Bram Cohen ([info]bramcohen) wrote,
@ 2006-01-12 13:33:00
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The Quantum Duelist
Pop science accounts of Schrodinger's cat have the infuriating property of rarely ever explaining what the experiment is about and instead give people the impression that quantum mechanics is probability: there is a certain probability that the cat is alive, and another that it's dead.

While it's true that probability is an important concept, and one which both has much more practical implications for the general public than quantum mechanics and is far less widely understood than it ought to be, it most definitely is not a quantum mechanical concept. Probability theory was worked out centuries earlier, and does not imply anything nearly as wacked out as schrodinger's cat.

To explain the bizarre nature of Schrodinger's cat, I will describe the strange case of the Quantum Duelist. Instead of a cat, the Quantum Duelist is a person, although like the cat he goes inside a black box which is left completely sealed for some period of time, and then when the box is opened the quantum state of the contents of the box are forced into a specific value, rather than the multiple interacting values which it has until it interacts with the outside world.

After entering and locking the black box, the Quantum Duelist flips a coin. If it comes up heads, he turns to the right, if it comes up tails, he turns to the left. Either way, he then takes ten paces forwards, turns around, and fires a gun straight ahead.

According to quantum mechanics, after the black box is opened, there's some chance that the duelist will be lying on the floor ten paces to the left, dead from a gunshot between the eyes fired by himself at a distance of twenty paces.

Unsettlingly, experiments clearly demonstrate that individual particles really do behave this way, so we can't dismiss quantum mechanics on the grounds of absurdity.



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[info]popefelix
2006-01-12 11:40 pm UTC (link)
It is worth noting that quantum mechanics says that there is some chance that you or I could run at a brick wall and, to our astonishment, pass right through. However, the chances of that happening are vanishingly small - smaller than 1 over the age of the universe in seconds.

The chances do get a lot better as things get smaller - quantum tunneling, as it's called, happens regularly on the scale of electrons.

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[info]bramcohen
2006-01-13 04:41 am UTC (link)
That's another one which gets rather misrepresented. The effect isn't 'passing through' the wall, it's 'teleporting past' the wall, and the main problem with that one is that it superficially appears to violate faster than light travel. Faster than light travel is far more bothersome to physicists than to lay people, as evidenced by the paucity of even 'hard' science fiction which bans faster than light travel, despite it being one of the most fundamental laws of physics.

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[info]popefelix
2006-01-13 01:08 pm UTC (link)
Well, you can probably place the blame for the misrepresentation you mention on people calling it "quantum tunneling" rather than "quantum teleportation." I've heard both.

As for FTL, I place the blame sqarely on hope, or perhaps dramatic necessity. I know that I, for one, hope to find some way of travelling faster than light (even on average, as in a Star Trek wormhole) because I want to be able, someday, to take a vacation to Alpha Centauri. :)

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[info]lupoleboucher
2006-01-19 02:24 am UTC (link)
Tunneling can be purely classical, actually.

The two things that weird people out about quantum mechanics are the wavelike nature of matter (which doesn't really bother me at all at this point), and measurement. Remove weird measurement thingees, and matter is just waves, and everyone in physics is happy again, because they can stop talking to confused pre-menopausal women with quartz crystal jewelry and cats named Ramtha.

For what it is worth, there is a paper kicking around my filing cabinet which draws a very evocative parallel between quantum measurement and secret cryptographic keys (it doesn't directly relate to quantum mechanical keys, but no doubt the idea inspired the analogy). I don't know if anyone followed up on it, because I stopped following the literature around that time. I'm guessing no; too original.

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[info]ciphergoth
2006-01-13 12:04 am UTC (link)
I am so stealing that analogy. Thank you.

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[info]deviantq
2006-01-13 12:12 am UTC (link)
I don't understand. Are you saying the wave function might collapse to both outcomes? Or are you saying it might never collapse and we might witness the superposition? In either case, what are you saying about the probability of that?

From what I would imagine (and I don't know the math, just the popsci), it seems like (to the outside observers) he is in a superposition of having fired from one position and having fired from another. From his perspective, his wavefunction collapses immediately after flipping the coin. When the wavefunction collapses in the observer's frame of reference (as the box is opened), it seems like it would have to be the same result. In other words, it's already collapsed in one point of view, and all we're doing is propogating that same collapse outside of the box.

Also, isn't this quite testable by experiment? Use a robot. Will we ever see this? It seems unlikely, but maybe my intuition isn't quantum enough.

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[info]bramcohen
2006-01-13 04:44 am UTC (link)
It's quite testable with individual particles, and yes it really works that way.

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Schroedinger's cat
[info]deviantq
2006-01-13 12:13 am UTC (link)
Would you say that this phrasing of Schroedinger's cat gets the point across? "The cat is neither dead nor alive (from the observer's perspective), but in a superposition of both states. It's not that it has a 50 % chance of either---that would imply that it's in one discrete state or another---but instead that it's in 'both,' effectively."

Or am I one of the masses who have been deceived by popsci books?

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Re: Schroedinger's cat
[info]bramcohen
2006-01-13 04:47 am UTC (link)
That summary totally misses the point. If that's all the equations implied, then it would be rather like the old battleaxe 'If a tree falls in the forest, and noone is around to hear it, does it make a sound?' The answer, of course, is yes. Quantum mechanics demonstrates actual phenomena which are far more unsettling than the sort of postmodernist questioning of reality which any stoned high school student could come up with.

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[info]steevven1
2006-01-13 12:26 am UTC (link)
What I don't understand about Schrodinger's Cat or the Quantum Duelist is that they both do in fact interact with the outside world. Every object has gravitational pull on every other object. The force of that gravitational pull is determined by its distance from the objects it's pulling on and it's mass. Therefore, in the case of the Duelist, he is changing gravitational pulls on things from his body and the gun by moving his body and the gun, which could not be determined without knowing his position. In the case of Schrodinger's Cat, if it were alive, him moving around, his breathing, the motion of his bloodstream, etc. would cause tiny gravitational pull changes on objects.

I realize that the gravity a human or cat's body would have is unbelievably small, but it is still something that interacts with the outside world.

I'd love for someone to explain this to me. Thanks.

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[info]trs80 [typekey.com]
2006-01-13 01:58 am UTC (link)
You want the theory of quantum gravity, which unfortunately no-one's come up with yet.

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[info]bramcohen
2006-01-13 04:41 am UTC (link)
One of the problems with quantum mechanics is that it doesn't play nice with relativity. Noone's been able to figure out an experiment which would force the issue though.

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Flawed analogy?
[info]mackys
2006-01-13 12:26 am UTC (link)
I think your analogy may be flawed. Assuming you mean that the quantum duelist corresponds to only a single particle, I don't think we can observe a state where he shoots himself.

QD says that when we observe a particle, it collapses completely into one state or the other. This corresponds to the duelist standing on either the left side or the right side (in both cases holding a smoking gun) when we open the box. These are the only two states that are possible post observation. He either fired from the right side of the box, or fired from the left side of the box. He cannot collapse into a state where he walked to one side of the box and fired from the other; that would be like opening Schrodinger's box and finding the left half of the cat alive, and the right half dead. If the cat and the duelist both correspond to a single quantum particle, then the quantum particle cannot split in half and each half do its own thing. The whole particle has to go one way or the other.

The duelist may, _before he is observed_, be in a state that is somewhat like being on both sides of the box simultaniously and both half-copies of himself shooting the other. And if one of the half copies should miss the other, that might influence what happens when we open the box. But when you do open the box and observe him, you force the quantum state to collapse. And it cannot "collapse" into a state that is half one kind and half the other.

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Re: Flawed analogy?
[info]bramcohen
2006-01-13 01:25 am UTC (link)
I'm sorry, but you're wrong. The two-slit experiment, for example, clearly demonstrates that particles can interact with themselves and yield a result which indicates that more than one 'possible' state actually happened.

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Re: Flawed analogy?
[info]rambletron3000
2006-01-13 02:21 am UTC (link)
The problem with that analogy is that also necessarily involves the (also hairy) wave-particle duality problem.

I've taken enough quantum physics only to know that I don't know what I'm talking about, but I'm not convinced that you're analogy is accurate. The double slit experiments shows that the two possible states can interact in the sense that they constrain the possible outcomes of each other, but I'm not sure that applies to any arbitrary interaction.

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Re: Flawed analogy?
[info]rambletron3000
2006-01-13 02:34 am UTC (link)
An alternate version of your scenario:

Assuming the bullets travel along the same path, just in opposite directions, the probability waves for their momentum and position may destructively cancel. It should be possible to open the box and find a duelist, but no bullet.

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Re: Flawed analogy?
[info]bramcohen
2006-01-13 04:40 am UTC (link)
No, that one can't happen, as it would violate conservation of energy. Cancellation patterns do show up in the dual slit experiment though.

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Re: Flawed analogy?
[info]rambletron3000
2006-01-13 04:50 am UTC (link)
Right. I was debating whether or not it's possible that it could disappear momentarily, though, which I think it theoretically could.

I'm still not sure parts of two different event paths could happen, though. I really think you would collapse to one path or the other, although you could have probability interference results constraining the outcomes.

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Re: Flawed analogy?
[info]bramcohen
2006-01-22 11:25 pm UTC (link)
I was actually thinking of the whole system acting like a single particle. One could easily describe the dual-slit experiment with a runner bumping into himself, although that wouldn't be any intuitively different to the general public other than being less dramatic.

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Back to the original complaint
[info]piddyx
2006-05-16 11:46 pm UTC (link)
I wonder why they don't teach the double-slit experiment instead of exposing people to the schroedinger's cat analogy.

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Re: Flawed analogy?
[info]darius
2006-01-13 05:00 am UTC (link)
You need indistinguishable outcomes to see that kind of interference. If you want to be really sure it's not happening here, strip it down to a 2-particle system (duelist and bullet) with a contrived Hamiltonian. (There are histories where the bullet turns around and hits the duellist, but your experimental setup doesn't do anything to amplify them.)

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Re: Flawed analogy?
[info]bramcohen
2006-01-22 11:28 pm UTC (link)
Most likely one could boing it down to two particles and have them bump into each other after the box is opened. I don't know if that can be done exactly right - the analogy is really meant to view the whole duelist/bullet thing as a single particle, and the killing part is for dramatic effect.

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Re: Flawed analogy?
[info]malaya_zemlya
2006-01-13 06:58 am UTC (link)
Cancellation is not the same as interaction.

Most importantly, cancellation of two waves is a linear process and the bullet-duelist interaction isn't. In other words, when two waves cancel or reinforce they simply pass through each other, blissfully unaware of each other's presence. Basically, they live in parallel universes. We see them cancel only because our own universe in a mix of these. Not a mix in a sense "vodka is a mix of water and alcohol" but rather in a sense "oblique is a mix of horizontal and vertical"

Getting shot in a head is anything but peacieful coexistence :) So that's not what QM would predict I think. At the very worst, you'd see two half-guys-half-bullets at the opposite ends of the box, but no graphic violence.

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Re: Flawed analogy?
[info]bramcohen
2006-01-22 11:30 pm UTC (link)
It's a little more complicated than just linear, hence quantum computation, although it is true that quantum computation apparently can't be used for arbitrary computations.

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Re: Flawed analogy?
[info]audi100quattro
2006-01-13 03:05 pm UTC (link)
Quantum cryptography relies on the photon being reduced to one state when observed. Quantum computing, a bit less so.

The act of observation is being overlooked here, we're not actually observing the photon in the middle of it's path in the two-slit experiment. We're merely observing the outcome of the experiment as a whole. I would have to agree with mackys in that when we to observe a photon, we would see it reduced to a state. Which is to say, when we try to measure a photon, we do get a specific wavelength/Quantum number.

From my small amount of study into QM, I've also learned enough to know I've learned nothing. Most Quantum Physicists will gladly admit the same. I could be wrong, it's been a while.

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No probability, only real outcomes
[info]limusine
2006-01-13 04:58 pm UTC (link)
I agree that probability often confuses concepts. So, supposing that we do a large enough number of experiments (say lots of boxes and duelist) will we end up with all these?
-duelist in perfect health in right side
-duelist in perfect health in left side
-duelist shot in right side
-duelist shot in left side
-two half duelists shot with half bullets

I'm supposing a simplification: duelist-particle only interacts with bullet-particle, and bullet-particle only interacts with duelist-particle (which means these particles do not interact with themselves)

Are there more possible outcomes?

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Re: No probability, only real outcomes
[info]bramcohen
2006-01-22 11:35 pm UTC (link)
In the dual slit experiment, it's a single particle (this two-particle business confuses the issue a lot). In any one given run of the experiment, the particle winds up hitting a specific point on the opposite side of the slits, but over the long run the distribution of hits will be the same as the interference pattern of a whole bunch of particles all released at once. The bizarre thing is that this interference pattern happens when the particles are put through one at a time, so each individual particle has to interfere with itself.

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[info]cat_of_dreams
2006-01-13 05:59 pm UTC (link)
My understanding is the biggest confusion over the whole dual state, collapsing waveform aspect, is that neither is actually occurring when we measure the particles. The only methods we have of measuring individual particles involve altering them in known ways then observing how they change to measure their state before we altered them. The waveform is collapsed by an outside force that we introduce to allow us to measure the particle, in it's pure state quantum particles do not collapse until some other force acts upon them.

For instance a photon detector destroys a photon by absorbing it into a material that emit electrical current when struck. The photon may have been in an infinite number of states before detection, but due to the nature of our detection scheme only one state can be detected. The detected state tends to be the most probable. In the dual slit experiment, both paths are equally probable so the interference pattern is observed. However is the paths were made to be no longer equally probable so that one slit was used 25% of time and the other 75% then the pattern would alter accordingly or perhaps disappear altogether.

The confusion with the quantum dualist analogy is that our gedanken observer is limited to a similar rule set as real observation of particles. While if the experiment were really done, a whole different level of physics would apply that does not behave along the quantum theory it attempts to explain.

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Wasn't the point of the cat
[info]brad_templeton
2006-01-13 08:07 pm UTC (link)
Also to probe the question of what is observation? Standard copenhagen had the wave function collapsing upon observation, collapsed for everybody. The cat experiment also asked the question of whether the cat was an observer, or just a bundle of entangled states, and whether humans were different.

In one view, the state is decided the moment the result of the quantum event is observed by the duelist, in some views the moment it is observed by the cat, and in other views, now seemingly false, the moment it interacts with anything or at least a measuring device.

Can you tell me the experiments that you think imply that the giant bundle of entangled states could collapse to a mishmash of the outcomes, including bullet one way and duelist the other? I don't believe double-slit implies this.

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Re: "Experiments clearly demonstrate... can't dismiss quantum mechanics"
[info]saltation_lj
2006-01-20 11:06 pm UTC (link)
not only experiments show that quantum mechanics is real: the chips your computer are using right now do too.

"coulomb tunneling" as electrons teleport/tunnel into adjacent paths is a major factor in the problems the big chip mfrs are having in further reducing, or rather: concentrating, chips.

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Re: Wasn't the point of the cat
[info]bramcohen
2006-01-22 11:40 pm UTC (link)
As covered in other comments, I didn't really mean to bring up all the two-particle issues, and added the killing part as a dramatic device. However, it's my (possibly incorrect) understanding that multi-particle systems still have uncertainty effects, it's just that the amount of uncertainty is much smaller due to their mass or something else being much larger.

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Particle-Wave 'duality'
[info]meltingupwards
2006-01-31 10:31 am UTC (link)
The problem is one of perspective. A particle/wave would more accurately be expressed as a wave/loop/string which vibrates... and is being observed as the interaction of this vibration with the 'plane' through which we filter our view of the 'wave'.

The explanation of the affect observed in a quantum particle teleportation device is that the wave/loop/string (or the filter 'plane') is affected such that the intersection of the 'wave' occurs at different points at different times (even in some special cases you might observe simultaneous intersections...)

If I rotate a (mathematical) 4d cube along any axis, from a 3d viewpoint I would see an apparent folding and unfolding of a cube like shape which would only momentarily resemble a normal 3d cube. The folding and unfolding which would be observed in a 2d observation would become more elaborate and inexplicable. Taken to 1d, the observed motion would become even more complicated. The key to 'tuning' this is understanding the tweaking (rate of spin, direction) of the rotation of one axis over another (or in combinations, and particularly in ratios to each other....) will result in very ordered patterns, in which you can see resemblance to many common structures in nature.

Consider the inherent spin of an electron. That it travels within wire no faster that about 11 feet an hour, but the signal that is transferred along it 'travels' in the spin at amazing speed. The energy is a vibration in and of itself. Thus, all matter is such.

I just boiled spaghetti, and the colander has a few strands hanging through. My super-observer point of view can see the strand that is the spaghetti (which may or may not be a closed loop)... I can see that it intersects with the colander (which conveniently has a curved surface, like our plane...) Now... as a lowly normal observer... I see a small round point which I can measure that it moves about... appears to be a particle, but then maybe... is it a wave?

Sorry for the treatise. Not what I had in mind when I started out. Maybe I'm full of it....

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A Late Thought
[info]nomenklatura
2006-02-09 11:00 pm UTC (link)
My Understanding of Schrodinger's Cat is that Schrodinger actually thought up this 'experiment' in order to show that there is something deeply different between quantum mechanical experience and classical mechanical experience. I believe he had no intention of making an actual analogy, if anything he was slightly skeptical of QM.

In essence what Schrodinger points out is the absurdity of thinking that quantum effects should be in any way classical and vice versa, that classical effects like a cat in a box with a geiger counter and some poison are not in any way quantum. After all, no one has ever seen an atom with their own two eyes, so why should we think it would bounce like a tennis ball?

An unresolved problem is what happens in the grey area between quantum and classical experience. In other words, how and when do classical (aka macroscopic) effects take over from quantum (microscopic) effects? The when is more or less known, but the how less so. It's not just a case of statistics 'adding up'. I've heard people like Roger Penrose say that what kicks in is gravity, and at this point I'm out of my depth.

All this to say that Bram's analogy is good, but it's not macroscopic reality. That's why it seems weird.

Thanks for bittorrent, by the way.

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