Heisenberg Uncertainty Principle not so "uncertain"?

Factual Questions
21

[QUOTE=lowbrass]
So is the idea that only a single particle goes through the slit at any one time an inference based on collective data? I’ve never really understood this.
[/QUOTE]
Oh no; it’s entirely possible to emit only one photon at a time, and observe the result (whether through one slit, or two, or however many); however, you can’t observe the voyage that the photon takes between inception and delivery.

In general, we’re not “uncertain” about quantum behavior; in fact, there are “rigidly defined areas of uncertainty and doubt,” built into the theory that predict the probability of the result very exactly. We just can’t say where in the distribution it will fall beforehand. Think of it as gambling on a univeral scale; you know exactly how much you’re going to lose, and the only question is how long it takes you.

Stranger

22

[QUOTE=Stranger On A Train]
Oh no; it’s entirely possible to emit only one photon at a time, and observe the result (whether through one slit, or two, or however many); however, you can’t observe the voyage that the photon takes between inception and delivery.

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Oh, I’m not asking if you can watch the voyage; I’m asking exactly how the process of emitting one photon and one photon only is accomplished. Do they actually look at some type of “target” and say, “Here’s the spot where the one photon hit - now let’s release another photon and see where it hits.” I rather suspect that isn’t really how it’s done.

23

As a slight hijack, how accurate would you say this dumbed-down cartoon explanation is? I found it actually quite helpful in understanding the concept of the double slit experiment.

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[QUOTE=Whack-a-Mole]
I could use a bit of clarification on “all paths” if those who know will humor me.

If I setup an experiment with my photon gun pointing at a detector 100 meters away and I setup another detector 25 meters ahead and 25 meters to the side will the closer detector that is not in a straight line to the photon source be the one to detect the photon first? Not sure I am explaining this well but if the photon takes all possible paths to the target straight ahead then one such path should persumably be the detector off to the side. If that detector gets the photon first then I would not expect to see the photon arrive at the detector further away.

My instinct here is that the detector to the side will not register a hit and I should expect the photon to go straight ahead to the more distant detector but clearly gut instinct is one of the first things to go out the window with all this. Yet I cannot see how the photon could take all possible paths and not be detected by the nearer detector.
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Your instinct is correct. All the paths going to the side detector cancel out. However, if you put a slit between the source and the two detectors then light will reach the one on the side. This is because there are no longer enough paths to cancel out.

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[QUOTE=Jayrot]
As a slight hijack, how accurate would you say this dumbed-down cartoon explanation is? I found it actually quite helpful in understanding the concept of the double slit experiment.


[/QUOTE]

It’s a very good explanation of what QM says is happening. Be aware, though, that it’s giving the Copenhagen interpretation of what causes the collapse of the wave function. There are also other interpretations.

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[QUOTE=Whack-a-Mole]

So, in an experiment where I shoot a photon at a target can the photon really take any possible path? If I time the whole thing very carefully wouldn’t I see the photon arriving at the target at a predictable time (the time it takes light to travel the shortest path from source to target)? If I do this then don’t I now know where the photon was on its travels? I know it is running at light speed and that is not variable. I know the distance it travelled and presumably there is only one shortest path so with a bit of math I should be able to know its velocity and position at any point during its travels with precision.

[/QUote]

Yes it can really take any path, but just about all the paths that don’t give you the path of least time will cancel out. But, you see, you can’t really know how long it took for the photon to reach the target because you don’t know for sure when it was emitted. (Energy / Time uncertainty)

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[QUOTE=lowbrass]
Oh, I’m not asking if you can watch the voyage; I’m asking exactly how the process of emitting one photon and one photon only is accomplished. Do they actually look at some type of “target” and say, “Here’s the spot where the one photon hit - now let’s release another photon and see where it hits.” I rather suspect that isn’t really how it’s done.
[/QUOTE]
Here is the result of an undergraduate experiment using single photons (in series) through a double slit apparatus. The rate of emission of the laser is so low (10[sup]5[/sup] photons/sec) that you almost certainly have only one photon in travel at any time. There’s no way to tell absolutely for certain, of course, without interfering with the photon, but the odds of having two coincident photons are very, very low, way at the tail end of the Poisson distribution which described photon emission.

A classical device that emits a single photon in a known direction on demand is essentially impossible, but physicists and eletrically engineering researchers are working on solid state devices that would act as single photon emitters–essentially a very small PIN diode (sometimes called a “qunatum dot” or “quantum diode”) which can act as a single photon emitter. Such devices exist, but not (yet) in commercial manufacture, with the intention of using them as the relays for optical quantum computers. I don’t know if anyone has performed a double slit experiment using such a device, but nonetheless, we know that single photons (and single electrons) emitted serially “through” both slits show a distribution the characteristic interference patterns of a wave-like entity, which is entirely in line with wave-like formulation of the Schrödinger equation. Why it works nobody really knows, exactly, but we know that it works and gives us accurate practical results.

Stranger

28

[QUOTE=Stranger On A Train]
Er, no. You’re conflating the notion of relativity–that there are no priviliged reference frames–with fundamental indeterminacy. These are two very different concepts.

[/QUOTE]

Do you propose something can conceptually have both velocity and location at the same time? Velocity is the derivative of position. For something to be differentiable at a given point it would have to be continuous at that point. For something to be continuous at a point it would have to be defined on some open interval containing that point. In case of mathematics, being differentiable implies continuity. In case of philosophical conceptualization of moving objects, this continuity (motion) implies an uncertainty in position, in the general sense it is infinitely small, but given a specific model various things can put a theoretical limit on this open interval. Of course this is philosophical and linguistic nitpicking, and math and physics remain the same which you know a lot better than I do. I guess that’s the problem of having a physicist for a father is that I grew up with the idea that you either have position or motion as a fundamental property but not both.

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[QUOTE=Ring]
It’s a very good explanation of what QM says is happening. Be aware, though, that it’s giving the Copenhagen interpretation of what causes the collapse of the wave function. There are also other interpretations.
[/QUOTE]
FWIW, that video is from What the Bleep Do We Know?

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[QUOTE=Whack-a-Mole]
Here’s the part I am confused on. This may be Newtonian thinking but I thought it still applied in the quantum world. It has been my impression that something like, say, a photon will take the shortest route possible when travelling from Point-A to Point-B.
[/QUOTE]

No, it takes every possible path. And “shortest” is actually minimizing not the distance but something called the “action” of the path. In classical (and semiclassical) mechanics a system moves between two states in such a way as to minimize (or sometimes maximize) the action.

In quantum mechanics, however, the action of every path is used to help determine the probability that the system follows that path. But it turns out that paths far from the classical path usually cancel each other out to give zero probability, while paths near the classical path reinforce each other to make it likely one of them will be picked. But there’s still enough play in the equations for the Uncertainty Principle to come into play.

31

[QUOTE=groman]
Do you propose something can conceptually have both velocity and location at the same time? Velocity is the derivative of position. For something to be differentiable at a given point it would have to be continuous at that point. For something to be continuous at a point it would have to be defined on some open interval containing that point. In case of mathematics, being differentiable implies continuity. In case of philosophical conceptualization of moving objects, this continuity (motion) implies an uncertainty in position, in the general sense it is infinitely small, but given a specific model various things can put a theoretical limit on this open interval. Of course this is philosophical and linguistic nitpicking, and math and physics remain the same which you know a lot better than I do. I guess that’s the problem of having a physicist for a father is that I grew up with the idea that you either have position or motion as a fundamental property but not both.
[/QUOTE]
There’s no problem whatsoever with a moving body having both position and motion. Of course, per Special Relativity, these properties aren’t absolute to some objective reference frame but are a function of the difference in motion between inertial reference frames, but that doesn’t mean that there is an inherent uncertainty in the classical description of the system, even as modified by SR. It does mean that there’ll be a difference in the measurements one makes in one frame and from another, but knowing the difference between those frames should allow “perfect” transformation.

In reality, there is a level of undercertainty in measurement, because any means of measuring or interpreting something is subject itself to your ability to calibrate the measurment tools by measuring them against something else, and so on, creating a homonucleus problem. “How does he know he has flies in his eyes if he has flies in his eyes?” This is, however, a distinct problem from quantum indeterminacy which states that for a given product of complementary parameters there is a fundamental and inviolate degree of precision below which one simply cannot distinguish between one state and another.

The problem with philosophical and (more to the point) linguistic “nitpicking” or rationale is that natural language is insufficiently precise and discrete to talk about science in a rigorous manner. Your use of the term “continuous”, for instance, to imply that there is no discrete value (that is, if I understand your argument correctly, that because a continuous interval is infinitely divisible it must not have discrete points) does not prevent us from talking about exact points on the interval in relation to an initial point. A function that is single valued will be continuously differentiable but will have an explicit value for every point on the interval. It’s no more impossble to define exactly both position and velocity from such a system than it is for Zeno’s Arrow to strike its target.

And in the case of a real world object–a basketball, say, or a ballerina–the distribution of its composite quantum wavefunction is such that the difference between where classical dynamics says it should be and where indeterminacy gives that it might actually be is so immeasurably tiny–not only really, really small, but actually below the level where measurement is even possible, even if one could somehow contrive to measure the position of such a massive object as a single composite value–that it is indistinguishable from a classical object. Basketballs and ballerinas do not flit back and forth across the floor randomly, but politely obey all of the long-standing models of physics and biomechanics that we’ve become comfortable with. That these models are a convenient fiction based upon fundamental behavior that is bizarrely predictable only in the stochastic sense is not the least bit fretful, and no more likely to suddenly give way than Ice-9 is to freeze Earth’s oceans.

[QUOTE=Contrapuntal]
FWIW, that video is from What the Bleep Do We Know?
[/QUOTE]
Even a stopped clock gets it right twice a day.

Stranger

32

Whack-a-Mole, can I suggest that you check out Richard Feynman’s QED: The Strange Theory of Light and Matter, which will describe the behavior of light as a relativistic quantized field. Conceptually, it’s essentially a retooling of Fermat’s principle of least time into the framework of quantum mechanics. In execution its obviously much more complicated, but in the end, it gives the same empirical results, and has been tested to a very high degree of accuracy with experiment, to the point that it’s sometimes referred to as the “jewel of physics”. Feynman’s explanation is only very moderately technical–a basic understanding of classical optics is all you need, I think, to appreciate his explanation–though in the end its still somewhat convoluted, as he describes (in Part 3, IIRC) how the various paths cancel each other out, which involves some mathematical handwaving that’s flaky but which works.

Stranger

33

[QUOTE=Stranger On A Train]
The problem (and what is often not made very clear in nontechnical explanations of interference experiments) is that once you detect the the photon (or electron, or whatever) you interact with it, and thus it can from that point only have travelled on that path. This will result in a “collapse of the wavefunction” (or whatever rationale you prefer), and the interference pattern produced in the case of the two slit experiment will disappear. This isn’t some foofy New Age-y pseudoscientific babble; by observing the particle, you interact with it and affect the result. Note that there is no indication that consciousness is required to “make this decision,” although clearly for us to have any awareness of it we have to inspect the system in some way, either by directly opening up the box and looking at the cat, or inquiring to Wigner’s friend about the state of things. However, before we look, all states/paths exist simultaneously.
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Except it really does seem as if a “consciousness” is required to collapse wavefunctions. I mean, if the photon is taking all paths then presumably before it passes through the slits one path slams into the table, another into the wall, the ceiling, the researcher, an alien hanging around Andromeda, Wigner’s friend and Scroedinger’s cat. As long as they are unaware of this though all seems well. But yet in some magical way the photon figures out that the thing it hits on the way into the slit that would tell someone it was there causes the whole thing to fall apart. Pretty clever on the photon’s part.

That the experiments work in this fashion I am not contesting. But it really does have a New Age-y feel.

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[QUOTE=Stranger On A Train]

Even a stopped clock gets it right twice a day.

[/QUOTE]
Or maybe just once?

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[QUOTE=Whack-a-Mole]
Except it really does seem as if a “consciousness” is required to collapse wavefunctions. I mean, if the photon is taking all paths then presumably before it passes through the slits one path slams into the table, another into the wall, the ceiling, the researcher, an alien hanging around Andromeda, Wigner’s friend and Scroedinger’s cat. As long as they are unaware of this though all seems well. But yet in some magical way the photon figures out that the thing it hits on the way into the slit that would tell someone it was there causes the whole thing to fall apart. Pretty clever on the photon’s part.

That the experiments work in this fashion I am not contesting. But it really does have a New Age-y feel.
[/QUOTE]
You have to understand that the entire business of waveforms collapsing is, as far as we know, nothing more than a mathematical formalism. We don’t see, observe, detect, or otherwise have any indictation of something actually collapsing or coalescing, or any residue thereof. The notion that all possibilities exist until someone deliberately looks at it works as a model, but it’s not the only choice, or indeed, even the least nonsensical of all options; hence the cry of physics professors for the “Shut up and calculate” interpretation. Even the adherents of the Copenhagen interpretation by and large didn’t believe in the literal physicality of waveforms collapsing right outside the envelope of perception, and the only true grace of the whole business is that it allows you deal with phenomena in a totally local fashion without any nonlocal connections or hidden ontology. If you give up and just accept nonlocality (and don’t worry too much about causality) then the nonsense about collapsing waveforms becomes just a way of dealing with the math without a shred of connection to the underlying reality.

From a larger perspective, extensions of the Copenhagen interpretations to some kind of model that involves only local reality are conceptually and metaphysically problematic. If everything around me only exists when I elect to perceive it, and ditto for you, how is it that our collective reality matches up so well when we meet? Worse yet, you may not even exist until I see you, and me you; who’s reality is the objective one? If I ask my friend Wigner to check with his friend about the cat, when does the whole system get resolved into a single collapsed waveform? When Wigner’s friend checks on the cat? When Wigner reports back to me? And what about the cat itself, who presumably has some notion that it is alive; can’t it self-determine its own state? (Never mind the fact that it can’t be a quantum system isolated in a classical box, and thus is locally connected to everything else around it.) It’s a metaphysical can of worms more unlikely than being injected into John Malkovich’s head and then spit out on the side of the New Jersey Turnpike.

Nah, New Age theories about quantum consciousness and other blah-blah are a bunch of hooey that appeal exclusively to the fact that the only things we know to be in common about quantum mechanics and consciousness is that we know very little about the underlying mechanics of either of them. There’s absolutely no indication that there is anything about the processes of cognition and self-awareness that aren’t governed by normal biochemistry and boring neurological connections, nor is there anything about the mechanics of objects on the quantum scale that requires consciousness–whatever that is–in order to resolve itself.

Stranger

36

[QUOTE=Whack-a-Mole]
That the experiments work in this fashion I am not contesting. But it really does have a New Age-y feel.
[/QUOTE]

No, no, no, no, no. Exactly the reverse.

The New Agers have latched onto the counterintuitive elements of physics to sell their woo-woo. This has been going on for decades. (The Tao of Physics came out in 1975.)

New Agers do not understand physics. They just see the effects of quantum mechanics and relativity and use them as magic wands to throw cloaks of pernicious pablum over the eyes of their followers.

Jeremy Bernstein

Peter Woit

(both from Wiki.)
Do not - do not - blame physics for being New Age-y. This is completely wrong. Physics makes it clear that our narrow-minded “common sense” view of the world is wrong in almost every way. This has been true since people realized that the earth was round instead of flat. In Haldane’s brilliant phrase, “The universe may not only be queerer than we suppose, but queerer than we can suppose.”

This is no way justifies a mystical view of the universe. We cannot understand the subatomic world from a macroscopic viewpoint. So what? We can examine that world mathematically, which is both a great achievement and a triumph of precise rationalism. The New Agers want you to give up that achievement and relegate it to the level of flat earthers.

Science is utterly amazing, mind-expanding, and wonderful in several senses of the word. The universe is larger and stranger than we can comprehend with our limited and provincial senses. That strangeness is not mysticism, however. Mysticism is blindness. Never confuse the two.

Stranger, I said directly that the small stuff is the guts of science. How could you have read that otherwise?

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FTR I am not advocating mystical interpretations of physics or the Universe. Just saying listening to it explained one sometimes gets a sense that some hocus-pocus is involved. I am clear that my sense of that comes from an incomplete understanding of what is going on.

[QUOTE=Stranger On A Train]
You have to understand that the entire business of waveforms collapsing is, as far as we know, nothing more than a mathematical formalism. We don’t see, observe, detect, or otherwise have any indictation of something actually collapsing or coalescing, or any residue thereof. The notion that all possibilities exist until someone deliberately looks at it works as a model, but it’s not the only choice, or indeed, even the least nonsensical of all options; hence the cry of physics professors for the “Shut up and calculate” interpretation.
[/QUOTE]

I thought there were real indications that the photon (or what have you) does indeed really go everywhere at once. Isn’t that the basis for quantum computers which have been shown to work based on this very premise? If it is all just a mathematical tool and not really happening how does a quantum computer do its thing?

And of course a simper one is a photon interferring with itself going through the double-slit experiment. If it is not in fact in two places at once how does the interference pattern get produced?

I’m probably missing something but I really thought there was a “reality” to quantum weridness and not just some handy ways to calculate things.

38

There are interpretations for the meaning of quantum weirdness. As Stranger wrote, there is no agreement about which interpretation is correct or whether all the interpretations will eventually prove to be inaccurate when a deeper theory is found.

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[QUOTE=Exapno Mapcase]
Stranger, I said directly that the small stuff is the guts of science. How could you have read that otherwise?
[/QUOTE]
I didn’t mean to be critical of your statement, only to emphasize that the “small stuff” is actually the core of science. It’s nice when somebody comes along and figures out a big chunk of the puzzle from all the smaller bits that were lying around the box, but if you look at the history of science and natural philosophy it becomes apparent that it’s never just one person who suddenly blew forth with some totally unexpected development. Einstein, for instance, is hailed as this amazing genius who saw something that nobody else did, and then did it again, and again, but in fact he was just fortunate to be on the leading edge of developing theory; if he hadn’t come along with his explanation of the photoelectric effect (leading to the notion of wave-particle duality) someone else most certainly would have, and his development of Special Relativity was contemporary with, and fortunately (for him) received attention before that of Poincaire who was working along identical lines. As for General Relativity, equal credit should be granted to David Hilbert and probably Hermann Minkowski for developing the mathematics used to describe GR. This is all “little stuff” (though very significant little stuff), as is digging up and classifying fossils, measuring climate conditions, categorizing insects, et cetera. Good science is hard and generally tedious work, a fact not appreciated by many (including, in my misspent youth, myself).

[QUOTE=Whack-a-Mole]
I thought there were real indications that the photon (or what have you) does indeed really go everywhere at once. Isn’t that the basis for quantum computers which have been shown to work based on this very premise? If it is all just a mathematical tool and not really happening how does a quantum computer do its thing?

And of course a simper one is a photon interferring with itself going through the double-slit experiment. If it is not in fact in two places at once how does the interference pattern get produced?

I’m probably missing something but I really thought there was a “reality” to quantum weridness and not just some handy ways to calculate things.
[/QUOTE]
These statements are all true, insofar as they mean anything at all. However, to talk of a photon–a point particle–being everywhere means that it’s not really a particle–it’s a field. However, unlike a field, it acts only at a point…so it’s a particle. Only it’s not…et cetera, ad nausum. The “reality” of quantum mechanics–such as we understand it at all–is that it is totally and completely nonintuitively different from anything we know, and whatever we’re describing with the math bears only the faintest resemblence to what is probably going on. Like the blind men in a room with an elephant, we can only infer from the bit we can touch what the gestalt of QM is. It’s handy and useful to think of it as a particle–sometimes–and also very worthwhile to treat it as a wave. Sometimes we can even treat it as being a bit of both, but only by giving up our absolute conception of what a particle and wave are.

[QUOTE=Exapno Mapcase]
There are interpretations for the meaning of quantum weirdness. As Stranger wrote, there is no agreement about which interpretation is correct or whether all the interpretations will eventually prove to be inaccurate when a deeper theory is found.
[/QUOTE]
In fact, it really doesn’t matter–at least from any practical standpoint–what interpretation you subscribe to. All interpretations that work end up giving the same result with no indiciation as to whether that interpretation was any better at predicting the result (or rather, the distribution of the result, since QM can only give us statistical measures, not discrete predictions) than any other interpretation. Do you like Copenhagen interpretation? Good on you, the waveform collapses, voila! Do you like consistant histories? Who am I to criticize? Do you like some version of Hugh Everett’s so-called “many worlds” interpretation? Well, it’s as good as any. Entertain thoughts of Bohmian nonlocal variables? Sit down, partner, and let me buy you a drink; it may not be any better than any other interpretation, but to quote The Tick, I like the cut of that man’s gibberish. In the end, it just doesn’t matter; they all give identically good (or craptastical, if you like) answers.

And if you think all of that sounds bad, try getting into to quantum field gravitation theories. There’s stuff in there that’ll make your hair curl.

Stranger