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Posts: 3430
Joined: Jan. 20 2004
From: Austin, Texas USA
Wave-particle duality
Since we seem to be on something of a science kick here once in a while, I thought this might be interesting to some of the members who have in the past brought up "wave-particla duality" in quantum mechanics. I once said, off-hand, something to the effect "Don't worry about it, it goes away in quantum field theory."
A recent thread on reddit, in the "Explain it like I'm Five" subreddit, gives what seems to me a fuller answer, in what are currently the second and third posts on the topic. I'm not the author of either of the replies.:
"Do computer simulations involving physics have to account for wave-particle duality? Has it posed an issue before?"
Answers:
"This is an interesting question. The answer is that it depends on the system you want to study. Just get something clear right off the bat, in the language of modern physics, the very idea of wave-particle duality is a bit artificial. The more modern view is that all elementary "particles" are excitation in a given field. For example, a photon is an excitation in the electromagnetic field, an electron is an excitation in the electron field, etc. So for example, if you have an emitter generating EM waves, you can think of it as a piston moving up and down on a body of water creating ripples that move outwards. In this analogy, the ripple is the energy associated with a photon. To sum up the intro, in the language of field theory, the particle and wave picture are simply useful approximations that capture the behavior of the fields.
Now which picture is more useful for a given situation depends on the specifics. For example, let's say you want to study how photons bounce around in a large slab of glass. At that point you can treat each photon as a little bullet whose trajectories are determined by geometric optics. This model works very well and it is routinely used in optical simulations. With it you can correctly estimate trajectories including changes by reflection, refraction, etc. However, now imagine that you are passing light through a very narrow structure. At this point you can no longer ignore the wave-like character of the light and you have to treat it using wave optics. At this point you get phenomena like diffraction, interference, etc.
However, while the two approaches I describe above may seem different, in the end they are not. Deep down the true solution comes from calculating the time dependent state of the EM field using Maxwell's equations. In this sense, geometric optics is simply a useful approximation when the wavelength of the light is much shorter than the features of the medium it is passing through. But in the end it's all about the fields. The same is true for electronic structure calculations, scattering cross-sections in particle physics, etc., etc.
[–]jam11249 8 points an hour ago I think this touches on the big point that when performing simulations we work within the framework of a given model. My mantra is that all models are wrong but some models are useful. Some models are sometimes useful but no models are always useful. A continuum nonlinear elasticity model is useful for looking at how a large piece of rubber deforms, but won't be useful at modelling a small number of crosslinked polymer chains. So the point I would raise is that if the features you are looking at are affected by an underlying mechanism, the mechanism will need be incorporated into the model. If not, then it is generally adding unnecessary complexity into already non-trivial problems. (Disclaimer, I'm speaking as an applied mathematician working on far more macro-behaviour than QM, but I'm pretty sure the argument carries over)"
Cool. I think most can accept that we have to think of it differently in different situations, but the measurement problem at it's heart is the problem. I was under the impression that with quantum computers, the idea of superposition, a similar duality to the wave/particle problem, is to the advantage of the computing power. In that case we confront the issue directly unlike the examples above. Again we come to the situation that we understand how nature works, but not why.
ORIGINAL: Ricardo Again we come to the situation that we understand how nature works, but not why.
The first great breakthrough of mathematical physics, Newtons's gravitational theory of the orbital motion of the moon and planets, was based on assuming the instantaneous action at a distance of gravity.
This was as big a problem for the late 17th and early 18th century to swallow as relativity and quantum mechanics have been for the 20th and 21st.
Another of Newton's assumptions/discoveries was the First Law: "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force."
Archimedes, certainly one of the greatest physicists of all time, thought that for something to keep moving, a force had to keep pushing on it. This was the fruit of extensive experience. It's what happens in our normal environment, where the forces of friction are often too subtle to be noticed by our unaided senses. Nearly 1900 years elapsed from the death of Archimedes until the publication of "Principia Mathematica." The First Law was a radical concept to the majority of the scientific world.
But I didn't have much trouble very accurately calculating missile trajectories and satellite orbits by Newtonian mechanics. I always got a kick out of how well it worked when done right.
I think we never really "understand" because our intuitive physics, which we begin to develop as babies, and continue to hone throughout life, is well adapted to throwing spears, shooting pool, and hitting baseballs, but not so good at how the universe behaves at high relative velocities, or at very small distances, since we have little or no sensory experience of relativity or quantum mechanics outside of the lab or the computer screen.
think we never really "understand" because our intuitive physics, which we begin to develop as babies, and continue to hone throughout life, is well adapted to throwing spears, shooting pool, and hitting baseballs, but not so good at how the universe behaves at high relative velocities, or at very small distances, since we have little or no sensory experience of relativity or quantum mechanics outside of the lab or the computer screen.
For lay people, and even some scientists I am sure, good analogy is necessary. For some topics, especially quantum scale stuff, that is very hard to come up with. Sagan did great with his "penalty of projection" analogy to higher spatial dimensions IMO. For quantum stuff, Feynman is pretty good. At least you FEEL like you understand what he is describing while he is doing it....then you try to explain what he says yourself and you find you are just not as good as he is.
Of course the trouble with many, if not most quantum and relativity analogies is that we try to use our intuitive physics, which is part of everybody's mental equipment, to explain things which are strongly counter-intuitive, such as the fact that quantum mechanics doesn't predict specific measurements, but only the probabilities of various measurements when precisely the same experiment is repeated.
On the contrary, our intuition tells us that, when you repeat an action, you get the same result as before. This intuition is so strong that Einstein, the most famous physicist of the 20th century, and one of the most influential of all time, insisted that quantum mechanics had to be incomplete. There had to be hidden variables that were not taken into account. He was proven wrong, after his death.
One could say (and I would say) that the mathematical formulations of physical theories are themselves analogies. But the analogies are very precisely formulated, and the correct manipulation of them requires a few years of study to master, at a minimum.
One example of such an analogy is the electromagnetic field. When Faraday suggested the existence of such an entity surrounding electric charges and currents, the tacit assumption was that the field consisted of motions in the "luminiferous ether" just as forces applied to an elastic solid would cause distortions and wave motions in it.
But a variety of experiments, Michelson and Morley being the most famous, failed to detect effects that would have to occur if the luminiferous ether existed. The electromagnetic field lost its material existence, and became a mathematical abstraction, though physicists and engineers still speak of it as though it were a "thing." Many would insist that it is a thing. That's the way it is often taught. I claim it is a mathematical abstraction invented by humans. Once the abstraction was defined correctly, mathematical operations served to predict the actions of charged particles and currents.
This illustrates the fuzzy boundary between "reality" and the ideas we invent to describe and predict what it does.
"Classical" physics conforms largely to the intuitions we start to develop by exploring our surroundings as babies, and develop more fully as we mature here on earth. Science and engineering students are required to participate in laboratory experiments to sharpen their intuition. Newton's giant leap into space is not too hard to follow for many. Solutions to Maxwell's equations of electromagnetism are not hard to visualize, with some practice and coaching.
But the mathematical analogies of quantum mechanics and relativity must bear the burden of innately counter-intuitive predictions. They are utterly foreign to our experience. As Feynman once said, with his lively wit, "No one understands quantum mechanics. You just have to follow the mathematics."
This from someone who understood quantum mechanics at least as well as anybody ever had, and far better than most.
I think we never really "understand" because our intuitive physics, which we begin to develop as babies, and continue to hone throughout life, is well adapted to throwing spears, shooting pool, and hitting baseballs, but not so good at how the universe behaves at high relative velocities, or at very small distances, since we have little or no sensory experience of relativity or quantum mechanics outside of the lab or the computer screen.
This is a relief. I was feeling pretty bad at not understanding the slightest thing about quantum physics, if only perhaps the odd zombie cat analogy. In the reddit discussion you posted, though I can understand conceptually what is meant by "excitation of a field", as soon as I try to map that on to "reality" I loose the little grasp I had to start with. A lot of it is simply that I am not conversant enough in mathematics to do as Feynman suggested and "follow the mathematics".
I would ask this though: do you think that our understanding of the world is inherently limited by our "mental set-up", for lack of a better word? In other words, is there a point beyond which we simply won't be able to go, not merely because it is counter-intuitive to us, but because of our biological constraints?
Even in most "intuitive" scientific theories, there is always the issue of the most basic axioms that are accepted but never truly explained. In one of Lawrence Krauss's Origins Project conferences, the panelists briefly discussed the limitations of science and mathematics. One of them jokingly imagined an encounter with an advanced alien race in which we showed them our tools for understanding the world. The alien condescendingly replied "oh, you still use mathematics?!". The other panelists laughed it off but you could tell there was some degree of unease at the idea that this tool is just that, a tool, albeit a very effective one, that we have made up.
The great French novelist Romain Gary (whose main contribution to US culture was proving that Clint Eastwood had no problem screwing other people's wives but cowered away from a duel as soon as he got caught. Cowboy indeed.) suggested in a Op. ed. back in the 70s that human morality had reached a plateau and that the only way forward would be dependent on our biological evolution (he was raising the issue of human nature and whether war and conflict would always be with us. He suggested that yes they would always be there, unless we somehow evolved into "something else"). This struck me as a compelling idea. I wonder if the same could be said of our ability to comprehend the world around us. The scientific tools we have created have allowed us to go much further than what would be expected of talking apes but I wonder how far these tools can bring us and, if these are indeed limited, whether it is biologicaly possible for us to devise other ones that would bring us even further.
I would ask this though: do you think that our understanding of the world is inherently limited by our "mental set-up", for lack of a better word? In other words, is there a point beyond which we simply won't be able to go, not merely because it is counter-intuitive to us, but because of our biological constraints?
I used to wonder and also assume this. That there are things to learn that are simply over all our heads. I think human imagination has already showed us that this is not really true. Sort of like artistic constraints on music composition, once you learn the parameters you realize there really are no limitations other than the physical ones. Take something simple like the periodic table of elements. Well, relatively simple. It contains tons of implied info about math, physics (both relativity and quantum), chemistry, even cosmology and evolution, such that it would easily function as some sort of translation to any other high intelligence out in the universe. Understanding what is possible will become so much easier once we know all the parameters, which we are still discovering. People sometimes want to make analogies between earth creatures, such as trying to teach calculus to your dog, but I seriously don't see it as that extreme, though it is fun to try to imagine that there might be such an advanced intelligence to our own. Language (abstract or "written" form) is key, and that is why we can communicate by hand signing with chimps. If it "seemed" interested, wouldn't we want to teach it more and more of what we know? It means there is hope for us IMO, to continue to learn more and more too.
quote:
The electromagnetic field lost its material existence, and became a mathematical abstraction, though physicists and engineers still speak of it as though it were a "thing." Many would insist that it is a thing. That's the way it is often taught. I claim it is a mathematical abstraction invented by humans. Once the abstraction was defined correctly, mathematical operations served to predict the actions of charged particles and currents.
I had it in my head at one point from reading, that a "field" would be the density or concentration of gauge bosons. So when you have more photons, gluons, etc you have a stronger "field". Passing through the Higgs "field", which is "big" because it is everywhere, is bumping into these Higgs bosons everywhere picking up "mass", and if you are a photon, you simply pass through them, or if you are an electron or nuetrino you skid past, but if you are W or Z they stick to you. Therefore the electromagnetic "field" would be a bunch of photons that electrons bump into. Where the field is weak is where there are less photons running about. That helped make some visual sense vs the pure math picture IMO.
The electromagnetic field lost its material existence, and became a mathematical abstraction, though physicists and engineers still speak of it as though it were a "thing." Many would insist that it is a thing. That's the way it is often taught. I claim it is a mathematical abstraction invented by humans. Once the abstraction was defined correctly, mathematical operations served to predict the actions of charged particles and currents.
I should have made it clear that in this quote I was referring to the classical electromagnetic field of Maxwell's equations, not the electromagnetic field of quantum field theory, which is often pictured as consisting of photons.
This is a relief. I was feeling pretty bad at not understanding the slightest thing about quantum physics, if only perhaps the odd zombie cat analogy. In the reddit discussion you posted, though I can understand conceptually what is meant by "excitation of a field", as soon as I try to map that on to "reality" I loose the little grasp I had to start with. A lot of it is simply that I am not conversant enough in mathematics to do as Feynman suggested and "follow the mathematics".
I would ask this though: do you think that our understanding of the world is inherently limited by our "mental set-up", for lack of a better word? In other words, is there a point beyond which we simply won't be able to go, not merely because it is counter-intuitive to us, but because of our biological constraints?
<snip>
Your question prompts a couple of observations, though the length of your post implies to me that it raises a number of different questions. My observations here address only a part of your post.
There are clearly limitations to the number of abstractions an individual can keep track of at once, and to the complexity of mental pictures that can be held in the imagination. This ability varies from one individual to the next, and can be cultivated through practice and instruction. But there are limits.
People have responded to this in at least a couple of ways. One is through abstraction and generalization in mathematics. A relatively familiar example is the development of vector analysis. There is a famous book called "A Course of Modern Analysis" by Whittaker and Watson, published early in the 20th century. It contains not a single illustration. Furthermore there are page after page containing lists of equations, one for each dimension. A three-dimensional problem is discussed with numerous sets of three equations, one each for, say x, y, and z, even though the equations may differ only in the name of the dimension.
Physicists and mathematicians in the latter half of the 19th century had begun to use a notation where all three dimensions were represented by a single symbol, called a vector. In fact, mathematicians soon realized that vector notation could very compactly represent calculations in an infinite number of dimensions.
This abstraction and generalization has proceeded apace in the 20th and 21st centuries, enabling more and more complex entities to be represented by fewer and fewer marks on paper. There is no apparent limit to this progression.
A second approach to outflanking human mental limitations has been the development of electronic computers. Their memories are vastly greater than human capacity for reading and writing data, and their calculations are extremely swift. There are even mathematical proofs that are embodied (in part) only in computer programs that produce and check gigabytes of data. Of course mathematicians debate whether it really is a proof, if only a computer can check it.
These days great progress is being made in cascaded neural networks, the outputs of one level of electronic neural nets being input to successively higher levels. The networks are "trained" by being given inputs, and being told whether the outputs are right or wrong. After sufficient "training" the networks can fairly reliably arrive at the right outputs for novel inputs. This process (called "deep learning") mimics to some extent the learning processes of animals. Work on this is just beginning to bear significant fruit. It is a new focus of work in artificial intelligence, and a lot of money and effort are being put into it. The usual optimistic predictions are being made, but the limits of this strategy have yet to be identified. We read about self-driving cars, but I haven't run across any accounts of significant scientific applications, though it would seem obvious to try giving it a shot.
As far back as the late 1960s I remember chatting over beer and enchiladas with a friend, who had been invited to address the International Congress of Mathematicians only a few years after getting his PhD, a tremendous distinction, one which was conferred only a few times in a century. He was speculating that a certain calculation could not be carried out because there were only a finite number of particles in the universe. But at that time, I think quantum computing had not seriously been considered. Certainly he and I were both unaware of its possibility at that time. The number of energetically achievable states of the individual particles is vastly smaller than the number of energetically achievable superpositions of states of numbers of particles, so I don't know what his evaluation would be today.
Is there a limit to our ability to understand the universe imposed by the structure of our brains? I don't know. I think there is a sufficiently vast field of ignorance to keep us occupied for the foreseeable future.
I would ask this though: do you think that our understanding of the world is inherently limited by our "mental set-up", for lack of a better word? In other words, is there a point beyond which we simply won't be able to go, not merely because it is counter-intuitive to us, but because of our biological constraints?
That has always been an interesting question, but one that, in my opinion, has already been answered. I think the remarkable discoveries in both quantum mechanics and relativity suggest that there is no limitation on our ability to continue to achieve greater understanding of the universe, both writ large and writ small. Just think of it. Dark matter, for example. We infer its existence from its effect on galaxies, stars, and other cosmological entities, but we do not know what it really is or consists of; only that it has mass. But that inferred existence will eventually lead to our understanding of what it is. Of that I am convinced.
I'll tell you one thing that I understand intellectually and intuitively but have always had a hard time picturing in my mind: the infinitely dense point, known as the "initial singularity," that contained all the mass, energy, and space-time in the universe, and the "Big Bang" that initiated the expansion of the universe from that infinitely dense point. I am comfortable with the idea of the initial singularity. What I have always had a hard time picturing in my mind is the expansion of the universe into the "nothingness" that I always picture it expanding into. Of course, the universe was not expanding "into" anything, as there was nothing to expand "into." But it has always been difficult for me to accept that there was nothing on the "other side," if you will, of the expanding universe. As I say, I completely understand it both intellectually and intuitively, but I have never been able to get past trying to picture it in my mind.
Bill
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And the end of the fight is a tombstone white, With the name of the late deceased, And the epitaph drear, "A fool lies here, Who tried to hustle the East."
Is there a limit to our ability to understand the universe imposed by the structure of our brains? I don't know.
Or if we were visited by some super-intelligent race (as, for instance in Childhood’s End), would we necessarily be able to understand all their technology, even if they tried to explain it to us?
When was the last time you tried explaining television to your cat?
ORIGINAL: Paul Magnussen When was the last time you tried explaining television to your cat?
Cats I have known have shown little interest in television. Recently, most have been quite interested in chasing "bugs" or pictures of fish on my iPad screen. To my mind this indicates a serious misconception on the part of the cat.
I don't have a dog or a cat now because I travel a lot, it would be inconvenient or impossible to take it with me, and it would be unfair to leave it behind.
If I had a dog, I don't think I could explain that it was kept indoors at night so the coyotes wouldn't eat it. But after surviving a few nights outdoors, I think the dog would have learned for himself that it was a good idea to stay in at night.
A cat might choose to stay out, since most cats like hunting more than most dogs do, and there are plenty of trees to climb in the neighborhood to stay out of reach of the coyotes.
Maybe the very existence of some of our ignorance will remain unknown to us, simply because of an inherent lack of interest? But thus far scientists have exhibited an almost annoying curiosity about matters of apparently little practical concern.
Thank you for your thorough reply. You're right that I probably threw in several implied questions in that post. I suppose one of the things I had in mind (bear with me because I haven't thought this through nearly as much as I should. I'm just spit-balling) was not so much whether we are limited in our ability to process information (since clearly we are but through the examples you mentioned we have found ways to bypass this limitation to a great degree) but rather whether it is possible that there is some "realm" of reasoning that is altogether inaccessible to us because of how our brains our wired. It was in this sense that I brought up axioms. It seems that we are necessarily limited to causal reasoning and its variations. Of course, those non-human animals that display reasoning abilities also follow the rules of causal reasoning so it just may be that that is all there is and any "advanced" intelligence would just be doing the same as the rest of us, albeit in more complex ways. I guess it would boil down to two questions: - Is it possible to reason outside of the principles of causality? - Is it possible for a being who is wired solely for causal reasoning to even conceive of a non-causal form of reasoning?
My hunch is that these questions aren't really worth pursuing and are probably nothing more than a contradiction in terms. I suppose I just find it fun to think about. And of course, I completely agree that there is still plenty of unknowns to keep us busy for a good while, if not "forever".
@BarkellWH Another one I struggle with is Hilbert's hotel. I can follow the logic of it just fine, but once I'm left with the conclusion that somehow there are infinities that are "bigger" than others, well, that's usually when I drop my book and decide to go practice a few falsetas...
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