I’m a physics Ph.D. student. There are people on this board who are a lot more qualified to comment than me, but here’s my take on things.
The article strikes me as somewhat wrong – or at least misleading – in several ways.
Up until the section entitled “Three conceptual problems with quantum mechanics”, it isn’t really explaining quantum mechanics at all, it’s giving an explanation for how quantum mechanics gives rise to classical mechanics. The explanation offered is kind of vague, but I don’t have anything major to criticize here.
It’s with the aforementioned section “Three conceptual problems with quantum mechanics” that the article really goes off the deep end. This section has three flaws:
It’s not describing those “conceptual problems” accurately.
Its explanation for them doesn’t make sense.
Those are (in my view) the wrong “conceptual problems” anyway.
Let’s go through the three “conceptual problems” listed in the article:
The article claims that the situation with quantum mechanics is analogous to the future – i.e., simultaneous possibilities can co-exist. It summarily dismisses determinism a “dismal view of the world”, and declares the rejection of determinism “a great triumph”, as classical mechanics “effectively deprived us of a future.”
What a load of garbage. I’m sure the pre-20th century physicists – who generally believed the world was deterministic (possibly with the exception of the human mind) – would be shocked to learn that they had “deprived themselves of a future.” :rolleyes: In the view of most scientists at the time, the reason the future couldn’t be known with certainty was that it’s impossible to have 100% accurate information about the present. The surprise with quantum mechanics is that even if you know all the information about your experimental system beforehand, you still can’t predict with certainty what the outcome of the experiment will be. This is what Einstein objected to when he said that he was convinced that God “does not throw dice.” Moreover, this is true of systems that aren’t goverened by human choices, so conflating this with free will is entirely missing the point. Quantum mechanics tells us that even systems that no one thinks of as having free will are inherently unpredictable, even given perfect information about the initial conditions.
The article also gets it wrong in conflating the issue of indeterminancy with Schrödinger’s cat – which is an illustration of superposition. Being in a superposition of two states isn’t the same as possibly being in one state or possibly being in the other. If you fire electrons at two slits (one at a time), in such a way that each electron has a 50% probability of going through the left slit and a 50% probability of going through the right, this is not the same as having each electron seemingly pass through both slits and interfere with itself. It’s not just that it’s randomly doing one or the other, it’s that it’s seemingly doing both at the same time. Writing off these problems as analogous to saying “Physics Cannot Predict the Future in Detail” is missing the point completely.
My best guess as to what this vague statement means is that it’s talking about non-locality. I.e., by making a measurement on one particle, it’s possible not only to influence its state, but to influence the state of a particle far away from it. The article dismisses this with the claim that “it is very hard to see how the only result of this-a probability associated with each destination-could be used to send a signal faster than light or violate any other cherished principle.” Non-sense – before quantum mechanics, locality was a cherished principle. Einstein (along
I agree with these clarifications. The problem comes from assuming the metaphysics properties of a particle; all we can really say is the state function is such that it allows the electron–if you interpret it as a particle–to pass thru one or the other slit. As CurtC points out, this interpretation is not justified; we could just as easily believe whatever makes up the electron went thru both slits, an interpretation that is sensible if you equate “state function” and “electron” in some way.
Personally (let me repeat that: Personally), I have always found this to be a needless complication of QM. Metaphysically, it says that since we can’t–by the rules of QM–determine which state the electron is in until it is observed, we must assume it is in all possible states simultaneously.
This, to me, makes the same mistake that classical physics made in assuming an underlying metaphysics. It is somewhat harmless physically–by definition the electron is in a state that can never be observed, i.e. never have any impact on the world–but it makes the matter seem far more mysterious than it is. It leads to gross misunderstandings of QM and the kind of endless philosophical debates that litter most pop-science discussions of QM.
The paradox of Schroedinger’s cat, to my mind, lies in the fact that one tacitly assumes a “delocalized combination of states” based on the limitless possibilities of the state function; if you assume instead that the condition of the cat is unknowable until the box is opened, there is no paradox, but of course this also carries a tacit assumption: Although the exact state of the cat is unknowable, we assume (thanks to philosophy) that something cannot both be and not be, and so ther cat is definitely in one state or the other (even if we can’t know which it is).
I really don’t think either interpretation is worth arguing, so I’m going to agree right here that QM can be viewed either way. The choice then is whether one metaphysically chooses to give a higher “reality” to the limitless possibilities of a mathematical function, or the philosophical implications of our current understanding of reality. That choice is personal–like all philosophical choices–but I’d ask that (1) people know they have these underlying assumptions when they make that choice, and (2) consider if the choice–while good for them–may lead others to misinterpret the real, observable theory of QM.
Perhaps I’m misunderstanding, but that assumption isn’t metaphysics – the superposition of multiple states is a necessary part of representing a quantum particle mathematically. If you take a system of electrons which occupy two states equally, you will get a different (wrong) answer if you treat them as a system in which half is completely in one state and half is completely in the other.
Schroedinger’s Cat is, in my opinion, one of the stupidest analogies ever formulated. It has caused more popular misunderstanding of quantum mechanics than just about anything else. The cat is not in a superposition of states. It is a macroscopic, classical object. Whether the cat is alive or dead before the box is opened is only a paradox in the way that a tree falling in the forest may or may not make a sound if no one is around. The cat is either dead or alive. Trees falling in forests make sounds.
(I’m not disagreeing with what you said, by the way, just using it as a platform from which to rant.)
Here’s where I know you’re going off the rails. Draw me a line. Go on. Draw a line separating classical from quantum. Where should we apply one set of rules and where should we apply the other?
All systems are quantum systems. All systems can be put into superposition. The trick is figuring out why macroscopic superpositions aren’t observed. Myself, I’m a fan of Penrose’s conjecture of gravitational decoherence, but really it’s an open problem.
I’m a physics Ph.D. student. I mention this only because the OP askes for opinions of those “better versed in physics” than he is. There are people on this board who are a lot more qualified to comment than me, but here’s my take on things:
The article strikes me as wrong – or at least highly misleading – in several ways.
Up until the section entitled “Three conceptual problems with quantum mechanics”, it isn’t really explaining quantum mechanics at all, it’s giving an explanation for how quantum mechanics gives rise to classical mechanics. The explanation offered is kind of vague, but I don’t have anything major to criticize here.
It’s with the aforementioned section “Three conceptual problems with quantum mechanics” that the article really goes off the deep end. This section has three flaws:
It’s not describing those “conceptual problems” accurately.
Its explanation for them doesn’t make sense.
Those are (in my view) the wrong “conceptual problems” anyway.
Let’s go through the three “conceptual problems” listed in the article:
The article claims that the situation with quantum mechanics is analogous to the future – i.e., simultaneous possibilities can co-exist. It summarily dismisses determinism as a “dismal view of the world”, and declares the rejection of determinism “a great triumph”, as classical mechanics “effectively deprived us of a future.”
What a load of garbage. I’m sure the pre-20th century physicists – who generally believed the world was deterministic (possibly with the exception of the human mind) – would be shocked to learn that they had “deprived themselves of a future.” :rolleyes: In the view of most scientists at the time, the reason the future couldn’t be known with certainty was that it’s impossible to have 100% accurate information about the present. The surprise with quantum mechanics is that even if you know all the information about your experimental system beforehand, you still can’t predict with certainty what the outcome of the experiment will be. This is what Einstein objected to when he said that he was convinced that God “does not throw dice.” Moreover, this is true of systems that aren’t goverened by human choices, so conflating this with free will is entirely missing the point. Quantum mechanics tells us that even systems that no one thinks of as having free will are inherently unpredictable, even given perfect information about the initial conditions.
The article also gets it wrong in conflating the issue of indeterminancy with Schrödinger’s cat – which is an illustration of superposition. Being in a superposition of two states isn’t the same as possibly being in one state or possibly being in the other. If you fire electrons at two slits (one at a time), in such a way that each electron has a 50% probability of going through the left slit and a 50% probability of going through the right, this is not the same as having each electron seemingly pass through both slits and interfere with itself. It’s not just that it’s randomly doing one or the other, it’s that it’s seemingly doing both at the same time. Writing off these problems as analogous to saying “Physics Cannot Predict the Future in Detail” is missing the point completely.
My best guess as to what this vague statement means is that it’s talking about non-locality. I.e., by making a measurement on one particle, it’s possible not only to influence its state, but to influence the state of a particle far away from it. The article dismisses this with the claim that “it is very hard to see how the only result of this-a probability associated with each destination-could be used to send a signal faster than light or violate any other cherished principle.” Nonsense – before quantum mechanics, locality was a cherished principle. Einstein published a paper (along with co-authors Podolsky and Rosen) arguing that quantum mechanics was incomplete, on the basis that in order to be complete it must violate locality. (This is known as the EPR paradox). Most physicists today accept non-locality as a fact of life, but to act as if it’s “not so weird” in light of our classical intuition is simply ridiculous.
That’s a pretty poor summary of the actual issue, which is that quantum-mechanical particles don’t have an exact position most of the time. The article’s first approach to the problem – writing this off as a classical phenomenon – is completely disingenuous (or it would be if the author knew what he’s talking about). The “third picture of classical mechanics” isn’t a classical description at all, it’s a description of the classical limit of quantum mechanics. One could say “quantum mechanics predicts that the uncertainty in a particle’s position is way too small to be noticed when we’re talking about classical mechanics (which deals primarily with macroscopic objects)” – but that’s not the same as saying classical mechanics predicts this uncertainty, which is utterly false. The article essentially says the former while pretending this means the latter.
The article’s second approach to the problem – noting that the indefiniteness in the particle’s position goes away when you measure its position – misses the point. There are observable consequences to the fact that quantum particles don’t in-general have a definite position. As I said above, being in two places at once is not the same thing as possibly being in one place or possibly being in the other. The weirdness isn’t that “we cannot say what the quantum particles look like when they cannot be seen”, it’s that we can definitively say that they don’t look like classical particles.
And yet, they do look like classical particles when we try to observe their position. That is, the act of attempting to measure the position of a particle changes the state of the system, in such a way that it forces the particle to have a well-defined position, even though it didn’t have one when it wasn’t being observed. In my view, this is the strangest (i.e., most counter-intuitive) aspect of quantum mechanics, and the article almost completely glosses over it. I’m not talking about the classical phenomenon that you can’t observe something without interacting with it (e.g., by bouncing light off of it). As I mentioned above, in quantum mechaincs observing one particle can change the state of a different particle, even if that other particle isn’t anywhere near where you were looking. Also, the way in which a particle changes when it’s observed is unlike any classical phenomenon (so far as I know).
It’s worth making this point a bit more explicitly. There are classical systems that don’t have a defined position – e.g., a wave. (It’s spread out in space, hence no single position.) If you want to make a wave more “bunched-up” in space, you can add a bunch of waves with different wavelengths together. So now the “wave-packet” has a better defined position, but at the cost of having a less defined wavelength. This is a classical example of the uncertainty principle. However, attempting to measure the wavelength of this classical wavepacket doesn’t cause all the other waves with different wavelengths to spontaneously vanish, leaving only a single randomly chosen one with a specific wavelength. But this is essentially what happens in quantum mechanics. The really weird part of quantum mechanics isn’t uncertainty, it’s wavefunction collapse. This issue seems to be lost on the author of that article.
I’m not saying quantum mechanics magically disappears, just that there are many regimes in which the effects become negligible or will average out to the point that we can use statistical methods. Room temperature cats are one of those regimes.
I don’t know what you mean by macroscopic superposition, but I suspect the problem is that you’re incorrectly applying single-particle thinking to a complex system. “Dead cat” and “alive cat” are not pure quantum states. You can’t define a basis in which those are pure states.
A cat is a collection of, say, 10[sup]25[/sup] particles. At room temperature, each particle only has a few states it can be in. So, while you can describe the cat by a many-body wave function in which every particle is in a superposition of its possible states, it isn’t useful to do so. The quantum effects completely average out – if a single particle changes state, it has a negligible effect on the whole. Describing a cat with a wave function makes no more sense than calculating the trajectory of a baseball by summing up the trajectories of the individual atoms.
Who said that the states in superpositions had to be pure? Just to verify, you do mean “pure state” as “density matrix of rank 1”, right?
Ohh, it’s not practical, you mean. Well of course not. That doesn’t mean that the ideas don’t apply. If that were the case then we couldn’t derive thermodynamics from statistical mechanics, which we do.
Basically your objection seems to be that when you have so many particles a lot of things “tend to average out” and in practice you’ll only see one or the other macroscopic state. This is all well and good, but you’ll hit your head on the ceiling if you keep waving your hands like that.
As I said before: how exactly classical mechanics is approximated by macroscopic quantum systems is still not completely settled, though there are various ideas. Most of them have a specific mechanism by which macroscopic superpositions decohere almost instantly.
OK, I’m pretty sure I don’t know what you’re talking about. What isn’t settled? Can you give me a specific example of what you mean by macroscopic superpositions?
A macroscopic superposition is exactly what you assert does not happen.
Here’s one simpler than the cat: a ball of matter in two slightly different positions. Why don’t we see this superposition? If it just doesn’t happen (as you first stated) then you have to draw a line between which sized balls do superpose and which do not. If it does, then waving your hands and saying “it all averages out” doesn’t mean anything. It’s not physics, it’s faith.
Most ideas I’ve seen for really dealing with it propose mechanisms for decoherence. That is, if you start with a macroscopic system in a superposition of two states, it evolves somehow into a simple mixture of the two states. The explanation most of these schemes give for why we don’t see these superpositions in the real world is that this decoherence takes place unimaginably quickly for macroscopic systems.
To go back to what started this: in Schrödinger’s experiment the cat does get put into a superposition of live and dead states, but they decohere into one state or another almost immediately, and definitely before the box can be open.
There was an article in popular science, or maybe discover last summer I read in the library that blamed macroscopic decoherence on gravity. The idea was a particle in two states or had to maintain gravitational fields for two states or more. Quantum particles which are pretty much ignorant of gravity’s effects don’t notice this, but macroscopic objects quickly shift to lower energy single quantum states under the energy load of their own gravitational fields.
The cat would either be murdered or saved by it’s own weight. Something oddly poetic about that.
I’m not even sure where to start here. Let’s first ignore the fact that a ball is made up of atoms and pretend that it is a structureless particle. Let’s pretend we know that it is moving at less than one Angstrom/second (an unreasonably precise assumption, but we’re setting an upper bound so no big deal), so the uncertainty in its position is given by the deBroglie wavelength:
lambda = h/(m*v)
= 6 x 10[sup]-34[/sup]/(0.1 kg)(10[sup]-10[/sup] m/s)
= 6 x 10[sup]-23[/sup] m
This is immeasurably small. An electron with the same uncertainty in its velocity would be significantly more delocalized simply because its mass (and thus momentum) is so much lower than that of a ball. The rules apply equally to all objects, but are only significant at the small length scales.
In any case, a ball is in fact a clump of (e.g.) 10[sup]25[/sup] atoms in a periodic lattice. The atoms are sitting in potential wells, with the electrons occupying angular momentum states required by the quantization of momentum and the Pauli Exclusion Principle. Valence electrons of neighboring atoms form bonding states which are superpositions of the valence electronic states of the isolated atoms. Quantum mechanics is in fact what makes the ball a ball. But it doesn’t require collective behavior of the atoms – they each occupy states according to their environment. The probability of a single atom occupying a position state to one side drops off quickly with distance from the center of the lattice potential, which can be quantified from the Heisenberg Uncertainty as above. The probability of two atoms simultaneously occupying states to one side in the same direction drops off as the square, just as the probability of drawing the ace of hearts twice in a row is 52 times less likely than simply doing it once. Take that probability to the power of 10[sup]25[/sup] and you see that the probability of all atoms occupying a state to one side is infinitesimal. Zero, for all practical purposes. That’s what I mean by the quantum effects averaging out in macroscopic systems like this.
So an unsupported assumption can manifest unobservable phenomenon. What’s the point? Why create elaborate theories to explain things one thinks should be true? That’s faith, not physics.
Even if that was not the case, there is nothing inherently paradoxical about Schrödinger’s experiment. Even if somehow the cat continued to exist in a superposition of live and dead states, why not? I mean the whole idea of it being a paradox relies on some magic inexplicable concept of life that we define as fixed. Unfortunately there is no magic “Schrödinger Exclusion Principle” that guarantees us that something cannot exist in a quatum superposition of being dead and alive at the same time for an arbitrary long period of time.
So what happens if you’re in a box instead of the cat. Well, you watch the detector and then you will eventually see it decay and kill you or somebody opens the box and lets you out before it happens. There’s no observable superposition that can happen from your frame of reference since you are part of the system to begin with. From the point of view of somebody outside, you are both dead and alive until observed as one or the other. There is simply no paradox much like there is no paradox with time dilation in relativity.
I guess in other words - the classical physics event continuity or consistency is already annihilated by special relativity. General relativity and Quantum Mechanics sweep the pieces under the rug. Schrödinger’s cat as described is as much of a logical problem as the Twin paradox - i.e. none.
With regard to this business with Schrodinger’s cat and macroscopic superpositions, I don’t think it’s as simple as you’re making it out to be. Arguments about wavelengths being small can explain why we don’t notice quantum uncertainty on macroscopic scales, or why I don’t exhibit diffraction when I walk through a doorway – but I don’t think that addresses the question of whether or not superposition states exist at a macroscopic level. That is, can a macroscopic object be in a superposition of two different observable states – something which is in principle allowed by quantum mechanics?
You might say that’s not a question of physics, since the act of observation projects the system into a single observable state, meaning such superpositions would be unobservable. But when does the projection occur? That depends on what a “measurement” in quantum mechanics actually is. Say we have a Schrodinger’s cat type experiment: an atom decays (or doesn’t), a detector detects the decay (or doesn’t), an cat-killing device responds (or doesn’t), a cat dies (or doesn’t), an experimenter looks in the box and sees a dead cat (or doesn’t)? At which stage in the process was the decay of the atom “measured” and projected onto either the decayed or undecayed state?
Again, one might ask “Who cares?”, so long as we know the projection happens some time before we (the experimenters) actually see the outcome. And unless we can set up some sort of interference to demonstrate the existence of this superposition state – like in the double slit experiment – then maybe that’s reasonable.
But personally I think some people get a little too carried away with the “shut up and calculate” approach. If the state of a system has real physical reality, then asking when the state undergoes a projection is a meaningful question about reality. And if you’re going to say the quantum state (i.e., the wavefunction in the Schrodinger picture) is just a useful mathematical construct for predicting the outcome of experiments, then I’d ask: are electrons just a mathematical device with no real existence? Are electric fields just a mathematical construct with no real existence? What about the chair I’m sitting in, or the table my computer sits on? Am I just thinking the thoughts I associate with typing because I believe they’ll result in my experiencing the thoughts associated with seeing words on a screen? Maybe philosophers think that way, but I’d suspect that most physicists believe deep down in their gut that they’re studying real things that actually exist, even while they’re giving lip service to the notion that they’re just trying to predict the results of experiments. If none of it’s real, why bother?
If you think that whole last paragraph is bull, so be it, let’s bring the discussion back to things that are measureable. There are some theories that macroscopic superpositions can’t exist – i.e., that there is some phenomenon that destroys superposition in systems of that scale – something other than the usual time-dependent decoherence of quantum mechanics. This would be some new physics (beyond quantum mechanics) that only shows up at macroscopic length scales, or perhaps in a way that depends on the amount of mass involved. Penrose’s theory (that mathochist mentioned) is one such idea. The thing is, these ideas are testable, at least to some degree. One can try to look for superpositions in mesoscopic objects (presumably by looking for interference effects, although I don’t know much about the specifics of these experiments). Obviously, the short decoherence times are a problem, but it’s possible that there’s a range where you should be able to detect quantum effects before decoherence, unless some other effect (beyond quantum mechanics) is destroying the coherence.
I heard Tony Leggett give a talk on this subject sometime last year, so that’s at least one prominent physicist (besides Penrose) who thinks these ideas may have merit. (Leggett mentioned tests using SQUIDs in particular.) Of course, there are equally prominent people who disagree.
I recall this article being a decent overview of some issues involving decoherence, the measurement problem, etc., but it was months ago that I read it (and I don’t have time to read it again right now) so I can’t vouch for it 100%.
I’m actually not asserting that a macroscopic sample of material can not ever be in a superposition of states simply by virtue of its size. Much of my thesis research was focused on liquid helium, a system which exhibits both superfluidity and Bose-Einstein condensation. Both phenomenon are examples of coherent quantum behavior at macroscopic length scales, and with all the work that has been done on trapped condensates it wouldn’t surprise me if someone is able to do some interesting interference work with macroscopic BEC samples.
What I’m arguing against is the tendency to apply superposition to any case where randomness exists. Is a box contained a pair of dice in a superposition of all possible rolls until it is opened? No. (Again, unless you are a member of the “if a tree falls in the forest” school of thought, but that’s philosophy, not science.) The measurement problem is not tied to human consciousness, but to the nature of interaction required to gain information from a system.
I assert that the cat-killing device is acting as the measurement in this case. Just as putting detectors over the slits in a two-slit experiment collapses the wave function and forces the electron to pass entirely through one slit or another, once the detector is present in the box, the atom can no longer remain in a superposition of decayed and undecayed states. Everything after that is randomness, and happens exactly as it would happen regardless if the box was open or shut.
The basic idea behind the Schrodinger’s Cat paradox, namely that the cat remains in a superposition of states until we open the box, is to me no different than arguing that the results of a two-slit experiment with detectors over the slits still show interference fringes until we turn our heads and look at the screen, at which point everything instantaneously changes in response to our gaze. It’s a bizarrely egotistical view of causality and science, in which the mere act of our attention causes physical changes.
I agree, up to a point. Useful theory can come from starting points which are not initially experimentally observable. (A case in point is Leggett’s theory that high-T[sub]c[/sub] copper oxide superconductors have d-wave symmetry – at the time, the current results were equally consistent with s-wave symmetry, until new experiments were developed to distinguish the two cases.) At the same time, however, many in the pop science community view quantum mechanics as a license to impose mysticism on science, usually as a result of not understanding quantum mechanics. (“If an electron can be in a superposition of spin up and spin down, then my foot can be in a superposition of wearing a shoe and a pumpkin.”) I find this to be highly counterproductive.
I think this may have been our disagreement. The plain reading of what you wrote before was that the cat does not superpose (ever). I did not mean that the superposition lasts until the box is opened. The entire state is entangled in a superposition of |decayed atom>|shattered vial>|dead cat> and |undecayed atom>|solid vial>|live cat>, but because the two states are so vastly different (in Penrose’s setup: have such different gravitational energies) the superposition decoheres almost instantaneously. The proposition of a mechanism of, or at least of a predicted timescale for, decoherence of superpositions as a resolution to the measurement problem is most definitely science and not philosophy. In fact, an experiment to test Penrose’s conjecture based on his original proposal is proceeding towards construction even now.
In brief: I meant that the superposition does exist, but decoheres very quickly. You meant (correct me if I’m wrong) that the superposition doesn’t happen in the way the original Cat story is told in the Copenhagen Interpretation.
