Quantum Mechanics in a nutshell

Factual Questions
1

Triggered (at least most recently) by this post, I find myself again wondering if it’s possible to have a reasonable facsimilie of a working understanding of quantum mechanics.

<this section, wherein I try to list what I think I know and ask what I think I don’t understand, has been typed, edited, finally deleted>

Can anyone recommend a layman’s guide that explains the truth and sidesteps any hokey metaphysics (I’m looking at you Zukav). Or is it within the boundaries of a message board to post an essential primer here?

2

Well, you could read George Gamow’s Mr. Tompkins series – that was an attempt by someone involved in the Quantum Revolution to write a popularizatyion of Quantum. I think his thirty Years that Shook Physics is better. But a better choice for the science might be **Where Does All the Weirdness Go?"
For my money, I think you’d do pretty well by getting an intro. quantum textbook. There are a lot of them with titles like Introduction to Modern Physics (McGervey, or Kennerd Richtmeyer, Lauritsen, and the entire world), or Quantum Mechanics (more than you can shake a quantum stick at).
How about the Feynman Lectures on Physics? He can take the abstruse and boil it down to the understandable, but you’ll need some math.

3

The absolute most important thing to understand about quantum mechanics is that it’s a wave theory. So start by trying to understand classical wave theories. Once you know those backwards and forwards, inside and out, then start on quantum mechanics, and you’ll find that it’s not so weird after all. Most of the features which seem weird in quantum mechanics are common to wave theories in general, and it’s just the fact that folks think of electrons and the like as classical particles that make them seem weird.

Of course, it’s also a particle theory, which is in fact where most of the quantization comes in. You have to be prepared to think in particle terms and wave terms at the same time, or at least to switch from one to the other with ease. But it’s not generally the particle aspects which trip people up.

4

The first book on QM that I read was In Search of Schrodinger’s Cat, by John Gribbin, which I still think is an excellent non-mathematical introduction. The Feynman Lectures are very good indeed, but rather more heavy. Definitely not an elementary introduction; he assumes a lot of previous physics and maths knowledge.

5

I read a book several years ago called “Taking the Quantum Leap” by an author named Wolf (or Wolfe? Wolff?) It did a very good job of explaining quantum physics in layman’s terms, with lots of simple, easy to understand illustrations.

6

I just finished thumbing through The Quantum Zoo, and it’s not bad at all. Easy to read with nice analogies.

7

[QUOTE=Nature’s Call]
Can anyone recommend a layman’s guide that explains the truth and sidesteps any hokey metaphysics (I’m looking at you Zukav). Or is it within the boundaries of a message board to post an essential primer here?
[/QUOTE]
I think introductory physics text and the like are going to be a bit beyond the “layman’s guide” level of explanation. At the request of a friend to whom I recently described (and appearantly really freaked out) the set-up, result, and implications of the dual slit experiement, I perused the local book stores in search exactly what you are asking for, and found Jim Al-Khalili’s Quantum: A Guide for the Perplexed. This is a pretty simple–but not simplistic–introduction on the principles of quantum mechanics from a strictly layman’s perspective. He does stuff like introduce the Schrödinger equation and briefly describe how it works, but he doesn’t delve into doing actual operations with it. I’m still working through it, so I can’t vouch for whether the cat is dead or alive in the end (quantum physics joke) but so far his presentation is both clear and, as much as any English explanation can be, comprehensive without droning on and on about thought experiments. The format is essentially written in small essays or articles with specific issues in sidebars, so you can pick it up without having to read fifty pages of mind-numbing analogies and put it down knowing less than you did before. Plus, it really has some beautiful illustrations and artwork.

One caution, though; don’t think that by reading this, or any other text on quantum mechanics, that you are going to “understand” QM. We can describe, in mathematical terms, the way in which things happen, but not the “How?” of them, and indeed it may be fundamentally impossible to functionally distinguish between one interpretation and another. All interpretations, and indeed the practical models that portray quantum mechanical behavior as alternatively a wave and a particle as Chronos describes, are an attempt to parse the mechanics of a non-classical, non-deterministic system in terms that we can at least understand in our experience. A photon or electron may be a wave (in some ways) but it’s not, analogies aside, like a wave on the ocean. And they may be particles, but they’re not little bits of stuff. Trying mentally to force them into the mold of classical, everyday objects is a recipe for frustration salad with a side order of bafflement breadsticks.

Stranger

8

Oxford University Press’s Very Short Introduction series is a real godsend for anyone trying to quickly get a good overview of a scientific (or other scholarly) topic. John Polkinghorne’s Quantum Theory: A Very Short Introduction in that series may be just what the OP is looking for. (Cheap, too!) I bought it a couple years ago and learned a lot from it.

9

As a synthetic chemist, I have a very laymans understanding of the QM principles. The minute someone throws a matrix of eigenvalues into the game I’ll fold, but I might be a good person to ask for just that reason. Besides, I’m just as likely to learn something as you are, and this stuff is pretty cool if you ask me.

Of course you would get a chemists perspective and maybe thats not what you are looking for.

10

[QUOTE=Chronos]
The absolute most important thing to understand about quantum mechanics is that it’s a wave theory. So start by trying to understand classical wave theories. Once you know those backwards and forwards, inside and out, then start on quantum mechanics, and you’ll find that it’s not so weird after all. Most of the features which seem weird in quantum mechanics are common to wave theories in general, and it’s just the fact that folks think of electrons and the like as classical particles that make them seem weird.
[/QUOTE]

I’d like to second this point. Superposition, coherence, interference, the uncertainty principle, discrete spectra, etc., whose appearance in a theory of atoms may at first seem puzzling, all occur in classical wave theories. Nevertheless, some weirdness is (so far as I know) uniquely quantum mechanical: indistinguishable particles are one example. The fact that unitary microscopic interactions somehow result in non-unitary “measurements” is another (not fully explained by decoherence, in my opinion.)

Of course, someone seeking a non-mathematical introduction to quantum mechanics probably won’t want to learn the mathematics of classical waves either. But searching for a book that discusses quantum mechanics by analogy to classical waves is a good idea nontheless. Unfortunately I don’t have one to recommend – in recent years all the books I’ve read on quantum mechanics are textbooks intended for students who need to learn calculations, not just concepts. I read a bunch of books for the popular audience when I was a kid, but back then I wasn’t educated enough to assess their quality, and now I don’t remember them well enough.

Although I’m too busy right now maybe later in the week I can hammer out some sort of ultra-bare bones intro to quantum mechanics (assuming another poster doesn’t do it first). I think at the very least it ought to explain:

  • why a quantum mechanical wave can look like a classical particle in certain limits (i.e., why don’t we notice the wave particle duality in the macroscopic world)

  • A discussion of what it means to choose a basis and to make a measurement in that basis (An analogy to passing light through a polaroid filter – as in the first chapter of Sakurai’s textbook, could be usefull)

  • some discussion of energy eigenstates and time evolution

  • probability amplitudes

  • relative phases and interference

  • the uncertainty principle explained in terms of wave packets

  • discreteness as related to a classical wave with boundary conditions

  • perhaps something about spin

  • perhaps something about indistinguishable particles and how their statistics differ from classical particles

Of course on looking at even this brief list, it’s a rather daunting task. Maybe if one of us says a little about one topic, and someone else adds a little about another . . . of course, if someone can find a book that says it all perfectly, then so much the better.

11

Thanks all! I just ordered The Quantum Zoo and Quantum: A Guide for the Perplexed.

While I’m waiting, here’s a bit of what I think I know: The double slit demonstrates the wave nature of fundamental particles. If one fires photons at a photographic plate through the double slit, the image that forms displays an interference pattern - a phenomenon consistent with how sound waves or ocean waves would behave. The “weirdness” begins when the photons are emitted one at a time. The same pattern appears, but how can that be? How does one photon interfere with the photons that had gone through long before?

The “explanation” is that something wave-like is propagating from photon source through to photographic plate, and that is a cascading set of probabilities as to the location of any one photon. While the exact location of any one photon cannot be known, a set of possible locations can be ranked in order of probability.

It’s my understanding the mathematical model that describes this propagation has been proven. But unlike classical mathematical models where one can draw a picture and label each component of the equation to explain what the model represents in the real world, the behaviour described by the quantum model defies description. In other words, no on really knows what happens between the beginning of an event and the taking of a measurement (which collapses the probability wave, eliminating all possibilities that had propagated to that point except the “chosen” one). It is this lack of knowing that gives rise to various Interpretations of Quantum Mechanics[sup]tm[/sup].

I think I understand the Many Worlds Interpretation. Is this seriously held to be a possiblility? What is the Copenhagen Interpretation?

I’ll stop here…

12

[QUOTE=Stranger On A Train]
He does stuff like introduce the Schrödinger equation and briefly describe how it works, but he doesn’t delve into doing actual operations with it. I’m still working through it, so I can’t vouch for whether the cat is dead or alive in the end …
[/QUOTE]

Well, you’re in good company: neither could Erwin! :smiley:

(And the fact that that joke is the one substantive thing I can add to this thread makes me avid to fight my own ignorance by following it. :))

13

[QUOTE=Nature’s Call]
While I’m waiting, here’s a bit of what I think I know: The double slit demonstrates the wave nature of fundamental particles. If one fires photons at a photographic plate through the double slit, the image that forms displays an interference pattern - a phenomenon consistent with how sound waves or ocean waves would behave. The “weirdness” begins when the photons are emitted one at a time. The same pattern appears, but how can that be? How does one photon interfere with the photons that had gone through long before?
[/quote]
It doesn’t need to interfere with the ones that have gone through before (although there are interpretations that posit precisely this, though not very popular ones); the photon exists as a statistical distribution, and while the behavior of any individual photon is unpredictable, a collection of photons will fit the distribution function precisely.

[QUOTE=Nature’s Call]
It’s my understanding the mathematical model that describes this propagation has been proven. But unlike classical mathematical models where one can draw a picture and label each component of the equation to explain what the model represents in the real world, the behaviour described by the quantum model defies description. In other words, no on really knows what happens between the beginning of an event and the taking of a measurement (which collapses the probability wave, eliminating all possibilities that had propagated to that point except the “chosen” one). It is this lack of knowing that gives rise to various Interpretations of Quantum Mechanics[sup]tm[/sup]
[/quote]
This is essentially correct. The mechanics of QM say nothing about the actual behavior of the system between action and observation. When we fire a cannon ball in the air and measure it’s resultant point of impact, we are assured that it has taken one of two possible ballistic paths (not accounting for aerodynamic losses, of course) but with particles on the quantum level they may have taken any path, or indeed, all of them simultaneously, and the options all average out (or cancel out) to the path it does take.

[QUOTE=Nature’s Call]
I think I understand the Many Worlds Interpretation. Is this seriously held to be a possiblility? What is the Copenhagen Interpretation?
[/QUOTE]
To be fair, all interpretations are, shall we say, equally absurd, and there’s no reason beyond asthetics or personal comfort to select one over the other. Nor is an interpretation necessary to do practical work with QM; whether the particle exists simultaneously in multiple worlds, or is a wavefront distributed through space in a strictly non-causal fashion, or obeys some nonlocal hidden rules, or somehow fulfills all of these interpretations simultaneously is neither here nor there when it comes to doing the calcuations, which just…work.

The Copenhagen interpretation, which is actually more of a recognition of the limits of perception and blind adherence to pragmatic working principles, is the most popular, but the argument could be made that this is due to the forceful personalities of Heisenberg, Born, and Bohr (all of whom are names that can be counted among the founding fathers of the field). I personally like to think in terms of the Bohm interpretation, which dispenses with locality (i.e. that things are locally causally connected) in favor of having the particle/waves as a potential spread out across space and able to communicate from one point to another instantaneously. This is, on the face of it, painfully inconsistent with Special Relativity, but if you squint and hold your mouth just so it’s not really a problem because this nonlocality can’t actually be used to violate causality. (The reason for this is complicated, but essentially you can’t have local hidden variables, and hence any single “spooky action at a distance” can’t be resolved as anything but noise.)

That this also causes problems with Special Relativity and quantum field theories like quantum electrodynamics worries me not a bit because (a) I think there’s room for nonlocality in QED while giving the appearance of locality , (b) it all averages out to the same conclusions as Special Relativity, so why worry about a few niggling inconsistencies in the underlying mechanics, and (c) I probably don’t know enough to be really frightened by the implications of nonlocality and how that’s totally going to screw up everyone’s day.

I hope it makes all of this as clear as the bottom of a coffeepot that’s set out with a skim of residue on the burner overnight.

Stranger

14

[QUOTE=Nature’s Call]
Thanks all! I just ordered The Quantum Zoo and Quantum: A Guide for the Perplexed.

While I’m waiting, here’s a bit of what I think I know: The double slit demonstrates the wave nature of fundamental particles. If one fires photons at a photographic plate through the double slit, the image that forms displays an interference pattern - a phenomenon consistent with how sound waves or ocean waves would behave. The “weirdness” begins when the photons are emitted one at a time. The same pattern appears, but how can that be? How does one photon interfere with the photons that had gone through long before?

The “explanation” is that something wave-like is propagating from photon source through to photographic plate, and that is a cascading set of probabilities as to the location of any one photon. While the exact location of any one photon cannot be known, a set of possible locations can be ranked in order of probability.

It’s my understanding the mathematical model that describes this propagation has been proven. But unlike classical mathematical models where one can draw a picture and label each component of the equation to explain what the model represents in the real world, the behaviour described by the quantum model defies description. In other words, no on really knows what happens between the beginning of an event and the taking of a measurement (which collapses the probability wave, eliminating all possibilities that had propagated to that point except the “chosen” one). It is this lack of knowing that gives rise to various Interpretations of Quantum Mechanics[sup]tm[/sup].
[/QUOTE]

I’m a little squeamish about the language “No one knows what happens,” although it’s more or less accurate. I hesitate because I think it’s a bit different than “no one knows” in the usual sense.

Example 1: No one knows if there is life in other solar systems. That’s because at this point we don’t have the technological means to make that determination. (Or perhaps because we haven’t been smart enough or lucky enough to make that determination with the technology we have.)

Example 2: If I drive down the street at a constant speed, “no one knows” whether I’m moving and the street is standing still, or whether I’m standing still while the street (and the rest of the world) moves underneath me. In this sense “no one knows” because you can choose to define “motion” either way. Whether I’m moving relative to the ground or the ground moves relative to me is a matter of taste, not a matter of physics.

It’s possible that quantum mechanics is more like the second example. That is, the different interpretations seem to make exactly equivalent predictions, so there’s no way to distinguish one from the other. In that case, I’m not sure whether it’s still meaningful to say “the world is this way” or “the world is that way.” It could be that in some sense they’re just two different ways of saying the same thing. In which case, I’d hesitate to say “no one knows” what’s happening.

The Copenhagen interpretation is the “old school” interpretation of quantum mechanics promoted by Bohr and Heisenberg, and so far as I know it’s still the most common interpretation offered in QM textbooks. There’s various versions of the Copenhagen interpretation, but in a nutshell, it just says “When someone makes a measurement, the wavefunction collapses.” There’s no explanation of why the wavefunction collapses, and usually “measurement” isn’t particularly well defined either.

Perhaps it would be helpful if I explain what I mean by wavefunction collapse. (I’ll mark it off with asterisks for those who want to skip the details.)

Wavefunction collapse basically means that the state of the system changes in an irreversible way. Normally, quantum mechanical systems evolve in such a way that you could run the evolution backwards and get back to the system you started with. That’s called “unitary” evolution. But (in the Copenhagen interpretation) measurement is the exception to this rule. It’s “non-unitary”.

To understand the difference, it helps if you understand the idea of a superposition. If you have a two solutions to a wave equation (or some other homogenous linear differential equation), you can take a sum of the solutions and get a new solution. E.g., it’s possible to have light of a particular frequency (i.e., a particular color), but you can also have white light, which as I’m sure you know is a mixture of colors.

Quantum mechanics also obeys a wave equation, so the same sort of thing is possible. So say we have two possible states of an atom (call them state 1 and state 2). You can then have a state that’s a superposition (i.e., sum) of the two:
1 + 2

An example of a unitary transformation would be one that maps state 1 to state 2, and state 2 to minus one times state 1.

1 + 2 –> 2 - 1

This can be readily reversed. Just map state 1 to minus one times state 2, and map state 2 to state 1

2 - 1 –> 1 - (-2) = 1 + 2

The key point here is not that we got back our particular choice of initial state (1+2). The point is that we would have gotten back our initial state no matter what it was.

An example of a non-unitary transformation would be one that maps both states to state 1

1 + 2 –> 1

Of course we could get back our initial state by mapping 1 to 1+2. But this transformation wouldn’t work for every initial state. Suppose we started with just state 1 and applied both transformations.

1 –> 1 –> 1+2

This doesn’t give us back what we started with. Thus, it’s not a unitary transformation.

The main problem with the Copenhagen interpretation (at least, in my view) is that measurement produces a non-unitary transformation (wave function collapse) – any yet, any measuring device ultimately consists of atoms which interact with the system you’re studying, and we expect these interactions to be unitary. So how do you combine a whole bunch of unitary (reversible) transformations and get something which is non-unitary (not reversible)? There have been some efforts to explain this since Copenhagen, but in my opinion none are entirely satisfactory.

The Many Worlds interpretation gets around the problem by saying (roughly) that every possible result of the measurement happens in some alternate universe. So even though it looks like the evolution of our particular universe is non-unitary, the evolution of the collection of all possible universes is still unitary. So the Many Worlds interpretation gets rid of non-unitary measurement, but at the expense of postulating an infinite number of unobservable worlds. Scientists strive to create theories with as few assumptions as possible, so a lot of them consider the introduction of infinitely many alternate worlds to be a worse problem than the one it solves.

“Is this seriously held as a possibility?” By some people, sure. But at least in my experience it seems that physicists either love the idea or hate it, with hate probably being the majority.

15

I don’t know about a love/hate dichotomy, there… Personally, I’m passionately ambivalent about it (and about most other interpretations of quantum mechanics). Which is not meant to be a joke, by the way, but I’m not sure how much better I can explain it.

16

[QUOTE=Chronos]
I don’t know about a love/hate dichotomy, there… Personally, I’m passionately ambivalent about it (and about most other interpretations of quantum mechanics). Which is not meant to be a joke, by the way, but I’m not sure how much better I can explain it.
[/QUOTE]
Interpretive Relativist! :wink:

Chronos may be ambivalent about it, but contemporaries of Hugh Everett III were downright unimpressed with his “relative state” interpretation, later known as the Many Worlds interpretation. (No doubt part of his dissatisfaction comes from not having the scheme eponymously named after him.) Although many leading physicists wouldn’t give Everett’s claims the time of day (Bohr reportedly brushed him off after he’d travelled to Copenhagen to meet him) it’s not as if he was completely off on a limb; his advisor was the famous John Wheeler who also advised Richard Feynman, Charles Misner, and Kip Thorne, and Wheeler did some work now and again with Everett’s relative state interpretation, though there’s no indication he (or Everett) took the notion of multiple worlds literally.

The “Many Worlds” by the way, are nothing resembling what you read or see in science fiction, with evil twins wearing facial hair and displaying aberrant behavior; the only interplay between the multiple universes comes at the level of quantum interactions, and indeed the term “Many Worlds” was applied much later by Bryce DeWitt who popularized the notion. (DeWitt wasn’t a flake either–among other honors he was awarded the prestigious Dirac Medal and the Einstein Award, but by popularizing the notion it was brought back into the consciousness it never gained originally.) The interpretation does offer some advantages in dealing with decoherence, allows for strict determinisim rather than probabilistic behavior, and it alieviates the whole vagueness regarding the actuality of “waveform collapse” that the Copenhagen people strenuously avoid talking to. According to some proponents, it should be considered a falsifiable theory, but I don’t understand how it is any more or less falsifiable than any other interpretation.

Anyway, Everett not getting the kudos he believed due him, turned his back on quantum mechanics and went to work for defense consultants, using his background in game theory and operations research to maximize the effectiveness and reliability of ICBM delivery systems. Hell hath no fury like a physicist scorned, I guess.

Stranger

17

Tim314, A couple of times in the post below, you mention “indistinguishable particles.” I would like to hear more about this.

-FrL-

[QUOTE=tim314]
I’d like to second this point. Superposition, coherence, interference, the uncertainty principle, discrete spectra, etc., whose appearance in a theory of atoms may at first seem puzzling, all occur in classical wave theories. Nevertheless, some weirdness is (so far as I know) uniquely quantum mechanical: indistinguishable particles are one example. The fact that unitary microscopic interactions somehow result in non-unitary “measurements” is another (not fully explained by decoherence, in my opinion.)

Of course, someone seeking a non-mathematical introduction to quantum mechanics probably won’t want to learn the mathematics of classical waves either. But searching for a book that discusses quantum mechanics by analogy to classical waves is a good idea nontheless. Unfortunately I don’t have one to recommend – in recent years all the books I’ve read on quantum mechanics are textbooks intended for students who need to learn calculations, not just concepts. I read a bunch of books for the popular audience when I was a kid, but back then I wasn’t educated enough to assess their quality, and now I don’t remember them well enough.

Although I’m too busy right now maybe later in the week I can hammer out some sort of ultra-bare bones intro to quantum mechanics (assuming another poster doesn’t do it first). I think at the very least it ought to explain:

  • why a quantum mechanical wave can look like a classical particle in certain limits (i.e., why don’t we notice the wave particle duality in the macroscopic world)

  • A discussion of what it means to choose a basis and to make a measurement in that basis (An analogy to passing light through a polaroid filter – as in the first chapter of Sakurai’s textbook, could be usefull)

  • some discussion of energy eigenstates and time evolution

  • probability amplitudes

  • relative phases and interference

  • the uncertainty principle explained in terms of wave packets

  • discreteness as related to a classical wave with boundary conditions

  • perhaps something about spin

  • perhaps something about indistinguishable particles and how their statistics differ from classical particles

Of course on looking at even this brief list, it’s a rather daunting task. Maybe if one of us says a little about one topic, and someone else adds a little about another . . . of course, if someone can find a book that says it all perfectly, then so much the better.
[/QUOTE]

18

[QUOTE=Frylock]
Tim314, A couple of times in the post below, you mention “indistinguishable particles.” I would like to hear more about this.
[/QUOTE]
Fundamental particles (electrons, quarks, gauge bosons) can be identified only by their inherent physical properties like mass, spin, electric charge, color charge, et cetera, which are exactly the same for each particular type of particle; for instance, all electrons have an electric charge of ?1.6022 × 10?19 coulomb, a rest mass of about 0.511 MeV/c2, and a spin of 1/2. The only way you can tell one electron from another is by physically observing it, and the longer you observe it the harder it gets to locate it; the indeterminancy (uncertainty) principle says that the momentum gets larger the better you know the position, or alternatively the waveform gets all smeared out until you can’t predict where it’s going to be next. This is convenient in the sense that you can then treat the behavior of collections of particles in a purely statistical fashion without worrying what’s going on with any individual, but it’s very disturbing, to some people at least, that you can’t determine what’s going on with an individual particle beyond quick peeks, and you can’t tag and follow the same particle around. Thus, the behavior of particles on the quantum level is not deterministic as it is with classical objects.

Now, this notion was esthetically displeasing, and also not just a little showstopping in terms of getting a “deeper understanding” of QM, and so it was proposed by Einstein and others that there are actually hidden variables (properties or behaviors) that make each and every particle unique. <insert your own Monty Python’s The Meaning of Life joke here> The EPR paradox was intended to display this incompleteness of QM; instead, physicis John Bell formulated a theorem which used some inequalities to demonstrate that if there are hidden variables, they are “nonlocal”; that is, not causally available (observed by a local observer). This means that while there may be distinguishing characteristics between one like particle and another (aside from position and momentum) you won’t be able to measure these parameters, or at least not all together, which gives you essentially identical particles, with the added frustration that they are now spread out and act instantaneously at distant “nonlocal” points in space.

This made a lot of people very unhappy, but it has been demonstrated experimentally, so…that’s reality as we know it.

Stranger

19

[QUOTE=Stranger On A Train]
Fundamental particles (electrons, quarks, gauge bosons) can be identified only by their inherent physical properties like mass, spin, electric charge, color charge, et cetera, which are exactly the same for each particular type of particle; for instance, all electrons have an electric charge of ?1.6022 × 10?19 coulomb, a rest mass of about 0.511 MeV/c2, and a spin of 1/2. The only way you can tell one electron from another is by physically observing it, and the longer you observe it the harder it gets to locate it; the indeterminancy (uncertainty) principle says that the momentum gets larger the better you know the position, or alternatively the waveform gets all smeared out until you can’t predict where it’s going to be next. This is convenient in the sense that you can then treat the behavior of collections of particles in a purely statistical fashion without worrying what’s going on with any individual, but it’s very disturbing, to some people at least, that you can’t determine what’s going on with an individual particle beyond quick peeks, and you can’t tag and follow the same particle around. Thus, the behavior of particles on the quantum level is not deterministic as it is with classical objects.

Now, this notion was esthetically displeasing, and also not just a little showstopping in terms of getting a “deeper understanding” of QM, and so it was proposed by Einstein and others that there are actually hidden variables (properties or behaviors) that make each and every particle unique. <insert your own Monty Python’s The Meaning of Life joke here> The EPR paradox was intended to display this incompleteness of QM; instead, physicis John Bell formulated a theorem which used some inequalities to demonstrate that if there are hidden variables, they are “nonlocal”; that is, not causally available (observed by a local observer). This means that while there may be distinguishing characteristics between one like particle and another (aside from position and momentum) you won’t be able to measure these parameters, or at least not all together, which gives you essentially identical particles, with the added frustration that they are now spread out and act instantaneously at distant “nonlocal” points in space.

This made a lot of people very unhappy, but it has been demonstrated experimentally, so…that’s reality as we know it.

Stranger
[/QUOTE]

Thanks for that.

It seems to me that if it is right to say there are distinct particles, then we are committed to the view that there is some characteristic of each particle which constitutes it as distinct from the other. I think we are committed to this view even if we also think (and even if its also true) that there is no way for us, even in theory, to measure that distinguishing characteristic.

If, on the other hand, we want to say that there is no such distinguishing characteristic, then it seems to me we are committed to the view that the two particles are not distinct.

But what do others think?

-FrL-

20

[QUOTE=Frylock]
It seems to me that if it is right to say there are distinct particles, then we are committed to the view that there is some characteristic of each particle which constitutes it as distinct from the other. I think we are committed to this view even if we also think (and even if its also true) that there is no way for us, even in theory, to measure that distinguishing characteristic.
[/QUOTE]
Not necessarily; electrons and quarks are fundamental building blocks which can’t be divided (so far as we know). Even if we can identify them uniquely at any instant by their position and momentum (to a certain level of precision), it doesn’t follow that they, or any simple, regular system built therefrom is in any other way distinguishable from like systems. Only when you get to the point of having many, many interacting particles (to the point that the probability distribution of its location is smaller than the nominal size of the system itself) do systems acquire uniqueness in a measurable way.

This doesn’t preclude “hidden” properties, but they can’t be “local”; that is, they can (and have to) share their properties with other particles, including themselves, at distant points in space, which violates Lorentz invariance, i.e. the speed of light limit of propogation of information. However, since the variables are hidden, the only way you can extract this information from them is through inference by comparing the states at different points–in the case of an entangled pair of elecrtrons, the spin orientation (up or down)–and this has to be done by a classical channel, so the total rate that useful information can be transferred is still limited to the speed of light, and thus makes them effectively causally connected in conformance with Special Relativity. Wheh.

This whole hidden variable business, however, is just a way of getting away from the appearance of probabilistic behavior and putting fundamental mechanic of nature back on a firmly deterministic, pseudo-classical footing without getting away from realism (i.e. that things exist without being “observed” or measured) the way the Copenhagen interpretations do. Strictly speaking, there’s no reason that it has to be that way, other than it is more esthetically appealing and doesn’t throw an apparently impenetrable barrier (“Pay no attention to the man behind the curtain!”) to further understanding of physics. It also doesn’t truck with the grammatically tortured voodoo of “it turns out the way it is because that’s the way it had to to be this way” tautology that though experiments with Copenhagen (and other probabilistic interpretations) inevitably lead to. But we can’t prove that there are hidden variables (although we can disprove that there are local hidden variables) nor can we demonstrate or falsify the necessary nonlocal realism.

Stranger