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Tiniest Lamp Spans Quantum, Classical Physics

kdawson posted more than 5 years ago | from the just-small-enough dept.

Science 59

Urchin writes "Physicists in California have made the smallest ever incandescent lamp using a carbon nanotube as the filament. The nanotube is so small it behaves as a quantum mechanical system but it's just large enough that the classical physics rules of thermodynamics should apply. Analyzing the light emitted from the tiny light will give the team a better picture of what happens in the twilight zone between the quantum and classical worlds." The New Scientist article doesn't mention the researchers' surprise, as the abstract does: "Remarkably, the heat equation and Planck's law together give a precise, quantitative description of the light intensity as a function of input power, even though the nanotube's small size places it outside the thermodynamic limit."

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Carbon nanotubes (1, Funny)

Anonymous Coward | more than 5 years ago | (#27786721)

Is there anything they *can't* do?!

Re:Carbon nanotubes (0, Offtopic)

Gerafix (1028986) | more than 5 years ago | (#27787023)

They can't turn into a dog or a cat and thus disprove evolution. Evolution was just a theory after all. - Texas Board of Education.

Re:Carbon nanotubes (0)

Anonymous Coward | more than 5 years ago | (#27787335)

Behold my carbon nanotube cat:
.

There is no such thing as classical physics... (2, Insightful)

A beautiful mind (821714) | more than 5 years ago | (#27786729)

...of course. It's just that the rules we recognize as classical laws of physics work well enough at that scale for us not to notice the effects that had to be explained by quantum physics.

Re:There is no such thing as classical physics... (-1, Troll)

Anonymous Coward | more than 5 years ago | (#27786831)

Yes, and the name given to these laws is "Classical Physics". QED

Re:There is no such thing as classical physics... (4, Insightful)

pablomme (1270790) | more than 5 years ago | (#27786861)

Obviously. Which isn't to say that the concept of a classical regime versus a quantum one isn't useful. You wouldn't describe the motion of a baseball using Schroedinger's equation: it's perfectly possible, but impractical.

Any information we can get about the transition between the two regimes is very valuable indeed.

Re:There is no such thing as classical physics... (4, Insightful)

DriedClexler (814907) | more than 5 years ago | (#27787009)

Obviously. Which isn't to say that the concept of a classical regime versus a quantum one isn't useful. You wouldn't describe the motion of a baseball using Schroedinger's equation: it's perfectly possible, but impractical.

Good point. I was browsing Douglas Hofstadter's I Am a Strange Loop recenlty, and he made a great point about levels of description. He notes that when we discover "X is reducible to the more fundamental phenomenon of Y", people seem to think that means Y is more important and useful. But, he says, that discovery is equivalent to "Y can be ignored at the level X". That is, even though there might be a lower-level description, the discovery of enough regularity at that level is also useful since it means a simpler way to describe what's going on.

Re:There is no such thing as classical physics... (2, Insightful)

Rich0 (548339) | more than 5 years ago | (#27788619)

Agreed. If quantum mechanics were truly practical then we chemists would be out of jobs. :)

Re:There is no such thing as classical physics... (1)

Impy the Impiuos Imp (442658) | more than 5 years ago | (#27791707)

...and so would prostitutes.

Re:There is no such thing as classical physics... (0)

Anonymous Coward | more than 5 years ago | (#27791189)

yes, and then the pitch could both be and not be a strike, but not if you look.

Re:There is no such thing as classical physics... (1)

mr_mischief (456295) | more than 5 years ago | (#27792301)

Any pitch can be both a strike and not a strike until the home plate umpire calls it, especially at a Cardinals/Cubs game. With 60,000 in attendance, you can have around 30,000 arguments about what the call should be, but only one call.

Re:There is no such thing as classical physics... (1)

wdef (1050680) | more than 4 years ago | (#27796805)

"You wouldn't describe the motion of a baseball using Schroedinger's equation: it's perfectly possible, but impractical."

Solving certain classical problems with quantum theory (and getting the right answers) is a typical graduate level homework question. There's a classic advanced textbook of quantum problems that's full of this sort of thing.

Re:There is no such thing as classical physics... (1)

pablomme (1270790) | more than 4 years ago | (#27797415)

Which is not incompatible with my point. When a way of solving a particular problem is impractical, the only value such solution may have is as an academic exercise. You'll learn a lot from such an exercise as long as you realize it's just that, an exercise.

If you really use quantum mechanics for a purely classical problem in your research, you are a lousy researcher, because you are being unable to focus on the important parts of the problem and neglect those that do not matter, thus wasting time and resources.

Re:There is no such thing as classical physics... (1, Interesting)

Anonymous Coward | more than 5 years ago | (#27788005)

Your statement is true about all physical laws. They are just rules that work well enough to predict events, but that doesn't mean they are whats really happening.

Re:There is no such thing as classical physics... (1)

Impy the Impiuos Imp (442658) | more than 5 years ago | (#27791737)

This is true. Quantum Mechanics' "true randomness" could sit atop a perfectly deterministic deeper reality. When Einstein said he believed in "reality", he meant there were definite objects out there with definite properties. QM wipes that away -- *at that level*. Of course, an even deeper reality would basically make the QM level a sort of virtual world, which doesn't exactly help Einstein's case, even if it were to be deterministic. The "real stuff" he believed existed would now be twice-removed, so to speak, from "reality".

Re:There is no such thing as classical physics... (1)

wdef (1050680) | more than 4 years ago | (#27796779)

With the proviso that the differences in those rules between the two paradigms reflect quite different views of reality (though luckily with some comparable mathematical structures such as transformations that allow a good deal of extrapolation of concepts from 19C physics into the quantum realm - greatly helping how we conceive of quantum ideas that really have no exact macroscopic equivalent).

Re:There is no such thing as classical physics... (1)

Gallomimia (1415613) | more than 4 years ago | (#27798775)

You're right. As the article implies it's now known as thermodynamics. It can also be called Newtonian physics. Our moms tell us we have two ears and one mouth therefore we should listen twice as much as we speak. Unfortunately for this site and its linked articles we have ten fingers and only two eyes.

The whole point of the beautiful minds studying this nanotube filament is to observe something that truly does require the calculations from both old physics and new physics (call them whatever you want, but know what the difference is) in order to model and predict the behavior of.

California Environmental laws! (5, Funny)

spineboy (22918) | more than 5 years ago | (#27786791)

I'm sorry - but they will have to switch it out for a really tiny compact fluorescent bulb.

Re:California Environmental laws! (0)

Anonymous Coward | more than 5 years ago | (#27786873)

A tiny LED would give even better efficiency. Coupled with the tiniest power supply, we could microilluminate the microscopic world!

Re:California Environmental laws! (4, Funny)

JonTurner (178845) | more than 5 years ago | (#27786905)

Queue the "how many physicists does it take to change a nano lightbulb?" jokes...

Re:California Environmental laws! (0)

Anonymous Coward | more than 5 years ago | (#27787433)

Cue, not queue. Cue means to trigger/make ready. Queue means to build a... queue. Not that hard, yo.

Re:California Environmental laws! (1)

SEWilco (27983) | more than 5 years ago | (#27790499)

He must have been referring to the cueing of scientists to apply for funding, and the resulting queue of funding applications.

Re:California Environmental laws! (1)

jbeaupre (752124) | more than 5 years ago | (#27787459)

Physicists don't change lightbulbs. They rewrite theory to account for darkness.

Re:California Environmental laws! (1)

M8e (1008767) | more than 5 years ago | (#27787539)

Ten Ångströms?

Allow me to say (1)

OeLeWaPpErKe (412765) | more than 5 years ago | (#27790345)

Let's just hope this isn't true. Then again, given how rational lawmakers are, let's just hope nobody asks the police to find out.

An incandescent lamp??? Arrest them! (0, Offtopic)

DriedClexler (814907) | more than 5 years ago | (#27786867)

How dare they build an incandescent lamp! Where's the outrage? Don't you guys here think that incandescents should be banned? Since they're wasteful and all?

Or maybe you take the "non-absurd" position that incandescent bulb usage should be allowed, just as long as a central committee approves of your intended usage?

Because the truly absurd position is to just cap the total emissions and let people do whatever they want within that limit, right?

(Flamebait, I know, but some people really don't understand the implications and inefficiency of banning incandescent light bulbs.)

Re:An incandescent lamp??? Arrest them! (2, Funny)

Gospodin (547743) | more than 5 years ago | (#27787777)

It gets even worse: they're using a CARBON filement! Carbon, people! It's worse than plutonium!

How many physicists... (5, Funny)

Red Flayer (890720) | more than 5 years ago | (#27786875)

How many quantum physicists does it take to change a light bulb?

One. Two to do it, and one to renormalise the wave function.

Re:How many physicists... (4, Funny)

Drakkenmensch (1255800) | more than 5 years ago | (#27787311)

You Fool! You altered the outcome by observing it!

Re:How many physicists... (4, Funny)

Red Flayer (890720) | more than 5 years ago | (#27788027)

That was the point. We did not know if it had been changed already or not.

As soon as we observed it, it collapsed into a changed state. (Well, half the time. The other half it collapsed into an unchanged state.)

Furthermore, we had an additional problem... we made the mistake of measuring how fast we were moving the bulb. As soon as we did that, we lost track of where the damn thing was.

Re:How many physicists... (1)

hebertpa (457332) | more than 5 years ago | (#27790441)

So what they are saying is that the problem the whole time with quantem mechanics has been a lack of lighting. Maybe that we help them observ the direction of a particle and know where it is.

Re:How many physicists... (1)

SQLGuru (980662) | more than 5 years ago | (#27791087)

They are just trying to shed a new light on the subject.....

Re:How many physicists... (1)

JLDohm (741501) | more than 5 years ago | (#27791951)

The answer was {0 (no one really understands Quantum Mechanics), 1 (Changing the bulb did leave him in an excited state), 2 (One to do it, and one to observe)...}

Once you looked in you probably found the answer was a linear combination of quantum physicists and maintenance workers

Re:How many physicists... (1)

drcesteffen (1236780) | more than 5 years ago | (#27841805)

The wave function of all quantum physicists says the probability some physicist will have the energy to change the light bulb is spread across all physicists. It does not imply any physicist has sufficient energy to change the light bulb. So changing the light bulb may be impossible.

Also (1)

KrimZon (912441) | more than 5 years ago | (#27786965)

Awwwwww! It's so wickle!

*ahem*

Anyway...

Silly Scientists? (-1, Redundant)

stevew (4845) | more than 5 years ago | (#27787049)

This sounds like the most useless research I've ever heard of. Don't these guys know that Incandescent light bulbs are going to be illegal after 2012? I mean - what is the point? They're not going to be able to sell the darn thing.

Now - if they were figuring out a way to make a Compact Florescent lamp (CFL) without Mercury - now that would be a hot seller!

Re:Silly Scientists? (1)

InfiniteLoopCounter (1355173) | more than 5 years ago | (#27787625)

Okay. It's fine you didn't read the article, given this is /.

It's tolerable you didn't read the summary -- again, this is /.

But to mistake a humorous post by another reader about the banning of incandescent lamps for a serious one... where does this madness end?

I mean - what is the point? They're not going to be able to sell the darn thing.

This is research we are talking about here. Lots of good stuff usually comes out as a bi-product down the track.

Re:Silly Scientists? (1)

stevew (4845) | more than 5 years ago | (#27792547)

Someone has his funny-bone permanently out of joint.

This was something like the fourth post too when it was originally contributed... so the "redundant" mod probably wasn't really fair. - but it is /.

New lightbulb? (3, Interesting)

nausea_malvarma (1544887) | more than 5 years ago | (#27787279)

This experiment is important because it reveals something about physics. However, I wonder if this could also lead to practical inventions. Could a high intensity energy efficient light bulb be made from millions of tiny nanolamps clumped together?

Re:New lightbulb? (0)

Anonymous Coward | more than 5 years ago | (#27792885)

Yeah, imagine a Beowulf cluster of these babies!

arXiv (1)

HaeMaker (221642) | more than 5 years ago | (#27787391)

I looked, the full paper isn't there, anyone else find it? I hope they are able to post it.

Re:arXiv (1)

cream wobbly (1102689) | more than 5 years ago | (#27817649)

Don't worry. Half the time people will look and it will be there.

Crud (4, Funny)

SnarfQuest (469614) | more than 5 years ago | (#27787399)

I just replaced all the lamps in my house with these, but they just don't seem to brighten up the room like the old ones, and now my cat is missing.

The things we must endure for global warming to be a success.

Imagine (5, Funny)

commodoresloat (172735) | more than 5 years ago | (#27787701)

Reading Beowulf under the light provided by a cluster of these lamps!

Headlights for nanobots. (1)

olsmeister (1488789) | more than 5 years ago | (#27788655)

Now, we just need to invent a nanoCCD, and devise a way to switch from high beam to low beam.

How many to replace (2, Funny)

Nom du Keyboard (633989) | more than 5 years ago | (#27788979)

Okay you went and blew the light, I know I left the replacement bulb around here somewhere, but every time I look at it it disappears.

Very important kind of experimentation! (5, Insightful)

bughunter (10093) | more than 5 years ago | (#27789673)

The history of science suggests that exploring the intersection of two bodies of theory is a very important kind of experiment. It was Thomas Young's double slit experiments [wikipedia.org] , Planck's study of blackbody radiation [wikipedia.org] , and Einstein's work with the photoelectric effect [wikipedia.org] that revealed the necessary clues to the quantum theory that resolved the paradox of the apparent wave/particle duality of electromagentic radiation.

It took 19th century classical physicists an entire century to resolve this issue, so long that the discipline became a little stagnant and some folks were beginning to claim that physics had explained everything there was to explain. However, Planck's work was especially important in revealing the quantized energy nature of light that was the key to opening up 20th century physics. [wikipedia.org]

Anyway, to keep this short, I suggest that we find ourselves in a similar situation. Our current models have been played out, and are leaving a lot of important questions unanswered. There are a few candidate theories that hold promise but aren't supported by observations. Looking at the cracks between our building blocks worked before -- it opened up whole universes of possiblility. We need to keep doing it. This experiment is a great example of that kind of work.

Re:Very important kind of experimentation! (1)

SQLGuru (980662) | more than 5 years ago | (#27791027)

I agree. In programming, it isn't the normal case that usually has the bug, but the boundary case.

Re:Very important kind of experimentation! (4, Insightful)

radtea (464814) | more than 5 years ago | (#27791547)

that resolved the paradox of the apparent wave/particle duality of electromagentic radiation.

We didn't actually resolve the paradox, we just showed that we didn't have to resolve it to do useful calculations. The legacy of positivism and the Copenhagen Interpretation has been to simply sweep the whole question under the carpet.

Even modern approaches that attempt to explain the central question of quantum theory, which is "How does the classical world arise out of quantum phenomena?" don't actually answer it. They just make you feel better about it, distracting you from the fact that they have explained nothing. The whole Many Worlds approach is like this: it actually says nothing about why consciousness experiences only one of the many possible outcomes, despite its rather clever intellectual edifice.

To look at it another way, if all you knew about was the quantum universe of smoothly evolving probability densities, you would never guess at the existence of the classical universe at all. You would never suspect there was such a thing as "wavefunction collapse" (or any of its conceptual equivalents in different interpretations.) You would simply be aware (insofar as awareness might be possible in such a universe) that the various components of wavefunctions decohere smoothly over time due to interactions and entanglements with systems that have many degrees of freedom. You would not under any circumstances say, "Hey, all the components of that wavefunction just vanished except for this one!" Yet that is what WE say all the time, and no one has a clue as to why it happens.

My own take on this is that far from being some bizarre quantum phenomenon, consciousness is fundamentally classical in a way that physics is not. This is a Kantian view, that there are necessary conditions to consciousness that are more restrictive than the general conditions of existence.

So far, no empirical test of any interpretation of quantum mechanics (except experimental violations of Bell's Inequalities, which rule out any local causal interpretation) have been proposed. It may be that systems like this one will allow for novel tests, and in any case they are likely to put a finer point on the fundamental question even if they get us no closer to answering it.

Re:Very important kind of experimentation! (2, Funny)

narcc (412956) | more than 4 years ago | (#27796715)

I think I'm required to tell you to "shut up and calculate".

Re:Very important kind of experimentation! (2, Interesting)

wdef (1050680) | more than 4 years ago | (#27796871)

You would simply be aware (insofar as awareness might be possible in such a universe) that the various components of wavefunctions decohere smoothly over time due to interactions and entanglements with systems

Actually, a very great and quite under appreciated physicist, HS ("Bert") Green, did show with colleagues that this collapse does occur just because of the interaction between systems and that mathematically it is not the least bit mysterious or spooky. Why the name of this man, who Max Born called "brilliant", is not better known has to be the real mystery.

See http://www.science.org.au/academy/memoirs/green.htm [science.org.au]

In 1958 Bert published one of his best papers [53]. It was entitled 'Observation in Quantum Mechanics' and addressed one of the outstanding problems of modern physics, namely the process by which indeterminate superpositions in quantum mechanics become converted to the determinate, although possibly unknown, alternatives of ordinary macroscopic physics. For many years the prescription of von Neumann, usually called the 'collapse of the wave packet', was the accepted view of how this happened. As it assumed that some processes outside quantum mechanics had to be invoked, even going so far as involving the brain of the human observer, people were not comfortable with it, although it seemed the only possible answer. The best known representation of this difficulty appears in the well-known SchrÃdinger's cat paradox. Bert, together with a number of others such as Wakita and Ludwig, found a much more satisfying explanation, which is basically still the received description, although nowadays in various forms. The idea was to suppose that a measuring apparatus could be of almost any form so long as it was very complicated, that is, contained a very large number (often for mathematical convenience taken to be infinite) of components such as molecules or electrons. The system being measured could be microscopic. When the two systems interact, any 'interference terms' in the state of the microscopic system become vanishingly small purely as a consequence of the size of the measuring instrument. There are, of course, many processes in nature in which a human observer is not involved â" especially before homo sapiens evolved â" and the von Neumann description is quite unable to say how these could happen. However with Bert's theory all one has to do is to replace the measuring apparatus by the environment to bring about the necessary disappearance of interferences. The only place where this very satisfactory explanation might run into some difficulty is in the early evolution of the universe, where there is no environment!

Re:Very important kind of experimentation! (1)

radtea (464814) | more than 4 years ago | (#27800253)

Fascinating! Thanks for the link--the role of decoherence became clear to me in the '90's, and there's a whole little group pushing it as the solution to this problem as if it was new.

I never published on the topic because it rapidly became obvious to me that it in fact says nothing about the real problem. There's a subtle bait-and-switch going on. Decoherence doesn't actually address the problem: why is there a classical world at all? Why aren't we aware of the damned probability distributions, coherent or otherwise? And why does the charge of the electron only show up in one place, not spread (incoherently) all over the place?

Decoherence explains why we don't see interference patterns everywhere, but it says nothing about the ontology of the wavefunction, or of consciousness, which to me is the real issue. It takes for granted that conscious experience is classical, but that's the whole point. As Max Born said, "WHY must I treat the apparatus as classical? What will happen to me if I don't?!" THAT is the question, and decoherence does not address it at all.

It is still fascinating that Green came up with this back in the '50's. The journal he published in (Nuovo Cimento) is not first-rank, although still respectable. The real reason his work wasn't given the attention it perhaps deserves is more likely to be the internal politics of the academic community.

Re:Very important kind of experimentation! (0)

Anonymous Coward | more than 5 years ago | (#27825801)

This is not explanatory, more a bit of induction:

Why don't you see the dark intervals when your eyelids blink closed?

Why do you see a continuous moving picture instead of about 24 or 30 frames per second?

Why do you see flicker fusion?

Why do you observe discrete still images or flickering when the flicker rate is slowed? What happens when you accelerate at relativistic velocities relative to a flickering light source? What does a movie look like through a telescope as you increase or decrease your recession velocity relative to the stationary screen? What happens when you are stationary with respect to the screen but the projector's recession velocity with respect to the screen changes? Pay attention to focus (and aperture and flux) of both the projector and your eyes.

Take a boundary condition where you are separated at a spatial distance such that the flux of photons from the screen falling on your cornea (yes, not retina; although you could simplify and consider that case without the lens) is small enough to count the individual photons in principle, while you're at rest with respect to the screen, which in turn is at rest with respect to the projector, so that the photons are detectable by your retinal cells. Arrange things so that the influence on your retina of other sources of visible light is made negligible and remove obstacles between you and the screen; free space is the goal.

Your brain is now reacting to a tiny slice of a fairly substantial system; but is definitely tied to the reflection of the photon by the screen, its passage through the film or filter after its generation (or atlernatively its generation by an LED or equivalent).

If you move such that you increase the spatial distance from the screen, the photon flux reduces because your cornea subtends a smaller area of the conceptual spheroid centred at the screen. Conversely, if you move closer to the screen, the flux of photons increases. As long as you are stationary relative to the screen at each measurement, you see a bigger slice of the picture. At some point as you close on the movie screen you stop seeing individual photons and start noticing optical fusion effects both temporally (you start noticing a persistent dot of brightness rather than occasional quick blinks of various colours), spatially (the dot expands into a recognizable image).

Eventually, at a close enough distance, "classical movie" emerges.

As with other physical experiments, this is reversible, so if you recede from a movie screen eventually you end up with such a small number of photons falling on your retinal opsins that you encounter tiny enough numbers of photons (in principle, even single ones) that you can determine that you are seeing "quantum world". (Consider this if you replace the movie screen with a classically constant monochromatic omnidirectional light source).

This does not go into hidden variables since information is being carried by photons travelling through free space. There is a clear time-like separation between reflection (or emission in the case of the monochromatic omnidirectional radiator) and the interaction with the retinal opsin. We can probably eliminate most environmental pollution experimentally to avoid decoherence of the photons en route (otherwise we have biiiig problems with astronomy in general (factoid: the radiation at the top of Earth's atmosphere from magnitude 0 stars is 1000 photons per second per cm^2 per angstrom at 5500 angstroms (by definition on the Vega standard)).

We can use large spatial distances to play with constructive and destructive interference involving tiny numbers of photons too, and expect to see the usual wave particle duality depending on the relationship between the quantized events (emitters/reflectors of countably small fluxes of photons) and your visual system (i.e., interference depends on synchronization both in terms of the time of arrival at the cornea and the frequency of the photons; the rate of arrival (I think!) is less important in the limit of unfused flickering).

At the bottom all of these visual observations by you are quantum interactions. The photons hitting your retinal opsins (and the chain of molecular reactions leading into your primary visual cortex) have some of their degrees of freedom correlated with (a) the emission from the monochromatic omnidirectional radiator or (b) the screen and the projector (and the original recording devices...). These events are all within the intersection of the light cones of the various systems, i.e. they are contiguous in space-time. All the interactions are local. There are no hidden variables. Predictions can only be statistical because although there are no hidden variables, there are lots of them that propagate very quickly when analysing the |no_light_noticed> case, and the opposite case is also rife with possible explanations for |light_noticed> that are not correlated with the distant projecting system; many of these are non-vanishing if we substitute a "more objective quantum detector" for you.

There is no need to abandon the linear evolution of Schroedinger equations for the relevant systems (even when combining them), and it agnostic about whether QM or GR is a complete theory.

It also accepts that there may be interfererence patterns everywhere that go undetected because of how detection and correlation works:

A pigeon (with a different flicker fusion rate and a sensitivity to a broader range of photon frequencies) will detect a transition from "clasical movie" to "discrete still pictures", from "continuous dot" to "blinking dot" at a closer spatial distance from the projector/radiator, and will have a different view of relativistic doppler shift. Pigeon eyes are also smaller and are arranged differently from ours. So would pigeons with analogous technology have a different boundary between classical and quantum worlds from us?

In particular, do pigeons perceive interference patterns differently?

Just wait for the follow-on (0)

Anonymous Coward | more than 5 years ago | (#27789687)

Soon you'll be able to get PHAT TOOB sound from an integrated circuit!

I expect a ticker-tape parade for our new hero, (2, Funny)

idontgno (624372) | more than 5 years ago | (#27789689)

Nanoscale Inanimate Carbon Rod! [wikia.com]

Wrong "world's tiniest" to be working on right now (2, Insightful)

plasmacutter (901737) | more than 5 years ago | (#27790223)

They would make a lot more money by making the world's tiniest violin with nano-tubes, and mailing it to, in order:

bank executives
auto executives
the **AA and member companies
right-wing talking heads seen in recent clips on episodes of the daily show.

I would like to know (1)

Khyber (864651) | more than 5 years ago | (#27794569)

What the luminous efficiency of this? Could the carbon nanotube perhaps include other elements to produce a different spectrum or color temperature?

Imagine a flexible light-up sheet of carbon nanotubes. With color? Ultra-resolution screens?

There is no such thing as classical physics... (1)

clint999 (1277046) | more than 4 years ago | (#27797331)

You would simply be aware (insofar as awareness might be possible in such a universe) that the various components of wavefunctions decohere smoothly over time due to interactions and entanglements with systems
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