Write4u, here are a few more thoughts on wave function collapse.
Wavefunction collapse is an explicitly non-unitary time evolution of whatever wavefunction is under consideration and that is what is sometimes controversial. Schrodinger's equation tells us that systems evolve unitarily and wavefunction collapse tells us that systems evolve non-unitarily.
One major criticism of the Copenhagen interpretation is that it doesn't clearly explain when the universe follows the unitary evolution and when it follows non-unitary evolution. That makes it an incomplete theory at best.
Anyways, only unitary evolution --- often goes under the name the Many Worlds Interpretation of quantum mechanics. However I think this is a pretty bad misnomer as it gets pretty scifi pretty quick and people start talking about divergent universes etc. when what is going on is really just as you describe, the universe is just undergoing unitary evolution which leads to entanglement and superposition states.
As far as we* know the universe has subjective components as well. For example, I have a feeling or experience what it feels like to observe an electron in the spin up state (perhaps I have an apparatus that lights up a different colored light depending on the spin state measured by some spin measuring apparatus).
Suppose we have a pair of totally anticorrelated photons. You measure one of them, then you'll know the outcome of the other one. The phrase "the measurement simultaneously affects the other particle" is not physical, because until you actually measure the other particle, you can't even notice anything different. There is no "effect". The only thing we can meaningfully talk about is the two measurements of the two particles. Now, depending on the reference frame, one will come before the other (or they are simultaneous) and whatever we measure, one result will imply the other.
Bell's theorem explains that if you try to simulate an entangled quantum system by modelling a quantum system with a classical stochastic variable the result has to be non-local. However, quantum systems described by Heisenberg picture observables, which are represented by Hermitian operators, not classical stochastic variables. The particles each exist in multiple versions that can interact with one another in interference experiments, which is why they can't be described by classical variables. Each particle's observables describe quantum information about the relations between the different versions of each particle, but this information can't be revealed by measurements on either particle alone.
This is why I think that the term "the particle simultaneously affects the other particle" is not very good, because it implies something like an active link - but depending on the reference frame particle A would affect particle B or the other way round. There is no "one particle affecting the other". Only if you are in a specified reference frame, it looks like there is an immediate influence of one particle on another.
I think most modern physicists would probably subscribe to the idea that our subjective thoughts are correlated with the physical state of our brains and bodies. In fact, we might go so far as to suppose that mental states a one to one with physical states.
Your interpretation is not compatible with this naive dualist perspective. Concerning the interpretation that a person's body would be in a superposition of having experienced both a spin up and spin down electron. What mental state would they be in? You could say it is random at the end of the measurement. Say the person's mind experiences spin up right after the measurement. But what about 10 seconds after the measurement? Supposing the wave function should still be a superposition of the person's body having seen up and down. So do the dice get rolled again to determine what the person experiences in this new instant? Is it random from instant to instant which experience we have?
Is there a rule that says if your mental state experiences spin down at the end of the experiment it will also experience spin down 10 seconds later despite the wavefunction having equal weight for both probabilities? If so our theory should probably be able to describe that rule.
Or is it somehow possible for a person to have multiple simultaneous, and contradictory experiences? This has implications for what is meant by one's personal identity.
What the many worlds interpretation fails to do is provide any account whatsoever for how physical states are correlated with subjective experience. This comes for free in classical physical theories so we typically don't think of this as being a desiderata for physical theories. This comes in classical theories because we can say the E&M fields which hit our eyeballs move charges in our optical nerves which affect the neurons in our brain, and because our mental states are correlated with the physical state of our bodies (possibly in a 1:1 way) it is clear that measurement results should cause us to experience particular things. It is not so clear quantum mechanically however. What the Copenhagen interpretation, or spontaneous collapse, does is to basically jam this correlation between mental and physical states back into the theory by hand by demanding that the system collapses into one state or the other so that we can avoid the conundrum of people having manifold simultaneous experiences.
In any case, there are many philosophical issues here that I'm not able to present in a very coherent way but I did want to share some of my thoughts and some references.
See: Decoherence and the Quantum to Classical Transition
by Maximilian Schlosshauer, © 2007. A great intro to decoherence that can help you avoid some traps that come with thinking about decoherence in the context of unitary evolution and the many worlds interpretation generally.
*Or at least I
The second proposed solution to the measurement
problem, affirms that wave functions are complete representations of physical systems but denies
that they are always governed by the linear differential equations of motion. The strategy behind this approach is to alter the equations of motion so as to guarantee that the kind of superposition that figures in the measurement problem does not arise. The most fully developed theory along these lines was put forward in the 1980s by Ghirardi, Rimini, and Weber and is referred to as “GRW”; it was subsequently developed by Philip Pearle and John Stewart Bell (1928–90).
According to GRW, the wave function of any single particle almost always evolves in accordance with the linear deterministic equations of motion, but every now and then—roughly once every 109 years—the particle’s wave function is randomly multiplied by a narrow bell-shaped curve whose width is comparable
to the diameter of a single atom
of one of the lighter elements. This has the effect of “localizing” the wave function—i.e., of setting its value at zero everywhere in space
except within a certain small region. The probability of the bell curve’s being centred at any particular point x
depends (in accordance with a precise mathematical rule) on the wave function of the particle at the moment just prior to the multiplication. Then, until the next such jump, everything proceeds as before, in accordance with the deterministic differential equations.
For isolated microscopic systems—those consisting of small numbers of particles—jumps will be so rare as to be completely unobservable. On the other hand, for macroscopic systems—which contain astronomical numbers of particles—the effects of jumps on the evolutions of wave functions can be dramatic. Indeed, a reasonably good argument can be made to the effect that jumps will almost instantaneously convert superpositions of macroscopically different states like particle found in A + particle found in B
into either particle found in A
or particle found in B
A third tradition of attempts to solve the measurement problem originated in a proposal by the American physicist Hugh Everett
(1930–82) in 1957. According to the so-called “many worlds
, the measurement of a particle that is in a superposition of being in region A and being in region B results in the instantaneous “branching” of the universe into two distinct, noninteracting universes, in one of which the particle is observed to be in region A and in the other of which it is observed to be in region B; the universes are otherwise identical to each other. Although these theories have generated a great deal of interest in recent years, it remains unclear whether they are consistent with the probabilistic character of quantum
mechanical descriptions of physical systems.
One of the important consequences of attempts at solving the measurement problem for the philosophy
in general has to do with the general problem of the underdetermination of theory by evidence. Although the various noncollapse proposals, including Bohm’s, differ from each other on questions as profound as whether the fundamental laws of physics
are deterministic, it can be shown that they do not differ in ways that could ever be detected experimentally, even in principle. It is thus a real question whether the noncollapse theories differ from each other in any meaningful way.
In a famous paper published in 1935, Einstein
, Boris Podolsky
(1896–1966), and Nathan Rosen (1909–95) argued that, if the predictions
of quantum mechanics
about the outcomes of experiments are correct, then the quantum
mechanical description of the world is necessarily incomplete.
A description of the world is “complete,” according to the authors (EPR), just in case it leaves out nothing that is true about the world—nothing that is an “element of the reality” of the world. This entails that one cannot determine whether a certain description of the world is complete without first finding out what all the elements of the reality of the world are. Although EPR do not offer any method of doing that, they do provide a criterion
for determining whether a measurable property of a physical system at a certain moment is an element of the reality of the system at that moment:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that physical quantity.
This condition has come to be known as the “criterion of reality.”
Suppose that someone proposes to measure a particular observable property P
of a particular physical system S
at a certain future time T
. Suppose further that there is a method whereby one could determine with certainty, prior to T
, what the outcome of the measurement
would be, without causing any physical disturbance of S
whatsoever. Then, according to EPR, there must now be some matter of fact about S
—some element of reality about S
—by virtue of which the future measurement will come out in this way.
EPR’s argument involves a certain physically possible state of a pair of electrons that has since come to be referred to in the literature as a “singlet
” state or an “EPR” state. Whenever a pair of electrons is in an EPR state, the standard version of quantum
mechanics entails that the value of the x
-spin of each electron
will be equal and opposite to the value of the x
-spin of the other, and likewise for the values of the y
-spins of the two electrons.
Assume that there is no such thing as action at a distance: nothing that happens in one place can cause anything to happen in another place without mediation—without the occurrence of a series of events at contiguous
points between the first location and the second. (Thus, the flipping of a switch in one room can cause the lights to come on in another room, but not without the occurrence of a series of events consisting of the propagation
of an electric current
through a wire.) If this assumption of “locality” is true, then it must be possible to design a situation in which the pair of electrons in the ERP state cannot interact with each other and in which, therefore, any measurement of one electron would cause no disturbance to the other. For example, the electrons could be separated by a great distance, or an impenetrable wall could be inserted between them.
Suppose then that a pair of electrons in an EPR state, e
1 and e
2, are placed at an immense
distance from each other. Because the electrons are in an EPR state, the x
-spin of e
1 will always be equal and opposite to the x
-spin of e
2, and the y
-spin of e
1 will always be equal and opposite to the y
-spin of e
2. Then there must be a means of determining, with certainty, the value of the x
-spin of e
2 at some future time T
without causing a disturbance to e
2—namely, by measuring the x
-spin of e
1 at T
. Likewise, it must be possible to determine with certainty the value of the y
-spin of e
2 at T
, without causing a disturbance to e
2, by measuring the y
-spin of e
1 at T
. By the criterion of reality above, therefore, there is an “element of reality” corresponding to the x
-spin and y
-spin of e
2 at T
; that is, there is a matter of fact about what the values of e
-spin and y
-spin are. But, as discussed earlier, it is a feature of the standard version of quantum mechanics that it is impossible to determine the simultaneous values of the x
-spin and y
-spin of a single electron, because the measurement of one always uncontrollably disrupts the other (see above The principle of superposition
). Hence, the standard version of quantum mechanics is incomplete. Parallel arguments can be constructed by using other pairs of distinct but mutually incompatible observable properties of electrons, of which there are literally an infinite
If the existence of an EPR state entails an infinity of distinct and mutually incompatible observable properties of the electrons
in the pair, then the statement that the EPR state obtains—because the EPR state does not specify a value for any such property—necessarily constitutes
a very incomplete description of the state of the pair of electrons. The statement is compatible with an infinity of different “true” states of such a pair, in each of which the observable properties assume a distinct combination of values.
Nevertheless, the information that the EPR state obtains must certainly constrain the true state of a pair of electrons in a number of ways, since the outcomes of spin measurements on such pairs of electrons are determined by what their true states are. Consider what sorts of constraints arise. First of all, if the EPR state obtains, then the outcome of a measurement of any of the above-mentioned observable properties of e
1 will necessarily be equal and opposite to the outcome of any measurement of the same observable property of e
2. In other words, whenever the EPR state obtains, the true state of the pair of electrons in question is constrained
, with certainty, to be one in which the value of every such observable property of e
1 is the equal and opposite of the value of the same observable property of e
There are statistical sorts of constraints as well. There are, in particular, three observable properties of these electrons—one of them is the x
-spin, and the others may be called the k
-spin and the l
-spin—that are such that, if any one of them is measured on e
1 and any other on e
2, the values will be opposite one-fourth of the time and equal three-fourths of the time.
At this point a well-defined question can be posed as to whether these two constraints—the deterministic constraint
about the values of identical observable properties and the statistical constraint about the values of different observable properties—are mathematically consistent with each other. In 1964, 29 years after the publication of the EPR argument, the British physicist John Bell showed that the answer to this question is “no.”
Thus, the EPR state implies a mathematical contradiction. The conclusion of the EPR argument, therefore, is logically impossible. It follows that one of the two assumptions on which the EPR argument depends—that locality is true (there is no action at a distance) and that the predictions of quantum mechanics regarding spin measurements on EPR states are correct—must be false. Since the predictions of quantum mechanics regarding spin measurements are now experimentally known to be true, there must be a genuine nonlocality in the workings of the universe
. Bell’s conclusion
, now known as Bell’s inequality or Bell’s theorem, amounts to a proof that nonlocality is a necessary feature of quantum mechanics—unless, which at this writing seems unlikely, one of the “many worlds” interpretations of quantum mechanics should turn out to be correct.
GRW, the Ghirardi, Rimini, and Weber theory, originated as an attempt to get away from the imprecise talk of "measurement" that plagues the orthodox interpretation.
GRW and all collapse theories want to reconcile the mathematics of quantum mechanics, which suggests that subatomic particles exist in a superposition of two or more states, with the measured results, which only ever give us one state. We can easily prepare an electron to have a spin
that is mathematically both
down, for example, but any experimental result will yield either
down and never a superposition of both states. The orthodox interpretation, or the famous Copenhagen interpretation of quantum mechanics, posits a wave-function collapse every time one measures any feature of a subatomic particle. This would explain why we only get one value when we measure, but it doesn't explain why measurement itself is such a special act.
GRW escapes the ideas that measurement is a special act or that some specific part of measuring a subatomic particle causes the particle's wave function to collapse. At the same time, GRW theory is compatible with single-particle experiments that do not observe spontaneous wave-function collapses; this is because spontaneous collapse is posited to be extremely rare. However, since measurement entails quantum entanglement, GRW still describes the observed phenomenon of quantum collapses whenever we measure subatomic particles. This is because the measured particle becomes entangled with the very large number of particles that make up the measuring device.