Slashdot Mirror
Scientists Teleport Information Between Ions a Meter Apart
erickhill writes with word that scientists from the University of Maryland have successfully transferred information from one charged atom to another without having it cross the intervening space of about one meter. The academic paper is available in the journal Science, though it requires a subscription to see more than the abstract.
Scientists have previously teleported unmolested qubits between photons of light, and between photons and clouds of atoms. But researchers have long sought to teleport qubits between distant atoms. Light's high speed of travel makes photons good transporters of information, but for storing quantum information, atoms are a much better choice because they're easier to hold on to. 'This is a big deal,' comments Myungshik Kim, a quantum physicist at Queen's University Belfast in the United Kingdom. 'To store information as it is in quantum form, you have to have a teleportation scheme available between two stationary qubits. Then you can store them and manipulate them later on.'"
Are they positive?
Qubit molester insists entanglement was consensual, stay tuned for details at 11.
All sources regarding quantum entanglement/teleportation are quite adamant that you can't use it to actually send information instantaneously. Despite there being "spooky action at a distance", any discernible information had to be transfered when you separated the photons themselves at sub-light speeds. In this case it would be atoms, but I assume it still applies? The article lists applications as super-fast quantum computers (I guess any functional quantum computer could be considered fast at what it does) and quantum encryption (a real application I've heard applied to quantum teleportation, though the encrypted data itself still has to travel at c or less).
So, am I right, and this is basically the same ol' non-instant-communication but still quite cool kinda teleportation, only using atoms instead of photons? I'm just checking.
The enemies of Democracy are
Is there any other kind?
TFA (The Science News article) states 'instantly' and I can't actually read the academic paper (bugmenot doesn't seem to have a working login) but does anyone who's more familiar with this area know whether or not it's actually limited to the speed of light, or if we're actually seeing something that's capable of moving faster.
The article makes it sound as though it's instantaneous, but has this actually been measured to show that it's instantaneous or is the relatively short distance at which the "teleport" is performed only making it seem as though it were instantaneous? The implications of something like that are freaking sweet, but I don't really want to get my hopes up.
From the article they are saying that the entanglement has occurred, etc.... they also say that they know the entanglement occurs 1/100M times or so.
My question... If observation destroys the situation they describe, how to they know the entanglement happened at all?
Anyone know?
Okay I am not a physicist, but am interested in understanding a bit more about what is going on here.
Is the following description (model) a reaonably accurate portrayal of what is happening here?
We have two atoms (A1 & A2) that are in two different (non-entangled) quantum states (Q1 & Q2), at two locations (L1 & L2) separated by 1 m, at which point we allow A1 to interact (quantum mechanically) with a photon which then is 'transmitted' along the vector (L2-L1) and is then 'received' at L2 and allowed to interact with A2 to evolve its quantum state. The process is repeated a finite number of times, after which A2 is left in a quantum state Q1 (the initial state of A1). Or does A2's state simply approach Q1 with some non-zero but bounded error?
If so, can you answer these questions and if not, how does the difference between my model of what is happening and what is actually happening effect the validity of the question and its answer (to the extent that it is still valid)...
Throughout these interactions is the state evolution of A1 minimal so that the state is still near or identical to Q1 and these two atoms are now entangled or is the initial atom A1 left in a vastly different quantum state Q3? Or perhaps we can exchange the two quantum states (obviously this would require bi-directional photon communication).
If the final state of A1 is different then its initial state, can we modify the procedure to allow A1 & A2 to converge on a common state Q3?
Is the 4-momentum part of this quantum state (obviously the position is not)?
If you are cloning a state Q1 which has a corresponding energy E1 how does that energy relate to the cumulative energy of the transmitted photons (I assume the process isn't reasonably efficient), and is that difference dependent on the initial energy of the A2 atom?
The idea of instant communication is quite fascinating, but it doesn't really apply to this study. The communication they showed is not truly instantaneous, as it relies on the transport of photons from one atom to another (read the abstract, which says as much).
My mother always knew what I had done without anyone telling her. Or whatever I was going to do before I took action. I hear other mothers have the same ability. Therefore, all mothers must exist in some state of constant quantum communication with each other.
Every mans' island needs an ocean; choose your ocean carefully.
Any use of the word "instantly" is, quite simply, hype. It's instantaneous like an "instant message" is instantaneous. Not that this isn't a cool discovery; it is. But it's not teleportation and it's not instant communication.
Adds a whole new meaning to the term: wireless.
"It's the height of ridiculousness to say for those 9 lines you get hundreds of millions."
Just think, if they can figure out how this works or at least how to exploit it. You could use these for secure long distance communication. No more cell towers, just entangle some particles, put one in a rack and the other in the cell phone.
I am curious to know if this "spooky action at a distance" as Einstein referred to it, is faster than light communication. We won't know this until we put one in a Mars rover and launch it. I would also be interested to know if these particles are entangled in another dimension outside of space time. I hope this can be figured out in our lifetime.
Yeah. I will try to give a simplified explanation to non-experts (I'm just a curious guy myself):
First you entangle two particles. Then you let one travel somewhere. (If at bumps into another particle on that way, the particle loses the entanglement.)
Now if you "measure" the first particle, the "wavefunction" (the entanglement) of both particles collapses in a specific way.
By measuring that traveled particle, you can get the information on how the other particle got manipulated when it lost the entanglement.
The nice thing about this is, that it is instantly. There is no measurable delay.
So you could theoretically entangle a ton of material with another ton of material, and then send the first ton up to some remote planet. (Which of course would take very long. But you could send it at very high speeds which no human could survive too. For example by using a rocket that uses nuclear explosions as propulsion.)
Say you have defined, that you can use 0.5 kg of material every year for each side, and split the ton in such "blocks". Then you just write the outgoing 0.5 kg block (you collapse the entanglement) over the year, and read the incoming 0.5 kg block at the end of every year. By using a special encoding, you can detect where the data ends, and where the data collapsed trough your measurement. Or you just pipeline the to-be-written data on both sides, and read at the end of every month, week, day, hour, minute, second... whatever is most reasonable. (Making it a buffered transfer of blocks.)
This would give you a thousand years of infinite-speed (depending on your read rate) communication with the bandwidth of 0.5 kg of material per year (~1,37 g per day). (The amount of bits depends on the material.)
Any sufficiently advanced intelligence is indistinguishable from stupidity.
Thank you for the explanation, that was very helpful.
One more question, about measurement. Is there any way to know that measurement has taken place at the other end and your local qubit has collapsed? Or would determining that constitute a measurement in and of itself, meaning if it hadn't been collapsed it then would be so you wouldn't know what happened? I mean, I know the answer is you can't communicate instantly, I'm just figuring out why (mostly to help explain to people with roughly my same layman's understanding of physics why instant communication is impossible).
The enemies of Democracy are
Ok, who voted for the beammeupscotty tag?
I can't think of a worse place to be beamed, than 'up scotty'.
You have two entangled particles A and B and send particle B somewhere else. Then you take a reading of A and call this reading X. You don't really know what is the meaning of X - did you observe it first or did someone else observed B first but you do know that if someone observed B next he will certainly get reading X back to him. Thus it's useless for communication.
The only way this seems useful to me is if we need to keep something perfectly identical to something else, but it can't work that way either, since quantum effects don't work on bigger scales (nothing's preventing you from smashing particle B but it won't affect particle A at all, right?)
It's sort of pointless on a bigger scale - tear a piece of paper in the dark, then send one piece in another room, come back to the first one and turn on the light - you can certainly declare the the shape of the tear of the other piece will perfectly match what you have here :) In other words, there's no analogy we can use, at all, for any communication purpose.
-- Sig down
Hey physics types: So I take it this can in no way lead to the future development of the transporter?
Seems clever, but how do you detect disentanglement?
This, coupled with the earth apparently being a giant hologram...Can someone say, custom reality?
Synopsis
...for kurzweilAI.net
One more question, about measurement. Is there any way to know that measurement has taken place at the other end and your local qubit has collapsed? Or would determining that constitute a measurement in and of itself, meaning if it hadn't been collapsed it then would be so you wouldn't know what happened?
A good question. Now, determining if the thing has collapsed would require a measurement. Any interaction that could be used determine the state is a measurement of the state. But, that doesn't mean it's impossible to tell the difference, in the sense that we still know that's what happens.
Consider the opposite scenario: One system does not or can not 'know' that the other has been measured. That constitutes what they call a 'local hidden variable theory'. In other words, that the state of the system/particle isn't actually undefined and never was - it had a 'hidden' value, one that you just didn't know about until you measured it. That's the only alternate explanation for how the thing can 'know' which value to assume once it's measured (e.g. clockwise polarization for a photon if it was entangled with a photon that'd been measured as counterclockwise-polarized)
I'm almost hesitant to call it an 'alternative' explanation, because it's really the simpler idea. The states aren't genuinely undetermined, it's jus that we don't know what it is. However, it's also the wrong explanation - because of http://en.wikipedia.org/wiki/Bell's_theorem. A brilliant bit of work that showed you could in fact test and measure whether there were such local hidden variables. There aren't. Quantum weirdness won the battle.
So you can tell that the states are genuinely undefined, and you can tell that this collapse occurs instantly. But you can't tell whether the collapse has actually occurred in any particular case. Now that I think of it, if you could, it would allow for FTL communication since you could communicate by, say, measuring or not measuring one of the particles at some predetermined points in time.
Is there any way to know that measurement has taken place at the other end and your local qubit has collapsed?
Crash course in quantum mechanics, perhaps this explains it: a binary quantum mechanical system is in a linear superposition of states A and B. That is, it is either 100% A, or 100% B, or anything in between; for example 70% A and 30% B.
Now if you measure, you would only get "pure" results, i.e. purely A or purely B. If the system was pure (i.e. 100% B) before the measurement, you get what it was. If the system was mixed (say, 70-30), and you had the chance to measure the system more than once, then you get A in 70% of the cases, or B in 30%. For example: make 1000 copies of the system, and measure each of them. Roughly 700 (give/take a few) would be A, roughly 300 would be B.
The biggest problem is that you don't have 1000 exact copies -- unlike with classical information, basic QM forbids cloning of a system. So you basically have one shot, and if you happen to measure B, you'll never know whether it was because of a 100% pure B state, or simply because you "got lucky".
I mean, I know the answer is you can't communicate instantly, I'm just figuring out why (mostly to help explain to people with roughly my same layman's understanding of physics why instant communication is impossible).
While the "quantum information" is being transfered instantaneously, the problem is that the quantum state is not transfered 1:1 onto the target. It is ... "twisted". Imagine that like x*A+y*B (-> teleport ->) y*A+x*B. Now you know that the numbers x and y mean the same in both systems -- you just don't know exactly how they would be twisted after the teleportation. There are 4 possibilities how they can be twisted, and all 4 are equally probable, there's nothing you can do to favor the one over the other.
However, after the teleportation, the guy at the source can tell how they have been twisted (because the teleportation act itself is a measurement, which's result tells him exactly what happened), but the guy at the target does not.
So at first, even if the guy at the target knows that the atom has been "teleported", he stil doesn't know which one of the 4 twisted flavors of the original atom he got. If he just takes a "wild guess" and tries to measure, he'll get a statistical result which reveals absolutely no information about the actual coefficients.
The target-guy needs the source-guy to tell him which of the 4 twists occured, or in short: needs an information transfer in order to be able to "untwist" his atom and have an exact copy.
Again, the important part is that if the target-guy does not "untwist" his atom, but instead decides to go away and measure it anyway, he'll have an overall chance of 50-50 (regardless of the original x and y) to measure either A or B, so there's no information whatsoever that he could gain, not even from repeating the experiment.
It's the "twist" that makes the twist with teleportation... :-)
An Explanation of Bell's Theorem
This experiment is about the teleportation of qubits, not to be confused with the 1982 experiment involving the teleportation of Q*bert, wherein, after falling off the bottom of his pyramidal cubes, the protaganist would teleport back to the top of said pyramid.
Cracking explanation. Cheers!
OMG!!! Ponies!!!
In all seriousness, we could indeed be frickin' teleporting to work in the next 100 years. Or shorter. Let's hope we invent time travel first, so we don't have to.
What makes you think there's a difference? Walking across town would appear instantaneous if you went back the precise amount of time it takes you to walk there, except that you'd be that much older when you arrived.
Forget thrust, drag, lift and weight. Airplanes fly because of money.
This type of thing is interesting in the realm of secure communications. Information does and can not travel faster than the speed of light, so don't get hung up on that. What you DO have is a communication medium like, say, fiber optics. By using a quantum medium, the state becomes disrupted upon measuring it. This means that each end can account for the other's measurement and thus be unconditionally certain that no other party has read the transmitted message. This is ideal for operations such as key distribution. I'd note that this process would actually be slightly slower to communicate than fiber optics. You have to send a traditional message over a non quantum wire communicating to the other party when and how to measure the quantum state. It's only application, arguably, is in network security. Quantum COMPUTATION, however, is a different subject. This is not that.
Holy crap! The feminism thing is a tad too much to digest:
Scientists have previously teleported unmolested qubits
Unmolested?? Where they expecting that these female ions would be molested by male ions on their way to their homes???
Why The Fuck they can't use normal words like "unchanged", "bit copy".
This feminism thing has gone too far...
I hope we go back to the pre-WW2 era when women were easier to control and men worked...
"Doing what i can, with what i have." ~ Burt Gummer
Assuming something like this works at much longer distances, this could be applied to interplanetary and interstellar communication.
Imagine a martian colony being seamlessly connected to the internet on earth through circuits which utilize this kind of information.
VLC FOR MAC IS DYING! IF YOU DEVELOP, PLEASE SAVE IT!!
http://tech.slashdot.org/tech/08/08/06/0043220.shtml
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
I was just thinking that, but I don't think you can tell when a particle is measured without measuring it which then collapses the waveform anyway.
cat
The mods didn't get the joke, but I did.
Weaselmancer
rediculous.
http://www.davidjarvis.ca/dave/entanglement - Introduction to Q.E. without math.
How much it faster then speed of light?
orson scott card's a visionary. See?
to call quantum entanglement "teleportation".
Interesting.... Forgive my gross misunderstanding but is it possible to make a pair where they both have a higher chance of being A than B when observed. In an extreme case 90% chance of it being A for both particles, but the other particle still has to be B.
Thus you could convey the information that the other particle was read at the other end and thus take it in turns to send information, synchronising so you know the other side has already been `written' to. There would only be a 10% chance of misreading.
2 entangled quantum states are like 2 magic coins. When you flip one coin and it comes up heads, the other coin comes up tails.
Now, suppose I flip my coin, and your 100 light years away. You don't know if I have flipped my coin or not, nor if it came up heads or tails. You flip yours, it comes up tails, you now know mine must have come up heads. What information has passed between us? ALL we each know is how the other's coin came up. There is no way to use that fact to communicate anything else.
Now, you CAN use it as say an encryption key, but the encrypted data STILL needs to be transmitted between both parties, and that is subject to relativistic limitations.
So, in some sense a quantum state is 'teleported' between two entangled systems, but no actual information is exchanged which is of any use to anyone. Where it becomes interesting from a computing perspective is when you teleport superpositions of states, which allows you to store or move qbits around reliably and accurately (because they don't have to actually travel through the intervening distance, where they would most likely be perturbed). You still can't transmit information instantly because there is classical information required (how the other guys 'coin' flipped) required to interpret whatever answer you get.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
Here's an illustration of the non-tranmission of information via entanglement.
Suppose we have a pair of 'magic coins'. Either coin can be flipped and come up either heads or tails, and the other coin will always come up the opposite.
Now, suppose 2 people meet in New York and agree that they will meet again in Oslo if Amy's coin comes up heads and Bill's coin comes up tails, or they will meet in Sidney if Bill's coin comes up heads and Amy's coin comes up tails. Then Amy goes to Peking and flips her coin. It comes up heads, so she meets Bill in Oslo.
The information, which city they will meet in, was AGREED ON BEFORE HAND, it wasn't 'transmitted' by the flip of the coins. The information was in Amy's head when she went to Peking, it traveled by a classical channel governed by relativistic limitations.
This can be seen explicitly if you assume that Amy and Bill DIDN'T agree on which face of the coins meant Oslo or Sidney. In that case when Bill and Amy flip their coins they DO know that their opposite number's coin came up the other way, but neither of them knows which city to go to! In other words, no information was conveyed between them BY the flip of the coins.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
Or else they could be stealing our precious music industry's songs at the speed of light!
Because you would have to AGREE BEFOREHAND on what each collapse MEANT. Each series of measurements on each end is RANDOM. Thus all each end of the channel knows is a random number. They each know the SAME random number (or its inverse which is the same thing). It is just a random number, it contains no information.
In order for information to be passed, the two sides would have to agree (by communicating using a classical channel) as to what they would interpret their random numbers to mean. The information thus ALREADY EXISTS at each end of the quantum channel and no new information is passed beyond that by the quantum channel.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
I think now would be a good time to do a field test on Bush/Cheney.
Salut,
Jacques
The researchers then measured the first atom, thus destroying the delicate quantum information it contained, and also destroying the entanglement. That left the original qubit intact in only the second, recipient atom, completing the teleportation.
If this works, then theoretically couldn't an attacker entangle a third qubit with the original two, measure that (and destroy the entanglement), and leave the two originals unchanged?
(yes I know there's a prodigious amount of handwaving here, but it's *entangled* handwaving)
Suppose Bob and Amy entangle 2 coins so if one comes up heads, the other comes up tails. Now they go away from each other and each flip their coin. All they know is that the other's coin came up opposite to that, and which way the two together came up is random. If they want the way the two came up to 'mean' something, they have to agree on that meaning BEFORE they go apart (or by radio etc). THAT is the information, and it wasn't transmitted 'faster than light', it was carried in their heads or it was carried by radio etc.
The actual situation is a bit more complex than that, but from an information perspective this the right way to think about it.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
Because the measurements you each make at each end are RANDOM. You each know that the measurements made by the other end are the same as yours, but that doesn't amount to 'information'. You would have to agree beforehand what EVERY possible sequence of random values would be when it was actually measured, which means all the information you could possibly transmit would have to be carried with each party (subject to classical relativistic mechanics).
Thus you each DO 'know' something when you do your measurements, but that knowing in and of itself is uninformative, and neither party has any control over WHAT is transmitted.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
The flaw in your reasoning is you cannot TELL by looking at your qubit whether or not the other qubit has been measured yet or not. Thus the scheme you propose is simply impossible.
All the two sides can determine is that they each end up with the same measurements whenever they DO measure their entangled states. Unless they agree beforehand on what that information means it is just a random number which they both share.
No information has passed from one end of the channel to the other.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
quantum mechanics, lol.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
But what I don't understand is why, if you can still transfer that an atom has been teleported... And if there are 4 possible 'twists', then why cant you send between 1 and 4 atoms - the first is the message carrier, no following atom means twist 1, 1 following atom means twist 2, etc.
Please explain for me, someone! >.
That's a common misconception about teleportation: You don't *actually* transfer atoms. You transfer only quantum-mechanical properties.
The target matter has to already exist at the other end. What you do is transfer the quantum-mechanical properties of one atom at site #1 onto an atom at site #2, without actually *knowing* (or having to know :-) what the atom at site #1 looked like in the first place. All you know at the end of the day is that, if you done it right, atom at #2 looks exaclty like the one at #1 used to look like.
Interesting.... Forgive my gross misunderstanding but is it possible to make a pair where they both have a higher chance of being A than B when observed.
At the sending end, yes. At the receiving end, not. That's the key problem: the receiving end is in one of the four states of maximum uncertainty, called the "Bell states". Each of the state is equally probable, and until you know *exactly* which one of the four it is, you cannot extract any useful information other than pure randomness out of the process -- *regardless* of how the source was prepared (i.e. even if the source was prepared to be purely A, you'd still get a 50-50 chance of measuring either A or B after teleportation, if you don't have any knowledge about which Bell state your target system is immediately after teleportation).
Look up for "EPR Paradoxon" and "Bell states" in the usual physical journals. Start with Einstein et al., Phys. Rev. 47 / 777 (1935) -- that was the first time it was theoretically described -- and work all your way up until Bennet et al. Phys. Ref. Lett. 70 / 1895 (1993), when it was experimentally proven for the first time. Be sure to have a copy of J.S. Bell's "Physics 1" from 1964 lying around.
Second thought: you might want to read tbe Bennet paper first and work click way through the references downwards until you read the Eintein/Podolsky/Rosen one. Then read your way up again through the trail of clicks you left behind.
Oh, and get a decent book on quantum mechanics. Althoug a little non-standard, it's actually undergrad stuff, if you bother to read the papers I told you...
Bell's theorem (which is a logical argument) and common sense (which we base logical arguments upon) are at odds. So the physicists side with "spooky action at a distance" because it's more phun. They've been taking the "magic" path ever since Einstein and relativity came along and said reality is unintuitive (which it is, but it follows from his assumptions which were based on observation). Witness "dark matter" and "dark energy" and "string theory".
Back to the topic at hand, no one can explain what is different about a particle whose wave function has "collapsed" and one that hasn't. If you can tell the difference, then you can use entangled pairs to communicate instantly at a distance. One person makes a measurement or not, and the other guy checks for the collapsed-ness of his particle - instant transmission. But since no one knows what the collapse means we just chalk it all up as magic - or unknowable, or parallel universes, etc... By the way, the collapsedness of the particles wave function is therefore a hidden variable that we don't have access to. This proves the existence of hidden variables in contradiction to Bell's theorem, and offers the distinct possibility that the spin is also there all along as a "hidden variable".
I thus predict that an overturn of at least one assumption in Bell's theorem will be one of the biggest headlines in physics some time this century.
In an over simplified way :
* you move them apart
If the balls where quantic, both box would weight exactly half a ball until opened.
The boxes contain both state at the same time : ball and no ball.
Only when opened the boxes will make up their mind and choose which state their are in.
* no magic necessary, no teleportation happens, since the state of both boxes is fixed from the start
That's where the difference between quantum mechanics and normal everyday macroscopic physics kicks in : with quantum physics the state of the boxes is NOT fixed from the start.
If you could roll back time and restart the experiment, the ball could very well end up in the other box, with a 50% probability.
Of course, you can't roll-back time. So scientist resort to more complicated experiments to prove that. See the references that the other /.ers gave you.
"Sufficiently advanced satire is indistinguishable from reality." - [Tips: 1DrYakQDKCQ6y52z6QbnkxHXAocMZJE61o ]
n/t
The states aren't genuinely undetermined, it's jus that we don't know what it is. However, it's also the wrong explanation - because of http://en.wikipedia.org/wiki/Bell's_theorem. A brilliant bit of work that showed you could in fact test and measure whether there were such local hidden variables. There aren't. Quantum weirdness won the battle.
This is true, but to be clear, Bell's Theorem shows that the correlation between spatially-separated measurements predicted by local-hidden-variables theories is less than the correlation predicted by QM (i.e., QM predicts the measurements are _more_ correlated than local hidden variables can make them). Now that the experiments have been performed, QM is generally considered the winner.
He can't. He's basically saying that his measurements will impose a pattern on the series of particles one one side, and a correlated pattern on the series of particles on the other side. The _problem_ is that the patterns are random on both sides.
Seriously, FTL signaling enables reverse causality (i.e., future events affecting past events). And that just isn't going to happen.
I don't think you can tell when a particle is measured without measuring it which then collapses the waveform anyway.
Sort of. Neither side can tell when the wavefunction collapses due to the other side performing a measurement. Both sides see completly random (but correlated) results from their measurements. It is that randomness that prevents superluminal signaling.
At no point can either Amy or Bill determine whether or not the other coin has been flipped. All they can say for sure is that WHEN IT IS, it will come up a certain way. Maybe it already has been flipped, maybe it hasn't. The only way to find out would be using a classical communications channel.
There is a CORRELATION between the two 'coins' with entanglement, but there is NO causality. Flipping one coin does NOT cause the other one to flip, this has actually been verified by various iterations of experiments testing Bell's hypothesis. The logic is a bit trickier and my simple analogy isn't good enough to explain it, but in actual quantum mechanics if one flip caused the other, then certain experiments could be devised which would have different results than if the two flips are merely 'coincidence'.
This is one of the amazing things about QM. There is actually NO causality anywhere in QM, only a distribution of the probabilities in a particular special type of function space. Causality is an emergent phenomenon which only exists at the 'macroscopic' level. Even then it isn't absolute. I believe it was Stephen Hawking who once quipped that Cthulhu could materialize in the middle of the Pacific Ocean at any moment and no law of physics would be broken.
There are a LOT of other interesting ideas which come out of this, like questions about the meaning of entropy, which leads into questions like the Anthropic Principle.
"Malo periculosam, libertatem quam quietam servitutem." -- Jefferson
BWAHAHAHAHAHAHAHAHAHAH!!!!
Qubit molester!
BWHAHAHAHAHAHAHAHAH!!!
Richard Steven Hack - This sig is TOO GODDAMN SHORT TO DO ANYTHING USEFUL WITH! MORONS!
And for their next feat, they will teleport a cat!
Disclaimer: The opinions and actions of the US Gov't are in no way representative of those held by this author or its ci