Remember when I asked for suggested topics for an upcoming Bloggingheads discussion with David Albert about quantum mechanics? The finished dialogue is up and available here:
I would estimate that we covered about, say, three percent of the suggested topics. Sorry about that. But perhaps it’s better to speak carefully about a small number of subject than to rush through a larger number.
And I think the dialogue came out pretty well, if I do say so myself. (And if not me, who?) We started out by laying out our respective definitions of what quantum mechanics “is,” in terms that should be accessible to non-experts. (One user-friendly answer to that question is here.) Happily, that didn’t take up the whole dialogue, and we had the chance to home in on the real sticky issue in the field: what really happens when we observe something? This is known as the “measurement problem” — it is unique to quantum mechanics, and there is no consensus as to what the right answer is.
In classical mechanics, there is no problem at all; you can observe anything you like, and if you are careful you can observe to any precision you wish. But in quantum mechanics there is no option of “being careful”; a physical system can exist in a state that you can never observe it to be in. The famous example is Schrodinger’s cat, trapped in a box with some quantum-mechanical killing device. (Someone must write a thesis on the ease with which scientists turn to bloodthirsty examples to illustrate their theories.) After a certain time has passed, the cat exists in a superposition of states: half alive, half dead. It’s not that we don’t know; it is really in a superposition of both possibilities at once. But when you open the box and take a look, you never see that superposition; you see the cat alive or dead. The wave function, we say, has collapsed.
This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”
In our dialogue, David does a good job at laying out the three major schools of thought. One, following Niels Bohr, says “Yes, you really do need a new law, the wave function really does collapse.” Another, following David Bohm, says “Actually, the wave function doesn’t tell the whole story; you need extra (`hidden’) variables.” And the final one, following Hugh Everett, says “You don’t need a new law, and in fact the wave function never really collapses; it just appears that way to you.” This last one is the “Many Worlds Interpretation.”
I want to actually talk about the pros and cons of the MWI, but reality intervenes, so hopefully some time soon. Enjoy the dialogue.
Dear ST,
when you know what is classical and what is not and you know how both interacts you are done. You should try with thermodynamic limit, i.e. putting this limit to infinity. No need for a strange and useless universe proliferation (fairly good for science fiction writers) and some external entity to help you to come out of weirdness.
Marco
Marco,
It seems to me that you are presuming there exists anything that is truly classical. But if this were true, these classical systems would allow us to get around the uncertainty principle, which would make quantum mechanics inconsistent.
Dear Jason,
I am just assuming that uncertainties are depending on the number of particles much in the same way as happens in statistical mechanics (t->-ibeta) so that, if the number of particles is large enough, you are in a pure classical realm. I mean something like Delta x = O(1/sqrt(N)) and Delta p = O(1/sqrt(N)). Then this object is classical. Rather I just note that a simple mathematical fact, that is the equivalence in quantum mechanics between thermodynamic limit and semiclassical approximation, is generally missed by well trained physicists.
Marco
The real question is whether quantum interpretations pertain to what is happening with nature, or whether they are what happen in the mind of a physicist.
They have some utility in certain problems, but I doubt whether quantum interpretations have anything existential about them. Quantum interpretations probably should not be taken that seriously.
Lawrence B. Crowell
Sorry, I meant
Delta x/ and Delta p/ = O(1/sqrt(N))
being and average values.
Marco
Marco,
But it’s still not a pure classical realm, only approximately so. It may be a very good approximation as far as any of our observations are concerned, but it’s still an approximation.
And you don’t get away from the many worlds that are a consequence of decoherence theory by simply referencing the classical realm. To get rid of them, you have to explicitly exclude them by adding some new dynamics to the theory.
Dear Jason,
For all practical purposes as claimed by environmental decoherence people supporting multiverse. I can say that also Dirac distribution cannot be realized in Nature but just fairly well approximated until my head does not hit a wall and I can understand what an approximation means…
Marco
ST,
James Robson on Aug 10th, 2008 at 9:16 am:
“I had always intuitively rejected the “many worlds” interpretation as inelegant and a bit too star trek for my tastes. ..where can I find an (accessible) exposition of the maths behind it?”
Here.
I still like Jerome Rothstein’s information theoretic interpretation.
All I can say in defense of this view, is it allowed me to sleep at night no longer wondering what quantum mechanics “really means”.
Delusional? Perhaps. But a good night’s sleep is a good night’s sleep.
e.
MWI adherent’s site: “And the Winner is… Many-Worlds! (the many-worlds interpretations wins outright given the current state of evidence)”
It looks like MWI proponents are starting to act like string theorists.
“mathematician”:
What a brilliant insight! Thanks for clearing things up for me. Previously I was deluded by all that lengthy evidence and argument; but it took someone of your caliber to point out to me that, clearly, MWI can’t be right, because, after all, its proponents think it’s right, and it’s obviously impossible to think you’re right while simultaneously being right! I mean, look at string theorists: they think they’re right, and everybody knows they’re a bunch of morons. Q.E.D.! Why didn’t I see it before?
(/sarcasm)
James: “I had always intuitively rejected the “many worlds” interpretation as inelegant and a bit too star trek for my tastes. However, some of this discussion… ”
I think ultimately it boils down to whether you are too chicken to *really* believe in the wave-function or not. I don’t mean you as in you, James Robson, but the universal You.
Theoretical physics is about believing your theories until they blow up in your face. It is not enough that they merely make you uncomfortable.
mathematician: “It looks like MWI proponents are starting to act like string theorists.”
Being a string theorist, I have to say that string theory is in a far weaker place than many worlds. 🙂 The wave function is simply the most fantastically tested object perhaps in the history of physics, and the many worlders merely want to attribute reality to it.
As I have said repeatedly, many worlds is only about taking the wave function literally. This point is perhaps even moot from a scientific perspective, as long as we don’t come up with an experimental way of distinguishing between various interpretations. I cannot think of a way to test between Copenhagen and many worlds (I am no expert and have never really read/thought about either). Naively, it seems to me that anything that many worlds would call apparatus can be accommodated into Copnhagen by expanding the definition of the system. (Again, the wave function of the universe might be one place where this might not be true, so perhaps there is some extraordinary way in which cosmology can pick out the right interpretation. But let me stop speculating.)
So this entire discussion, while fun, is only about us, and not about science. I personally like many worlds because despite the popular feeling that it is too extravagant (because of, well, the many worlds), I think it involves far less conceptual baggage than Copenhagen. In particular, I prefer a fully quantum mechanical world without any ad-hoc classical fixtures.
QED
ST,
I think you can potentially verify the many worlds interpretation by looking at the boundary between collapse and no collapse, particularly if the interaction that generates collapse of the wavefunction in question is not used to perform any measurement. Doing so forces any theory of wavefunction collapse to explain how the collapse occurs in terms of physical processes, instead of whether or not a system was measured. The Copenhagen interpretation simply fails to do this, so any observation of collapse without measurement, and especially some physical mechanism providing gradual turn-on of collapse, completely destroys the Copenhagen picture.
This test, it turns out, has been performed:
http://prola.aps.org/abstract/PRL/v77/i24/p4887_1
John,
The concept of energy flowing through time and actualizing potential events is not analogous to quantum observation. Classically, energy impinges dynamically on a system and causes it to undergo some specific process. Classically, the cat dying is a dramatic event.
In the quantum case, the observation of the cat dead is a direct transition to the already accomplished state. Presumably an energy transfer had occurred while the box was closed, without producing information. Then, when the box was opened, information appeared without an energy transfer. This is in stark contrast to the everyday world in which energy and information change at the same time.
How can you take the wave function realistically? It is complex valued! 🙂 or for the Dirac field quaternionic valued. The problem is that we really don’t know what it means to take a quantum wave function in any realistic way. We might opt for MWI, or other might prefer Bohm, but these are really mathematical constructions which can’t be easily set in some sort of “quanta are real” certaintude.
Lawrence B. Crowell
Lawrence,
Why does the fact that the wavefunction is complex valued have anything to do with whether or not we should take it realistically?
Anything which we regard as real is something which makes a detector “click,” make a CCD pixel activate, register a voltage or add a bit to a computer register. In other words what is real are things like particles, or as Johnson put it “I kick it and it kicks back.” Even general is a theory involving the relationships between particles — it is really not a theory primarily focused on spaces or points in space. Things such as wave functions, fields, and spaces or spacetimes are really our mathematical constructions.
Lawrence B. Crowell
Except the complex phase invariance of these particles leads to conservation of electric charge. Is electric charge not a directly-measurable property?
Furthermore, one can measure differences in complex phase by observing interference patterns from particles that take different paths of different lengths.
So I don’t honestly see how your objection has any merit.
I see decoherence coming up again, it seems the elephant in the quantum container. There was a good discussion of decoherence in the thread linked at http://blogs.discovermagazine.com/cosmicvariance/2008/07/07/everything-you-every-wanted-to-know-about-quantum-mechanics-but-were-afraid-to-ask/#comments. One of the “justifications” for what I call “art deco” because I don’t think it’s a genuinely viable concept, was that the wave function can be thought of as comprised of a bunch of other components, such as the innumerable positions a particle could have etc. (But so could a classical wave be so imagined by mathematical decomposition, with no particular consequences ….Why don’t the waves just remain interacting like classical waves, which have no basis for splitting up into versions of localized interaction?)
Then, under “decoherence” each of these position components gets entangled with a version of the target/observer (in my rather sloppy rephrasing of the general idea) and ends up in its own little world and so on (but why there should be separate worlds for the different ways to hash out instead of the whole mess just staying superposed together, escapes me along with the rest of the hat trick.) However, note that in QM each of those “components” like the portion of the wave going down one path and the portion going down another, have amplitudes (well, amplitude over volume) less than one. IOW, they are the partial amplitudes for the particle appearing in each particular possible place (simplistically put in an example that we can construct at least.)
But when a given “observation” makes the particle “appear at the observed location” the amplitude of the locally condensed-down wave concentrates back into amplitude “one”. That isn’t the same as each little Fourier subwave being led off into it’s own little dream world, where each would keep its own lesser amplitude. See, the whole wave has to pile back into that one little space, and if we multiply the outcomes then we have to increase the *total* amplitude of all the “worlds” combined – they have to borrow from each other in effect. I don’t think that works, because you can’t just get it out of the waves and their interactions (either the total amplitude should concentrate into *one* unique spot and take away from the other places – and thus no multiple outcomes, or the dividing up of the wave must leave each version in an attenuated state (with who knows what type of possible outcome.)
And there are ironies, such as the attempt to say both that quantum interpretations don’t or can’t matter since all we have is the outcome and predictive schemes, but that nevertheless decoherence is the way to explain what happens! And note ST claiming that measuring instruments have some way of interacting with the wave functions of particles that somehow results in a localized detection, well does that make them special after all? Is a simple screen waiting for an electron to hit “somewhere” such a thing and how does it really concentrate the entire wave into one spot, and yet somehow also concentrate the whole wave into some other spot elsewhere (elsewhere on the screen *and* elsewhere in a sense we don’t even understand.) If art deco can explain the waves ending up in the way we finally observe them, why does it still need to split up all the possible results?
Like I have said, IMHO art deco is a trick based on circular reasoning and hidden assumpit0ons, as well as sidestepping the issue of apportioning amplitude. Look at comment # 161, from a person who apparently would like to support deco but appreciates the problematical nature of the idea.
Hi Lawrence B. Crowel,
It would seem from #54, and to some extent #69, that you adopt a rather solipsistic attitude to any attempt to “understand” the Universe. It all occurs in the “Physicist
Look at it this way. You can consider a point in spacetime x, which under different coordinate conditions define a metric g_{ab}(x) and g’_{ab)(x), which are of course coincident. Yet in ADM relativity you then find in the subsequent time slice that the two metrics have pushed x to different points, say y and z. So for all we work hard to learn geometry and the rest, general relativity is not really about spaces — it is about the relationship between particles. The goedesic deviation equation tells us how two particles will move relative to each other. All the geometry stuff is really mathematical modelling.
Feynman in many ways made a point of this. He worked to illustrate what happened with particles. He did not get caught up in lots of wave function talk or about the mysteries of QM waves. I tend to hold much the same viewpoint, in particular when it comes to quantum interpretations.
Our models are descriptions of nature, and they have some value in that sense in informing us how nature functions. Yet by admitting what we work on are model systems we can avoid getting caught in intellectual traps — such as people in the early 18th century who worried about the reality of gravitational lines of force.
Lawrence B. Crowell
I don’t get why people think MWI completes QM. It claims that the observer, as he knows himself, is only a small region within an expanding state space of his “actual” existence, but it doesn’t explain what makes him occupy one region rather than another.
Perhaps he chose it? That is a clever cop-out. Since there is no known way to model consciousness in a physical theory, you sweep the mystery of decoherence under the rug of conscious choice. Not only is there still a mystery; there is now the second mystery of why this choice should have precisely the same statistics as Copenhagen randomness.
The only thing MWI completes is the equation journals of the pencil-pushers at the laboratories. That is not what physics is supposed to be about.
Neil B.,