A thousand years from now, the twentieth century will be remembered as the time when we discovered quantum mechanics. Forget wars, computers, bombs, cars and airplanes: quantum mechanics is a deep truth that will continue to be a part of our understanding of the universe into the foreseeable future.
So it’s kind of embarassing that we still don’t understand it. Unlike relativity, which seems complicated but is actually quite crystal clear when you get to know it, quantum mechanics remains somewhat mysterious despite its many empirical successes, as Dennis Overbye writes in today’s New York Times.
Don’t get me wrong: we can use quantum mechanics quite fearlessly, making predictions that are tested to the twelfth decimal place. And we even understand the deep difference between quantum mechanics and its predecessor, classical (Newtonian) mechanics. In classical mechanics, any system is described by some set of quantities (such as the position and velocity), and we can imagine careful experiments that measure these quantities with arbitrary precision. The fundamentally new idea in quantum mechanics is that what we can observe is only a small fraction of what really exists. We think there is an electron with a position and a velocity, because that’s what we can observe; but what exists is a wavefunction that tells us the probability of various outcomes when we make such a measurement. There is no such thing as “where the electron really is,” there is only a wavefunction that tells us the relative likelihood of observing it to be in different places.
What we don’t understand is what that word “observing” really means. What happens when we observe something? I don’t claim to have the answer; I have my half-baked ideas, but I’m still working through David Albert’s book and my ideas are not yet firm convictions. It’s interesting to note that some very smart people (like Tony Leggett) are sufficiently troubled by the implications of conventional quantum mechanics that they are willing to contemplate dramatic changes in the basic framework of our current picture. The real trouble is that you can’t address the measurement problem without talking about what constitutes an “observer,” and then you get into all these problematic notions of consciousness and other issues that physicists would just as soon try to avoid whenever possible.
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.” It’s not too much to ask, I think. It would also be great if everyone could explain the distinction between bosons and fermions. Someday I will write a very short book that explains the major laws of modern physics — special relativity, general relativity, quantum mechanics, and the Standard Model of particle physics — in bite-sized pieces that anyone can understand. If it sells as many copies as On Bullshit, I’ll be quite happy.
Sean said:
We’ll, I don’t know exactly what you mean, but if I had to guess I’d say that you are (and if you aren’t now you are on the path to be) a believer in nonlocal hidden variables.
What I was thinking was…
If Schroedinger wanted the state of this:
|no decay of an unstable radioactive atom>|alive> + |decay>|dead>.
So that we can give the state |alive> some probability.
But an atom can not kill a cat.
I guess people used radioactive material to give alive this meaning of probability…
If the box contains a detector to trigger a gun or something,
the system state is:
(|no decay of an atom>+|decay>)|alive>
—> measurement by a detector ( = projection op., |decay>(decay|. This is guess. But if I express measurement process in a projection op,…)
After projection process, the state is in pure(?).
Then there’s no need for distinguishing between QM and CM, no need for probability concept.
—>triggering act ( =op., |dead cat>(alive cat| )
—>dead cat
What I wanted to say with *the amount of radioactive material and exposure time* was…:
The cat had never been in the QM’al probabilistic state, it was in the 100% alive state.
Or QM system and CM system can not be mixed in the first place.
And wanted to give wave function some meaning of time, though I’m not sure what I was thinking…
Hmm…yeah, this is odd 🙂 Sorry if I distracted the thread.
Of course, quantum gravity potentially raises the stakes in this discussion, although the implications are at least as obscure as quantum gravity itself. This recent preprint is interesting:
Observables in effective gravity
(hep-th/0512200)
Authors: Steven B. Giddings, Donald Marolf, James B. Hartle
Aaron – the fact that we can only perceive one branch of the density matrix seems no more problematic to me than the fact that if someone were cloned then there would be end up being two people, each perceiving their own reality (and having memories consistent with the pre-cloning events).
Though I’m certainly willing to be corrected, as far as I can see decoherence seems to solve all the conceptual problems of QM – there no longer seems to be any need to assign a special role to the observer or to define what constitutes an observation.
Also I’m not sure about Sean’s statement “what we can observe is only a small fraction of what really exists”. What is it that exists that we can’t observe? Sure we can’t observe the ordered pair (x,p) of a particle but under standard interpretations of qm this doesn’t exist either. Or maybe I’m misunderstanding something…
The wavefunction is the thing that really exists and can’t be observed. The position and momentum don’t even exist independently, much less simultaneously.
Of course, I also believe that “it is useful to think that…” is indistinguishable from “it is true that…”, but that’s the subject for another discussion.
“the fact that we can only perceive one branch of the density matrix seems no more problematic to me than the fact that if someone were cloned then there would be end up being two people, each perceiving their own reality (and having memories consistent with the pre-cloning events).”
There is, as far as I know, no physical derivation of the significance of the reduced density matrix. Decoherence tells us that microscopic systems entangled with macroscopic systems do not exhibit interference between macrostates of the macroscopic system. That doesn’t tell us why this should have anything to do with our perception. We perceive a classical world, and I don’t know of any reason why this should be so.
A lot of common misinformation and misinterpretation of QM and G/S Relativity seems to be due to people resorting to a logical fallacy – drawing conclusions from an analogy.
The way I interpret the process of building a Physical description, one needs to be able to express it within a rigorous Mathematical framework and come up with some testable consequences of the theory. The qualitative interpretation of the Mathematical description in terms of familiar concepts is what seems to lead to most of the confusion about the issue.
Sean – sorry if I’m being slow, but I don’t really see why in principle you can’t measure the wavefunction (at least upto an overall phase). Clearly you can’t do it by trying to measure the position directly since then the particle will simply collapse (or appear to collapse) to a position eigenstate. But is there some reason that there can’t exist another measurement process that gives you the wavefunction (upto phase) to arbitrary accuracy? (There doesn’t seem to be a really obvious fundamental reason like HUP.)
The article linked to below, entitled “On the End of a Quantum Mechanical Romance” is by a philosopher, not a physicist, but it seems very relevant to the discussion.
http://psyche.cs.monash.edu.au/v2/psyche-2-19-mulhauser.html
Aaron – as far as I understand it, in each branch the states are near coherent (the Heisenberg inequality is close to being saturated) and since (in everyday units) Planck’s constant is small, it appears that all the uncertainties ((delta x),(delta p) etc.) are small in each branch and hence we can approximate by classical states to get a good classical effective theory for each branch.
As for why each branch can’t perceive another branch, well if the Hilbert space splits as H = H_1 + H_2 after decoherence (just say there are two sectors) then you should be able to show that each sector can’t “observe” the other sector. To be more specific, starting from |p_1(0) >
Sorry, that last message seems to have been cut off from about half way through (probably due to formatting problems, although it was OK on the preview). Never mind.
michaeld– The intuitive idea is straightforward: you probe the wavefunction by “measuring an observable,” and whenever you do that the original wavefunction is perturbed away from its state. It’s true that it’s somewhat difficult to make a rigorous statement, although people have tried to prove a no-measurement theorem (see also here); I’m not at all an expert. There is a well-established no-cloning theorem that says you can’t duplicate a wavefunction without disturbing it; this is close to what you want, since if you could measure the wavefunction precisely, you could just go ahead and prepare another system in the same wavefunction, which is forbidden by the no-cloning theorem.
It’s only when you trace over the measurement apparatus (to get the reduced density matrix) that you get orthogonality. The question is why is this a relevant procedure.
If the wavfunction of the Universe :
http://www.geocities.com/capecanaveral/hangar/6929/h_kaku2.html
for instance is partially true?..then the shroedinger cat inside-box, cannot ever be killed, for even for cats, part of their wavefunction is outside the box, and thus it may allready be in a partial existence inside another Universe? …theoretically I can deduce that, according to feline stastistical laws, there are NINE feline Universe.
As an afterthought, there is probably one Universe for every day of the cats week, which may or maynot be nine? 🙂
QR,
One’s nine lives can be quickly extinquished when you sing the “wrong phrases” in a choir group? Which ever it is that day? 🙂
So then, does it becomes a matter of survival to “me-ow” intune?
Imagine, “censoring” to become a potent force in recognition? As a opposition?
Naw, I am sure we are all stronger in our convictions then this?
Momentum and Position talks set mind to wonder on the significances that followed from the days talks here
So much to remember.
@Sean:
The wavefunction is the thing that really exists and can’t be observed. The position and momentum don’t even exist independently, much less simultaneously.
Actually, no, Heisenberg’s principle is that one cannot measure the two to arbitrary precision at the same time. It most definitely does not say that the two do not exist simultaneously. The point of HUP is about how well we can know a generalized coordinate and its canonically conjugate generalized momentum, not whether they exist at the same time. The basis transformation from the Lagrangian to the Hamiltonian would be, um, problematic, if half of the space for the Hamiltonian didn’t exist, don’t you think? Physically, some generalized equivalent of energy would be go missing in the description of the system
The intuitive idea is straightforward: you probe the wavefunction by “measuring an observable,” and whenever you do that the original wavefunction is perturbed away from its state.
Whether the wavefuntion is perturbed depends on what you are measuring. Some things yes, some things no — if the operators commute, then you can measure away until you’re out of observables associated with commuting operators (at least in principle, though I’d bet that practically speaking, the set of observables you can do this with is always pretty small, maybe even sets of 1). Either that, or someone seriously needs to rewrite the old school Caltech way of teaching graduate quantum (the gent who taught my class was of that noble pedigree; also, this is opposed to quantum field theory, which while we didn’t get much into, so I make the disclaimer that I realize that I need to learn some new tricks, but hey, we’re talking about quantum mechanics, not QFT or QCD or other areas where I am on much less sure ground).
@Cat:
You seem to have hit upon the reason Schrodinger came up with his gedanken experiment — he is reputed to have thought the Copenhagen interpretation was too problematic, hence the desire to come up with a demonstration of absurd reasoning to score points.
agm– I hope your Caltech professor taught you that, when you perform a measurement of a certain observable, the observation returns an eigenvalue of that observable and the wavefunction is subsequently in a corresponding eigenstate. That’s the collapse of the wavefunction, or whatever you want to call it. Of course, if you’re lucky enough that the wavefunction is already in an eigenstate, there need be no evolution, but that’s certainly not the generic case.
Your argument about the uncertainty principle is precisely the mistake I was arguing against: we shouldn’t think of position and momentum as things that exist but can’t be simultaneously measured, we should think of the wavefunction as what exists, and observations as something that only tell us about part of it.
I’m interested in the role of the observer, and in particular the nature in which consciousness comes into play. I am of the faith (scientific though be it) that consciousness is a physical phenomena, and so the act of observation, according to current theory, would be interactions between collections of observer matter particles, force particles, collections of observed matter particles and the like, by my (and physics’) admittedly limited knowledge of the universe. Of course, I could be wrong. What do you think?
If there are cases when making an observation does not change the state of a wavefunction (i.e., when the wavefunction is an eigenstate of the observable before making the observation), then my description is correct. The generic case is irrelevant — the question is whether such an observation is possible, not how many systems one can come up with where one could make such a series of measurements. And I explicitly mentioned this in my parenthetical comment.
And I made no mistake. Throwing the physical analogue I presented in the trash, the mathematical framework requires both generalized coordinates and either generalized velocities (Lagrangian description) or the relevant generalized momenta (Hamiltonian description). Either way, HUP makes a statement about the about their relation, not their existence. It’s a property inherent in the description.
Pedantry, yes. Error, no.
“Plato” so true! 😉
Observer dependence is contained within GR/SR? and also Observer dependence is a contributing factor for QM, where the wavefunction is really the 2-D re-formulation of the 3-D description of a lcoal Particle, its a “particle-function” spread out as a field of waves?
A particle inside a box is tangable stuff:
http://pancake.uchicago.edu/~carroll/universelab05/img8.html
so interpretation of forms via E=mc2, can be shown that the dimensionality of the expressed energy, is not a translation in non similar dimensions?
A 2-D field energy, say the force particles, are not 3-D ‘waves’ that can “pile up one on top of the other”, and as stated in a post above by agm, the P.E.P relates particles of a 3-D ‘tangable’ matter in space?.. to exclude other ‘like’ energies at one location of space.
Where as the H.U.P is an exclusion principle of Time parimiters. A change in space-time, is a change in dimensional location of structure makeup.
You can observe a 3-D particle in spacetime, you can locate a 3-D particle in 2-D, space what you cannot observe is a 2-D field inside a 3-D particle.
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.” It’s not too much to ask, I think
Hmm, here is a live experiment that can help you determine whether you are asking for too much or not … [I hope most of the commenters at ‘slashdot’ have a college degree].
Sean – thanks, I think I understand now (about why we can’t measure the wavefunction). That’s very interesting.
Quantum mechanics is very mysterious. However, the Heisenberg uncertainty relation, which is often held up as a central element of quantum mechanics, is not the mysterious part. Uncertainty relations are a consequence of working with waves, and have little to do with the quantum nature of quantum mechanics.
Even classical waves, like water waves, obey uncertainty relations. In the case of classical waves, the uncertainty relates the position and spacial frequency (the number of waves per distance, which is the reciprocal of the wavelength). If dx is the uncertainty in the position (roughly the length of the wave packet) and d(1/l) is the uncertainty in spacial frequency (the spread of the wave’s Fourier transform) then the uncertainty relation is:
dx d(1/l) > 1/(2 pi)
In order to get a good measurement of the spacial frequency (or wavelength) the waves need to be spread out over a large distance, making their position very spread out. To get a good measurement of the position the waves need to be very bunched up, making it difficult to pin down the spacial frequency.
There is also an uncertainty relation relating time and frequency
dt df > 1/(2 pi)
Quantum mechanics identifies momentum with spacial frequency and energy with frequency via:
p = h/l
E = hf
where h is Planck’s constant. This leads to the usual uncertainty relations:
dx dp > h/(2 pi)
dE dt > h/(2 pi)
For me, this removed the mystery of the uncertainty relations. Uncertainty relations are a result of working with waves, whether they are water waves or wave functions.
The mysteries of wave function collapse and entanglement remain. I think that decoherence removes wave function collapse from the theory, shifting the issue even more sharply to entanglement. Entanglement is the only thing left keeping me awake at night, but it keeps me awake often.
Gavin
As Dumb Biologist I suscribed to the decoherence idea: it´s quantum mechanics all the way up! This obviously solves all problems: the world is deterministic but it is impossible to know, even in principle, the state of a system with arbitrary precision. That´s why we can only make statistical predictions. To be honest I don´t really know to what extent the wavefuctional collapse has been rigorously “explained” in the literature (yes, I said wavefunctional, like it or not the world is described by a quantum field theory). But this collapse should be our interpretation of a dinamical instability of entangled states involving several particles (or quanta) that happens in quantum field theory. The eigenvalues of the operator we are measuring should be the “attractors” of the (quite complicated) dynamical evolution.
I don´t like the discussion of the collapse of the wave function of particles. The world is not like that, what is reduced is a wavefunctional, and I think that the instability that we associate with the collapse is a phenomenon that takes place only in a quantum theory of fields, not particles.
IN: I agree! Always good to see someone being reasonable in a discussion like this instead of postulating experimentally unverified nonunitarity magic.