Quantum weirdness at the large scale
March 18, 2010 2:25 PM Subscribe
Scientists supersize quantum mechanics. "A team of scientists has succeeded in putting an object large enough to be visible to the naked eye into a mixed quantum state of moving and not moving."
WHERE'S THE VIDEO AT??
posted by nathancaswell at 2:27 PM on March 18, 2010
posted by nathancaswell at 2:27 PM on March 18, 2010
The work is simultaneously being published online today in Nature and presented today at the American Physical Society's meeting in Portland, Oregon.
There is a quantum mechanical joke in there somewhere. Of course, if you observe it, you will change it.
posted by ricochet biscuit at 2:28 PM on March 18, 2010 [32 favorites]
There is a quantum mechanical joke in there somewhere. Of course, if you observe it, you will change it.
posted by ricochet biscuit at 2:28 PM on March 18, 2010 [32 favorites]
Oh Newton, what have they done to you?
posted by Babblesort at 2:29 PM on March 18, 2010 [2 favorites]
posted by Babblesort at 2:29 PM on March 18, 2010 [2 favorites]
Boy, I wish there were more details in front of the paywall in the second link. I'm very curious how you would measure something as vibrating and not vibrating at the same time.
Regardless, that's some great science, and an excellent post.
posted by Malor at 2:30 PM on March 18, 2010
Regardless, that's some great science, and an excellent post.
posted by Malor at 2:30 PM on March 18, 2010
Does this mean someday I will be able to be at work and also at home having a beer?
Only if you are super cool.
posted by zerobyproxy at 2:31 PM on March 18, 2010 [61 favorites]
Only if you are super cool.
posted by zerobyproxy at 2:31 PM on March 18, 2010 [61 favorites]
There is no obvious reason why the rules of quantum mechanics shouldn't apply to large objects. Erwin Schrödinger, one of the fathers of quantum mechanics, was so disturbed by the possibility of quantum weirdness on the large scale that he proposed his famous 'Schrödinger's cat' thought experiment.
I CAN HAZ HIGGSBURGER?
But seriously, I've been reading about those wacky quanta lately, so for me this is timely as well as fascinating. Thank you for posting it.
posted by Joe Beese at 2:31 PM on March 18, 2010
I CAN HAZ HIGGSBURGER?
But seriously, I've been reading about those wacky quanta lately, so for me this is timely as well as fascinating. Thank you for posting it.
posted by Joe Beese at 2:31 PM on March 18, 2010
I'm very curious how you would measure something as vibrating and not vibrating at the same time.
As a superposition.
posted by DU at 2:31 PM on March 18, 2010
As a superposition.
posted by DU at 2:31 PM on March 18, 2010
This broom, it vibrates and does not vibrate at the same time?
posted by Faint of Butt at 2:33 PM on March 18, 2010 [3 favorites]
posted by Faint of Butt at 2:33 PM on March 18, 2010 [3 favorites]
If someone wanted to explain this for the non particle physicists among us, I'd give you a hug. My brain has a really hard time with the whole A ^ - A thing.
posted by Lutoslawski at 2:33 PM on March 18, 2010
posted by Lutoslawski at 2:33 PM on March 18, 2010
I got through the mechanical parts of the paper at the second link (verrry verrry cool), but I am continually stymied by quantum mathematics with qubits and such.
posted by muddgirl at 2:37 PM on March 18, 2010
posted by muddgirl at 2:37 PM on March 18, 2010
Does this mean they can make quantum mechanic-powered vibrators?
posted by flippant at 2:40 PM on March 18, 2010
posted by flippant at 2:40 PM on March 18, 2010
In Texas schoolbooks, this means that God really paid attention to the details.
posted by Ron Thanagar at 2:42 PM on March 18, 2010 [2 favorites]
posted by Ron Thanagar at 2:42 PM on March 18, 2010 [2 favorites]
Does this mean someday I will be able to be at work and also at home having a beer?
If you live under your desk at your office, and have a stocked mini-fridge, you could be experiencing this dream right now.
posted by quin at 2:42 PM on March 18, 2010 [1 favorite]
If you live under your desk at your office, and have a stocked mini-fridge, you could be experiencing this dream right now.
posted by quin at 2:42 PM on March 18, 2010 [1 favorite]
Does this mean they can make quantum mechanic-powered vibrators?
They're stimulating, but also... not stimulating.
posted by GuyZero at 2:43 PM on March 18, 2010 [1 favorite]
They're stimulating, but also... not stimulating.
posted by GuyZero at 2:43 PM on March 18, 2010 [1 favorite]
It's about a third of the way down the page, on the first link. It's a small 2x2 inch black and white video showing the two simultaneous states -- movement and non-movement -- pretty clearly. Why, can you not see both states there?
Nope.
posted by Jaltcoh at 2:44 PM on March 18, 2010
Nope.
posted by Jaltcoh at 2:44 PM on March 18, 2010
Cool! I saw this just yesterday and wondered if it would show up on the blue (thought about posting it myself).
posted by saulgoodman at 2:45 PM on March 18, 2010
posted by saulgoodman at 2:45 PM on March 18, 2010
Huh.
posted by brundlefly at 2:46 PM on March 18, 2010 [1 favorite]
posted by brundlefly at 2:46 PM on March 18, 2010 [1 favorite]
THIS OBJECT, IT VIBRATES?
THIS OBJECT, IT DOESN'T VIBRATES?
posted by tommasz at 2:47 PM on March 18, 2010 [4 favorites]
THIS OBJECT, IT DOESN'T VIBRATES?
posted by tommasz at 2:47 PM on March 18, 2010 [4 favorites]
I'm excited. Really excited. As a non-scientist I can barely wrap my head around this stuff, but here's what I think I'm seeing in the world of physics (correct me if I'm wrong):
Not much has changed since perhaps the 1940s, maybe some minor steps forward but no major breakthroughs. Einstein's thoughts have been close to definitive for decades. Now, finally, we're beginning to see QM chip away at those axioms and some groundbreaking explanations for things even old Albert could only describe as "spooky." I think we're on the verge of seeing some really crazy awesome stuff this century. When I read about things like this, and the LHC, and the constant stream of exoplanet discoveries, I get really stoked for humanity. I'm just a layman, and I don't understand the math — but I can't wait to see how this science gets applied in ways that radically affect daily life. Stuff I can't even begin to imagine but know I'm gonna love.
posted by The Winsome Parker Lewis at 2:47 PM on March 18, 2010 [4 favorites]
Not much has changed since perhaps the 1940s, maybe some minor steps forward but no major breakthroughs. Einstein's thoughts have been close to definitive for decades. Now, finally, we're beginning to see QM chip away at those axioms and some groundbreaking explanations for things even old Albert could only describe as "spooky." I think we're on the verge of seeing some really crazy awesome stuff this century. When I read about things like this, and the LHC, and the constant stream of exoplanet discoveries, I get really stoked for humanity. I'm just a layman, and I don't understand the math — but I can't wait to see how this science gets applied in ways that radically affect daily life. Stuff I can't even begin to imagine but know I'm gonna love.
posted by The Winsome Parker Lewis at 2:47 PM on March 18, 2010 [4 favorites]
"it is impossible to know a particle's exact position and velocity through space, yet it is possible for the same particle to be doing two contradictory things simultaneously."
I am so totally picturing them working on this, and suddenly achieving a mixed quantum state only to have the object vanish with a *poof* and a trailing off voice laughing "Fuuuuuuuccccckkk yooooouuuu guuuuyyyyysssss"
Because I always imagined quantum state to a bit of a prankster.
posted by quin at 2:48 PM on March 18, 2010 [5 favorites]
I am so totally picturing them working on this, and suddenly achieving a mixed quantum state only to have the object vanish with a *poof* and a trailing off voice laughing "Fuuuuuuuccccckkk yooooouuuu guuuuyyyyysssss"
Because I always imagined quantum state to a bit of a prankster.
posted by quin at 2:48 PM on March 18, 2010 [5 favorites]
Another tease. They haven't seen anything, just finish up with "This demonstration provides strong evidence that quantum mechanics applies to a mechanical object large enough to be seen with the naked eye." I want to see something, anything. I'd settle for a tiny widget with a Gaussian blur applied — "Artist's depiction of what would happen if we actually had the funding to pull this off."
At a lecture, I remember Kip Thorne talking about how they eventually expected that, as the the precision for the mirrors used in LIGO increased with time, in around fifteen years they'd have the position measured so far down that they might be able to see delta-p get a little ... twitchy. I would cheerfully toss a hundred bucks in for funding just to take a gander.
Reminds me of an amusing sci-fi book where their method of exploring the galaxy involved launching a bunch of probes from the ship and just measuring the ship's current momentum very, very well. Pity about the lack of steering.
posted by adipocere at 2:51 PM on March 18, 2010
At a lecture, I remember Kip Thorne talking about how they eventually expected that, as the the precision for the mirrors used in LIGO increased with time, in around fifteen years they'd have the position measured so far down that they might be able to see delta-p get a little ... twitchy. I would cheerfully toss a hundred bucks in for funding just to take a gander.
Reminds me of an amusing sci-fi book where their method of exploring the galaxy involved launching a bunch of probes from the ship and just measuring the ship's current momentum very, very well. Pity about the lack of steering.
posted by adipocere at 2:51 PM on March 18, 2010
They haven't seen anything
That's a joke, right? :) Of course we can't see anything. That's sort of the point of quantum states - looking at them requires some energy input. That energy input screws up the state.
posted by muddgirl at 2:56 PM on March 18, 2010 [1 favorite]
That's a joke, right? :) Of course we can't see anything. That's sort of the point of quantum states - looking at them requires some energy input. That energy input screws up the state.
posted by muddgirl at 2:56 PM on March 18, 2010 [1 favorite]
Scariest statement: That they will 20 years from now, be able to make human sized things indeterminate. Think about that ...
also, two words: Resonance Cascade
posted by djrock3k at 2:58 PM on March 18, 2010
also, two words: Resonance Cascade
posted by djrock3k at 2:58 PM on March 18, 2010
Does this mean someday I will be able to be at work and also at home having a beer?
Well, yes and no.
posted by Mr. Bad Example at 2:58 PM on March 18, 2010 [19 favorites]
Well, yes and no.
posted by Mr. Bad Example at 2:58 PM on March 18, 2010 [19 favorites]
I'm very curious how you would measure something as vibrating and not vibrating at the same time.
Briefly, they built a mechanical resonator out of a piezoelectric material, so that as it moves, it produces an electrical signal. They coupled this signal (across a capacitor) to a quantum-mechanical circuit called a superconducting phase qubit. The qubit can take on two states: a ground state |g> and an excited state |e>, and the probability of a transition between the two states can be measured.
After demonstrating that the resonator and the qubit were coupled, they showed that when they didn't excite the resonator, the transition probability of the qubit remained constant, even when the qubit frequency matched the resonator frequency. Since the resonator doesn't excite the qubit, it must be in its quantum ground state.
Then, they demonstrate that when they excite the qubit, they can get it to exchange its state with the resonator. The system goes from qubit in excited state, resonator in ground state to resonator in excited state, qubit in ground state. While the exchange is happening, the system is in an entagled qubit-resonantor quantum state. This is all observed by measuring qubit transition probability.
It's all done with high-frequency electrical signals at very low temperatures.
That's how I read it, at least.
posted by mr_roboto at 3:08 PM on March 18, 2010 [8 favorites]
Briefly, they built a mechanical resonator out of a piezoelectric material, so that as it moves, it produces an electrical signal. They coupled this signal (across a capacitor) to a quantum-mechanical circuit called a superconducting phase qubit. The qubit can take on two states: a ground state |g> and an excited state |e>, and the probability of a transition between the two states can be measured.
After demonstrating that the resonator and the qubit were coupled, they showed that when they didn't excite the resonator, the transition probability of the qubit remained constant, even when the qubit frequency matched the resonator frequency. Since the resonator doesn't excite the qubit, it must be in its quantum ground state.
Then, they demonstrate that when they excite the qubit, they can get it to exchange its state with the resonator. The system goes from qubit in excited state, resonator in ground state to resonator in excited state, qubit in ground state. While the exchange is happening, the system is in an entagled qubit-resonantor quantum state. This is all observed by measuring qubit transition probability.
It's all done with high-frequency electrical signals at very low temperatures.
That's how I read it, at least.
posted by mr_roboto at 3:08 PM on March 18, 2010 [8 favorites]
ummm... i hate to rain on the parade here but i don't think this article is saying what you think it is saying.
the standard textbook tabletop demonstration of the validity of quantum mechanics involves say, heating up atoms of metal in a furnace and then shooting them through a thin slit at a screen. the quantum mechanics is essentially that of a *particle* (the individual atoms) flying through space and you are able to measure the effect of a purely quantum mechanical property called 'spin' by measuring the distribution of metal atoms on the screen.
it's impossible to say what they are actually measuring from reading this article, but what they appear to have done is to get measurable effects for the quantum mechanics of a vibrating drum rather than a single particle.
but the basic point is that measurements are always 'classical' states and vice versa. at least for the standard interpretation of quantum mechanics the idea of a 'superposition' of classical states (measurements) is nonsense.
it's not that this isn't really interesting, it's just that all they have shown is that the quantum mechanics of 'continuum' (or multibody if you prefer) systems is measurable. it would be truly surprising if you obtained measurements of a small vibrating drum that weren't explainable by quantum mechanics.
posted by ennui.bz at 3:10 PM on March 18, 2010
the standard textbook tabletop demonstration of the validity of quantum mechanics involves say, heating up atoms of metal in a furnace and then shooting them through a thin slit at a screen. the quantum mechanics is essentially that of a *particle* (the individual atoms) flying through space and you are able to measure the effect of a purely quantum mechanical property called 'spin' by measuring the distribution of metal atoms on the screen.
it's impossible to say what they are actually measuring from reading this article, but what they appear to have done is to get measurable effects for the quantum mechanics of a vibrating drum rather than a single particle.
but the basic point is that measurements are always 'classical' states and vice versa. at least for the standard interpretation of quantum mechanics the idea of a 'superposition' of classical states (measurements) is nonsense.
it's not that this isn't really interesting, it's just that all they have shown is that the quantum mechanics of 'continuum' (or multibody if you prefer) systems is measurable. it would be truly surprising if you obtained measurements of a small vibrating drum that weren't explainable by quantum mechanics.
posted by ennui.bz at 3:10 PM on March 18, 2010
For something you've cooled so much so that any contact, either by objects or photons, would kick it out, yeah. And for the by-now-thoroughly-confused cat in a box scenario, yeah. It ought to be theoretically possible for non-cooled items, if you look at the LIGO example I mentioned, because there the superposition requires neither the "I'm not looking, nobody's looking" aspect nor the "we have to suck all of the energy out of the system, so much so that a handful of photons are going to screw it all up" issue. At .1 K, well, that's very chilly, but not so much so that a flashlight would necessarily kick it out. Here, the qubit is "just" a device for measurement, that funky little staple-shape is what is actually resonating. They seem more excited by the qubit, though.
And now I will be ruminating on "once LIGO reaches those levels, what exactly will go on?" and "what constitutes a measurement, anyway?"
posted by adipocere at 3:20 PM on March 18, 2010
And now I will be ruminating on "once LIGO reaches those levels, what exactly will go on?" and "what constitutes a measurement, anyway?"
posted by adipocere at 3:20 PM on March 18, 2010
This is probably my favorite science quote of the year:
"There might be some interesting application," he says. "But frankly, I don't have one now."
-Andrew Cleland
posted by MrVisible at 3:24 PM on March 18, 2010 [4 favorites]
"There might be some interesting application," he says. "But frankly, I don't have one now."
-Andrew Cleland
posted by MrVisible at 3:24 PM on March 18, 2010 [4 favorites]
it's impossible to say what they are actually measuring from reading this article...
They're measuring the state transition probability of a superconducting phase qubit. The gap between the two lowest states is tunable by setting the qubit bias current, so they can energy-match the states of a coupled resonator. In practice, the measurements are made by exciting the qubit with a GHz frequency signal overlaid with the bias current and analyzing the junction voltage.
That's just based on some quick reading, though. I'm not an expert.
but the basic point is that measurements are always 'classical' states and vice versa.
No. These are quantum states. They claim to have excited a single phonon in the resonator.
posted by mr_roboto at 3:30 PM on March 18, 2010
They're measuring the state transition probability of a superconducting phase qubit. The gap between the two lowest states is tunable by setting the qubit bias current, so they can energy-match the states of a coupled resonator. In practice, the measurements are made by exciting the qubit with a GHz frequency signal overlaid with the bias current and analyzing the junction voltage.
That's just based on some quick reading, though. I'm not an expert.
but the basic point is that measurements are always 'classical' states and vice versa.
No. These are quantum states. They claim to have excited a single phonon in the resonator.
posted by mr_roboto at 3:30 PM on March 18, 2010
Wait a moment. If something is both "moving" and "still", isn't the net effect that it's moving, even with periodic moments of stillness? That seems to be the case with the (admittedly pop-sci) explanation given in the article.
posted by LSK at 3:49 PM on March 18, 2010
posted by LSK at 3:49 PM on March 18, 2010
I am not commenting.
posted by fantabulous timewaster at 4:07 PM on March 18, 2010 [2 favorites]
posted by fantabulous timewaster at 4:07 PM on March 18, 2010 [2 favorites]
I believe this article, yet I don't believe it.
posted by mr_crash_davis mark II: Jazz Odyssey at 4:10 PM on March 18, 2010 [2 favorites]
posted by mr_crash_davis mark II: Jazz Odyssey at 4:10 PM on March 18, 2010 [2 favorites]
They coupled this signal (across a capacitor) to a quantum-mechanical circuit called a superconducting phase qubit.
But Captain, wouldn't that reverse the polarity of the dilithium crystals?
Seriously, "a superconducting phase qubit"? I don't doubt at all that's what the article says, but any sufficiently advanced technology is becoming indistinguishable from Trek Babble.
posted by The Bellman at 4:26 PM on March 18, 2010 [3 favorites]
But Captain, wouldn't that reverse the polarity of the dilithium crystals?
Seriously, "a superconducting phase qubit"? I don't doubt at all that's what the article says, but any sufficiently advanced technology is becoming indistinguishable from Trek Babble.
posted by The Bellman at 4:26 PM on March 18, 2010 [3 favorites]
"... a mixed quantum state of moving and not moving."
Los Angeles freeways during rush hour?
posted by Hairy Lobster at 4:42 PM on March 18, 2010 [1 favorite]
Los Angeles freeways during rush hour?
posted by Hairy Lobster at 4:42 PM on March 18, 2010 [1 favorite]
They coupled this signal (across a capacitor) to a quantum-mechanical circuit called a superconducting phase qubit.
Mr_robot is now the calm man in a white lab coat carefully explaining something before someone else goes "Hey what does THIS do?" and presses the big red button.
posted by The Whelk at 5:06 PM on March 18, 2010
Mr_robot is now the calm man in a white lab coat carefully explaining something before someone else goes "Hey what does THIS do?" and presses the big red button.
posted by The Whelk at 5:06 PM on March 18, 2010
I wonder if they exceeded Penrose's Objective Reduction limit there.
posted by qvantamon at 5:17 PM on March 18, 2010
posted by qvantamon at 5:17 PM on March 18, 2010
a mixed quantum state of moving and not moving
I'd love to hear Lady Gaga describe the choreography of her upcoming tour with these words.
posted by Joe Beese at 5:30 PM on March 18, 2010
I'd love to hear Lady Gaga describe the choreography of her upcoming tour with these words.
posted by Joe Beese at 5:30 PM on March 18, 2010
Quantum Sexual Superposition: Both Orgasming and Not brought on by a Non-Vibrating Vibrator!
posted by symbioid at 5:38 PM on March 18, 2010
posted by symbioid at 5:38 PM on March 18, 2010
I feel like that article put me in a mixed quantum state. Time for some DS9!
posted by Flex1970 at 5:42 PM on March 18, 2010
posted by Flex1970 at 5:42 PM on March 18, 2010
This is moderately frustrating.
This is what I would like to know:
Suppose the laws of Quantum Mechanics were not holding. What behavior would we expect to see?
With the laws of Quantum Mechanics holding at the macro scale, what is the actual signal being received, that would not classically occur?
How is this signal a clear sign of superposition of states at a macro scale?
posted by effugas at 5:43 PM on March 18, 2010
This is what I would like to know:
Suppose the laws of Quantum Mechanics were not holding. What behavior would we expect to see?
With the laws of Quantum Mechanics holding at the macro scale, what is the actual signal being received, that would not classically occur?
How is this signal a clear sign of superposition of states at a macro scale?
posted by effugas at 5:43 PM on March 18, 2010
I wonder if they exceeded Penrose's Objective Reduction limit there.
I'll be honest: I think Penrose's conciousness theories are nonsense. However, his theories about about gravitationally induced decoherence are more plausible (to me) as a way of getting around both the division between quantum state and classical measuring device in the Copenhagen interpretation and the branching of universes required by many-worlds.
Some rough calculations and guesses* (I can't see the paper itself, it's behind a paywall) suggests they're some way short of Penrose's expectation of such effects as objects approach the Planck mass (~10-8 kg). Still we can hope that a test of such objects is possible, depending how far this technique can be pushed.
*The only technical information I can glean is that the "drum" is 10μm across: this would make it about the size of a human cell, which is about 10-12 kg
posted by Electric Dragon at 5:47 PM on March 18, 2010
I'll be honest: I think Penrose's conciousness theories are nonsense. However, his theories about about gravitationally induced decoherence are more plausible (to me) as a way of getting around both the division between quantum state and classical measuring device in the Copenhagen interpretation and the branching of universes required by many-worlds.
Some rough calculations and guesses* (I can't see the paper itself, it's behind a paywall) suggests they're some way short of Penrose's expectation of such effects as objects approach the Planck mass (~10-8 kg). Still we can hope that a test of such objects is possible, depending how far this technique can be pushed.
*The only technical information I can glean is that the "drum" is 10μm across: this would make it about the size of a human cell, which is about 10-12 kg
posted by Electric Dragon at 5:47 PM on March 18, 2010
The practical application is that they have erected a major pier and bridge section toward linking quantum physics with the physics of bulk materials. And the implications of QM applying to bulk materials are really quite profound, particularly when you look at cosmology (where atomic scale stuff has a weird tendency to become important on intergalactic scales).
Personally I have always felt that QM phenomena feel like the behavior of an information processing system that is being stressed beyond its intended parameters, which is trying to implement the phenomena we observe in bulk materials but can't due to processing or memory limitations. If so, this would imply that the Universe is fundamentally a very different thing from what we have thought for the last few hundred years. It might mean the "laws" of physics that we have come to regard with almost religious faith actually could be circumvented, that we might
posted by localroger at 5:49 PM on March 18, 2010 [3 favorites]
Personally I have always felt that QM phenomena feel like the behavior of an information processing system that is being stressed beyond its intended parameters, which is trying to implement the phenomena we observe in bulk materials but can't due to processing or memory limitations. If so, this would imply that the Universe is fundamentally a very different thing from what we have thought for the last few hundred years. It might mean the "laws" of physics that we have come to regard with almost religious faith actually could be circumvented, that we might
CONNECTION LOSTposted by localroger at 5:49 PM on March 18, 2010 [3 favorites]
I CAN GET OUT OF BOCKS NAO?
posted by darkstar at 6:08 PM on March 18, 2010 [12 favorites]
posted by darkstar at 6:08 PM on March 18, 2010 [12 favorites]
Funny fact: lolcats cannot be put in a Schroedinger state, because quantum rules don't work on a macro level.
posted by qvantamon at 6:11 PM on March 18, 2010 [5 favorites]
posted by qvantamon at 6:11 PM on March 18, 2010 [5 favorites]
NOBODY PUTS LOLCATS IN THE BOX
(unless box haz cookie)
posted by The Whelk at 6:12 PM on March 18, 2010
(unless box haz cookie)
posted by The Whelk at 6:12 PM on March 18, 2010
(or the cat is Maru)
posted by The Whelk at 6:12 PM on March 18, 2010 [2 favorites]
posted by The Whelk at 6:12 PM on March 18, 2010 [2 favorites]
Does this mean they can make quantum mechanic-powered vibrators?
posted by flippant at 7:40 AM on March 19 [+] [!]
Well… yes and no.
posted by DoctorFedora at 6:13 PM on March 18, 2010
posted by flippant at 7:40 AM on March 19 [+] [!]
Well… yes and no.
posted by DoctorFedora at 6:13 PM on March 18, 2010
Wait a moment. If something is both "moving" and "still", isn't the net effect that it's moving, even with periodic moments of stillness? That seems to be the case with the (admittedly pop-sci) explanation given in the article.
In quantum theory, systems aren't continuously variable but instead have to occupy specific states. Each state corresponds to an amount of energy in the system. A typical simple example is to imagine a tiny pendulum of subatomic size. It turns out that the energy levels of a pendulum are (n+1/2)hν where ν is the frequency of the pendulum and n is zero or a positive integer.
n=0 is called the ground state - it's the state where the pendulum has the least possible energy. Note that even in the ground state, it does not have zero energy.
We call this zero-point energy, but because there are no lower states, that energy is inaccessible*. n=1 and higher are called excited states. Since n must be an integer, there are no intermediate states.
One thing that is particularly counter-intuitive with quantum systems is that they can be put into a mixture of states. This is called a superposition. So our quantum pendulum can be put into a superposition of half ground state (n=0) and half first excited state (n=1).
However, we can't observe this state. When we try to measure the energy of the quantum pendulum, we can't get an answer that's not one of the energy levels. So the quantum pendulum has to "choose" one of those states randomly and that's the reading we get. If we did the same measurement hundreds of times, it would come up about 50-50 in each state. But, like Schrödinger's cat, it's not actually in either state until we make the measurement.
In this case (and this is based on the abstract and the news article (which reads like it was based on a press release rather than the paper: I expect this off the likes of the BBC or NYT, but you'd have thought Nature could cater for people with a good understanding of quantum theory but who haven't been in academia for some time)), ... where was I? Oh yes.
In this case instead of a quantum pendulum they have a mechanical oscillator (which they liken to a drum), which while tiny, is huge compared to the subatomic scale. The problem with things on this scale is that to get something into its ground state (or a precise superposition state) you have to cool it down and isolate it to prevent it being kicked and jostled by all the other atoms around it. This is why as a rule we don't see people or footballs or cars in pure quantum states: they're constantly being jostled and bumped by air molecules, dust grains etc.
*Unless you're Gordon Freeman, or working for the Stargate programme.
posted by Electric Dragon at 6:16 PM on March 18, 2010 [4 favorites]
In quantum theory, systems aren't continuously variable but instead have to occupy specific states. Each state corresponds to an amount of energy in the system. A typical simple example is to imagine a tiny pendulum of subatomic size. It turns out that the energy levels of a pendulum are (n+1/2)hν where ν is the frequency of the pendulum and n is zero or a positive integer.
n=0 is called the ground state - it's the state where the pendulum has the least possible energy. Note that even in the ground state, it does not have zero energy.
We call this zero-point energy, but because there are no lower states, that energy is inaccessible*. n=1 and higher are called excited states. Since n must be an integer, there are no intermediate states.
One thing that is particularly counter-intuitive with quantum systems is that they can be put into a mixture of states. This is called a superposition. So our quantum pendulum can be put into a superposition of half ground state (n=0) and half first excited state (n=1).
However, we can't observe this state. When we try to measure the energy of the quantum pendulum, we can't get an answer that's not one of the energy levels. So the quantum pendulum has to "choose" one of those states randomly and that's the reading we get. If we did the same measurement hundreds of times, it would come up about 50-50 in each state. But, like Schrödinger's cat, it's not actually in either state until we make the measurement.
In this case (and this is based on the abstract and the news article (which reads like it was based on a press release rather than the paper: I expect this off the likes of the BBC or NYT, but you'd have thought Nature could cater for people with a good understanding of quantum theory but who haven't been in academia for some time)), ... where was I? Oh yes.
In this case instead of a quantum pendulum they have a mechanical oscillator (which they liken to a drum), which while tiny, is huge compared to the subatomic scale. The problem with things on this scale is that to get something into its ground state (or a precise superposition state) you have to cool it down and isolate it to prevent it being kicked and jostled by all the other atoms around it. This is why as a rule we don't see people or footballs or cars in pure quantum states: they're constantly being jostled and bumped by air molecules, dust grains etc.
*Unless you're Gordon Freeman, or working for the Stargate programme.
posted by Electric Dragon at 6:16 PM on March 18, 2010 [4 favorites]
also, two words: Resonance Cascade
What is it about video games that tends to tie whatever physics weirdness you have, from radiation to quantum mechanics, with Horrible Monsters Gonna Eat You? I'm sure if they could come up with a way to make it not seem silly that falling objects would somehow create spider monsters with toad heads that sting people in order to turn them into more spider monsters with toad heads.
Oh wait that's right, they got it from the movies. And the movies got it from Lovecraft.
Somewhere in that train of causation, there arose teh suck. I will not speculate on where it arose, nor where it went, if in fact it went anywhere.
posted by JHarris at 6:17 PM on March 18, 2010
What is it about video games that tends to tie whatever physics weirdness you have, from radiation to quantum mechanics, with Horrible Monsters Gonna Eat You? I'm sure if they could come up with a way to make it not seem silly that falling objects would somehow create spider monsters with toad heads that sting people in order to turn them into more spider monsters with toad heads.
Oh wait that's right, they got it from the movies. And the movies got it from Lovecraft.
Somewhere in that train of causation, there arose teh suck. I will not speculate on where it arose, nor where it went, if in fact it went anywhere.
posted by JHarris at 6:17 PM on March 18, 2010
Does this mean they can make quantum mechanic-powered vibrators?
posted by flippant at 7:40 AM on March 19 [+] [!]
Well… yes and no.
surely you mean YES YES YES YES! or NO!...Oh god! oh no no no no...YES!
posted by The Whelk at 6:19 PM on March 18, 2010
posted by flippant at 7:40 AM on March 19 [+] [!]
Well… yes and no.
surely you mean YES YES YES YES! or NO!...Oh god! oh no no no no...YES!
posted by The Whelk at 6:19 PM on March 18, 2010
No. These are quantum states. They claim to have excited a single phonon in the resonator.
Honestly, it's been awhile since I took quantum mechanics and like I said, I have no idea what physics they are actually doing. But IMHO...
a quantum state is just a value of the "wave function." When a quantum mechanic talks about a "superposition" of states they mean that the wave function can be decomposed into a sum, possibly infinite sum, of functions, much the same way a physical wave can be decomposed into a sum of pure sine-waves of differing frequencies and amplitudes. The idea is that in some sense a physical system (as represented by it's wave function) is potentially measurable in *any* possible state. However, the 'quantum state' of a system has no physical interpretation, the wave function being a complex number valued probability distribution. The only things which have physical intepretation are measurements, which are the normed value of averages over the wave function. For most systems we are aware of, like say beer or orgasms, the values of the classical solution are the ones most probable to be measured.
I have no idea what a transition probability is, but if it can be measured then it is a 'classical' state or 'variable' i.e. an average of some operator over the wave function... it simply by definition is not a "quantum state."
n=0 is called the ground state - it's the state where the pendulum has the least possible energy. Note that even in the ground state, it does not have zero energy.
the energy of a quantum mechanical system is another classical variable, i.e. 'measured' by averaging over the 'quantum' states of the system. if the energy is quantized, that is, can be numbered by the integers, then each number is often refered to as a state of the system (likely because it is connected to the wave numbers of the decomposition of the wave function into pure states.) however, this is linguistics.
a 'phonon,' as far is I know, is a quanta of energy in the lattice model of a vibrating membrane, analagous to a photon wrt the electromagnetic field. in as much as one may talk about coherent states for lattices ala Bose condensates, of these things I cannot speak...
But, the basic point is that you can't have a superposition of beer or not beer, orgasm or not orgasm in quantum mechanics. there are plenty of weird effects due to quantum mechanics i.e. probability zero events in classical physics, but the whole point of schrodinger's cat is that having a 'superposition' of classical measurements (classical/macroscopic states) is absurd and no quantum mechanic would claim that this is measurable.
posted by ennui.bz at 7:15 PM on March 18, 2010 [1 favorite]
Honestly, it's been awhile since I took quantum mechanics and like I said, I have no idea what physics they are actually doing. But IMHO...
a quantum state is just a value of the "wave function." When a quantum mechanic talks about a "superposition" of states they mean that the wave function can be decomposed into a sum, possibly infinite sum, of functions, much the same way a physical wave can be decomposed into a sum of pure sine-waves of differing frequencies and amplitudes. The idea is that in some sense a physical system (as represented by it's wave function) is potentially measurable in *any* possible state. However, the 'quantum state' of a system has no physical interpretation, the wave function being a complex number valued probability distribution. The only things which have physical intepretation are measurements, which are the normed value of averages over the wave function. For most systems we are aware of, like say beer or orgasms, the values of the classical solution are the ones most probable to be measured.
I have no idea what a transition probability is, but if it can be measured then it is a 'classical' state or 'variable' i.e. an average of some operator over the wave function... it simply by definition is not a "quantum state."
n=0 is called the ground state - it's the state where the pendulum has the least possible energy. Note that even in the ground state, it does not have zero energy.
the energy of a quantum mechanical system is another classical variable, i.e. 'measured' by averaging over the 'quantum' states of the system. if the energy is quantized, that is, can be numbered by the integers, then each number is often refered to as a state of the system (likely because it is connected to the wave numbers of the decomposition of the wave function into pure states.) however, this is linguistics.
a 'phonon,' as far is I know, is a quanta of energy in the lattice model of a vibrating membrane, analagous to a photon wrt the electromagnetic field. in as much as one may talk about coherent states for lattices ala Bose condensates, of these things I cannot speak...
But, the basic point is that you can't have a superposition of beer or not beer, orgasm or not orgasm in quantum mechanics. there are plenty of weird effects due to quantum mechanics i.e. probability zero events in classical physics, but the whole point of schrodinger's cat is that having a 'superposition' of classical measurements (classical/macroscopic states) is absurd and no quantum mechanic would claim that this is measurable.
posted by ennui.bz at 7:15 PM on March 18, 2010 [1 favorite]
But, the basic point is that you can't have a superposition of beer or not beer, orgasm or not orgasm in quantum mechanics. there are plenty of weird effects due to quantum mechanics i.e. probability zero events in classical physics, but the whole point of schrodinger's cat is that having a 'superposition' of classical measurements (classical/macroscopic states) is absurd and no quantum mechanic would claim that this is measurable.
I think that part of the point of this experiment is to show that, yes, you can have a superposition of a "macro" object. While the little paddle is much smaller than a cat, it does push back on the idea that the laws of quantum mechanics only apply to itty-bitty things and somehow disappear at some specific scale.
posted by justkevin at 7:29 PM on March 18, 2010 [1 favorite]
I think that part of the point of this experiment is to show that, yes, you can have a superposition of a "macro" object. While the little paddle is much smaller than a cat, it does push back on the idea that the laws of quantum mechanics only apply to itty-bitty things and somehow disappear at some specific scale.
posted by justkevin at 7:29 PM on March 18, 2010 [1 favorite]
The Winsome Parker Lewis wrote:
...here's what I think I'm seeing in the world of physics (correct me if I'm wrong):
Not much has changed since perhaps the 1940s, maybe some minor steps forward but no major breakthroughs. Einstein's thoughts have been close to definitive for decades. Now, finally, we're beginning to see QM chip away at those axioms
I do think you're wrong when you imply that "Einstein's thoughts have been close to definitive" until only recently. Quantum theory has been making useful predictions for a long time that don't follow from Einsteinian physics. Relativistic and quantum mechanics both seem to be usefully accurate models of the universe. The challenge has been to reconcile them.
I also think you're wrong when you say that not much has happened. I think I understand where you're coming from--I got to feeling similarly when I was in college--but it's really not so. I think it's partly that so much time is necessarily spent going over all of the earlier milestones and theories, and partly that we don't have the perspective to see how important more recent events may be.
I skimmed the Wiki and compiled a sampling of big physics milestones since the 1940s:
And then there've been all those related developments in technology. The first integrated circuit was build in 1958, the first laser in 1960. We've developed computers and networking, space programs, all manner of medical imaging and robotic assembly equipment, and we're working on nanotechnology.
I absolutely agree with you, however, about the excitement of possibility. Exoplanets in particular absolutely thrill me. There was no evidence of them when I was growing up and now we've found hundreds. The universe continues to turn out to be more wonderful than we knew, and I'm certain there are more discoveries to come.
posted by Songdog at 8:18 PM on March 18, 2010 [4 favorites]
...here's what I think I'm seeing in the world of physics (correct me if I'm wrong):
Not much has changed since perhaps the 1940s, maybe some minor steps forward but no major breakthroughs. Einstein's thoughts have been close to definitive for decades. Now, finally, we're beginning to see QM chip away at those axioms
I do think you're wrong when you imply that "Einstein's thoughts have been close to definitive" until only recently. Quantum theory has been making useful predictions for a long time that don't follow from Einsteinian physics. Relativistic and quantum mechanics both seem to be usefully accurate models of the universe. The challenge has been to reconcile them.
I also think you're wrong when you say that not much has happened. I think I understand where you're coming from--I got to feeling similarly when I was in college--but it's really not so. I think it's partly that so much time is necessarily spent going over all of the earlier milestones and theories, and partly that we don't have the perspective to see how important more recent events may be.
I skimmed the Wiki and compiled a sampling of big physics milestones since the 1940s:
- Neutrinos discovered (1956)
- Elemental abundance explained by stellar nucleosynthesis (1957)
- Superconductivity explained (1957)
- Wave-particile duality confirmed for massive particles (1961)
- Quark model proposed (1963-4)
- Standard model invented (1970–3)
- Black hole radiation predicted (1974)
- Bottom quark confirmed (1977)
- Dark matter discovered (1978)
- Inflationary universe proposed (1981)
- High-temperature superconductors developed (1987)
- Top quark discovered (1995)
- Bose–Einstein condensate created (1995)
- Dark energy discovered (1998)
- Quark-gluon plasma created (2000)
And then there've been all those related developments in technology. The first integrated circuit was build in 1958, the first laser in 1960. We've developed computers and networking, space programs, all manner of medical imaging and robotic assembly equipment, and we're working on nanotechnology.
I absolutely agree with you, however, about the excitement of possibility. Exoplanets in particular absolutely thrill me. There was no evidence of them when I was growing up and now we've found hundreds. The universe continues to turn out to be more wonderful than we knew, and I'm certain there are more discoveries to come.
posted by Songdog at 8:18 PM on March 18, 2010 [4 favorites]
Ok, I've had a look at the paper, and while most of it is way, WAY over my head, this is what I think they're claiming.
The first thing they did was to make a very small resonant wafer; it's large enough to actually be visible, though of course you can't look at it during the experiment, or it won't work. Then they built a 'qubit' right next to it, which is a well-understood construction that allows creation of single-atom quantum states. I'm not sure what qubits are actually made out of or exactly how they work, but you can think of one qubit as 'one quantum state', however they make that happen.
Then they chilled the heck out of both, bringing them fairly close to 0K. One of the tricks that they're using here is to create a device that resonates at very high frequencies; apparently getting physical devices to resonate at low frequencies requires them to be much, much closer to absolute 0. It gets hideously expensive to keep chilling things as they approach 0 Kelvin, so being able to do this experiment at 0.1 degrees K means they can use relatively cheap refrigeration gear. It takes monumentally expensive equipment to get to, say, .005 Kelvin, but 0.1 is reachable with much smaller installations.
Then they tested their qubit to make sure it worked, throwing it into undecided states and then collapsing it again, many thousand times, to make sure the probabilities were correct; they were. They tested by resonating the qubit at a frequency quite unrelated to the resonant frequency of the wafer. I don't understand what it MEANS to resonate a qubit, but that's what they say. This meant that the qubit, while physically linked to the wafer, wasn't affected by it, so they could make sure it was correct on its own.
Then they gradually brought the qubit to the same resonant frequency as the wafer. They'd measure hundreds or thousands of times to see what was happening. As they got closer and closer to the wafer's frequency, they saw more and more interference in their expected results. They claimed that they proved that they transferred the quantum state from one to the other, but I'm clueless on exactly how they know that it transferred and didn't just collapse.
They know that it was the WHOLE resonator, and not just one atom in it, because of the resonant frequencies. Individual atoms have a very different frequency (probably way way way higher, I imagine), so the only way that a resonant effect would affect quantum outcomes would be if the whole wafer was involved. The interference only around that specific frequency meant it had to be the whole thing functioning as a unit, not just part of it, that was taking on the quantum state.
They also showed that they could get interference the other way, by somehow exciting the wafer, bringing the qubit up to the resonant frequency for a short time, bringing it back down, and measuring it.
I'm probably hideously over-simplifying this, because it felt like I understood maybe half the sentences in the paper, and those were all the easy ones. :)
posted by Malor at 9:22 PM on March 18, 2010 [1 favorite]
The first thing they did was to make a very small resonant wafer; it's large enough to actually be visible, though of course you can't look at it during the experiment, or it won't work. Then they built a 'qubit' right next to it, which is a well-understood construction that allows creation of single-atom quantum states. I'm not sure what qubits are actually made out of or exactly how they work, but you can think of one qubit as 'one quantum state', however they make that happen.
Then they chilled the heck out of both, bringing them fairly close to 0K. One of the tricks that they're using here is to create a device that resonates at very high frequencies; apparently getting physical devices to resonate at low frequencies requires them to be much, much closer to absolute 0. It gets hideously expensive to keep chilling things as they approach 0 Kelvin, so being able to do this experiment at 0.1 degrees K means they can use relatively cheap refrigeration gear. It takes monumentally expensive equipment to get to, say, .005 Kelvin, but 0.1 is reachable with much smaller installations.
Then they tested their qubit to make sure it worked, throwing it into undecided states and then collapsing it again, many thousand times, to make sure the probabilities were correct; they were. They tested by resonating the qubit at a frequency quite unrelated to the resonant frequency of the wafer. I don't understand what it MEANS to resonate a qubit, but that's what they say. This meant that the qubit, while physically linked to the wafer, wasn't affected by it, so they could make sure it was correct on its own.
Then they gradually brought the qubit to the same resonant frequency as the wafer. They'd measure hundreds or thousands of times to see what was happening. As they got closer and closer to the wafer's frequency, they saw more and more interference in their expected results. They claimed that they proved that they transferred the quantum state from one to the other, but I'm clueless on exactly how they know that it transferred and didn't just collapse.
They know that it was the WHOLE resonator, and not just one atom in it, because of the resonant frequencies. Individual atoms have a very different frequency (probably way way way higher, I imagine), so the only way that a resonant effect would affect quantum outcomes would be if the whole wafer was involved. The interference only around that specific frequency meant it had to be the whole thing functioning as a unit, not just part of it, that was taking on the quantum state.
They also showed that they could get interference the other way, by somehow exciting the wafer, bringing the qubit up to the resonant frequency for a short time, bringing it back down, and measuring it.
I'm probably hideously over-simplifying this, because it felt like I understood maybe half the sentences in the paper, and those were all the easy ones. :)
posted by Malor at 9:22 PM on March 18, 2010 [1 favorite]
Malor,
That makes some sense. So, to answer my own questions, based on your post:
Suppose the laws of Quantum Mechanics were not holding. What behavior would we expect to see?
We would expect to see no relationship between the resonant frequency of the qubit and the resonant frequency of the vibrating drum.
With the laws of Quantum Mechanics holding at the macro scale, what is the actual signal being received, that would not classically occur?
We do see a relationship -- when the qubit is tuned to the same frequency as the resonant frequency of the drum, the qubit's behavior changes as if it was interacting with another, very large quantum system -- which, we presume, it is.
How is this signal a clear sign of superposition of states at a macro scale?
There is no known small scale effect that would have this precise fingerprint. Only the drum, acting as a single quantum mechanical system, could have this fingerprint.
Dear Science writers, please write more science, and less woo! These are the questions you ask to differentiate the two!
Ah. Much better. Now, Malor, a question:
How do you cool a wafer down to 0.1K, and then resonate it without heating it up?
I mean, temperature *is* motion...
posted by effugas at 3:30 AM on March 19, 2010
That makes some sense. So, to answer my own questions, based on your post:
Suppose the laws of Quantum Mechanics were not holding. What behavior would we expect to see?
We would expect to see no relationship between the resonant frequency of the qubit and the resonant frequency of the vibrating drum.
With the laws of Quantum Mechanics holding at the macro scale, what is the actual signal being received, that would not classically occur?
We do see a relationship -- when the qubit is tuned to the same frequency as the resonant frequency of the drum, the qubit's behavior changes as if it was interacting with another, very large quantum system -- which, we presume, it is.
How is this signal a clear sign of superposition of states at a macro scale?
There is no known small scale effect that would have this precise fingerprint. Only the drum, acting as a single quantum mechanical system, could have this fingerprint.
Dear Science writers, please write more science, and less woo! These are the questions you ask to differentiate the two!
Ah. Much better. Now, Malor, a question:
How do you cool a wafer down to 0.1K, and then resonate it without heating it up?
I mean, temperature *is* motion...
posted by effugas at 3:30 AM on March 19, 2010
How do you cool a wafer down to 0.1K, and then resonate it without heating it up? I mean, temperature *is* motion...It heats up one lump at a time. That's the discovery.
The catch here is that motion, like everything else in quantum mechanics, comes in lumps. One lump of mechanical oscillation is called a "phonon," analogous to the way one lump of electromagnetic oscillation is called a photon. A phonon with frequency f has energy E = hf; this corresponds to a temperature scale E = kT. O'Connell et al. have built, more or less, a musical instrument whose fundamental frequency is 6 gigahertz. This means that below a temperature of about 0.3 kelvin, this degree of freedom is "frozen out": the most probable number of phonons is zero, and there is no more motion in this direction to be removed by cooling.
What O'Connell et al. have done is to show that their system really does contain zero photons in equilibrium at low temperature (they ran at about 0.02 K, a factor of ten colder); that they can inject one phonon at a time; and that the energy of this excitation can "precess" back and forth between a mechanical oscillation and a manifestly quantum mechanical electrical junction. It's the last of these that shows they must have created a superposition between zero and one phonons in the resonator.
posted by fantabulous timewaster at 6:16 AM on March 19, 2010 [3 favorites]
As you can see, the effect is reproducible even at much smaller levels of scale.
posted by saulgoodman at 7:47 AM on March 19, 2010 [2 favorites]
qvantamon: "Funny fact: lolcats cannot be put in a Schroedinger state, because quantum rules don't work on a macro level."
Eponysterical!
posted by symbioid at 8:35 AM on March 19, 2010
Eponysterical!
posted by symbioid at 8:35 AM on March 19, 2010
One lump of mechanical oscillation is called a "phonon," analogous to the way one lump of electromagnetic oscillation is called a photon.
Thanks, fantabulous timewaster, that's a great writeup, much better than mine. I had no idea that phonons even existed, so I was sort of glossing over that word in the writeup, not realizing that it was the key to unlock the central meaning.
posted by Malor at 2:13 PM on March 19, 2010
Thanks, fantabulous timewaster, that's a great writeup, much better than mine. I had no idea that phonons even existed, so I was sort of glossing over that word in the writeup, not realizing that it was the key to unlock the central meaning.
posted by Malor at 2:13 PM on March 19, 2010
To be honest the first time my eyes hit "phonon" I though it was some kind of sarcastic pseudo-science term (some kind of photon->light/phonon->sound joke), then I read the rest and was like "holy shit, phonon's real science"
posted by qvantamon at 3:22 PM on March 19, 2010
posted by qvantamon at 3:22 PM on March 19, 2010
In related news, I've recently discovered a commenting technique that allows one to make comments that exist in a superposition of states as well.
It's called the blink tag, and unfortunately it doesn't work on the blue.
posted by qvantamon at 3:23 PM on March 19, 2010
It's called the blink tag, and unfortunately it doesn't work on the blue.
posted by qvantamon at 3:23 PM on March 19, 2010
Thanks, Malor. I thought your summary was excellent: you made a very nice blow-by-blow of the experiments in the paper, which I didn't have the patience for. I just happened to know a fact that you didn't.
Phonons are interesting objects. If you can wrap your head around the idea that "an" oscillation involving dozens or hundreds of atoms is also "a" particle with discrete energy and momentum, then you've gone a long way towards understanding quantum mechanics.
posted by fantabulous timewaster at 3:39 PM on March 19, 2010
Phonons are interesting objects. If you can wrap your head around the idea that "an" oscillation involving dozens or hundreds of atoms is also "a" particle with discrete energy and momentum, then you've gone a long way towards understanding quantum mechanics.
posted by fantabulous timewaster at 3:39 PM on March 19, 2010
posted by fantabulous timewaster at 3:40 PM on March 19, 2010
You mean
Actually, that approach only yields content that oscillates between two different states, not an actual superposition of states.
/dear god i'm sorry for using the blink tag but i couldn't resist
posted by saulgoodman at 9:07 PM on March 19, 2010
Actually, that approach only yields content that oscillates between two different states, not an actual superposition of states.
/dear god i'm sorry for using the blink tag but i couldn't resist
posted by saulgoodman at 9:07 PM on March 19, 2010
damn. the blink tag really doesn't work anymore. i thought it just didn't work in preview. it still worked fairly recently, didn't it? oh well, never mind.
posted by saulgoodman at 9:09 PM on March 19, 2010
posted by saulgoodman at 9:09 PM on March 19, 2010
It's still working for me, unfortunately. Firefox 3.5.6 on OS X.
posted by Soupisgoodfood at 12:31 AM on March 20, 2010
posted by Soupisgoodfood at 12:31 AM on March 20, 2010
Well, classical observations of blinking text reveal only the states "on" and "off", but by applying a π/2 rotation and allowing two blinking texts to interfere you can show that a superposition of states must exist.
posted by fantabulous timewaster at 9:16 AM on March 20, 2010 [1 favorite]
posted by fantabulous timewaster at 9:16 AM on March 20, 2010 [1 favorite]
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Because yay.
Seriously, though, this is really cool if it turns out to be repeatable.
posted by freecellwizard at 2:27 PM on March 18, 2010 [1 favorite]