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Hi again everyone!
Interest seems to be waning based on viewers/comments, so please if you’re reading these entries, let me know! I enjoy writing these and I’ll keep contributing regardless, but if there isn't much interest the blog will become less of a priority for me and I might switch to posting every other week or so.
Today’s topic is exciting though, so maybe it’ll inspire more conversation.
Lesson 5: Quantum Entanglement
+ Show Spoiler +Entanglement is a weird and beautiful and purely quantum mechanical phenomenon. It’s quickly becoming the center of attention in quantum information, communication, and cryptography, so it’s definitely a concept worth being (at least vaguely) familiar with. Before we discuss entanglement as we know it today, let’s go back to the rise of quantum theory and the drama it inspired… Throughout the 1920s and 1930s Albert Einstein voiced many concerns he had with quantum theory. You've probably heard the popular Einstein quote “God does not play dice”? Or a more illuminating statement went something like “I would like to think the moon is there, even when I’m not looking at it”. Quantum theory, however, states that “only after we measure a property value of a particle does that property gain physical reality - before we measure it we must consider it to be in a superposition of many states”. This was his big issue with quantum. In 1935 Einstein, Podolsky, and Rosen (EPR) published a paper that addressed this issue. In this paper, they presented the first scientific definition of “reality”, a term we should be familiar with: "If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."In other words, if you can know something without measuring it, then the measurement did not influence that particular something, so it must have existed before being observed and therefore must be “real”. Read that sentence a couple of times and I swear it’ll make sense.  Another important word to know when we discuss entanglement is “locality”. The principle of locality states that an object can only be influenced by its surroundings, and that these influences travel continuously through space/time, and the speed at which they travel is capped by the speed of light. Classical physics follows this principle. Pretty much everything we know of follows this principle. Einstein believed that entanglement, which challenges reality and locality, was the fatal flaw of quantum theory. So what is entanglement? In lesson 2 we learned that we can describe systems with wave functions. If you have a system of multiple particles that are entangled, you have a wave function that describes the system as a whole; it is not possible to describe an individual particle independently, as its properties are intimately tied to the rest of the system. Let’s consider an example that illuminates both the concept and Einstein’s issues with entanglement... Now, it is a known property of two entangled photons that they must have orthogonal polarization. Say we have a pair of entangled photons and separate them by very large distances. I have one, you have the other. I measure the polarization of my photon and its vertical; yours must be horizontal. Even though we never observed the second photon and therefore might think it’s still in a superposition state, since it was described by the wave function of the entangled system, when I collapsed the wave function by measuring my photon’s polarization, yours had to take on a definite value too. Not just any value, the value required by properties of entanglement. This has been proven experimentally. Understandably, Einstein didn’t like this. The “communication” between these entangled photons is instantaneous. We could be on other sides of the solar system and my measurement would immediately influence your photon. This violates special relativity, something Einstein was particularly fond of.  Einstein’s solution to this apparent paradox was to assume that particles possess “hidden variables”; intrinsic properties that are fixed when the particle is created, thus eliminating the need for super-luminal communication. The mysteries of entanglement are really already fixed facts- we just can’t see them because quantum theory is incomplete; it doesn't account for these hidden variables. This would support the notions of realism and locality. This so-called EPR paradox plagued the reputation of quantum theory and caused many arguments between the legendary physicists until 1965, when Bell came along with his famous theorem. Bell published a paper titled “ On the EPR Paradox” that introduced the famous “Bell inequalities” and “Bell’s theorem”. The theorem states that no theory of “hidden variables” can ever reproduce the predictions of quantum mechanics. In other words, quantum is right. There aren't any hidden variables that could explain everything that can actually be observed. I came across an awesome, non-physics example that illustrates the idea of these inequalities, if you’re interested... + Show Spoiler +Borrowed from this site...Consider our collection of objects with fixed properties to be a collection of people. And let their fixed properties be the following: • A: Sex ("Male" or "Female") • B: Height (over 5' 6" ("Tall") or under 5' 6" ("Short" - don't be offended!)) • C: Eye color ("Blue" or "Green") Then, no matter which group of people you are dealing with, you are always able to issue the following statement (inequality): "The number of short males plus the number of tall people, male and female, with green eyes will always be greater than or equal to the number of males with green eyes. I absolutely guarantee that for any collection of people this will turn out to be true.“ After Bell’s paper, many experiments were carried out and to this day quantum theory holds. Entanglement is a purely quantum mechanical phenomenon with no classical analogue. This severely bothered Einstein, but in today’s world it’s something we’ve become relatively comfortable with. Quantum is weird, but as far as we know, it’s correct. Today, we are at the point where we’re trying to use entanglement to do stuff. You can find lots of papers that discuss entanglement in quantum communication applications if you feel like searching the internet a little. I just want to mention two interesting recent discoveries… Entanglement between photons that don’t coexist in time+ Show Spoiler +Last year some experimentalists demonstrated that not only can we entangle particles separated by large distances, we can entangle particles that don’t coexist in time! This was demonstrated experimentally, I think about a year ago. The researchers entangled two photons, 1 and 2, and measured the polarization of 1. Then they entangled a second pair of photons, 3 and 4. The polarization of 2 and 3 were measured simultaneously, causing them to be entangled via something called “projective measurement”. This, therefore entangled 1 and 4. The entanglement was confirmed by measuring 4’s polarization… but photon 4 didn’t even exist when they measured the polarization of 1! Yet somehow 1 influenced the state of a photon that would exist in the future. See the paper hereIf you've taken any physics (or even chemistry) class, you've probably heard of entropy and how it only increases, and how this can give us the “arrow of time”. Time increases in the same direction entropy increases. A broken coffee cup doesn't put itself back together, so if we see that on a video, we know its being played in reverse. Well, very recently it was proposed that perhaps there is another way to view the arrow of time based not on entropy, but on entanglement. A particle alone can be described by a wave function and is said to be in a “pure state”. When it interacts with another particle, it becomes entangled and is then in a “mixed state”; its wave function is mixed with the other particle’s. This leads to correlations between the two (one photon is vertically polarized, the other is horizontally polarized). As particles join this system, their properties also become correlated. The basic idea, then, is that the arrow of time points in the direction of increasing correlation. It’s an interesting concept that I don’t know enough about to go into extreme detail, so check out these links for more info: The original thesis that proposed these ideasA more reader-friendly article
So that’s entanglement for you! As always, thanks for reading and all feedback is appreciated! I’m already starting to run low on ideas for topics, so if there is some physics-y thing you want to learn about, request it!
 
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United States24633 Posts
I feel like entanglement is something that we just don't understand. It forces us to think differently about other established theories. Hopefully we will continue to make breakthroughs on this.
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence.
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i'm a "quantum field theory" guy
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All this stuff is super interesting, even for someone like me that doesn't (have time to) understand the math behind it.
It all sounds a bit like magic.
By the way, I have heard of a guy that suggests that ER=EPR.
(Einstein Rosen Bridges equals EPR quantum entanglement)
Or in other words, that two entangled quantum particles are connected by a wormhole.
http://arxiv.org/abs/1306.0533
If this was true, it would be a solution to the Black Hole Information Paradox and provide a link between general relativity and quantum mechanics.
http://en.wikipedia.org/wiki/Black_hole_information_paradox
There is a lot of controversy around this, mainly because it builds on a concept called Firewall, which would violate some laws of Einstein.
http://en.wikipedia.org/wiki/Firewall_(physics)
This is also preceded by a big fight between Leonard Susskind and Stephen Hawking.
People are basically still trying to figure it out, but it sounds interesting nonetheless.
Susskind also gave a lecture on this:
+ Show Spoiler +
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On May 26 2014 02:08 micronesia wrote:
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence.
Wow you're pulling that piece wayyyy out of context and kinda missing the point.
A broken coffee cup doesn't put itself back together, so if we see that on a video, we know its being played in reverse.
The affirmation here is that given that the entropy of the universe can only grow over time then we can redefine the arrow of time as pointing towards an entropy increase.
@OP I'm not sure you made clear enough (and I'm not even sure you agree on it) that entanglement as most people now see it doesn't actually lead to faster than light information transmission and doesn't break special relativity. Or at least that what's most people I talk to/read/watch/attend conferences seem to agree on. Maybe you could properly express your opinion or what you've benn thaught on this?
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--woops quoted insted of edit--
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United States24633 Posts
On May 26 2014 05:02 FakePseudo wrote:Show nested quote +On May 26 2014 02:08 micronesia wrote:
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence. Wow you're pulling that piece wayyyy out of context and kinda missing the point. Show nested quote +A broken coffee cup doesn't put itself back together, so if we see that on a video, we know its being played in reverse. The affirmation here is that given that the entropy of the universe can only grow over time then we can redefine the arrow of time as pointing towards an entropy increase. I see your point but I don't see it as taking the example way out of context.
I think what you described is what I said: "illustrate the concept for the layman." You are just giving the OP the benefit of the doubt regarding my concern. My worry is that many readers will falsely be lead to believe that the reason why the coffee cup can't be put back together is because the broken system has a higher entropy, which is not true, and also not what the author was getting at.
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I am still reading these! They are great! I read 3&4 on my phone though, and cannot make any posts on it. Sorry for being silent but I'm reading them!
Do you, btw, believe in any particular interpretation of quantum physics? I have come to lean towards the MWI interpretation, after reading an explanation of it on Less Wrong http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ . That guide was pretty awesome for someone like me, as it was the first guide that actually explained things and not just said "it's totally weird and you have to trust us". This is what made me more interested in the math of quantum physics (the Less Wrong guide has practically none).
The entanglement across time was interesting and I haven't heard it before, but I think I can image it (very roughly and probably incorrectly, but whatever).
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On May 26 2014 02:08 micronesia wrote:
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence.
That was by no means supposed to prove anything, it was just a simple statement to say "this is how we usually define the arrow of time" before presenting the idea relevant to this post. The focus here is on entanglement, not stat mech.
On May 26 2014 05:02 FakePseudo wrote:
@OP I'm not sure you made clear enough (and I'm not even sure you agree on it) that entanglement as most people now see it doesn't actually lead to faster than light information transmission and doesn't break special relativity. Or at least that what's most people I talk to/read/watch/attend conferences seem to agree on. Maybe you could properly express your opinion or what you've benn thaught on this?
You're correct that I didn't make that clear enough, and I definitely should have. As far as I know, entanglement can't lead to faster-than-light communication of classical information. Even the photon example I threw out there is way over simplified, as how these "measurements" are done and what the outcomes truly are is pretty complicated. A decent, easy to understand explanation that goes into more correct detail can be found here.
I know I haven't replied to everyone's comments yet, but I will! This stuff is not something I'm intimately familiar with, so the input is very much appreciated. I'm definitely learning a lot with you all on this one.
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On May 26 2014 06:24 airen wrote:Do you, btw, believe in any particular interpretation of quantum physics? I have come to lean towards the MWI interpretation, after reading an explanation of it on Less Wrong http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ . That guide was pretty awesome for someone like me, as it was the first guide that actually explained things and not just said "it's totally weird and you have to trust us". This is what made me more interested in the math of quantum physics (the Less Wrong guide has practically none).
First, thanks for your continued support!
Honestly this isn't something I've put much thought into. I believe in math that is consistent with experiments, haha. I guess my views align closest to the common Copenhagen interpretation, but I don't really want to limit myself to any particular view. The different interpretations are definitely interesting, though, and something I'd like to become more familiar with one day. Maybe one day really soon now that its been brought to my attention again 
I just ran into the less wrong site while I was posting my last reply, before I saw your reply. I linked their discussion on the no-communication theorem. I haven't read anything else there but that seems like a good site to keep on hand.
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On May 26 2014 06:01 micronesia wrote:Show nested quote +On May 26 2014 05:02 FakePseudo wrote:On May 26 2014 02:08 micronesia wrote:
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence. Wow you're pulling that piece wayyyy out of context and kinda missing the point. A broken coffee cup doesn't put itself back together, so if we see that on a video, we know its being played in reverse. The affirmation here is that given that the entropy of the universe can only grow over time then we can redefine the arrow of time as pointing towards an entropy increase. I see your point but I don't see it as taking the example way out of context. I think what you described is what I said: "illustrate the concept for the layman." You are just giving the OP the benefit of the doubt regarding my concern. My worry is that many readers will falsely be lead to believe that the reason why the coffee cup can't be put back together is because the broken system has a higher entropy, which is not true, and also not what the author was getting at.
Say again...??
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Thanks for posting this, I've been hooked for the past 20 minutes...
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So the EPR paradox was resolved and we now know that quantum physics cannot be represented by classical physics.
Now my question is, to what degree has quantum physics an observable effect on the real world?
If an electron can have a random quantum state, how does this affect atoms and molecules?
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On May 26 2014 08:12 EatThePath wrote:Show nested quote +On May 26 2014 06:01 micronesia wrote:On May 26 2014 05:02 FakePseudo wrote:On May 26 2014 02:08 micronesia wrote:
Regarding your entropy example: "a broken coffee cup doesn't put itself back together," I hope you just used it to illustrate the concept for the layman rather than to actually provide evidence of the irreversibility of entropy, as it really does not serve as such evidence. Wow you're pulling that piece wayyyy out of context and kinda missing the point. A broken coffee cup doesn't put itself back together, so if we see that on a video, we know its being played in reverse. The affirmation here is that given that the entropy of the universe can only grow over time then we can redefine the arrow of time as pointing towards an entropy increase. I see your point but I don't see it as taking the example way out of context. I think what you described is what I said: "illustrate the concept for the layman." You are just giving the OP the benefit of the doubt regarding my concern. My worry is that many readers will falsely be lead to believe that the reason why the coffee cup can't be put back together is because the broken system has a higher entropy, which is not true, and also not what the author was getting at. Say again...??
Giving him the benefit of the doubt, he could be saying that the lack of full context could mislead a laymen about what exactly is meant by entropy. If you take two images of a mug, one broken and another unbroken, you can't necessarily say which "state" has more entropy because you need a context (and with that context, a timeline). For example, if the mug was initially broken and was then put back together, you can bet that the unbroken mug "state" has more entropy. But this point is rather pedantic imo. It's practically impossible to explain entropy to a laymen "satisfactorily" because it really is just an abstraction built upon a bunch of other abstractions, all connected by a specific mathematics. Talking about in English is going to be inexact and possibly misleading almost no matter what you do.
On May 26 2014 16:46 urboss wrote:
So the EPR paradox was resolved and we now know that quantum physics cannot be represented by classical physics.
Now my question is, to what degree has quantum physics an observable effect on the real world?
If an electron can have a random quantum state, how does this affect atoms and molecules?
If you're asking "what are things that we see that classical mechanics simply could not explain?" well things like lasers quite simply could not exist. Even if we were somehow totally wrong about how they do work (we aren't), classical mechanics has no explanation whatsoever for them, not even ballpark afaik.
Other things like that are transistors (everyone says that but I think only engineers really only understand what that is). Essentially all modern electronics could not function without these devices. There's also all the quantum-information-theory-related stuff. Quantum cryptography, quantum computing, quantum signal processing (e.g. I think atomic clocks are somehow made more accurate by removing quantum noise - something classical physics couldn't even begin to explain).
Then there's quantum tunneling and teleportation. Good luck explaining those with classical physics.
If you're asking "what are things a person could see with their senses that classical physics can't explain?" then you're talking about macroscopic quantum phenomena. The only two I can think of off the top of my head are superconductivity (you can actually see the transition when this happens) and maybe something with Bose-Einstein condensates (I don't actually know this one for sure, never done any experiments with them).
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Thanks, I guess my question is rather directed toward normal-ass atoms and molecules, what we can find inside our cells.
If an atom consist of particles that behave randomly, does that have an effect on the atom itself?
Or in other words, does the atom show random behavior in the interaction with other atoms or are those interactions completely deterministic?
What I'm trying to get at:
Is our brain completely deterministic or are random thoughts a theoretical possibility?
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On May 26 2014 17:58 urboss wrote:
Thanks, I guess my question is rather directed toward normal-ass atoms and molecules, what we can find inside our cells.
If an atom consist of particles that behave randomly, does that have an effect on the atom itself?
Or in other words, does the atom show random behavior in the interaction with other atoms or are those interactions completely deterministic?
What I'm trying to get at:
Is our brain completely deterministic or are random thoughts a theoretical possibility?
These questions are much more complex and deep than I think you are appreciating.
About determinism, it is essentially a dead concept as far as "ultimate" concepts go. That is a whole big barrel of monkeys and a much larger conversation than can be had in this thread.
As far as practically speaking, the answer may be slightly different.
It's virtually unthinkable to model a macroscopic object as a sum of quantum systems. Even just writing down the equations would take more atoms in graphite/ink and paper than there are available in the visible universe. Not a lot of people recall that kind of thing when trying to "extrapolate" quantum ideas to the macroscopic world.
The other big (huge) factor is the concept of wave collapse. All the randomness that people associate with quantum mechanics stems from uncertainty about outcomes in highly isolated systems. Once systems come in contact with other systems, they tend to get disturbed. This disturbance often equates to a "measurement" which collapses all the involved wave functions - and thus there is no longer any randomness left in the systems. If you are trying to model e.g. the brain as a (ridiculously) large system of isolated quantum systems, then your model will eventually break down and revert to a classical model because all the systems will have some kind of interdependence and will thus disturb and "measure" each other and collapse all the wave functions. That means, essentially, that by the time anything interesting happens, it is almost certainly happening classically, i.e. deterministically.
Most of the utility that we (as humans) get out of quantum mechanics in daily life is not from randomness but from quantization effects. In other words, taking things that would otherwise be continuous and saying they're made up finite bits and bobs and so only so many can "fit" here and there etc.
To answer your question more directly: ultimately, somewhere in the universe and likely even on our planet there are (macroscopic or otherwise) effects from quantum mechanics on our environment (and thus on ourselves) such that over a long enough period of time, these effects will add up to a non-negligible difference in outcome vs. what would have happened classically. What that period of time is I couldn't tell you. It might be measured in seconds or millennia. Someone's brain somewhere will 100% have a random thought generated, following this logic.
Probably not the answer you're looking for, but I hope it gives you something to consider.
/edit - My instinct is to say: definitely yes, people have random thoughts all the time. But I'm not sure I could make an argument to convince someone that it's true simply using experimental fact.
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On May 26 2014 17:58 urboss wrote:
Thanks, I guess my question is rather directed toward normal-ass atoms and molecules, what we can find inside our cells.
If an atom consist of particles that behave randomly, does that have an effect on the atom itself?
Or in other words, does the atom show random behavior in the interaction with other atoms or are those interactions completely deterministic?
What I'm trying to get at:
Is our brain completely deterministic or are random thoughts a theoretical possibility?
DefMatrixUltra gave a lot of nice input, I'm just going to add on a little...
I agree with him that this question is super, super deep and these sort of conversations tend to go back to creator-related arguments.
Really though, determinism as a macroscopic, all-encompassing, phenomenon isn't supported. As DefMatrixUltra said, "It's virtually unthinkable to model a macroscopic object as a sum of quantum systems. Even just writing down the equations would take more atoms in graphite/ink and paper than there are available in the visible universe."
Consider something like trying to model the solar system... a simple solar system with a sun and two planets and absolutely nothing else ever around to disturb us. The system can be completely described by Newton's gravitational law. We solve the equations and we know forever ever after what the system will do. It's totally deterministic. The planets orbit the sun and everything is great. What if we displaced one of the planets just a tiny bit, and pushed it closer to the sun? (say it was hit by a really super fast meteor or something). Then all hell breaks loose. Maybe not today, maybe not in a hundred years if the displacement was really small, but eventually that planet is going to do something crazy like collide with another planet or get ejected out of orbit entirely because it's no longer in a classically stable location. This behavior is still completely deterministic- its called deterministic chaos- but this chaos is rooted in extreme sensitivity to initial conditions.
We start our orbits out perfectly and they live on forever and ever happy as can be. We start them off a few miles out of place and the entire system falls apart. (this is an exaggeration, of course, but it illustrates the point).
Can quantum uncertainty in the initial conditions of something give rise to macroscopic effects based on this idea? Probably. I don't have any examples on hand and haven't really thought about it much until now, but why not? So in that case, even if we thought our system was "deterministic", the uncertainty that isn't taken into consideration classically could have profound effects on whats observed.
That might be a stretch and other people might not like that argument, but meh. Take it for what you will and read DefMatrixUltra's response, too.
Describing behavior of a macroscopic system containing many many parts using the wave function approach for each part of this system is impossible, if only because we do not have the time (literally, people just haven't existed long enough to write everything out) or the computational power to perform such calculations. Instead we get by using statistics to bridge the gap between quantum and classical behavior.
I started writing this response when I rolled out of bed at 5am and would really like to put more thought into before I say too much, but I thought I'd go ahead and post something anyway to start organizing my thoughts. Like I said, universal determinism is a hugeee and loaded subject. There's lots of literature around that gives some thought provoking ideas, so go follow the wikipedia trail wherever it will lead and I'll sure you'll learn a lot about the subject.
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Thanks for your answers, it shows me that there is a lot of stuff one has to consider.
All the randomness that people associate with quantum mechanics stems from uncertainty about outcomes in highly isolated systems. Once systems come in contact with other systems, they tend to get disturbed. This disturbance often equates to a "measurement" which collapses all the involved wave functions - and thus there is no longer any randomness left in the systems.
This stuff confuses me.
Is "measurement" something tangible that can itself be represented by a wave function?
Also, you say that "measurement" collapses all the wave functions in real systems.
Does that mean that quantum physics only applies to a highly isolated system?
Or in other words, does it mean that quantum physics cannot be used to explain the real world?
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On May 27 2014 20:37 urboss wrote:
Is "measurement" something tangible that can itself be represented by a wave function?
The measurement is an actual, physical measurement, its not something we represent mathematically. Take this as a simple example- we have a photon and its wave function tells us that the photon has a 50/50 chance of being vertically/horizontally polarized. This wave function is just a solution to the Schrodinger equation, its just a mathematical construct. We send it through a polarizer: if it goes through, it was vertical; if it doesn't, it was horizontal. We measured the polarization, and it took on a single value. This is what we call “collapsing” the wave function. We’re really just collapsing/removing the uncertainty of our knowledge. Before we knew there was a 50% chance it was vertical, after we measure we know for sure what the polarization is.
Also, you say that "measurement" collapses all the wave functions in real systems.
Does that mean that quantum physics only applies to a highly isolated system?
It applies to all systems, theoretically. Just like Newton’s law of gravitation applies to all systems. But when we calculate the speed of a falling object, do we include the forces of gravity exerted by every single other object in the universe? Of course not. Those forces are real, they are there, but we can still learn a great deal about our falling object even if we ignore them.
The quantum mechanics you solve as an undergrad, and even ever, really, apply to highly idealized systems. Physics in general applies to highly idealized systems. It applies everywhere, but we make a lot of assumptions and simplifications that allow us to solve the problem. In many cases this is good enough. Like solving the equations that describe how a laser work- we neglect a lot of complicating factors, but our end result describes very closely what we see in reality. Same thing with the spectral lines of hydrogen- and those are some pretty fancy undergrad quantum calculations.
So in short, quantum is everywhere. We solve highly idealized systems because reality is complicated.
Or in other words, does it mean that quantum physics cannot be used to explain the real world?
I think this was stated before, but quantum is needed to describe many, many things in the real world. Every topic I've blogged about so far. Something as simple as interference patterns in the electron beam double slit experiment. The electronics in your cell phone. Magnetism, even. Quantum is everywhere in the real world. In many situations the normal person encounters on a daily basis, classical physics is good enough to explain what’s going on, but not always.
I hope that clears things up a little? If not feel free to keep up the questions, and I (or someone else) can try re-wording things or explaining from a different angle.
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Thanks, this makes sense now.
To come back to the initial question, it seems that the problem with randomness was something that was addressed in 1980 by Quantum Decoherence.
I'm just pasting from Wikipedia:
When the Copenhagen interpretation was first expressed, Niels Bohr postulated wave function collapse to cut the quantum world from the classical. This tactical move allowed quantum theory to develop without distractions from interpretational worries. Nevertheless it was debated, for if collapse were a fundamental physical phenomenon, rather than just the epiphenomenon of some other process, it would mean nature were fundamentally stochastic, i.e. nondeterministic, an undesirable property for a theory. This issue remained until quantum decoherence entered mainstream opinion after its reformulation in the 1980s.
Do you by chance know how Quantum Decoherence solves the problem with randomness?
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On May 27 2014 20:37 urboss wrote:Thanks for your answers, it shows me that there is a lot of stuff one has to consider. Show nested quote +All the randomness that people associate with quantum mechanics stems from uncertainty about outcomes in highly isolated systems. Once systems come in contact with other systems, they tend to get disturbed. This disturbance often equates to a "measurement" which collapses all the involved wave functions - and thus there is no longer any randomness left in the systems.
This stuff confuses me. Is "measurement" something tangible that can itself be represented by a wave function? Also, you say that "measurement" collapses all the wave functions in real systems. Does that mean that quantum physics only applies to a highly isolated system? Or in other words, does it mean that quantum physics cannot be used to explain the real world?
First I want to address quantum decoherence. I don't imagine it's easy to investigate as it's based very heavily on the mathematical framework used to study quantum mechanics. It's a combination of ideas from that framework, more or less, and that makes it a fairly abstract kind of concept. Essentially, though, quantum decoherence is the concept I'm referring to when I'm saying that a whole of lot of quantum systems all next to each other and all interacting will quickly start to look like a classical system.
Your questions about measurements are very on point. The fact is: we don't know what exactly constitutes a measurement. In fact, we've kind of defined it in the reverse way in that a measurement is basically "whatever collapses the wave function." 'Measurement' is a nice word for scientists to use because we need to measure things to get our bearings and to make sense of everything. It turns out that doing this (recovering information from a system) always seems to collapse the wave function. So observing a system (getting a look at its insides) always collapses it. But that verb "observe" is very mischievous and gets a lot of journalists and laymen into trouble. A rock can be an observer in that it can disturb and collapse a quantum system - it just can't relay back to us any useful information.
The rough picture we have at the moment is that anything that reacts in a tangible sort of way with a quantum system will collapse that system. Things bumping into it. Things exerting strong magnetic/electric potentials on it. But specifically it's hard to say.
Consider a single atom (a collection of protons, neutrons, and electrons). The usual picture we have of atoms is that the protons and neutrons are more or less in the "middle" where they are, and the electrons exist in a superposition where their locations and paths aren't fixed until they're "measured." In a chemically and electrically neutral environment, there are (in general) not any strong external influences on atoms. Put this atom inside the brain. It's kind of "next to" a whole bunch of other atoms. But if they're chemically neutral (i.e. none of them desperately want another electron or are trying to rid themselves of an extra) and the environment is electrically neutral "enough" then maybe their quantum-like traits are preserved for some time until the system is sufficiently disturbed.
But it's difficult to actually know for sure one way or the other. My personal instinct (i.e. I couldn't convince anyone it's true) is that atoms in our brain often have their electrons in a quantum state, if only for very small amounts of time. But the fact that we don't know exactly what it is that constitutes a measurement makes it difficult to say either way. What kind of interactions and what strength of interactions can disturb a quantum system so that it collapses the wave function? That's a question for which we'd all very much like a definitive answer.
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On May 27 2014 22:16 urboss wrote:Thanks, this makes sense now. To come back to the initial question, it seems that the problem with randomness was something that was addressed in 1980 by Quantum Decoherence. I'm just pasting from Wikipedia: Show nested quote +When the Copenhagen interpretation was first expressed, Niels Bohr postulated wave function collapse to cut the quantum world from the classical. This tactical move allowed quantum theory to develop without distractions from interpretational worries. Nevertheless it was debated, for if collapse were a fundamental physical phenomenon, rather than just the epiphenomenon of some other process, it would mean nature were fundamentally stochastic, i.e. nondeterministic, an undesirable property for a theory. This issue remained until quantum decoherence entered mainstream opinion after its reformulation in the 1980s.
Do you by chance know how Quantum Decoherence solves the problem with randomness?
You're asking terribly deep questions, I like it.
A few comments into this thread airen asked if I subscribed to any particular "interpretation" of quantum mechanics. I replied with Copenhagen, which basically believes in the wave function and the collapse of it when we take a measurement.
Interpretations are just ways of making sense out of everything, or at least trying to. There are tons of different interpretations, and decoherence is another way to view things.
How it solves the problem with randomness, in very simple terms, is something like this:
Take the photon example again, except this time we don't want to think about "collapsing the wave function". The wave function is what it is, but then something (read: our polarizer) interacts with it. As a result of this interaction, the wave functions of the photon and polarizer become entangled with each other. Our nice, coherent wave function that described our photon has interacted with something, and therefore has lost its coherence, it de-cohered and became entangled with the environment.
Are you familiar with the concept of interference? You add two sine waves together and if they're both at values greater than 0 at one point, they experience constructive interference- the total wave is bigger than the individual waves. If one is positive and one is negative, the destructively interfere and the total wave can be smaller or even zero at that point. Well a wave function is, as expected, a bunch of waves. We get probabilities of things happening by (sort of) squaring the wave function, and when we do this we get interference terms...
The role of interference is key in the concept of decoherence, but that requires math that's probably a little too sophisticated to be useful for me to explain... so take these statements as you will. In classical physics, which is not random, you don't get these "interference" terms in expressions for the probability of something happening. In quantum, you do. Decoherence, mathematically, actually removes these interference terms from the probability expressions, leaving just the classical result.
Instead of seeing a "superposition" of lots of possibilities (the wave function), we have a classical statistics.
Maybeeee that answered your question? I think this is still a pretty active area of research. People are always arguing about what quantum means and what something is doing before you measure it and stuff like that.
No one knows what the correct way to think about everything is... its nice to be familiar with the different explanations though. Most of the popular ones agree with what we know to be true about physics. Which interpretation is "right" or "wrong" is, in my opinion, a debate that probably won't ever end or be supported with definitive proofs.
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I just want to say this thread has been fun to watch, keep it up.
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Argh, only just found this blog series and will read and reread, so please keep on keeping on. =)
What makes this stuff so fascinating is that it deals with the concept of Reality itself and how we think about it.
All we have is math and logic and interpretations, and we don't even know what constitutes an observer? AAAH!
I remember waay back when I first read about the light particle/wave duality and how that boggled my mind leading
to all sorts of questions that made my head hurt at the time. Well gosh darn it, THIS time maybe I have the brain cells, I'll follow the links to other links and figure this all out and return with the Truth of Everything.
Well, probably not. But I will read with interest, and ponder with the rest of you.
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I don't have much to say on the subject, but I found this article about a recent study where a team managed to "teleport" information across a distance of 10 feet using quantum entanglement.
Here's the article: http://phys.org/news/2014-05-team-accurately-teleported-quantum-ten.html
Some really interesting stuff! It shows how quantum theory can be used practically. Perhaps one day we will have super fast quantum computers
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On June 03 2014 21:27 sorrowptoss wrote:I don't have much to say on the subject, but I found this article about a recent study where a team managed to "teleport" information across a distance of 10 feet using quantum entanglement. Here's the article: http://phys.org/news/2014-05-team-accurately-teleported-quantum-ten.htmlSome really interesting stuff! It shows how quantum theory can be used practically. Perhaps one day we will have super fast quantum computers
Does anyone knowledgeable have something to say about this? I'm very skeptical of nonlocal information transfer, and everything I've read ends up explaining these events as a misunderstanding about the nature of the observation -- where the intervention really occurred that caused the measurement to happen. But I'm no expert and I'm curious what others think about this.
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I read through the Science paper a couple of times today, so here is a quick summary in very simplified words(since not everyone has a university account that gives them access to all those journals... or has patience to decode):
So Alice has a qubit (bit of quantum information) she wants to teleport, q1. Alice also has q2 which is entangled with Bob's q3. Alice has to measure q1 and q2. These measurements yield information that tell Bob how to "decode" the measurement he got. (Oversimplified, but think of Alice measuring the polarization of a photon and defines north as "up". If her polarization is "down", she has to tell Bob the definition of her axes so he knows that north means up. Make sense?) The catch: Alice has to call Bob on the phone to tell him her results; this still requires the classical distribution of information.
This is a complicated experiment because it requires Alice to get a lot of information out of one single measurement, and it requires that Bob's q3 retains coherence (it isn't interfered with before he deliberately measures it). This sort of thing has been done before but never over this large of a distance. They had more success with this experiment because they used matter qubits--nuclear spins have long coherence times, nitrogen vacancy centers allow for longer entanglement duration. Compare to photons which are difficult to measure and retain these properties for much shorter time scales.
Why is this called teleportation? Well, the information that was located with Alice appeared on Bob's end. However, he needed a key to know what he was looking at.
If anyone else read the paper and got something different from it, please please chime in. This is not an area of research I'm involved with, so I could very easily be misinterpreting something.
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On June 04 2014 07:18 Ideal26 wrote:
I read through the Science paper a couple of times today, so here is a quick summary in very simplified words(since not everyone has a university account that gives them access to all those journals... or has patience to decode):
So Alice has a qubit (bit of quantum information) she wants to teleport, q1. Alice also has q2 which is entangled with Bob's q3. Alice has to measure q1 and q2. These measurements yield information that tell Bob how to "decode" the measurement he got. (Oversimplified, but think of Alice measuring the polarization of a photon and defines north as "up". If her polarization is "down", she has to tell Bob the definition of her axes so he knows that north means up. Make sense?) The catch: Alice has to call Bob on the phone to tell him her results; this still requires the classical distribution of information.
This is a complicated experiment because it requires Alice to get a lot of information out of one single measurement, and it requires that Bob's q3 retains coherence (it isn't interfered with before he deliberately measures it). This sort of thing has been done before but never over this large of a distance. They had more success with this experiment because they used matter qubits--nuclear spins have long coherence times, nitrogen vacancy centers allow for longer entanglement duration. Compare to photons which are difficult to measure and retain these properties for much shorter time scales.
Why is this called teleportation? Well, the information that was located with Alice appeared on Bob's end. However, he needed a key to know what he was looking at.
If anyone else read the paper and got something different from it, please please chime in. This is not an area of research I'm involved with, so I could very easily be misinterpreting something.
Thanks very much, all the cogent details that I was looking for!
It would seem that this is good progress for reasons of stability and reproducibility, without having done any groundbreaking miracle ansible stuff, which the headlines always make it out to be. But of course one wonders if there's a clever way of arranging your qubits so a modicum of classical information will decode them all.
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EPT
