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.
Lawrence,
Then why is it that gravitational waves exist, if gravity is just about relationships between particles?
Jason #65: A belated thanks for the link – I saw your message only now. Anyway … If you are saying that the experiment you pointed to verifies that decoherence is real, I fully agree. But I do not consider that to be an experimental test of many worlds vs. Copenhagen.
Many worlds is an “explanation” why we are in one of the decohered branches (as opposed to another) with some probability. But a true adherent of Copenhagen can still get away with the claim that this is some kind of staggered collapse. Afterall, the time-line for collapse is not really fundamental to the whole Copenhagen interpretation (even though, perhaps, Bohr himself might have believed that the collapse was instantaneous).Of course, it becomes increasingly contrived to differentiate what is classical and what is quantum in the Copenhagen interpretation in light of such macroscopic deoherence experiments, but then again, there has never been a precise difference between the two to begin with! The only real way to tell what is quantum in Copenhagen is to do an experiment like the above!!
As I said in a previous post, as long as we are willing to be fuzzy about what is classical and what is quantum (and that is the fundamental reason why I prefer many worlds), we can always expand the definition of the system.
Mathematician: Love, I mean LOVE, your pithy one-liners. 🙂
“As I said in a previous post, as long as we are willing to be fuzzy about what is classical and what is quantum (and that is the fundamental reason why I prefer many worlds), we can always expand the definition of the system.”
Just in case anybody is still reading this: I meant that the distinction between classical (observer) and quantum (observed) is not a priori well-defined in the Copenhagen view. And that is why many worlds is appealing to some of us.
Physics doesn’t need “MWI adherents”, “Copenhagen adherents”, etc..
“Adherents” generally don’t have a good track record of getting things right.
The last “adherents” in physics to have gotten it right were the “gluon adherents”.
ST,
I think the problem that experiments like that pose for the Copenhagen interpretation is that it forces the interpretation to become more specific in what is meant by “measurement”. The basic Copenhagen interpretation simply fails to explain what’s going on here, and it needs to be buttressed with some new machinery to more accurately describe the collapse, making the Occam’s Razor case for the MWI even stronger.
Jason Dick: Then why is it that gravitational waves exist, if gravity is just about relationships between particles?
—————
Maybe with gravitons? Physical models and its mathematics are really similar to art in a way. They are representations of what we observe in the natural world. They are representations of the world, but the particular geometrical structures we appeal to are not necessarily how nature is organized. In our more modern world Newton’s lines of force have been replaced by spacetime curvatures. We are less inclined to see on a fundamental basis a gravity field according to a radial vector field — even though we can do all sorts of Gauss law calculations and predict planetary orbits. These representations are useful up to the limit they permit us to predict things about the world. Ultimately what is real in science is what makes a detector record a value. Physics is an empirical science after all.
Lawrence B. Crowell
At the risk of kicking a dead horse (darn horse just keeps getting up!) I must insist that the hidden variables view of Bohm has much more going for it than MWI – for one reason. You will find in Feynman’s illustration with electrons, and I think also with Young’s of photons in the 1800s, that the that the build up of interference at the target occurs even when there is space (in time) between individual particles being released.
This is not my interpretation – this is not something that needs to be further tested to prove – it has already been shown in experiments that Feynman – to his discredit – made very little fuss about, if I remember right. But it is a big thing. In fact you could say that in a perfectly cold environment of 0 degrees K that state that exists in the path in the vacuum to the target between the two slits will exist indefinitely. At that temperature that path could exist for eons and be perfectly preserved. If one doesn’t describe the physical vacuum through which this path is carved a “hidden variable” then I say its only a matter of semantics. If one looks at it this way, and one is intellectually honest, one must describe it as something that acts like a hidden variable. It also shows that the evolution of “state” in the vacuum is directly related to the passage of energy and information and that this is what we are really describing when we discuss the passage of time.
Jason, (anyone
Neil,
“How can the Bohm interpretation account for the gradual turn-on of wavefunction collapse in carefully-designed experiments?”
Jason,
I actually find the use of “lines of force” visualization quite useful. The vacuum isn’t a unified whole as such but has some granularity which can be broken down to Planck length increments. One can represent each of these increments as possessing a random line of force whose orientation can be altered. The passage of a photon, or any particle for that matter, through this quantum foam will have an effect on the orientation of that force. If you pass a particle through this quantum foam there will be a meandering path created whose average value will be a vector formed from the initial velocity and energy of the particle at launch. To get the least meandering path one would want to irradiate the path before launch to target to completely randomize the “foam”.
One this initial particle has arrived at the target, and assuming the system is completely isolated from outside energy, a fairly straight path will be created in the vacuum. As each following particle is launched the lines of force created by previous particles will create an interference. It really behaves no differently than what Faraday discovered 200 years ago but in a granular and discontinuous way. As long as particles are launched at a low enough angle to previous launch velocities a predictable interference will build up.
But once you launch particles or radiation transverse to the path its like scattering billiard balls. Its very unpredictable what the final result will be. In essence the previous predictable interference path is destroyed. You have essentially randomized all these tiny lines of force and have started the process of re-initializing the experiment that we started at the beginning. But one doesn’t have to completely reinitialize in “one swell foop”. One can do it in small increments at various points on the path and divide it in time
“To get the least meandering path one would want to irradiate the path before launch to target to completely randomize the “foam”.”
I should have said that after randomizing the path you will get the least “deviation” from the initial trajectory along the entire path when subsequently shooting a photon or electron through it. “Meandering” probably isn’t too scientific a description. In effect the particle then acts like a particle and not a wave by randomizing information from previous particles.
Except particles don’t interfere with previous particles. They interfere with themselves.
“Except particles don
Hi, again, Lawrence B. Crowell,
Thanks for your reply to my comment.
You seem to try to give an analogy to the QM interpretation issue using a GR equivalent. Your example uses the ADM formulation but I’m not sure why this particular formulation is need to make your point?
Certainly, it would seem (from the tediously philosophised “hole argument” – if nothing else) that GR teaches that the geometry (i.e. the coordinitised set of spacetime points) is nothing more than a bookkeeping device (well this is not entirely true as the associated topology and dimension, for example, seem to be fairly relevant, at least classically).
We are left without the props of any special coordinate systems constructed with measuring rods and clocks and so, unless the events in question occur at the same spacetime point, then the interpretation is up for grabs (ish…) and strange things can seem to happen. I agree this is odd, and I happen to think that relativity (even special) is, in the long run, harder to comprehend than QM. It just seems easier at first.
However, even in GR things still happen at definite coordinate “points” with definite “momenta” (how measured – what meaning? Ok, granted…) But we seem easily able to ignore the new situation and retain the Newtonian clockwork comfort of our childhoods.
Not so with QM.
As for Feynman – I think one of his greatest legacies was pedagogical and he instilled real understanding in generations of students. I never had the pleasure of meeting him, but still I find it hard to believe that he would be satisfied with the ignorance that we currently have regarding the understanding of Qm. (As I said, I don’t really know so I shouldn’t speculate)
Also – why did Einstein move us beyond the “people in the early 18th century who worried about the reality of gravitational lines of force.”?
For purely practical, experimental reasons?
-James.
Eric,
Then how do you explain the Aharonov-Bohm effect?
Maybe someone can reiterate what the Aharonov-Bohm effect actually is. Its been too long since I read about it.
About Mark’s question, I don’t believe the Transactional Interpretation is compatible with the quantum factoring algorithm. That is, the naive understanding of the Transactional Interpretation leads you to believe that factoring is in randomized polynomial time, which is generally not believed by computer scientists (and this would extend to any problem in BQP, which is much less believable). And I’ve looked for some description of the Transactional Interpretation that goes beyond this naive understanding, and was unable to find it. This is entirely consistent with Domenic Denicola’s comment that it is believed that the Transactional Interpretation only works with one particle.
On a related topic, I have never been able to make sense of the factoring algorithm in Bohm’s interpretation (although at least you can see where the computational power is coming from in that interpretation). Can anybody help me here?
Eric,
The Aharonov-Bohm effect is an effect where magnetic fields outside the path of the electron have an effect upon its phase. Basically, if you have a two-slit experiment, and place a solenoid between the slits, turning on the solenoid shifts the interference pattern. Note that the magnetic field never actually crosses the paths of the electrons.
Of course, this effect is well-understood in terms of normal quantum mechanics, but it just reinforces the statement that it’s actually the phase of the individual particles that are interfering with one another. Since the various particles are often not produced with coherent phases, it makes no sense for the interference to be between particles.
Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?
(I don’t know what BQP is. I’m just going by the context.)
Thanks. That was a great Diavlog. I would like to see you do another one on QM with Anton Zeilinger, and I’d pay money to see one between Zeilinger and Albert. It reminded me that I don’t really get the MWI or why people like it.
Tell if I’m wrong here: The MWI means that there are branches of the wavefunction where the most improbable series of events actually do occur. For example, there’s a branch of the wavefunction of the universe where every quantum experiment done on earth after this post results in the least probable of outcomes. Doesn’t the fact the we don’t ever see anomalous outcomes of quantum experiments (such as a quantum coin flip that keeps coming up tails for the rest of your life) mean that the MWI doesn’t work?
I don’t quite get Albert’s obsession with the idea that taking the MWI seriously precludes someone’s being surprised at extremely unlikely quantum events. Sure, the theory predicts with probability one that such events will happen. So what? That just means that it predicts with probability one that someone (somewhere in Hilbert space) will find themselves in a position to be quite surprised.
Albert seems to think that this surprise is somehow illegitimate because there’s no basis (within the theoretical resources of the MWI) for any background expectation of what “should” happen. That is, it was inevitable that there would be a person who sees a million z-spins in the same direction; I am that person; there’s no reason to think I “should” (even in a probabilistic sense) have been some other person. There are two things to say in response.
1. Isn’t Albert’s objection resolved by the pretty weak assumption that one expects to experience macrostates (so to speak) that arise from a large number of different microstates, just because if all the microstates happen (as the MWI proposes) then there’s nothing to choose between them and most people will be in positions to observe one of these “likely” macrostates? But this is just thermodynamics and Albert wrote a good book on that so I imagine he knows what he’s talking about.
2. I’m not sure there’s a problem even without that assumption. Do you really need a background expectation of what should happen in order to be legitimately “surprised”? Isn’t it enough to say that this kind of surprise is legitimate when what one observes is an outlier among the set of things that could have happened? Who cares, looking backwards, what was likely or not? Even if it turned out that (given the initial conditions & dynamical principles of the universe) it was inevitable that all the electrons I’m looking at would have their z-spins up, I would still find that fact to be worthy of note, or if you prefer, “surprise.”
(I suppose the Born probability rule prevents the analogy with thermodynamics from being very good. But isn’t that the problem one should be talking about, not this attempt to derive facts about how physics works from human notions of “surprise”?)
Christopher,
His objection, as near as I could tell, was in the deriving of probabilities from the MWI. After all, if all outcomes occur, why should we be surprised by any outcome that has non-zero probability?
Here’s how I look at it. Imagine that we are sitting here before conducting an experiment. The experiment in question is a quantum-mechanical version of flipping a coin many times: we’re going to perform a quantum mechanical measurement of a system that has two possible states. Before performing the experiment, I’m going to make a definitive statement about what I expect to see and what I don’t expect to see. For example, if we make 100 “flips”, I don’t expect to see all heads or all tails as outcomes. In fact, I expect to see that the number of flips will be approximately 7 flips away from 50 heads.
Now, in the MWI, why am I justified in making this statement? Consider that immediately after the experiment, “I” will have split into 2^100 different worlds, and will observe every single outcome. There will be a “me” after the experiment who observes the 100 heads result. There will be a “me” after the experiment who observes the 100 tails result. But I can still be firmly justified in expecting to see around 7 flips away from 50 heads because nearly all of these 2^100 future me’s, each of whom has equal amplitude, will not see these outcomes. Therefore I might imagine that by making these choices, I’m choosing to attempt to say as much as I can about what will happen in the future as accurately as I can. I do this by maximizing the selves who are unsurprised by the outcome and minimizing the selves that are surprised. Because this game is completely isomorphic to just dealing with probabilities, we might as well consider it such.
Jason,
I may have misunderstood, but I thought that Albert’s objection (if that’s the right word — probably “puzzle” is better) had to do with how the post-experiment “you” who sees 100 heads should think about the probabilities. Why should that instance of you find the 100-heads result surprising? (After all, the objection goes, the MWI predicted with certainty that this version of “you” would exist.) I won’t repeat my answers to this objection. I’m not even sure they’re all that good, especially since it isn’t the case that all possibilities in configuration space occur with equal probability. (Unless perhaps that is the case, and the Born probability rule is more apparent than real — but I don’t know the physics or the math remotely well enough to have any wisdom on that question.)
It’s surprising because most of the observer amplitude finds very different results. For the typical observer to see one instance of 100 heads in a row, the experiment would need to be repeated around 10^30 times.
To contrast this to a different system, think about winning the lottery. The probabilities are such that it is no surprise whatsoever that somebody wins the lottery quite frequently. But if, for example, I purchased one lottery ticket a week, I would be very, very surprised if that somebody turned out to be me. By analogy to the coin flip scenario, it makes sense to equate the observers in the 2^100 different worlds as being different observers that share the same past worldline. Because they each have equal amplitudes, and because so few of them experience events like 100 heads in a row, it only makes sense to be surprised when I find myself in that situation.
Now, then, going back to looking at the experiment beforehand, the point remains that we have one observer that splits into many. If we were to consider adopting a strategy to ensure that the amplitude of this observer that is not surprised by the result is maximized, we’d find that the best strategy the observer can adopt is to make use of the Born formula and to consider the future possibilities as probabilities, despite the fact that they all occur.