You can consider them to be so, but only at the expense of their uniqueness, leading to something like a Many Worlds- or Many Minds-view, which both have more troubles than most other interpretations (the preferred basis and probability problems, for instance).
In fact, while it appears on the surface to neatly do away with the problem of how we only ever see one definite measurement outcome—we don’t: there’s a version of us that sees spin up, and a version that sees spin down—there’s really an underlying circularity smuggled in: the split into ‘me’, ‘measurement apparatus’ and ‘measurement object’ is a basis-relative notion, so that there is this split depends on the notions of ‘me’, ‘measurement apparatus’, and so on, but those are already classical notions. So the explanation of how we observe the particular apparently classical outcomes we do hinges on the classical notions that divide the quantum state up into more-or-less neatly delineated subsystems—which is something not at all obvious from being given the quantum state itself. Hence, the can is just kicked down the road.
Thanks, this seems to be true. I only have a very superficial understanding of QFT (QED). I continually try to understand better by reading Wiki articles. With limited success.
But that doesn’t prevent me from seeing that “particles” and “waves” are nonsense, that we know a better explanation and that it is only up to me to study it.
I don’t see why nature would have to be a priori constrained by / limited to “classical” explanations or elementary school math. If more complex math, complex numbers, Hilbert spaces, Hermitian operators and whatnot is what it takes to understand nature then that’s up to me to learn.
The experiments that show that (for example) photons strike single atoms and ionize them (rather than giving a little bit of energy to a bunch of atoms like a wave might be expected to do), or that show that the same electrons that produce an interference pattern can be counted like particles when looking at chemical reactions make thinking about a field interpretation seem a little unnatural. Reality seems to be composed of a surprising mixture of wavy and particle-y aspects, and attempting to interpret it as just one or another (and I’m taking “field” to be another way of talking about a continuous (and thus wavey) kind of thing) eventually leads to awkwardness.
Well, waves vs. particles may be a little old-fashioned as a way of thinking about it, but the underlying issue is alive and well even today. The basic idea is that of complementarity: there exist pairs of properties of a physical system that are not simultaneously definite (as quantified by the uncertainty relation). Bohr, who came up with the notion, also used to talk about the complementarity between the ‘space-time picture’ and the ‘claim of causality’, which is even more old-fashioned; basically, the space-time picture is the description of a system in terms of (coordinate) position and time, while the ‘claim of causality’ is the description in terms of momentum and energy.
This relates to wave/particle duality, since a ‘particle’ is ultimately a state with a perfectly definite position (an eigenstate of the position-operator), while a ‘wave’ is a state with a definite frequency (which is a state with a perfectly defined momentum, an eigenstate of the momentum operator). So the wave-aspect of a quantum system really just relates to the well-definedness of its momentum, while the particle-aspect conversely relates to position. If you increase its localization, you force the system to become a relatively sharply defined wave packet, which will have a very ill-defined wavelength, and vice versa.
There are many other examples of complementary properties in this way (essentially, all quantities where the associated operators fail to commute), and the phenomenon also extends to quantum field theory (where the field and the conjugate field obey canonical commutation relations).
Since I am trying to understand quantum theory, would you mind clarifying this when applied to the double slit experiment?
ISTM that, if you define a particle like this and use it to explain the results of the no-detector-at-the-slits double slit experiment, there is no particle that goes through either slit. There are only particles that arrive at the detector.
As Chronos says, you can essentially consider that to be the case. The particle-aspect won’t be manifest at the double slit (otherwise, there would be no interference), but only upon making the position-measurement at the screen. Once you measure the localization of the photon at the slit (i. e. when you obtain which-path information), it becomes more ‘particle-like’ thereby, and the interference pattern disappears.
Thanks, I thought that a particle based explanation typically says that the particle goes through both of the slits. (How do they define the particle? As the whole wave state?)
Feynman, the great particle guy, I think said that the particle briefly turns into a wave. At least he said it’s false that there’s a particle that goes either through the one slit or the other, it has to be one of the two. That idea is wrong.
Except that Bohmian mechanics would say that. And it is not wrong, either.
With QFT you would say that the electron field takes in a blip of energy, churns for a while, then spits out the energy as another blip according to the fair and balanced distribution of energy created by the whole situation. (I’m not clear on position operators in QFT, I guess you can use them too in some cases if you want?)
I feel like I know where I want antechinus’ question to go, but will use a different setup to ask it.
Standard double slit experiment setup, two slits and a screen, let’s say one meter away. I drop a second screen into the setup half a meter away from the slits. This second screen is small, and only blocks a small portion of the area.
When the wave of a single photon passes the half meter point, the wave encounters the small screen. Does the entire wave function collapse at that point or does it only collapse if the resulting collapse has the photon striking the small screen?
Or, if you will, if the photon ‘may’ be detected at the half meter point, must the wave function collapse at that point? Does it even matter if it does or doesn’t?
The way the word ‘particle’ is used here basically infers from having detected something particle-like that what’s been going through the slit likewise must’ve been particle-like. So, since you always detect photons in neat little chunks, photons are particles; if photons interfere with themselves, then the particle ‘must have gone through both slits’.
It’s a little simpler if you just think of the superposition of a particle in two distinct location. This won’t be an eigenstate of the particle operator, hence, not truly a particle in that sense, but it’ll be kinda like a particle over here, and a particle over there; only upon detection do we see it appear in one place. The parlance of saying ‘the particle is in two places at once’ parallels that of saying ‘the particle went through both slits at once’.
With Bohmian mechanics, the particle alone doesn’t give the full phenomenology, though. Rather, each quantum system is described by the usual quantum mechanical wave function (the ‘pilot wave’), plus a perfectly definite position variable (which is what makes BM a ‘hidden variable’ theory). The pilot wave produces a potential, which determines how the particle moves. This potential will be influenced by distant configurations—such as the presence of a second slit, or of a measuring apparatus (this is the non-locality of Bohmian mechanics). Depending on this, the motion of the particle (the value of the position variable) changes. The trajectories of the Bohmian particles in the double slit experiment have become a somewhat iconic picture for this interpretation.
You have to be careful with position in quantum field theory. There’s no straightforward position operator, since position becomes a parameter of the theory (like time in quantum mechanics—in fact, you can consider quantum mechanics a quantum field theory in 0+1 dimensions, that is, in just the time dimension). Field values vary across time and space.
I think I tried to answer that above. The basic gist is, the more information about the location you extract (and screening does give you some location information even if the photon doesn’t interact with the wall), the less visible the interference fringes are going to be.
The one thing I don’t like about quantum mechanics explanations is when people start saying all this stuff is “strange”, “mysterious” or “incomprehensible”. (Which Feynman himself is guilty of. That’s where he’s wrong.)
It is a simple experiment and a plain observation. You can explain it and understand it to any level of detail you care to be interested in.
It’s no more mysterious than pressing a key on your keyboard and seeing the pattern of light on your monitor change in response. You can learn about computers and understand computers to the most impossible gory level of detail you care about (which I have, that being my field).
I think that there are genuine puzzles associated with quantum mechanics—stuff we quite simply don’t fully understand yet, and probably shouldn’t expect to, since nobody guarantees us that the theory is the final word. There were lots of things puzzling about Newtonian mechanics—for instance, the instantaneous action at a distance of the gravitational force—which were only explained by later theoretical developments (i. e., General Relativity). That didn’t preclude it from being a perfectly sensible, useful scientific theory.
With quantum mechanics, it’s not so much about how something can be ‘both wave and particle’—other than our preconceptions, there’s nothing that says stuff in the universe has to conform to either picture. But there are genuine issues as to how what we ‘know’—i. e. what measurement outcomes we observe—affects what happens—why a quantum system changes from manifesting wave-like properties to particle-like properties after measurement, for instance.
The thing is, the theory itself doesn’t tell us what counts as a measurement, thus apparently forcing the introduction of either something like a buck-stops-here measure (the collapse), of additional variables that entail measurement is just an ordinary (more or less) discovery of information about a system (Bohmian mechanics), or of the rejection of the idea that there is, in fact, only one outcome observed at any time (many worlds). All of which result in further troubles.
But you’re right, blanket statements about quantum mechanics as introducing some special sort of mystery or magic are just ill-founded. Yes, there’s stuff we don’t yet understand, but, I mean, just take a look at the world—obviously we don’t understand the vast majority of what’s what. Just give us a little time, we’ve only really been at this for a couple of thousand years, at best!
About 90% of the weirdness of quantum mechanics just comes down to wave-particle duality. And that is something that, with a little work, a human can comprehend. So when someone who does comprehend it hears someone else talking about how “mysterious” and “weird” wave-particle duality is, it’s easy for them to say that person is being silly.
But then there’s that last 10% of weirdness, that comes from the violations of Bell’s inequality. That, I don’t think any human brain is capable of understanding. It’s not that our theories aren’t good enough, and some better theory would be comprehensible: Our theories are just fine. But our brains aren’t up to the task. Unfortunately, it takes a lot of explaining to even set up the situations where Bell’s inequality comes up, and so it almost never makes it into lay explanations of quantum weirdness (or rather, it makes it in, but explained incorrectly, to the point that sensible people again say “but that’s silly”).
I first read about Bell’s theorem in that stupid book Dancing Wu Li Masters where they make a big deal about how mysterious it is without explaining it far enough.
Years later I finally understood it (though right now I kinda forgot) I thought the quantum mechanical prediction was fine but I was bothered by the classical prediction.
Never was bothered about the nonlocality in that experiment. It’s a simple formula, predicting that phenomena in different places are connected. And they are. Why couldn’t the universe work like this? I rather thought it stupid to make such a big deal about how impossible this is, you can’t do that, it can’t be, why, well because I said so…
We observe the universe the way it is, we don’t tell the universe how to behave (why do they call it the “laws” of physics, anyway? Who do I sue when the universe breaks a Law of Physics?)
What it comes down to, is that there are certain things that we think should be obviously, intuitively true about the Universe. But if you put all of those things together, then you get Bell’s Inequality, which the real Universe, according to experiment, violates. Therefore at least one of those things that we believe are obvious, isn’t true. Which one? I dunno. Maybe the Universe really is nonlocal.
These aren’t distinct issues, though. Both are consequences of complementarity—the existence of incompatible observables with no simultaneously well-defined values. Bell inequalities are mathematically just necessary conditions for the existence of a joint probability distribution over the set of outcomes of an experiment—that is, they follow from the statement that if you have a set of observables A, B, C, and D, there exists a well-defined probability p(A,B,C,D) for all the possible values of A-D.
If now some of these observables are incompatible, then you couldn’t even in principle measure their values simultaneously—i. e., their simultaneous value has no meaning. But the requirement of them having a joint PD means that you can assign a well-defined probability to each of their simultaneous values—say, if A and B are incompatible (for instance, spin-measurements in different directions on the same particle), then you have a well-defined value for p(A = up, B = up), or p(A = down, B = up); but what should that mean if you can never simultaneously measure both?
So, Bell’s inequalities (examples of which were first derived by George Boole in the 1860s) are really only expected to hold if you require the existence of these nonsensical (given complementarity) probability assignments. Their violation then just follows from the rejection of the requirement that non-simultaneously measurable observables should nevertheless have meaningful joint probabilities—which is not so weird, really.
The existence of joint probability distributions is equivalent to the usual assumption of local realism—if all of these observables have definite values at all times (realism), and the measurement of one doesn’t influence that of another (locality), then we can think of the possible measurement outcomes for all observables as an ensemble, and obtain probabilities from the relative frequencies of specific outcomes—say, (A = up, B = down, C = up, D = down)—within this ensemble. (Alternatively, the possible outcomes form the vertices of a convex polytope, and the polytope itself—the set of convex combinations of the vertices—is the space of the probability distributions; its hull is given by the set of Bell inequalities.)
Also, I think it’s something of an overstatement that these are the only mysteries of quantum mechanics. Another issue that has received lots of attention is the question of the status of the wave function—is it a physical field, or just a bookkeeping device encapsulating our knowledge of a physical system? This might seem academic, but it has real physical consequences.
Another question is why, if quantum mechanics violates Bell inequalities, it does not do so maximally—there are possible theories one can write down which lead to strictly stronger violations. What picks out the quantum predictions in this case?
Also, there are interesting issues regarding the understanding of part/whole relations. In particular, entanglement seems to suggest that the properties of a system do not inhere in its parts, but rather, in relations between these parts; but what’s a property without a bearer? What’s a relation without relata?
In recent years, also the question of dimensionality has received more attention. Quantum mechanics is usually formulated in abstract spaces with high dimensionality (indeed, infinite dimensionality for the case of continuous variables), so how does this relate to our 3D space? In general, the structure of Hilbert space isn’t all that naturally related to three dimensions.
And of course, what many people would consider ‘the big one’ (although it’s also related to the issue of complementarity above), the measurement problem. The usual unitary quantum evolution won’t generally yield specific values for the observables we’re interested in measuring, but tend to bundle them up in a massively entangled state. How does that resolve into our experience of unique outcomes? Do we need, as von Neumann thought, another dynamics that gets rid of the extraneous stuff? But then, when do we apply it? One experimenter’s measurement may be another’s unitary evolution. Or do we simply try to stick with the unitary dynamics, and hope to recover our experience as one ‘branch’ in a massively entangled ‘universal wave function’, as Everett held? Do we add hidden variables, following Bohm?
These are, I think, live questions, and far from idle speculation. In particular, they may point the way towards the development of new, more fundamental theories—just as the conceptual troubles of nonlocality in Newtonian mechanics pointed towards its completion in relativity theory.
The state is contained in the wave packet, though, not the particle (assuming I’m understanding Bohmian mechanics properly). Suppose you measure spin on Z, thereby filtering the wave packet into Z+ and Z- streams. Fine. We can do that again, and the Z+ stream will now be entirely directed to Z+, because the entire stream is in a Z+ state. But if we then measure X, the Z+ness of the stream is lost, and is now in an X+ and X- state. Does that count as a state change? I would say so, though the particle isn’t carrying that state.
I guess my view is that I can always fall back to Many-Worlds. If the universe needs to spin off a few more copies to make the physics work, so be it. I also think the universe is lazy, and only resorts to that when necessary.
I wouldn’t quite say that. But if the universe is doing a kind of lazy evaluation, then most of the time–when I just open the box normally and don’t perform a tricky interference experiment–it only has to evaluate the one branch. The universe only had to keep track of the quantum state of the one electron. The rest of it (our friend doing something or other based on the outcome) could wait.
The information is there, in principle, but it sure seems inaccessible to me. Like Hawking radiation–yeah, information wasn’t lost, but it’s maximally scrambled. Even if you could capture every bit of noise, you would need a quantum computer as large as the volume it’s working on to hope to decode it.
Still, you’re right. I am advocating for a modification of quantum theory. Too much of QM feels like the universe making approximations: quantized variables, probably quantized spacetime, the Bekenstein bound, event horizons, etc. So I think that noise at the lowest levels probably ruins some of the wilder possibilities. And that things like Galilean invariance are only approximations. It also makes me skeptical that quantum computers will ever really deliver the promised speedup. But I’ll eat crow if it turns out we can really built million-qubit QCs.
Hilbert space is a space completely unrelated to the three spatial dimensions of position, and there’s no reason to expect any sort of correspondence between them.
Sure, but that’s just the normal unitary evolution due to interaction with the Stern-Gerlach magnetic field; it’s not the measurement-induced indeterministic state collapse that’s usually meant by the state change upon measurement. It’s not in any way more troubling than the fact that a voltmeter influences every circuit it’s part of. In particular, the position of the Bohmian particle before any spin measurement will give exact information about the outcome of all future such sequences of measurements. So while a subsequent X-measurement renders the value of a prior Z-measurement invalid, the sequence of values for Z, X, Z you were going to get were always already contained in the state of the system.
In a sense, you can think of it as just determining the particle’s position ever more closely, by constraining it to half-spaces: that you found it in the upper half-space, then in the left one, doesn’t carry any expectation that the next measurement along the upper/lower axis should again find it in the upper half.
I think the many worlds interpretation does a significantly worse job of accounting for our experience than most others—simply because it’s not clear that we ought to have any experience at all, or even exist as a definite system, on that interpretation, the ‘split’ between us, the system we’re experimenting on, and the environment being a basis-dependent notion.
This already requires modification of quantum theory, though, introducing some way of keeping track of whether you’re performing a ‘tricky’ or an ‘ordinary’ experiment, which will, again, depend on things like classical arrangements of measurement apparatuses and the like.
Sure, but the sort of reasoning that sees the root of classicality in such noise-based scrambling simply won’t work if the information is still there in principle. It’s not a question of whether we can get at the information to measure the interference terms, it’s a question of whether we’re in a superposed state or not.
If quantum theory is the universe taking computational shortcuts, then it’s doing it in the worst possible way—simulating a quantum system is in general exponentially harder than simulating a classical system (that’s why people originally expected the possibility of a quantum speedup for computation, since obviously, quantum systems seem to be able to do this sort of thing efficiently).
Sure, but the point is that given the Hilbert space description of a system, that it’s a system in three dimensional space isn’t obvious at all. A wave function will typically depend on all the coordinates of the particles in a given setting; why group these into triplets to individuate the individual quantum systems?