In respect to cosmology, some would say that the Copenhagen Interpretation isn’t good due to the fact that there is no outside [classical] observer. So, how would you generalize quantum mechanics in a way that you can deal with cosmology as a whole and not just in a limited region?
The best attempt, in this case, would be to consult the best-known individuals that have been working on this problem, James Hartle and Murray Gel-Mann. I have looked up one of their papers on arxiv. Going back to 2006, there was a Solvay Conference where Hartle was invited to give a talk about this issue. One topic at the conference was on the quantum structure of space and time.
http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is a minimal set of principles for quantum theory abstracted from the modern quantum mechanics of closed systems, most generally the universe. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory allow for the further generalization that would be necessary were spacetime not fundamental. Emergent spacetime phenomena are discussed in general and illustrated with the example of the classical spacetime geometries with large spacelike surfaces that emerge from the `no-boundary’ wave function of the universe. These must be Lorentzian with one, and only one, time direction. The essay concludes by raising the question of whether quantum mechanics itself is emergent.
31 pages, 4 figures, contribution to the 23rd Solvay Conference, The Quantum Structure of Space and Time
Can you solve this problem within a fixed space with a fixed geometry? The geometry must be quantum and it must interact dynamically with the quantum matter that lives in it. And there is no outside where an observer can see a wave function collapse. Everything in the model is quantum and contained in the universe which could, for example, either be contracting, condensing, rebounding or re-expanding. I have no idea what Hartle meant by “…spacetime geometry is fluctuating”. Perhaps, it has no meaning outside of context. Maybe it would’ve been better had he uttered “indefinite”?
http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value.
A spacetime geometry history is intuitively akin to the trajectory of a particle. One cannot say, with certainty, which slit of shape it went through. Rolling on an assumption, I’m guessing that what Hartle means. He certainly does not introduce a “meta-time” in which the geometry oscillates. Basically, he’s talking about quantum uncertainty applied to spacetime geometry.
In relation to Copenhagen, you need to realize that an interpretation of quantum mechanics is “a statement which attempts to explain how quantum mechanics informs our understanding of nature”. The well-known “shut up and calculate” formulation attempts to do no such thing, therefore, it is not an interpretation. Stating otherwise simply means that one is not interested in interpretations and you don’t understand them. Understand that what I just typed previously is a prejudicial viewpoint that some physicists hold against engineers, in reference to what is known as the “shut up and calculate” formulation.
Now, you also have what is known as positivism in which quantum mechanics is only about the results of measurements and not about the reality existing without measurements. Essentially, it was the philosophy of Bohr. Positivism, as a concept, was effectively “disproved” (Is this philosophically possible?) back in the late 1960s. However, it did not end there. Positivism fails to prove that there are not abstract ideas, laws and principles beyond particular observable facts, relationships and principles of necessity, or that we cannot know them. Positivism ignores all humanly significant and interesting problems, citing its refusal to engage in reflection; it gives to a particular methodology an absolutist status.
There’s another one–the collapse interpretation. This is when the measurement is performed then the wave function collapses. Usually, it’s taken to require that the wave function represents an objectively-existing physically real wave field, which instantaneously collapses at an infinite speed. It sort of implies something in the realm of the Ghirardi-Rimini-Weber theoretical viewpoint. Now, if you recall in the Bohm-view, things are made of particles and those particles are guided by the wave so even though the objectively-existing real field (mathematically represented by the wave function) never collapses and particular branches are picked out by whichever one the particles deterministically end up in.
Don’t forget information interpretation. Some think the wave function does not represent reality but only the information about reality. Quite simply, this cannot be correct. In experiments regarding matter-wave optics, for example, you’ll find that it is possible to diffract, reflect, focus and interfere to do stimulated emission with the wave field–what is mathematically represented by the wave function. Clearly, this is experimental evidence for the objective existence of the wave. Now, if the wave can be subjected and utilized in such a process it logically follows that the wave field must exist in order to act and be acted upon. For instance, think of the two-slit experiment; it is not possible for a field representing “information” or “knowledge” to interfere with itself and to behave like it satisfies a wave equation if it does not in fact represent a real wave.
Any claims that the Copenhagen interpretation must be the logically preferred interpretation [for right-thinking physicists] cannot be correct. Then again, I’m an engineer–a research engineer–it’s not up to me to come to the defense of these physicists. Nevertheless, such claims often have their basis stemmed in a misunderstanding of what Copenhagen means but also from not giving a thought or two about the alternatives or from uncritical hero worship of [just insert the name of a scientist from the 1920s here]. In today’s world, it is untenable to regard the views of Bohr and Heisenberg in any sense of the word as standard or canonical. More like smoke and mirrors.
Let’s take this to another level as far as measurements and the Copenhagen interpretation go.
Say you have a system that’s a superposition of two states:
How exactly do you measure a system? Some would say by interacting with it but I don’t want to make the same mistake as Weinberg did. Weinberg would make the mistake in assuming ontological status to both the collapse of the wave function and to entanglement within the Copenhagen interpretation. A subtle mistake that it is, still in the distinction being made between a classical and quantum mechanical description of the measuring device.
The act of measurement is an interaction and it creates entanglement between the measuring device and the measured system. But entanglement itself is not a physical property of a system but rather a property of the system’s description in particular how the system is subdivided into component subsystems.
As to Weinberg’s critique of the Copenhagen interpretation:
Steven Weinberg in “Einstein’s Mistakes”, Physics Today, November 2005, page 31, said:
All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.
Where he says “this is surely wrong…”, he makes the mistake of identifying the laws governing the behavior of the physical system with the choice of the description of the system. The classical description of the moon is not wrong because it fundamentally obeys quantum mechanical rules. Rather, it is less than maximal. The critical issues is that we desire to speak in terms that are absolute about a specific outcome of a measurement. It dictates a classical description of the record of this measurement; there must be a classical/quantum cut between the piece of paper on which one writes down the result and the actual system for which this measurement is recorded.
Where Weinberg states that the act of measurement is treated classically in Copenhagen interpretation “which is obviously false”–that statement is false. The record of the measurement is what’s treated classically, or, at worst, the gross variables of the position and velocity of the measuring device, where applicable. The act [which is the variables of the measuring device interacting with the system] is left without detailed description except that it must obey the rules of quantum mechanics, i.e., one must be able to re-measure the system immediately and obtain the same result for the act to be called a “measurement”.
Where Weinberg speaks of the wave function evolving in a perfectly deterministic way and asks from where the quantum probabilities come, he is confusing subtly the wave function with the physical system. The probabilities were there from the beginning. The probabilities are what the wave function is modeling.
As to his problem with the Copenhagen interpretation [in regards to quantum cosmology], one could assert that it is the problem with quantum cosmology and not the Copenhagen interpretation in that it is ridiculous and meaningless to describe a wave function for the “universe as a whole” beyond a very trivial one of a one-dimensional mode space.
As far as the quantum treatment of the measurement process, remember, that measurement is a dissipative process. It is fundamentally an act of amplification and requires an entropy dump (heat sink). The “meta-system” of system + measuring device must then described within the parameters of quantum mechanics using density operators wherein both classical and quantum probabilities may be expressed. The “meta-system” evolves and quickly decoheres into a composite system with classical correlation between the measuring device with the appropriate record of possible outcomes in a classical set of probabilities which correlate with the various “collapsed” wave functions of the measured system. The entanglement gets shifted into the entropy dump.
That is the measurement process and it cannot be significantly altered without invalidating the device as the measuring device.
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