local entity, as explained below. Due to the lack of space, I will not go into the next tasks, those of the so-called hard problem and the doctrine of trialism, but will focus exclusively on the physics of human intention (D. Chakalov, Plasma magic? Q-Mind Digest, 12 November 2000). Neither classical nor quantum physics can explain what I call 'brain catastrophe', for different reasons, hence the only option available for revealing the physics of life is quantum gravity. The first hurdle on the road is, I believe, the collapse of wave function, keeping in mind also other "catastrophes", such as the vacuum catastrophe, which too has to be explained with quantum gravity. It is widely believed that the so-called collapse of the wave function can be either instantaneous or of finite duration. The first option is explored in standard texts in quantum mechanics: "Afterwards the system is in that particular eigenstate, selected from the original superposition, which corresponds to the eigenvalue actually obtained as the result of that measurement" (John Polkinghorne). We cannot, however, use temporal notions "before" and "after" the collapse, simply because we cannot logically relate things that do not exist: before the collapse there is no event, while after the collapse there is no quantum wave. Also, it is painfully clear that these two options run into insurmountable difficulties. The main question is: when does the quantum system jump into its eigenstate? Before, during, or after we measure its eigenvalue? If by 'before', 'during' and 'after' we imply the time read with a clock in an inertial frame -- and we simply do not have any other choice -- then it turns out that the question is ill-posed. There is no answer to it, simply because the standard QM is based on a "global", non-relativistic Newtonian "time", which has nothing to do with the theory of relativity. We can't mix apples with oranges, as explained by Erwin Schrödinger seventy years ago. (If it were possible, in Bohmian mechanics, to map the hidden "time" of quantum trajectories to the one read with a physical clock, as defined in General Relativity, I wouldn't be writing these lines.) There is a third option, explored at this web site, which employs the logical possibility of two components of time, global (non-relativistic, unphysical, and absolute) time and local (physical) time, as explained with John's jackets parable. I believe this new idea about time is essential for theoretical physics, brain science, and psychology. In essence, the theory has been proposed by Henry Margenau in 1940; the modifications suggested here are that a quantum state is a real entity in the global time only (called John-state), and with a new (to physics) ontological status resembling that of cognitive structures known as universals and Platonic ideas. (Every time physicists use math, they operate with Platonic ideas which do not change and are real in the sense explained above.) At a given value of the local time, as read with a physical clock defined in GR, the quantum systems has propensities to produce certain events, explicated in the local time (called John's jackets or 'interpolating states', A. Peres), with certain probabilities "during" the interaction with a macroscopic device. The lack of a global and unique time variable in the relativistic domain, as well as the relativistic causality rendering superluminal signaling unphysical (D. Beckman et al., quant-ph/0102043), do not permit a complete physical observation of any quantum system in its John-state. Just its localized 'jackets', in their local reference frames, but these 'jackets' can not represent the complete John-state due to Heisenberg relations excluding simultaneous observation of non-commuting observables. Strictly speaking, there is no time observable nor perfect clock. Hence a new theory of spacetime, with two components of time, is believed to be the only possible solution to the problem identified by Erwin Schrödinger seventy years ago, and then (hopefully) for developing a theory of quantum gravity, since it provides an essential division (Schnitt) between the system under study (John's jackets) and the rest of the Universe, in her John-state. The latter is a special ONE stateplaying the role of 'chooser' in quantum world. Hence it is possible not only to eliminate the intrusion of the observer in QM (cf. below) but also to avoid all logical, Catch-22 type contradictions in quantum cosmology: there can be no physical laws in the Beginning, referring to a still-not-existing classical world. Just pure math and cognition (also known as [John 1:1]). The initial idea is based on a simple, and certainly not original, suggestion for solving the first Zeno paradox -- the global time of John is inserted "between" the static snapshots of John's jackets, but we can not observe John with inanimate (dead) devices because of the so-called speed of light (with our brain -- maybe, but that's an open question pending experimental verification). Then I employ Leibnitzian harmonia praestabilita and Jung's principle of synchronicity (Carl Gustav Jung. Synchronizität als ein Prinzip akausaler Zusammenhänge. In: Carl Gustav Jung and Wolfgang Pauli, editors. Naturerklärung und Psyche. Rascher, Zürich, 1952), and offer simple interpretations of: (i) the unphysical unitary "evolution" of quantum systems: a peaceful co-existence of pure states (called here jackets) "during" von Neumann's Process II (The Mathematical Foundations of Quantum Mechanics, Princeton UP, Princeton, NJ, p. 351) is possible in the global time only; the mixed state just describes the lack of knowledge about the pure state it is in, cf. D. Aerts, quant-ph/0105109 and N.D. Mermin's "instruction sets"; (ii) the so-called collapse of state vector: an artifact of the geometry of spacetime, associated with non-living devices (the apex in spacetime cone can't accommodate more than one event); (iii) Schrödinger's cat and the double-slit experiment; (iv) the anthropic approach to cosmological constant problems (e.g., A. Vilenkin, hep-th/0106083) and the "miraculous" fine tune-up of the initial boundary conditions and other "coincidences", giving rise to life and intelligent observers: the accuracy of pinpoiting our Universe is one part in 10^{1230} (Roger Penrose; cf. also Lee Smolin); (v) the inevitable disappearance of the local time in background-independent theories and the notorious problem of time in quantum gravity: the evolution of the gravitational field should be given in terms of the global time, hence keeping together the foliation-independence and a preferred, albeit unphysical, reference frame for solving the problem of time; and (vi) the emergence of time and space in quantum gravity (C.J. Isham and J. Butterfield, gr-qc/9901024). But what is the nature of the global time? It is a component of time, together with the local time, of the putative universal time arrow. It is not something eternal. Not at all. It is a manifestation of a special ONE state of the whole physical universe, which irreversibly gains information after each and every step of the universal time arrow, being linked to God [John 1:1-4], examined here as the "source" of creatio-ex-nihilo. Specifically, I assume that there exists an infinite pool of unknown data and events, which may or may not happen, and which is stored in the "source" of creatio-ex-nihilo. Recall that we have information about 'things we know' and 'things we know that we don't know', but at a given instant of time we know nothing about 'things we still don't know that we don't know'. As John A. Wheeler put it, "Time is Nature's way to keep everything from happening all at once." (J.A. Wheeler, "Time Today", in Physical Origins of Time Asymmetry, J.J. Halliwell, J. Pérez-Mercader, and W.H. Zurek, eds., Cambridge UP, Cambridge, 1994, p. 1). Hence in order to explain time, we somehow have to "insert" the presumably infinite pool of unknown data and events, which is the reason for introducing a component of time, called here global time. This certainly needs explanation. Perhaps the best way to explain the nature of global time is by examining the phenomenon of entanglement (Verschränkung, Erwin Schrödinger). A clear mathematical and physical explanation can be found in Sec. "The Idea of Entanglement" in Chris Isham's Lectures on Quantum Theory. The last paragraph of this wonderful book reads: "The central issue in all this is really the phenomenon of quantum entanglement, and its striking contrast with the reductionist concepts of Western philosophy." See also Erast Gliner's Deon, distant entangled object, in gr-qc/0006072, and Ghirardi & Marinatto's "Entanglement and Properties". An explanation for pedestrians is offered by Nick Bigelow [Quantum engineering: Squeezing entanglement. Nature 409, 27-28 (2001)]: "Quantum entanglement between two particles is a spooky connection that means measuring one has an instant effect on the other. Connecting many atoms in this way would be the first step towards a quantum computer. "If a street magician with two identical coins told you he could predict which way up your coin would land -- heads or tails -- simply by tossing his coin first, you probably wouldn't believe him. But what if he told you that, because of the laws of physics, your toss had to turn out the same as his toss? Not convinced, you try it and find that, yes, it is true. And it remains true, time after time, toss after toss. By some mechanism, there is a surprising correlation between the behaviour of the two coins. What's going on? Well, it could be that these two coins have somehow been prepared in a remarkable quantum state known as an entangled state." If we were two-dimensional creatures residing in a 2+1-dimensional Flatland, we would be extremely puzzled by some spooky correlations of two or more events, caused by some mysterious 3-D object, which can also be "simultaneously" in two or more locations, and we would never be able to comprehend "how come the quantum", i.e., how is it possible that two or more things can be 'both many and one' (D. Bohm, Quantum Theory, Prentice-Hall, New York, 1951, Ch. 8, § 24). We can, of course, use tensor calculus and introduce some 'intrinsic' (or local) time, and hence avoid the global-time mode of the mysterious 3-D object (called otherwise 'ether') and a non-physical absolute reference frame, but then we will find out that "there is no time observable!", and our Flatland physicists will encounter the problem of time. This spooky ONE state, which provides the "instantaneous" correlation of two entangled states, resides in the global time only. I'm going here into the roots of the measurement problem in quantum mechanics, which is the central issue in many interpretations of QM, as well as in all research programs for quantum computing. This ONE state can not be observed nor manipulated with inanimate (dead) measuring devices, which renders an error-free quantum computing impossible. What we do, in our brains, can not be reproduced with dead machines. I will
offer a simple demonstration of the global-time mode of the human
brain. Look at the picture below, and think of two 'John's jackets',
|dead cat> (two faces) and |live cat> (vase), in the context
of the famous Schrödinger's cat.
However, can we think of some gauge field and gauge invariance that could provide invariant presentations of the John-state as |dead cat> (two faces) or |live cat> (vase)? The John-state is like a Platonic idea stored in the ONE state of the whole Universe. Once created, it does not change. Can we find the physics here? It is extremely difficult even to think of 'two or more things being both many and one'. Explaining the notion of "spin", for example, Wolfgang Pauli managed just to coin a new phrase, klassisch nicht beschreibbare Zweideutigkeit. To summarize, I conjecture that the so-called probability waves from quantum mechanics propagate in the global time only (no empty waves or Gespensterfelder for that reason). Same holds for the gravitational field, as stated in (v) above. In Einstein's General Relativity, the non-existence of a gravitational field stress-energy in the right-hand side of the field equations (and subsequently the purely geometrical interpretation of gravity as some sort of "curvature" of space-time) is due to the nature of global time, I suppose. As acknowledged by Albert Einstein, General Relativity is not a complete theory: "The right-hand side includes all that cannot be described so far in the Unified Field Theory, of course, not for a fleeting moment, have I had any doubt that such a formulation is just a temporary answer, undertaken to give General Relativity some closed expression. This formulation has been in essence nothing more than the theory of the gravitational field which has been separated in a somewhat artificial manner from the unified field of a yet unknown nature." (Surely Einstein was aware of the criticism by David Hilbert (David Hilbert, Die Grundlagen der Physik, Mathematische Annalen, Heft 92, S.1-32, 1924): "I assert that for the general theory of relativity, i.e., in the case of general invariance of the Hamiltonian function, energy equations corresponding to the energy equations in orthogonally invariant theories do not exist at all. I could even take this circumstance as the characteristic feature of the general theory of relativity." Quoted after: A.A. Logunov and Yu.M. Loskutov, Nonuniqueness of the predictions of the general theory of relativity, Sov. J. Part. Nucl., 18(3), May-June 1987, p. 179-187. Hence the conservation laws for energy, momentum, and angular momentum are in principle impossible, as shown by Anatol Logunov; for more references, click here.) Locally, the effect of the global-time mode of the Universe, called ONE state, is completely wiped out (I examine the case of inanimate matter only, in the macro-scale of 'tables and chairs'), and we can physically observe, with inanimate devices, just localized jackets in out past light cone, post factum only. A Machian-type Universe, in which the mass of physical bodies is determined dynamically by 'everything else in the Universe' -- the very same 'chooser' operates in the quantum world -- thus selecting one familiy of spacelike surfaces for one instant of the local time (cf. (v) above), can be designed only with some unphysical bootstrapping web, which I simply call global time. It is natural to expect that it will not be present in Einstein's General Relativity, which deals with physical jackets only, and also that the hypothetical "event horizon" and hence "black holes" may not exist at all, in a complete theory of quantum gravity. It is also natural to expect that one could find many more blueprints on the local time physics, left from the global-time mode of the Universe. As suggested by Chris Isham fifteen years ago, instead of quantizing gravity, one should seek a quantum theory which yields General Relativity as its classical limits (A. Davies and D. Sutherland, eds. Superstrings and Supergravity. Proceedings of 28th Scottish Universities Summer School in Physics. SUSSP, Oxford, 1986, p. 8). I can't think of any better way to provide a common denominator for QM and GR but by reconciling the principle of superposition (M. Tegmark and J.A. Wheeler, quant-ph/0101077, cf. Fig. 1) with general covariance. In both cases we're dealing with 'jackets' only, which do not have any individuality of its own. Only in the limiting case of classical mechanics, where the John-state can be safely ignored (Planck constant set to zero), we obtain the notion of 'objective reality out there'. Put it differently, the global time component of the universal time arrow, producing the ONE state (or John-state) of the whole Universe, can start from a very narrow John-state (quantum die, cf. Einstein's saying "God casts the die, not the dice"), accommodating effectively one jacket only, in which case we obtain classical mechanics and classical GR. It remains to be revealed what happens toward the other limit, and what could be the hierarchical structure of all John-state(s), perhaps resembling that of our cognitive structures. I will try to use some elementary math here: I conjecture that the 'volume' of the 'quantum die' or John-state varies in the open interval (0, infinity) , and hence what we call 'entanglement' can be safely ignored only in the limiting case of 'John-state approaching zero'. This is a very difficult notion to comprehend, however, because, if we use the example with Flatland (please see above), we have to think of entanglement as an effect of spacetime geometry which is smearing the individuality of objects on Flatland gradually, and by approaching the other limit, that of 'John-state approaching infinity', all objects on Flatland will be effectively "fused" into ONE state. As to theologians, perhaps they will argue that the case of 'John-state being strictly zero' is indistinguishable from 'John-state being strictly infinity', and that these two totally unphysical boundaries describe the physics of God. When our physical jackets deteriorate, they die, but where do we go? As a bonus, I have a model for brain dynamics which incorporates anticipation and feedforward from the outset, and is based on the solution of mind-body problem suggested by Wolfgang Pauli and Carl Jung more than fifty years ago. I've suggested just a new term for it, trialism. After twenty years of constant efforts, I have sufficient reasons to consider this project completed with success. It was an entirely private initiative (and obsession). No educational, research, private, or government institution has ever supported it, in any way whatsoever. No surprise, since I suggest to look to neurons rather than multi-billion-dollar accelerators for progress in physics. Who cares about taxpayers' money? There is a long list of individuals who helped me, on purely private basis, with their preprints and moral support. If I manage to publish my manuscript Physics of Human Intention (most likely on CD ROM), I will mention all of them. I will also try to explain there my ideas on the most important issue: the emergence of space and time in the universal time arrow, with two components of time, global and local. This will be highly speculative stream of thoughts, with references to some non-smooth topological transitions of the global-time mode of the Universe, which are supposed to 'project' instants "now" of the local time. The aim is to suggest a dynamical (in the global time) description of the peculiar "speed" of light, which is hiding the "duration" of preparation of the physical snapshots from the local time, and serves as a numerically finite but physically unattainable cut off or "boundary" of the physical part of the Universe, in its local-time mode. The idea, again, is not new at all; it is the old story about the Dragon chasing its tale. Once created [John 1:1], the Universe can not reach its "end" in the local-time mode, nor it is possible to trace its creative, non-unitary evolution in the local time back to the Act of Creation. It is logically impossible to reach something that is residing eternally inside you. Hence the new notion of 'logical infinity' suggested for the local-time mode of the cosmological time. Last but not least, let me say a few words about three popular collapse-free theories. Everett's interpretation of QM: Apart from schizophrenia, I don't see any relevance to brain science. Also, see Q23 in How do probabilities emerge within many-worlds?, by Arnold Neumaier. On the other hand, it could serve as a very helpful tool for explaining the idea of John's jackets, because the conservation of probability current is explicitly violated "during" the creative talk between John's jackets and their John-state. Cramer's transactional interpretation of QM: The atemporal hand-shaking medium, resembling the global-time mode of the Universe, does not create an arrow of time. The offer wave and the confirmation wave are completely canceled, producing a frozen snapshot of the Universe. See Quantum Interactions on Null Surfaces by Kevin Brown, and compare it with Ulric Neisser's cognitive cycle. And finally, Bohmian mechanics: I wish I knew how to find the 'active information' (B.J. Hiley et al., quant-ph/0010020) in the brain. Another problem is the back-action: Bohm's pilot wave can not accommodate any recoil from the guided particle, while the process of learning does include "back-action", as a two-way dialogue between John's jacket (e.g., an apple in the local time) and its Platonic idea (John-state, in the global time) of an apple per se. Apart from these difficulties, I regard Bohmian mechanics as the best source for insights, first because of the idea of pre-space, which is very close to the ideas of Pauli and Jung. In a recent paper, entitled Non-commutative Geometry, the Bohm Interpretation and the Mind-Matter Relationship, Basil Hiley wrote (Sec. 8): "What I have tried to argue above is that for quantum processes space-time is not the basic manifold in which quantum processes evolve. The basic process unfolds in this pre-space, which is not subject to the Cartesian division, res extensa-res cogitans. What I want to suggest that it is in this pre-space that mind and matter appear as different aspects of the same underlying process." The manuscript is available in PDF format from Prof. Hiley's web site at http://www.bbk.ac.uk/tpru/BasilHiley.html . To sum up, any of the three interpretations above, as well as any modal interpretation of QM, can be potential candidate for solving the brain catastrophe and mind-brain problem. I decided to try it with the standard QM, and I'm fully open to suggestions (1 Thess. 5:20-22). I sincerely welcome all questions, comments, and suggestions. The whole web site (626 KB, font Verdana included) can be downloaded from http://members.aon.at/chakalov/chakalov.zip
After unzipping into an empty folder,
please open index.html
with your web browser.
Printed below is my email from May 8th to fifty-two theoretical physicists. Pay attention to highlighted text (red).
D. Chakalov dchakalov@surfeu.at
Wednesday, 9 May 2001
------
Dear colleagues, May I request your opinion on the task stated in the subject of this email. Regarding the intrusion of the observer in QM, in a recent update of quant-ph/0011086 [Ref. 1], Bruce Rosenblum and Fred Kuttner wrote: "Physicists appropriately seek the least astonishing solution." I believe the least astonishing solution is to reconcile QM with STR. The problem: Since there are no events in quantum theory [Ref. 2], and the "instantaneous" collapse supposedly implies some preferred reference frame, as well as energy nonconservation and other untractable divergencies [Refs. 3-5], it seems to me that the task is by no means trivial. After seventy years of efforts, we still do not have a relativistic QTM [Ref. 6]. If so, we should seek novel ideas, and I believe the first choice is to abandon the two assumptions about the "duration" of the collapse, instantaneous or finite duration, and to explore the logical possibility of 'both - and' , http://members.aon.at/chakalov/readme1st.html It seems to me that this logical possibility leads to the idea of two kinds of time, global (unphysical and absolute) and local (physical), and the task is to embed the latter into the former. As a bonus, you might get the 'chooser' in QM, http://members.aon.at/chakalov/right.html#Note_2 http://members.aon.at/chakalov/right.html#crux which might (hopefully) be traced back to the emergence of the Universe, hence eliminating not only the observer in QM but also the anthropic principle and the "superluminal" correlation of CBR temperature fluctuations [Ref. 7]. Please excuse my intrusion into your field of professional expertise. Looking forward to hearing from you, Dimi
References [Ref. 1] Bruce Rosenblum,
Fred Kuttner. The Observer in the Quantum Experiment. Date (revised v2):
Mon, 7 May 2001 21:17:17 GMT,
"The observations encompassed by classical physics allowed the complete exclusion of a role for the observer. The world view suggested by the quantum experiment either challenges that exclusion or suggests new physical phenomena. There are hints of a different view of reality, and "[It is] likely that the new way of seeing things will involve an imaginative leap that will astonish us" [J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge Univ. Press, Cambridge, England, 1987, p. 27]. "Physicists appropriately seek the
least astonishing solution."
[Ref. 2] Anthony Sudbery. Diese verdammte Quantenspringerei. http://xxx.lanl.gov/abs/quant-ph/0011082 Anthony Sudbery: "A related problem
is that of relativistic invariance. A theory based on transitions between
states of the world requires these states to be defined universally at
each instant of time, and therefore has a definition of simultaneity built
in; in other words, it has a preferred frame of reference. Since the theory
makes the same predictions as conventional relativistic quantum field theory,
this frame of reference would not be experimentally distinguishable from
any other frame related to it by a Lorentz transformation, but as Bell
conceded in the final sentence of {Bell:beables}, "It seems an eccentric
way to make a world."
[Ref. 3] Stephen L. Adler,
Todd A. Brun. Generalized stochastic Schroedinger equations for state vector
collapse.
Stephen L. Adler and Todd A. Brun:
"The local equation has the defect that it leads to a divergent rate of
energy nonconservation in generic field theory models, indicating that
new ideas will be needed to achieve a satisfactory relativistic state vector
collapse model."
[Ref. 4]
GianCarlo Ghirardi. Local measurements of nonlocal observables and the
relativistic reduction process.
GianCarlo Ghirardi: "Our main concern
here will be the analysis of statevector reduction in a relativistic quantum
context and the identification of the basic features which any relativistic
reduction mechanism must exhibit.
See also: Paul
Busch. EPR-Bell Tests with Unsharp Observables and Relativistic Quantum
Measurement.
Paul Busch: "The crucial point lies
in making a difference between quantum mechanical objectivity, or value
definiteness, which can spread to spacelike distances, and relativistic
nonobjectivity, which pertains until the observers enter the forward lightcone
(causal future) of the measurement event.
[Ref. 5] Philip Pearle. Wavefunction
Collapse and Conservation Laws. Found. Phys. 30, 1145 (2000).
Philip Pearle: "It is emphasized
that the collapse postulate of standard quantum theory can violate conservation
of energy-momentum and there is no indication from where the energy-momentum
comes or to where it goes."
[Ref. 6] Erwin Schrödinger (1931). Specielle Relativitätstheorie und Quantenmechanik. Sitzungsber. Preuss. Akad. Wiss., phys.-math. Kl., Bd. 12, S. 238-247. See also: Asher
Peres. Classical interventions in quantum systems. II. Relativistic invariance.
"It thus appears that the notion
of quantum state should be reassessed. There are two types of states: first,
there are physically meaningful states, attached to spacetime points with
respect to which no classical intervention has a spacelike location. Then,
between any two such points, we may draw a continuous timelike curve and
try to attach a quantum state to each one of the points of that curve.
These interpolating states can indeed be defined as shown in the present
article, by considering a set of parallel spacelike hyperplanes. However,
states defined in such a way are merely formal mathematical expressions
and they have no invariant physical meaning."
[Ref. 7]
Edward W. Kolb. Dynamics of the Inflationary Era.
Edward W. Kolb: "One of the striking
features of the cosmic background radiation (CBR) temperature fluctuations
is the growing evidence that the fluctuations are
acausal. The CBR fluctuations
were largely imprinted at the time of last-scattering, about 300,000 years
after the bang. However, there seems to be fluctuations on length scales
much larger than 300,000 light years! How could a causal process imprint
correlations on scales larger than the light-travel distance since the
time of the bang? The answer is inflation." |