A thousand years from now, the twentieth century will be remembered as the time when we discovered quantum mechanics. Forget wars, computers, bombs, cars and airplanes: quantum mechanics is a deep truth that will continue to be a part of our understanding of the universe into the foreseeable future.
So it’s kind of embarassing that we still don’t understand it. Unlike relativity, which seems complicated but is actually quite crystal clear when you get to know it, quantum mechanics remains somewhat mysterious despite its many empirical successes, as Dennis Overbye writes in today’s New York Times.
Don’t get me wrong: we can use quantum mechanics quite fearlessly, making predictions that are tested to the twelfth decimal place. And we even understand the deep difference between quantum mechanics and its predecessor, classical (Newtonian) mechanics. In classical mechanics, any system is described by some set of quantities (such as the position and velocity), and we can imagine careful experiments that measure these quantities with arbitrary precision. The fundamentally new idea in quantum mechanics is that what we can observe is only a small fraction of what really exists. We think there is an electron with a position and a velocity, because that’s what we can observe; but what exists is a wavefunction that tells us the probability of various outcomes when we make such a measurement. There is no such thing as “where the electron really is,” there is only a wavefunction that tells us the relatively likelihood of observing it to be in different places.
What we don’t understand is what that word “observing” really means. What happens when we observe something? I don’t claim to have the answer; I have my half-baked ideas, but I’m still working through David Albert’s book and my ideas are not yet firm convictions. It’s interesting to note that some very smart people (like Tony Leggett) are sufficiently troubled by the implications of conventional quantum mechanics that they are willing to contemplate dramatic changes in the basic framework of our current picture. The real trouble is that you can’t address the measurement problem without talking about what constitutes an “observer,” and then you get into all these problematic notions of consciousness and other issues that physicists would just as soon try to avoid whenever possible.
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.” It’s not too much to ask, I think. It would also be great if everyone could explain the distinction between bosons and fermions. Someday I will write a very short book that explains the major laws of modern physics — special relativity, general relativity, quantum mechanics, and the Standard Model of particle physics — in bite-sized pieces that anyone can understand. If it sells as many copies as On Bullshit, I’ll be quite happy.
December 26th, 2005 at 11:37 pm
“Mathematics is always a continuum, linked to its history, the past – nothing comes out of zero” Atiyah
While mine is a layman perspective, it is evolving, as I learn.
The very nature of geometrical propensities are hard thing to resolve in my mind if they come from the quantum regimes, found as quantum geometries?
Yet, such inclinations were understood by Einstein with the help of Grossman in a classical sense? Dirac, at a quantum level, understood as well. Feynman developed from him? While these were matrices to consider, it still held geometrical insights by Dirac?
Am I missing something here that might have safely said that the discretium will prevail, and continuity slowly falls by the wayside?
Your points need to be constantly gone over and considered.
December 27th, 2005 at 12:03 am
I like the cute Schrödinger Cat.
December 27th, 2005 at 12:04 am
I enjoyed your plates
How are you going to introduce “superfluid” from early universe perspective?
“Symmetry breaking” would have to break from something?
December 27th, 2005 at 12:48 am
This is rather off-topic, but is there any chance you could give some opinions on the new Mansouri paper (astro-ph/0512605), which claims to explain away dark energy using a model that takes into account inhomogeneities and nonperturbative effects? (Note that this seems to be qualitatively different from e.g. the Kolb et.al. claims about perturbations causing the effect.) Especially in light of the recent Shapiro/Turner paper (astro-ph/0512586) that claims to find 5 sigma model-independent evidence for acceleration. I wonder if these two things can be reconciled? (By comparing assumptions about coordinate systems, …?) I’ve barely begun to read through the Mansouri paper but already I’m wondering what a specialist thinks. I always get confused about precisely which quantities correspond to experimental observations….
December 27th, 2005 at 1:17 am
Sean, don’t forget another smart Nobel laureate with doubts about QM: ‘t Hooft has been pounding the table about the possibility of a deterministic substructure for years (and yes, he does know about Bell’s inequalities). Speaking of the devil, he seems to have just submitted this reminder
http://www.phys.uu.nl/~thooft/gthpub/DiceWorld.pdf
to Physics World. Anyone with an interest in these questions could do worse than browse his list of publications at
http://www.phys.uu.nl/~thooft/gthpub.html
and read
http://arxiv.org/abs/hep-th/0104219
http://arxiv.org/abs/hep-th/0105105
http://arxiv.org/abs/quant-ph/0212095
December 27th, 2005 at 3:52 am
Cute cat…
I wonder that small amount of quantum mechanically acting atoms of radioactive materal could kill this big cute cat.
Is this possible because it’s just over simplified thought experiment?
I guess killing a cat needs quite amount of radioactive material and long time exposure, which in turn would not act quantum mechanically.
A system of (large particle number and long period of time) would not act QM’lly, so can not be described as superposition state of wave function. This is just my guess.
That radioactive half-life can not be seen as a sign of QM? Or can it be?
What Schroedinger wanted was to couple a QM system and a CM system, right?
Just layman’s curiousity…
December 27th, 2005 at 3:56 am
This was posted on my blog and thought I would pass it along ..
December 25, 2005
A CHRISTMAS TO REMEMBER
It was Christmas eve day and all through the house Two little children ran around like a mouse. The excitement was building. The moment was near. It would not be long be fore St. Nick would be here.
Christmas is shared due to divorce, this was dads year, it sadly turned into remorse.
Granted they were being fresh, as most kids are, but as I see it dad took it a little to far.
They were told they were bad & the gifts would go back, if they didn’t behave & stop the crap. As children this is what we’ve all been told, but to actually have it happen is out of control.
Christmas for these kids is the same for you & me, they woke with excitement to see what’s under the tree.
Except for these kids who were told they were bad, awoke on Christmas morn & instead being happy, they were very , very sad.
These children awoke from their beds with excitement & glee, to find NOTHING at all, under the tree.
They were sad & disappointed as most of us would be, Imagine how you would have felt at age 9 & 13, to find a bare tree.
Ya see, to them, Santa was a very nice man who lived long ago, that’s the story that is said, but as far as this house believes , he is now dead. Presents come from me & what I say goes, if I say NO gifts then that’s the way it goes.
Later that day when they returned home, their was toys for the boy & a bible book for the girl, sadly but true, she was told, that if you didn’t open your mouth to the courts & start your stuff, you would have received more, I have to pay for an attorney now & he walked away in a huff.
PLEASE E- Post your comments @ http://www.itsyourtownus.blogspot.com or E- MAIL me at teenieh1@optonline.net My goal is to have as many emails & or letters to show this Judge the mental abuse that is going on and must be stopped!!!!!!!
PLEASE e mail everyone you know & ask them to do the same ( a chain if you will ) I know I will receive a lot & hope this will help.
Sincerely yours, MOTHER.
December 27th, 2005 at 3:56 am
Having read D Z Alberts book:QME, some years ago, I found myself even more troubled by experience!
Then something triggered me to inqure further into QM and HUP, questions raised called for a re-read of Alberts book, and thus more of the same, it really is an amazing book.
Some basic problems I have formulated into:
1)Observation in three dimensions, does not equal measure in 2-dimensions.
2)A far-off measure translates to one-way observation.
3A local measure can only occur at a specific scale.
4)From a classical location of 3-D, 2-D objects being investigated do not return any precise values for measure or observation.
5)From a QM location to a Classical Location, accuracy prevails, Macro domains of 3-D, are easy, big ‘targets’ for Quantums to locate, and thus any 2-D Quantum can and will have absolute determination over a higher dimensional location.
6)Macro observers do not perform measure by default, you can ‘observe’ a finite speck of dust without altering it in any way.
7)Observation can operate in linear directions, one-way, but for measure, you need the information to be returned to the observer, and upon its return, this information must not interject with any other quantity, else it be not “true”.
8)Measure can NOT translate across different Dimensions ie (3-D to 2-D/2-D to 3-D) without a change in its value
occuring.
My confusion is further confirmed by my understanding of current theories of Q fields?
It seems to me that the interplay of (2-D) E-M waves and the Photon,(3-D), are really the same as stating that there is inter-dimensional correspondence occuring, over a number of obvious dimensional parimiters, and make the H.U.P work or not work?..because of the change in dimensions?, rather than the change in position?
So my really fundemental question is:Does the H.U.P really occur without a change in position, but with a change in dimensions?,,Thus does a change in dimension equal a change in position?
Sorry if I confuse the issue more than needed!
December 27th, 2005 at 4:01 am
Cat: Schrödinger-style feline-killing contraptions typically feature a radiation detector set up to trigger a macroscopic and lethal process (e.g. breaking a container full of poison gas, or firing a revolver at the darn animal). If an atom in the small radioactive sample decays, the detector triggers the cat-killer, and the cat dies… or does it?
December 27th, 2005 at 5:12 am
Sean-
This may turn into a blog post of my own, but for now, I’ll just point out that there are people who firmly believe in Quantum Mechanics, but take issue with your statement that
Chris Fuchs, in particular, has been espousing a “Bayesian” interpretation of Quantum Mechanics (check out e.g., quant-ph/0205039 ) — the wavefunction isn’t real; it’s all about information. This is uncomfortable, of course, for us as physicists: we want (need?) to be realists. There has to be a something out there for us to observe. But the wavefunction itself pretty much can’t be that beast, since it depends too much on what observations have happened (i.e., on what information you have).
December 27th, 2005 at 5:15 am
Hey Sean. Would you call it an “understanding” of quantum mechanics, if you can name the experiments, that makes the difference between QM and classical mechanics.
The high school education here kinda teaches that … so you kinda know what a double slit experiment is, or the photoelectric effect, but don’t really hear about a wavefunction.
Helge
December 27th, 2005 at 5:25 am
I still guess that “to trigger a macroscopic and lethal process” needs huge amount of radioactive material. Life do not die so easily…or do they?
“If an atom in the small radioactive sample decays, the detector triggers the cat-killer”
———but if this is how it works,
Does the property of QM disappear when the detector detects the decay of QM’al atom?
Or the system isn’t in the superposition state any more.
As soon as the decay is detected, the system is either in |live> or in |dead>. Not both.
The trigger executes only one state, not superposition state.
How about this? So the cat just becomes a measurement device in this case.
It’s the same if I remove the triggering detector in the killing process.
Conclusion:
QM system–>detection—>CM system.
i.e., Act of detection is boundary between QM system and CM system. Without detection these two can never be coupled. In other words, if a QM’al system ends up in a CM system after some amount of time, there was always measurement process between them.
Or the decaying itself is measurement, if the photon is not absorbed back in a given time after, or if the cute cat eats the photon, or if the detector eats it.
Nonsense?
December 27th, 2005 at 6:13 am
No dear Cat, I know this is frightful to you, but it’s quite enough for a single radioactive atom to decay for the detector to be triggered and have you poisoned, or shot, or whatever, by a thoroughly ordinary electromechanical Cat-killer.
Which brings us to the chain “QM -> detection -> CM” and the followup question: what exactly qualifies as “detection”? Is an inanimate Geiger counter hooked up to a Cat-killer all it takes to collapse the wave function to either |alive> or |dead>? If so, why? After all, the detector is also ultimately made of quantum mechanical entities, so why should it be special? Just because it’s larger? Then how large does it have to be, exactly? Or is observation by a conscious observer needed? If so, why? The observer too is also ultimately made of quantum mechanical entities, so this amounts to giving consciousness a special role transcending that of ordinary physical phenomena… and this is the point where most physicists give up and exclaim “shut up and calculate!”, leaving such questions for the philosophers of science to ponder.
December 27th, 2005 at 6:37 am
In quantum mechanics, the wavefunction is not real. Read what Heisenberg, Bohr and Von Neumann have to say about this.
This is not correct.
This is not correct either. You all know very well what it means to observe something.
Yes. Physicists need to get over their mental problems and start thinking seriously about consciousness. The current dogma in physics, materialism, or physicalism, as some call it, is in fact a form of religion, which asserts that the physical world is all there is. It is not. There is subjective experience. Subjective experience is not made of physical material. Materialists who get as far as thinking about this often respond by saying that “in a sense”, subjective experience is made of physical material, based on the observation that the brain is a physical object. But the brain and the mind are not the same thing, so in a more accurate sense than the aforementioned one, subjective experience is not a physical thing.
I should mention that there are ways that physicists deter one another from serious thought about consciousness. Accuse anyone who mentions it of believing in spirits. Suggest that thinking about such things constitutes philosophy and is therefore a waste of time. Suggest that in philosophy, everything is opinion and nothing can ever be known with certainty, and that therefore no rigour need be applied in the course of investigations – merely adopt an opinion and forget about it, because it doesn’t matter. These arguments are nothing more than immature schoolyard taunts. However, they have successfully persuaded several generations of physicists that ignorance is strength.
What you are asking for (which is the wrong thing to ask for), is that everything mentioned in the method of predicting experimental results should be a mathematical object which is defined and is a part of the theory. This is not possible. Quantum mechanics is little more than induction – the probability of getting a particular experimental result is nothing other than the fraction of times that that result has been obtained before under similar circumstances.
The desire to remove references to “measurement”, “experiment” and an observer from the formulation of the inductive method, or to define them in terms of more elementary mathematical notions cannot be accomplished. You can only define things which are arbitrary, for example, I can define a vector space and then I know all about vector spaces because they have exactly the properties that I gave to them when I defined them. But I cannot define a duck. A duck is an empirical object, discovered in experience (yes, subjective experience), and the properties of ducks must be discovered by examination, not by definition.
Physics is sufficiently distinguished from mathematics already by the fact that it takes account of the results of experiments.
There are therefore two branches of theoretical physics:
1. Applied mathematics, which considers the application of mathematical formulae to the aggregated results of experiments for the purposes of organising them into a system, rather than leaving them as a mere aggregate.
2. Metaphysics, which considers the conditions of the possibility of an experimental result. All experimental results can be encountered only in experience, therefore metaphysics is the study of the conditions of the possibility of experience, which include *time*, and *causation* (because the inference from an observed effect to a putative cause is necessary for all interpretation (including interpretation of empirical data), and interpretation (of empirical data) is necessary for experience).
Physicists today know nothing about metaphysics, and use it merely as a label to insult their enemies. So theoretical physics today has only one branch, applied mathematics, and the process of doing theoretical physics consists in the practice of producing mathematical formulae and then checking to see if they produce the right predictions. Where do the formulae come from? They come from the minds of great men, from insight and from principles. But what is the name of the systematic investigation of these principles, since the insight of a great man is merely a dogmatic assertion of authority, and can never be acceptable as a foundation for a science?
The investigation is called metaphysics, and metaphysics was studied by the founders of quantum mechanics, but is not studied any more, and that is why nobody today has a clue what they were talking about. Instead today there is just materialism, which asserts that physical matter is “fundamental” (the people are fundamentalists, you see), and have not given enough attention to subjective experience, and the conditions of its possibility (including space and time) are not material.
December 27th, 2005 at 7:42 am
My apologies. Of course, the desire can be accomplished, but what is desired cannot.
December 27th, 2005 at 7:43 am
http://en.wikipedia.org/wiki/Conformal_field_theory
It wouldn’t be right I think to deviate to the Future of Quantum Mechanics without out understanding how Hooft began his thinking in terms of Holography?
December 27th, 2005 at 7:52 am
#10 Andrew Jaffe and Sean
As I understand this topic (not well, but learning) quantum physics from a Bayesian point of view probably goes back to Bohr, or at least to Edwin Jaynes’. Einstein was looking at the realities of nature, describing at an *ontological* level. And Bohr was thinking on the *epistemological* level, not describing reality but, instead, information about reality. It’s about the difference between our knowledge of reality, and reality itself.
Writing about quantum physics from a Bayesian point of view:
Edwin Jaynes Probability: http://bayes.wustl.edu/etj/node1.html
For example the papers: “Probability in Quantum Theory”, “Clearing up Mysteries- the Original Goal”.
Plus this one, “Role and Meaning of Subjective Probability: Some Comments on Common Misconceptions.”
from here:
Giulio D’Agostini – Probability and Statistics
http://www-zeus.roma1.infn.it/~agostini/prob+stat.html
(and this one too.. some parts in Italian:)
Quantum Mechanics and Probability (+Confidence Intervals)
G. D’Agostini — 18/01/2000: http://www-zeus.roma1.infn.it/~agostini/clw_qm.html
Bohr said: “There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature _is_. Physics concerns what we can say about nature.” In his statement, he is stressing the information processing aspect of science. Although Einstein and many physicists would disagree with him and say that science is about learning what is reality, and what are its ‘laws’, Bohr is pointing out that any theory about reality can have no consequences testable by us, unless that theory can also describe what humans can see and know. If one incorporates human information into science, i.e. the original “logical inference” as described long ago by Bernoulli and Laplace, the quantum mechanical mud becomes clearer.
December 27th, 2005 at 8:04 am
If, somehow, you could measure observables with eigenstates like |dead> + |alive> you could kill just by observing
December 27th, 2005 at 8:12 am
Aa layman, history, is very important to me.
It is interesting that calorimetric design might of helped solve some of the issues with “spooky action at a distance?” While this created some consternation, one where we might never have understood these connections as with Einstein, today, it is much different?
Entanglement and it’s history in development help to reveal some of these interactive features?
So we set up the “circumstances” for early universe “information” to interact(glast), or, we “measure” the effect of colllisions in Onion skins?
But somethings go beyond this.
Are reduced from a fifth dimensional perspective, to two? Bekenstein bound and horizon mapping help to keep the blackhole interior in perspective?
December 27th, 2005 at 8:24 am
I don’t think it’s ever realistic to expect every “educated” college-degree person to understand what even “wavefunction” means. I would draw a line at Heisenberg uncertainty, stated in a non-mathematical language.
We spend too much time surrounded by physicists to think that everyone must know what we are talking about – however many PhD/Master students in biology will have trouble doing simple calculus assignments, never mind humanity majors in college!
Remember that most educated people out there think that Einstein’s theory of relativity has proven that “everything is relative”, and some will give you an example of how time passes by faster when you are doing something fun, as opposed to slowly killing time when you are bored as Einstein’s “time” relativity.
I wish someone did Jay-walking show, aka Jay Leno going to the mall to ask average Joe basic physics questions – 0.00001% of population (professionally trained physicists) would find this type of show hillarious!
A short book describing everything in layman’s term would be great, but using words like “wavefunction” assuming everyone understands what it means will make it sound like gibberish to non-physicists and trivial “dumbing physics down” book to physicists.
December 27th, 2005 at 8:38 am
Ponderer, perhaps these things should be taught in secondary school. Just like art and literature, physical theories like Quantum mechanics, relativity etc. are also part of our culture. So, some popular books about these subjects should be compulsory reading.
December 27th, 2005 at 8:50 am
JUst for some clarity then?
December 27th, 2005 at 9:00 am
Or here?
December 27th, 2005 at 10:15 am
Isn’t it even worse than that? I thought certain properties did not even exist until measured. Otherwise you’re describing a hidden variables theory.
George
December 27th, 2005 at 10:40 am
I had some problem with the phrasing of that sentence, since I am not sure what “really exists” really means. One viewpoint I am sympathetic to is that physics is all about results of measurments, and other things may or may not “exist”, but if they do not make any measurable difference maybe they can be left out of the discussion. In that spirit I never understood what is the measurment “problem”, is it just the lack of a convenient mental image or is there something more concrete?
(candidate for the latter is the emergence of classical physics out of the quantum world).
December 27th, 2005 at 10:50 am
But if physics is merely the results of measurements, how can it attain algorithmic compression? You need some conceptual framework to understand those measurements, and that is (at least) as much a part of physics as numbers in a column. Physical theories are notoriously underdetermined by measurements.
George
December 27th, 2005 at 11:02 am
George, I am not claiming that every element of the theory has to be a measurable quantity, just that one has to be minimalist in what is claimed to “exist”, and listen to the theory instead of trying to validate one’s favorite mental pictures (which are after all derived from a very narrow range of experience). Lot of the discussion about “intepretation” seem to me not to offer any measurable differences between the alternatives, though some of it (more recently) seems much more concrete.
December 27th, 2005 at 11:03 am
Moshe, re the measurement problem you could perhaps worry about things like the standard gedanken-experiment used to illustrate Bell’s inequalities (the one due to Bohm, where two particles in a spin singlet state go off in opposite directions, eventually to hit polarization detectors) modified to have one detector orientation randomly selected at the last moment, when it’s too late for the information to reach the other detector even at the speed of light. QM says it doesn’t matter, the correlation between polarizations measured at the two detectors is unaffected. Experiments with photons confirm it. So the wavefunction is collapsing instantaneously over a spacelike separation, light cone be damned. Granted, you can’t use spin correlations to exchange information at superluminal speed, but many would (and do) argue that the spirit of relativity doesn’t sit well with this state of affairs.
December 27th, 2005 at 11:08 am
I am completely unsympathetic to the positivist idea, that things only “exist” if they can be measured. I think physics is about understanding, and if some concept provides a more powerful and economical understanding of how the universe works, I’m happy to say that it exists, whether or not I can measure it directly, and whether the notion involves quarks, the Big Bang, or the quantum-mechanical wavefunction. I do appreciate that there are people out there who disagree, and this disagreement is one of the things that makes it hard to explain quantum mechanics to non-experts — we don’t even agree about it ourselves!
George, in my view it’s misleading to say that certain things don’t exist until they are measured — that’s taking a backwards view, that there really is something called “the position of the electron,” but it doesn’t somehow “exist” until we measure it. I’m arguing for a much more straightforward interpretation: the wavefunction exists, and from it you can calculate the probability of different measurements, but there really is no such thing as “the position of the electron” in the classical sense. Observations don’t map isomorphically onto reality.
December 27th, 2005 at 11:12 am
Andrew and Amara– Perhaps some day I will be convinced that it’s not useful to think that wavefunctions are real, but in the meantime I should just note that Bohr and Heisenberg and Schrodinger and Einstein all were lousy philosophers, and spouted all sorts of nonsense about quantum mechanics and reality. They may occasionally have been right, and these are certainly smarter people than me, but I don’t think they get much benefit of the doubt on this particular set of issues. The modern stuff is interesting, but I don’t know anything about it.
December 27th, 2005 at 11:20 am
Sean, I am also unsympathetic to the positivist idea, what I said above is that in my mind things “exist”, and can be a useful part of the theory, only if they affect the results of measurments, I don’t need them to be measurable directly themselves. I would be happier if different interpretations would have measurable differences, so the question could be in principle decidable, maybe they do…
December 27th, 2005 at 11:25 am
Hi, Moshe. You ask:
If you regard quantum mechanics as a recipe for predicting the results of measurements, and essentially one no different from the principle that the probability of a result is given by the fraction of times that result has been obtained before under similar circumstances, then it is not necessary that the classical world should emerge from quantum mechanics. Statements about the classical world, such as “the cup is on the table” are statements about the actual results of experiments (namely, the state of affairs), rather than a statement about the method which needs to be used to predict results.
That is, the classical world is to be found in the results of experiments and not in the formulae used to predict them. What I’m trying to say is that if we want to interpret something which will tell us what really exists, we should apply our interpretive powers to the empirically given data, rather than the method for processing and predicting it.
A lot of attention has been drawn to the fact that the “cut” between the classical and the quantum world is arbitrary to a large extent – we can include the measuring device in the quantum world and regard our own experience of seeing it as a measurement, and so on. When we include more and more of the classical world into the quantum world, the cut moves to the retina, up the optic nerve, and into the brain. The quantum formalism allows us to predict results regardless of whether we consider our predictions to be predictions of events in our brain, images on our retina, pointers of measurement devices, or locations of subatomic particles. However, the transition from “I see a green spot” to “the electron is at this location” is called interpretation, and quantum mechanics has to be able to work at any level of interpretation. That is why, whenever all of the predictions made by quantum mechanics has been taken into account, what remains is pure, uninterpretable randomness. (Incidentally, this relation to interpretability is what necessitates the occurrence of the “classical” world in the understanding of quantum mechanics – causation, in which every effect has a determinate cause must necessarily be present in order for any interpretation of experimental results).
Best,
R.
December 27th, 2005 at 11:27 am
Fair enough, but “things exist only if they affect the results of measurements” is a more slippery standard than it first appears (and, I would argue, not a very good one). Does the Big Bang exist? What about things that are outside my current light cone?
Of course, the wavefunction certainly effects the results of measurements — I change the wavefunction, the experiments give different results.
December 27th, 2005 at 11:53 am
Why not just leave it at “There are things that exist and are measured/observed; there are things that probably exist and can plausibly be measured/observed; there’s the rest which science cannot address.”
I thought decoherence pretty much resolved the observer/observed “paradox” in QM experiments. Being an aggregate of sufficiently many particles and their frenzied interactions, the observer and their apparati simply fail to behave in a measurably quantum manner, whilst some ion in a trap, which we measure using a minimum amount of interaction, does. The rest about quantum cats and the quantum nature of consciousness, and so forth, is nothing but metaphysical flapdoodle reflecting our evolved classical bias regarding “reality”.
Wasn’t it Feynman who said trying to “understand” it will make you nuts? Shut up and calculate, and all that? Why does this quantum vs. classicle false dichotomy continue to bug people, as it is, after all, a falsehood?
December 27th, 2005 at 12:02 pm
If we take the wave function to exist then we have to reconcile ourselves to e.g, something that might be a light-year across suddenly collapsing to a point when an observation is made. It is slightly less likely to make one seasick if one takes the wavefunction to be a description, containing in itself what is knowable.
December 27th, 2005 at 12:06 pm
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.”
And I could feel just as strongly that “every educated person” should know, say, the basic mechanism of transmission of genetic information, or that anyone with a college degree should be able to tell me the difference between natural selection and genetic drift. And a classics scholar would have her own shibboleths, a poet hers, a lawyer yet another set, and so on and on.
We all tend, I think, to over-rate our own specialized branches of study. It might be nice if every education could provide a basic grasp of philosophy, law, biology, physics, chemistry, mathematics, a handful of languages, visual arts, music, literature, etc etc etc — but I don’t think it’s possible, and I think it a bit presumptuous to say, in effect, “everyone should follow that field which interests me most”.
December 27th, 2005 at 12:07 pm
Sean, I now understand the sentence in question and agree with it. I would also, with some discomfort, grant the existence for things that are inferred from a theory that is itself well-tested. What I am uncomfortable with is discussions of what is the “correct” way to think about a theory, as long as these different intepretations don’t have any measurable differences.
December 27th, 2005 at 12:11 pm
As we can never really “know” which is the “real” situation, what does it matter whether we get seasick or not? If one wishes to approach the concept without a dose of dramamine, one can comfort themselves with the idea that large objects are composed of a large number of particles, feverishly interacting, and hence no particle or collection of particles within that system can remain in a superposition for very long.
Either way, you get the same answer, so, again, what is the problem?
December 27th, 2005 at 12:13 pm
Decoherence ultimately doesn’t explain anything; that’s the problem. If you want to claim that it’s QM all the way up, the ultimate question is then turned into, ‘why do we only perceive one branch of the wavefunction’ which is fuzzy enough to make me run away.
December 27th, 2005 at 12:14 pm
Sean-
Actually, I was being much less a positivist (and even less a philosopher!) than you are giving me credit/blame for. A bit of technical stuff follows: The problem with the ‘reality’ of the wavefunction becomes most evident when you start dealing with the full density matrix (i.e., so-called mixed states), which is the most general way of describing a quantum system. The problem is, there’s no unambiguous way to split the density matrix between the ‘quantum probabilities’ described by wavefunctions and the ‘classical probabilities’ that describe our lack of information about which wavefunction is the correct description. (And this is all aside from other problems, such as the interpretation of the wavefunction/density matrix within special relativity, of which the EPR paradox is the most famous symptom.)
But yes, something out there is certainly real. It’s not all in our heads (not mine, anyway; I’m not smart enough). And let me be a bit more careful: you did use the word “useful” — I agree that it’s “useful” to think of the wavefunction as real. It just might not be true. (And see the work of the aforementioned Fuchs on trying to construct a more operational definition of the wavefunction.)
December 27th, 2005 at 12:17 pm
I’ve always felt that if you corner most physicists and scratch away enough, you’ll find an instrumentalist, but I don’t think anyone actually thinks that way in practice; it’s more of a philosophical refuge against hard questions.
December 27th, 2005 at 12:30 pm
“Perception” is registering an observation, which involves an interaction, and so forth. Some collections of interactions have the rather subjective quality of being “conscious” of the interaction, I suppose, whilst others do not. Really, consciousness and perception have not proven themselves to be phenomena that cannot be explained in a purely classical framework, so I see no reason to jump ahead to the need to somehow reconcile perception with quantum reality. If classical mechanics is enough to describe all the parts of a brain being “conscious” (whatever that winds up meaning), then decoherence fully accomodates the “it’s quantum all the way up” description. Approximate classicality is probably good enough, and there’s no need to stay up nights wondering why we don’t “perceive wavefunctions”. It could be you need a classical (or the quantum approximation, which yields virtually the same result) system to “perceive” at all. I certainly don’t know whether that’s truly the whole story, but no one else does either, and it’s ultimately quite likely to be an answerable question. ‘Til then, “shut up and calculate” agnosticism seems the only scientifically valid opinion. The rest is empty philosophising, a product, I think, of the romantic notion that seemingly mysterious things must be really special somehow.
December 27th, 2005 at 12:49 pm
then decoherence fully accomodates the “it’s quantum all the way up” description.
No, it really doesn’t. Decoherence just tells you that the reduced density matrix approximately diagonalizes, but it doesn’t tell you anything about why that should be physically (or perceptually relevant).
If it’s quantum all the way up, there are no classical systems, but he fundamental tension is that we perceive a classical world. Decoherence looks like it ought to be relevant in explaining it, but as best I can see, all it does it make the relevant experiments much, much more difficult.
This isn’t completely philosophy, either. There is a fundamental dichotomy in the ‘interpretation’ of QM: collapse vs. no-collapse. These should be, in princile, experimentally distinguishable. In that sense, ‘interpretation’ is a misleading word. There is an honest physical question to be investigated here.
But until some clever experimentalist does an experiment that gives more than just vanilla QM, I subscribe to the ‘have no clue’ interpretation.
December 27th, 2005 at 1:20 pm
D. Biologist, I think some interpretations may be more easily be seen to be compatible with special relativity than others, i.e., may allow us to avoid phrases such as “super-luminal but carries no information”.
December 27th, 2005 at 1:37 pm
I guess we are left then to ponder the subject with our own devices?
If anything, the renewed debate “amongst the knowledgeable” helps to set up further information for us lay people.
December 27th, 2005 at 1:39 pm
Should read:
Ponder the subject
December 27th, 2005 at 1:46 pm
I rather thought that the “honest physical question” (being, I think: “Can we observe a system transitioning from an entangled collection of quantum entities in superposition to one that exibits approximate classical behavior in a measurable duration?) is being probed experimentally, especially in the field of quantum computing. I’m not sure how far along this area of investigation has proceded to something definitive, so I’ve been hesitant to come out in favor of decoherence any more than proposing it as perhaps a more philosophically satisfying model for those who choose to bother themselves with such matters.
If it possible to indentify measurable differences between one quantum interpretation or another (e.g., the collapse of the cat’s wavefunction is NOT instantaneous, ever, just too fast to feasibly measure), then I suppose it’s a scientifically relevant concern. If it isn’t, even in principle, then, again, how rational concern over quantum interpretations differs from any other form of philosphy other than “science” is not at all clear to me.
December 27th, 2005 at 1:58 pm
There are a whole class of experiments generally called “quantum eraser” experiments which probe this sort of thing, I think. Various people have predicted an irreversible collapse of the wavefunction. This could be measured in such experiments.
Decoherence is an honest physical effect that can be measured. It’s not an issue of philosophy. My personal belief, however, is that its explanatory powers are often overstated.
December 27th, 2005 at 2:19 pm
I think Newton’s laws of motion in their original form and in Hamiltonian form are indistinguishable, experimentally speaking. Nevertheless, the latter is more easily extended to quantum mechanics than the original formulation. That is why, IMO, interpretation is not merely philosophy. (Of course, these different interpretations of QM are not leading to multiple equivalent mathematical formulations, and perhaps that is part of the problem?).
December 27th, 2005 at 2:36 pm
#30 Sean and #40 Andrew:
I think that the Bayesians would say that the quantum mechanical probabilities involved inthe EPR scenario become simply Bayesian probabilities.
In 1998, I heard a talk by Ariel Caticha [1] describing a different way to treat state vectors. He calls the idea “array entropy”, which was originally introduced by Edwin Jaynes [2], but Jaynes thought that it was inadequate for the entropy of a quantum system. Caticha, however, expanded on Jaynes’ idea in a nice way. He assigned amplitudes and wave functions, not just to the system, but to _the whole experimental setup_.
[In the following, I synthesize a bit from Caticha's article. For the full article, get the conference proceedings [1] or look at the xxx server, where he he has two slightly earlier articles available:
http://xxx.lanl.gov/abs/quant-ph/9803086 “Consistency and Linearity in Quantum Theory”
http://xxx.lanl.gov/abs/quant-ph/9804012 “Consistency, Amplitudes and Probabilities in Quantum Theory”]
We know that one of the objectives of quantum theory is to predict the outcomes of experiments. Amplitudes are used to predict the outcomes of experiments, where, mathematically, the amplitudes are calculated via Hilbert norms (For the nontechnical people here, these norms, or inner products, are the means to measure the distance between wave functions). Interpreting the amplitudes can then be used to prove the Born postulate provided that amplitudes are assigned to the experimental setup. Caticha calls this extra assignment a “constraint” that the amplitudes be assigned consistently.
NOTE: Caticha says in his appendix that Born’s postulate is a theorem that has been independently discovered several times: A.M. Gleason, J. Rat. Mech. Anal. 6, 885 (1957); D. Finkelstein, Trans. NY Acad. Sci. 25, 621 (1963); J.B. Hartle, Am. J. Phys. 36, 704 (1968); N. Graham, in “The Many-Worlds Interpretation of Quantum Mechanics” ed. by B.S. DeWitt and N. Graham (Princeton, 1973). The limit N->infinity where N is the number of replicas of the system is further discussed in E. Farhi, J. Goldstone, and S. Gutman, Ann. Phys. 192, 368 (1989).
His approach, to consistently assign amplitudes to the experimental setup, is to assign a single complex number to each setup in a way that relations among the experimental parts translate into relations among the corresponding complex numbers. The consistency comes in by the requirement that if there are two different ways to compute this complex number, then the two answers must agree.
Caticha uses a path integral approach [3] to cover all possible combinations of starting points and interactions prior to the observing time. These lead to the same numerical value for the amplitude, that is, the outcome of the experiment. These amplitudes can then be inserted in the quantum mechanical equation of motion- the Schroedinger equation.
How to get from the Schroedinger equation to the Born postulate? The Born postulate states that the probability of N independent particles is the product of the wavefunction (amplitude-squared) for each of the particles, and the sum of each those is unity. [Note: here might be a connection to the Many Worlds Interpretation.] The Schroedinger equation is the equation of motion. Caticha shows that the connection can be made by using a Hilbert norm.
After Caticha shows the connection, he wants to evolve the system in time, and he does that with an entropy array. Once he applies the entropy array, then he can measure any observable in the system, and he says that the time evolution of states is “linear” and “unitary”.
So his is a Bayesian approach. If one adopts a Bayesian approach to probability, then the Schroedinger wave equation becomes a posterior probability describing our incomplete information about the quantum system, rather than wave functions that collapse in reality upon our observation.
Bohr’s Copenhagen Theory says that even when the QM state vector gives only probabilities, it is a complete description of reality in the sense that nothing more can ever be known; not because of technological limitations, but because of fundamental principles. But Jaynes seems pretty convinced (’Clearing Up Mysteries,the Original Goal’) about Bohr’s way of perceiving physics problems. He says that persistent in Bohr’s writings is a common logical structure which indicates that Bohr was never on the ontological level traditional in physics. Always he discussing not Nature, but our information about Nature, but that physics at that time did not have the vocabulary for expressing ideas on that level, so then his words appeared muddy.
On Dirac (the late Dirac was not a positivist, and the young Dirac was probably not either): I learned from Jaynes’ writings that Dirac was working with Harald Jeffreys (a Bayesian) side by side for a little while at St. John’s College, and he seems to have not realized what Jeffrey’s probability theory could offer, that is, a vehicle for expressing epistemological notions quantitatively. Jaynes said that if either Bohr or Dirac understood the work of Jeffreys, the recent history of theoretical physics might have been very different: they would have the language and the technical apparatus with which Bohr’s ideas could be stated and worked out precisely without mysticism. Had they done this, and explained clearly the distinction between the ontological and epistemological levels, Einstein would have understood it and accepted it.
References
[1] Caticha, Ariel, _Probability and Entropy in Quantum Theory_ in Maximum Entropy and Bayesian Methods_ (conf proceedings from MaxEnt’98 conference, Garching, Germany, July 1998), Kluwer Academic Publ., 1999. (BTW: This 9page mathematical paper is surprisingly readable..!)
[2] Jaynes, E.T. “Jaynes: Papers on Probability, Statistics and Stastical Physics,” edited by R.D. Rosenkrantz, Reidel, Dordrecht, 1983.
[3] R.P. Feynman, Rev. Mod. Phys. 20, 267 (1948); R.P. Feynman and A.R. Hibbs, “Quantum Mechanics and Path Integrals,” (McGraw-Hill, 1965).
December 27th, 2005 at 2:47 pm
Sean said:
We’ll, I don’t know exactly what you mean, but if I had to guess I’d say that you are (and if you aren’t now you are on the path to be) a believer in nonlocal hidden variables.
December 27th, 2005 at 3:42 pm
What I was thinking was…
If Schroedinger wanted the state of this:
|no decay of an unstable radioactive atom>|alive> + |decay>|dead>.
So that we can give the state |alive> some probability.
But an atom can not kill a cat.
I guess people used radioactive material to give alive this meaning of probability…
If the box contains a detector to trigger a gun or something,
the system state is:
(|no decay of an atom>+|decay>)|alive>
—> measurement by a detector ( = projection op., |decay>(decay|. This is guess. But if I express measurement process in a projection op,…)
After projection process, the state is in pure(?).
Then there’s no need for distinguishing between QM and CM, no need for probability concept.
—>triggering act ( =op., |dead cat>(alive cat| )
—>dead cat
What I wanted to say with *the amount of radioactive material and exposure time* was…:
The cat had never been in the QM’al probabilistic state, it was in the 100% alive state.
Or QM system and CM system can not be mixed in the first place.
And wanted to give wave function some meaning of time, though I’m not sure what I was thinking…
Hmm…yeah, this is odd
Sorry if I distracted the thread.
December 27th, 2005 at 4:02 pm
Of course, quantum gravity potentially raises the stakes in this discussion, although the implications are at least as obscure as quantum gravity itself. This recent preprint is interesting:
Observables in effective gravity
(hep-th/0512200)
Authors: Steven B. Giddings, Donald Marolf, James B. Hartle
December 27th, 2005 at 4:04 pm
Aaron – the fact that we can only perceive one branch of the density matrix seems no more problematic to me than the fact that if someone were cloned then there would be end up being two people, each perceiving their own reality (and having memories consistent with the pre-cloning events).
Though I’m certainly willing to be corrected, as far as I can see decoherence seems to solve all the conceptual problems of QM – there no longer seems to be any need to assign a special role to the observer or to define what constitutes an observation.
Also I’m not sure about Sean’s statement “what we can observe is only a small fraction of what really exists”. What is it that exists that we can’t observe? Sure we can’t observe the ordered pair (x,p) of a particle but under standard interpretations of qm this doesn’t exist either. Or maybe I’m misunderstanding something…
December 27th, 2005 at 6:14 pm
The wavefunction is the thing that really exists and can’t be observed. The position and momentum don’t even exist independently, much less simultaneously.
Of course, I also believe that “it is useful to think that…” is indistinguishable from “it is true that…”, but that’s the subject for another discussion.
December 27th, 2005 at 6:21 pm
“the fact that we can only perceive one branch of the density matrix seems no more problematic to me than the fact that if someone were cloned then there would be end up being two people, each perceiving their own reality (and having memories consistent with the pre-cloning events).”
There is, as far as I know, no physical derivation of the significance of the reduced density matrix. Decoherence tells us that microscopic systems entangled with macroscopic systems do not exhibit interference between macrostates of the macroscopic system. That doesn’t tell us why this should have anything to do with our perception. We perceive a classical world, and I don’t know of any reason why this should be so.
December 27th, 2005 at 7:35 pm
A lot of common misinformation and misinterpretation of QM and G/S Relativity seems to be due to people resorting to a logical fallacy – drawing conclusions from an analogy.
The way I interpret the process of building a Physical description, one needs to be able to express it within a rigorous Mathematical framework and come up with some testable consequences of the theory. The qualitative interpretation of the Mathematical description in terms of familiar concepts is what seems to lead to most of the confusion about the issue.
December 27th, 2005 at 8:05 pm
Sean – sorry if I’m being slow, but I don’t really see why in principle you can’t measure the wavefunction (at least upto an overall phase). Clearly you can’t do it by trying to measure the position directly since then the particle will simply collapse (or appear to collapse) to a position eigenstate. But is there some reason that there can’t exist another measurement process that gives you the wavefunction (upto phase) to arbitrary accuracy? (There doesn’t seem to be a really obvious fundamental reason like HUP.)
December 27th, 2005 at 8:32 pm
The article linked to below, entitled “On the End of a Quantum Mechanical Romance” is by a philosopher, not a physicist, but it seems very relevant to the discussion.
http://psyche.cs.monash.edu.au/v2/psyche-2-19-mulhauser.html
December 27th, 2005 at 8:46 pm
Aaron – as far as I understand it, in each branch the states are near coherent (the Heisenberg inequality is close to being saturated) and since (in everyday units) Planck’s constant is small, it appears that all the uncertainties ((delta x),(delta p) etc.) are small in each branch and hence we can approximate by classical states to get a good classical effective theory for each branch.
As for why each branch can’t perceive another branch, well if the Hilbert space splits as H = H_1 + H_2 after decoherence (just say there are two sectors) then you should be able to show that each sector can’t “observe” the other sector. To be more specific, starting from |p_1(0) >
December 27th, 2005 at 8:51 pm
Sorry, that last message seems to have been cut off from about half way through (probably due to formatting problems, although it was OK on the preview). Never mind.
December 27th, 2005 at 9:13 pm
michaeld– The intuitive idea is straightforward: you probe the wavefunction by “measuring an observable,” and whenever you do that the original wavefunction is perturbed away from its state. It’s true that it’s somewhat difficult to make a rigorous statement, although people have tried to prove a no-measurement theorem (see also here); I’m not at all an expert. There is a well-established no-cloning theorem that says you can’t duplicate a wavefunction without disturbing it; this is close to what you want, since if you could measure the wavefunction precisely, you could just go ahead and prepare another system in the same wavefunction, which is forbidden by the no-cloning theorem.
December 27th, 2005 at 9:28 pm
It’s only when you trace over the measurement apparatus (to get the reduced density matrix) that you get orthogonality. The question is why is this a relevant procedure.
December 27th, 2005 at 9:40 pm
If the wavfunction of the Universe :
http://www.geocities.com/capecanaveral/hangar/6929/h_kaku2.html
for instance is partially true?..then the shroedinger cat inside-box, cannot ever be killed, for even for cats, part of their wavefunction is outside the box, and thus it may allready be in a partial existence inside another Universe? …theoretically I can deduce that, according to feline stastistical laws, there are NINE feline Universe.
As an afterthought, there is probably one Universe for every day of the cats week, which may or maynot be nine?
December 27th, 2005 at 11:00 pm
QR,
One’s nine lives can be quickly extinquished when you sing the “wrong phrases” in a choir group? Which ever it is that day?
So then, does it becomes a matter of survival to “me-ow” intune?
Imagine, “censoring” to become a potent force in recognition? As a opposition?
Naw, I am sure we are all stronger in our convictions then this?
Momentum and Position talks set mind to wonder on the significances that followed from the days talks here
So much to remember.
December 28th, 2005 at 12:23 am
@Sean:
The wavefunction is the thing that really exists and can’t be observed. The position and momentum don’t even exist independently, much less simultaneously.
Actually, no, Heisenberg’s principle is that one cannot measure the two to arbitrary precision at the same time. It most definitely does not say that the two do not exist simultaneously. The point of HUP is about how well we can know a generalized coordinate and its canonically conjugate generalized momentum, not whether they exist at the same time. The basis transformation from the Lagrangian to the Hamiltonian would be, um, problematic, if half of the space for the Hamiltonian didn’t exist, don’t you think? Physically, some generalized equivalent of energy would be go missing in the description of the system
The intuitive idea is straightforward: you probe the wavefunction by “measuring an observable,” and whenever you do that the original wavefunction is perturbed away from its state.
Whether the wavefuntion is perturbed depends on what you are measuring. Some things yes, some things no — if the operators commute, then you can measure away until you’re out of observables associated with commuting operators (at least in principle, though I’d bet that practically speaking, the set of observables you can do this with is always pretty small, maybe even sets of 1). Either that, or someone seriously needs to rewrite the old school Caltech way of teaching graduate quantum (the gent who taught my class was of that noble pedigree; also, this is opposed to quantum field theory, which while we didn’t get much into, so I make the disclaimer that I realize that I need to learn some new tricks, but hey, we’re talking about quantum mechanics, not QFT or QCD or other areas where I am on much less sure ground).
@Cat:
You seem to have hit upon the reason Schrodinger came up with his gedanken experiment — he is reputed to have thought the Copenhagen interpretation was too problematic, hence the desire to come up with a demonstration of absurd reasoning to score points.
December 28th, 2005 at 1:09 am
agm– I hope your Caltech professor taught you that, when you perform a measurement of a certain observable, the observation returns an eigenvalue of that observable and the wavefunction is subsequently in a corresponding eigenstate. That’s the collapse of the wavefunction, or whatever you want to call it. Of course, if you’re lucky enough that the wavefunction is already in an eigenstate, there need be no evolution, but that’s certainly not the generic case.
Your argument about the uncertainty principle is precisely the mistake I was arguing against: we shouldn’t think of position and momentum as things that exist but can’t be simultaneously measured, we should think of the wavefunction as what exists, and observations as something that only tell us about part of it.
December 28th, 2005 at 1:42 am
I’m interested in the role of the observer, and in particular the nature in which consciousness comes into play. I am of the faith (scientific though be it) that consciousness is a physical phenomena, and so the act of observation, according to current theory, would be interactions between collections of observer matter particles, force particles, collections of observed matter particles and the like, by my (and physics’) admittedly limited knowledge of the universe. Of course, I could be wrong. What do you think?
December 28th, 2005 at 3:44 am
If there are cases when making an observation does not change the state of a wavefunction (i.e., when the wavefunction is an eigenstate of the observable before making the observation), then my description is correct. The generic case is irrelevant — the question is whether such an observation is possible, not how many systems one can come up with where one could make such a series of measurements. And I explicitly mentioned this in my parenthetical comment.
And I made no mistake. Throwing the physical analogue I presented in the trash, the mathematical framework requires both generalized coordinates and either generalized velocities (Lagrangian description) or the relevant generalized momenta (Hamiltonian description). Either way, HUP makes a statement about the about their relation, not their existence. It’s a property inherent in the description.
Pedantry, yes. Error, no.
December 28th, 2005 at 6:52 am
“Plato” so true!
Observer dependence is contained within GR/SR? and also Observer dependence is a contributing factor for QM, where the wavefunction is really the 2-D re-formulation of the 3-D description of a lcoal Particle, its a “particle-function” spread out as a field of waves?
A particle inside a box is tangable stuff:
http://pancake.uchicago.edu/~carroll/universelab05/img8.html
so interpretation of forms via E=mc2, can be shown that the dimensionality of the expressed energy, is not a translation in non similar dimensions?
A 2-D field energy, say the force particles, are not 3-D ‘waves’ that can “pile up one on top of the other”, and as stated in a post above by agm, the P.E.P relates particles of a 3-D ‘tangable’ matter in space?.. to exclude other ‘like’ energies at one location of space.
Where as the H.U.P is an exclusion principle of Time parimiters. A change in space-time, is a change in dimensional location of structure makeup.
You can observe a 3-D particle in spacetime, you can locate a 3-D particle in 2-D, space what you cannot observe is a 2-D field inside a 3-D particle.
December 28th, 2005 at 7:42 am
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.” It’s not too much to ask, I think
Hmm, here is a live experiment that can help you determine whether you are asking for too much or not … [I hope most of the commenters at 'slashdot' have a college degree].
December 28th, 2005 at 8:02 am
Sean – thanks, I think I understand now (about why we can’t measure the wavefunction). That’s very interesting.
December 28th, 2005 at 10:25 am
Quantum mechanics is very mysterious. However, the Heisenberg uncertainty relation, which is often held up as a central element of quantum mechanics, is not the mysterious part. Uncertainty relations are a consequence of working with waves, and have little to do with the quantum nature of quantum mechanics.
Even classical waves, like water waves, obey uncertainty relations. In the case of classical waves, the uncertainty relates the position and spacial frequency (the number of waves per distance, which is the reciprocal of the wavelength). If dx is the uncertainty in the position (roughly the length of the wave packet) and d(1/l) is the uncertainty in spacial frequency (the spread of the wave’s Fourier transform) then the uncertainty relation is:
dx d(1/l) > 1/(2 pi)
In order to get a good measurement of the spacial frequency (or wavelength) the waves need to be spread out over a large distance, making their position very spread out. To get a good measurement of the position the waves need to be very bunched up, making it difficult to pin down the spacial frequency.
There is also an uncertainty relation relating time and frequency
dt df > 1/(2 pi)
Quantum mechanics identifies momentum with spacial frequency and energy with frequency via:
p = h/l
E = hf
where h is Planck’s constant. This leads to the usual uncertainty relations:
dx dp > h/(2 pi)
dE dt > h/(2 pi)
For me, this removed the mystery of the uncertainty relations. Uncertainty relations are a result of working with waves, whether they are water waves or wave functions.
The mysteries of wave function collapse and entanglement remain. I think that decoherence removes wave function collapse from the theory, shifting the issue even more sharply to entanglement. Entanglement is the only thing left keeping me awake at night, but it keeps me awake often.
Gavin
December 28th, 2005 at 11:16 am
As Dumb Biologist I suscribed to the decoherence idea: it´s quantum mechanics all the way up! This obviously solves all problems: the world is deterministic but it is impossible to know, even in principle, the state of a system with arbitrary precision. That´s why we can only make statistical predictions. To be honest I don´t really know to what extent the wavefuctional collapse has been rigorously “explained” in the literature (yes, I said wavefunctional, like it or not the world is described by a quantum field theory). But this collapse should be our interpretation of a dinamical instability of entangled states involving several particles (or quanta) that happens in quantum field theory. The eigenvalues of the operator we are measuring should be the “attractors” of the (quite complicated) dynamical evolution.
I don´t like the discussion of the collapse of the wave function of particles. The world is not like that, what is reduced is a wavefunctional, and I think that the instability that we associate with the collapse is a phenomenon that takes place only in a quantum theory of fields, not particles.
December 28th, 2005 at 11:33 am
IN: I agree! Always good to see someone being reasonable in a discussion like this instead of postulating experimentally unverified nonunitarity magic.
December 28th, 2005 at 11:37 am
anon.: Though being reasonable and summarizing what is already known has its benefits, gazing into vague theoretical physics crystal balls is tantalizing to say the least.
December 28th, 2005 at 11:45 am
Like some, in presence and Entanglement, I am trying to “reason” in my mind as to the evolution of “light,” from the shadows on the wall. Yet, I am still held prisioner.
December 28th, 2005 at 2:06 pm
Sean, you say:
This is actually an extremely important point. This is what is called a practical attitude, and is almost universally regarded as meritorious. However, it makes confusion of theoretical and practical motivations into a principle, and as such can only do harm to one’s understanding, if one follows that principle. Because when one asks the question “Useful for what?”, the answer can never be “for the purposes of having a clear understanding”. The principle itself says that we should sacrifice a clear understanding for the purposes of achieving some unspecified goal.
The two are also not indistinguishable. To say that something is true is a statement of fact, a theoretical statement which reflects our knowledge about the state of affairs. To say that a particular decision or activity is useful is a statement about strategy, and one must already know what the goal is before one can determine whether the statement is accurate.
The statement that they are indistinguishable is therefore incorrect. However, it can be understood what you were trying to say from the expression “useful to think that …” This in itself presupposes that our acceptance of a particular statement as a true statement is somehow a voluntary action. This is the case for opinions and perhaps beliefs – that is, we adopt our opinions and beliefs voluntarily. But it is not the case for knowledge. I know that 2+2=4, and I cannot simply decide to know otherwise. The distinction between our own opinion and our knowledge is of fundamental importance and must be borne in mind in any investigation which is not to become mere poetry.
So what you were saying, in my interpretation, and please correct me if I am wrong, is that one should voluntarily adopt as one’s opinions and beliefs, and even regard as knowledge, those statements which it is useful to treat as true for practical purposes, even in cases where we know that they are not true. The practical purposes are left unspecified, although we might gather from the context that this has something to do with theoretical physics.
As I said, this makes confusion of theoretical and practical motives into a principle, and as such it commands that we should treat as true some statements which are not true, for the purposes of achieving some goal. However, it can never be advantageous, if the goal is to understand clearly, to regard a false statement as true or vice versa. Consequently the principle itself is incompatible with any purely theoretical investigation, although it may be suitable for a person who is only concerned with practical purposes. It is a principle for engineers, not for theoretical physicists.
We should, for practical purposes no doubt. We must ask ourselves why the confusion of usefulness with truth is so widespread, and indeed why it is frequently advocated and advertised, as though it carried some benefit. It certainly carries a certain effect on the mind of the host – the mind which accepts the principle and lives by it will not be able to succeed in purely theoretical endeavours, unless it is forcefully reminded by the strength of some authority that knowledge is not mere opinion, as happens in mathematics. A mind which leaves mathematics behind and seeks to investigate other matters may decide that rigour is no longer important, and may regard as true statements which are merely useful, but in so doing it restricts itself to practical matters, for in theoretical matters what we are concerned with is knowledge, not practical usefulness.
The usefulness of the principle is here revealed – it restricts the mind to practical matters, and this is useful if we wish to train engineers. If that is our purpose, it also suits us well to sneer at those who think of philosophy, to say that they are spouting nonsense and that those who restrict themselves to practical matters are praiseworthy. We should also tell everybody that in purely theoretical matters, everything is opinion and rigour is not required. Simply adopt an opinion and live with it, because the application of rigorous thought is a waste of time.
This is the dominant paradigm in modern theoretical physicics. We have raised an army of engineers and asked them to solve the problem of quantum gravity, in our wisdom.
But on the question of what we should think of as real, Heisenberg, in “Physics and Philosophy” says, as a criticism of the Bohm interpretation, that the real things are the things in ordinary three dimensional space, and that one must do violence to the notion of reality if one wants to regard a complex wave in configuration space as a real thing. I would say that I agreed with Heisenberg, if it were merely a matter of opinion, but it is not. Heisenberg is correct.
To say that Heisenberg is here spouting nonsense, that we are practical people, and that a complex wave in configuration space is just as real as the things in three dimensional space around us, and that any suggestion to the contrary is the same as the statement that the world doesn’t exist, is remarkably common. Why are so many people willing to do violence to the notion of reality? The things we see around us are real – what is the problem with that? It certainly doesn’t lead us to think that a cat is both dead and alive at the same time.
Incidentally, when one admits that another person is “smarter” than oneself, one cannot consistently accuse them of spouting nonsense if they have seriously and rigorously thought about a difficult subject and are attempting to explain it. It is more appropriate to say that one hasn’t understood what they have said. Indeed, the expression, “spouting nonsense” is nothing other than a statement that one doesn’t understand what was said, accompanied by derision. Derision is a social behaviour in which the derider suggests that he is himself worthy of imitation, while another is to be reviled.
The founders of quantum mechanics may not have been excellent philosophers themselves, but that does not mean that one should not study philosophy. If one wants to succeed in speculative endeavours in theoretical physics, one has the obligation to study philosophy, by which I mean investigate the subject rigorously for the sake of one’s own clear understanding. This does not mean that we should accept as truth something that somebody once said on the basis of their mere authority. Nor does it mean that we should read poetry or smoke a pipe while stating our opinions and beliefs, or even that we should adopt this or that opinion or belief, for we are here concerned with knowledge, not belief. It means rigorously studying the relation of mathematics and logic to empirically given data. It means acknowledging that rigorous thought must be applied to theoretical endeavours even if our colleagues deride us for it, because the use of derision, or an appeal to usefulness, to establish the truth of a statement is a logical error.
December 28th, 2005 at 3:10 pm
Aaron Bergman writes: It’s only when you trace over the measurement apparatus (to get the reduced density matrix) that you get orthogonality. The question is why is this a relevant procedure.
I realize that this is likely just pushing the same question off another level, but you trace over the states of the measurement apparatus because you don’t measure what they are (either because you’re not capable of making the measurement, or because you’re not interested in making the measurement). If you were to go to the trouble of measuring the state of your apparatus, you’d find another level of entanglement.
You don’t really need a macroscopic system to cause decoherence– single unmeasured quanta are enough to do the job (I remember somebody– Dave Pritchard, maybe– talking about atom interferometer experiments that set out to quantify this). The key is the “unmeasured” part– that’s why you do the trace over states, and destroy the off-diagonal elements of the density matrix.
In terms of even braoder questions, there was a talk at DAMOP a couple of years ago (the one in Tucson) where Wojciech Zurek (of no-cloning fame) was trying to derive the probability postulate (the idea that you square the wavefunction to get the probability distribution) from first principles. I didn’t see how it ended, because I had a plane to catch, but I wasn’t understanding much of the first half, anyway. It’s nice to know that frighteningly smart people are working on this, all the same.
December 28th, 2005 at 3:23 pm
If you were to go to the trouble of measuring the state of your apparatus, you’d find another level of entanglement.
Which is my point. Decoherence tells you something about relative states, but not why relative states are relevant to our perception. Tracing seems like an obvious thing to do given that we’re not measuring the exact state of the measurement apparatus, but I don’t know of any physical reason why it’s the right procedure other than that is seems to give the right answer. Michael Nielsen emphasized this a while ago.
I’d be surprised if you saw decoherence by entangling with a non-thermodynamic system as the vanishing of the off-diagonal terms arises, in my understanding, by the rapidly changing phases of the macroscopic system. Do you have a reference?
December 28th, 2005 at 5:00 pm
Making sense of the Non-sensical
Violation of the principle of complementarity, and its implications Shahriar S. Afshar
So for me how would you describe “this place” that Penrose is calling for in the new Quantum view?
December 29th, 2005 at 3:45 am
Dissident:Any comment for where I’m wrong?
I read wikipedia for the Schroedinger’s cat. Maybe I was wrong…
The problem of the cat was that:
“When the cat will die?”
If there’s quite amount of radioactive material, I can apply the half-life time. And can predict that the cat will die within half-life.
But, if there’s only one or several radioactive nuclei, we can’t predict when it will decay. In turn can’t predict when the cat will die. If the cat is very lucky, it can survive forever.
This is why I mentioned about quantity and exposure time. And the gibberish, “decaying itself is measurement.” I was forgetting…
Is the wavefucntion of nucleus different from the wavefuction of (an atom plus a photon)? I mean qualitatively(?). I don’t know what this means.: The probability that a nucleus would decay within 1 hour is 1/2.
Really, if there’s only one nucleus, the cat may survive for long time, even though half-life is just an hour.
Where am I wrong? Anybody, any comment?
December 29th, 2005 at 5:37 am
Cat, what you are talking about now is not specific to quantum mechanic, it’s generic probability theory. Knowing the probability of an event is not the same as knowing when or even that it will occur within a certain amount of time. This is true whether the event is an atom decaying or your rolling a double-6 in a game of dice.
In the Schrödinger’s Cat gedankenexperiment, this uncertainty is put to good (?) use by closing the box with the Cat in it and then refraining from looking inside for a while. Did that radioactive atom decay (thereby triggering the Cat-killer apparatus) or not? Until we open the box and look inside, we don’t know; we only know the probability.
And this is where the interpretational issue arises: deos this mean that until we open the box and look inside, the Cat is in a superposition state of |dead> and |alive>? And if so, what does that mean?
December 29th, 2005 at 11:03 am
In the below sense I am talking about how perception is shifted from what we had always understood.
A Fifth Force?
December 29th, 2005 at 1:01 pm
Is this because we’re working with an ensemble of decohering environments rather than a specific one? That is, the result of decoherence is a multi-branch wavefunction because it is an ensemble average across decohering environments. If we could follow a particular case, we’d always end up with one branch? (we wouldn’t be happy with a measuring apparatus that didn’t do this).
December 29th, 2005 at 1:46 pm
I’m intrigued by Sean’s view that the wavefunction is “real” and “exists”. I know it’s probably impossible to give exact meaning to such terms; but, Sean, would you attribute the same “reality” and “existence” to, say, the Hamiltonian of a classical system or, say, the partition function in statistical mechanics? Hope I’m not asking a silly question.
December 29th, 2005 at 2:41 pm
“it’s generic probability theory.”
—then do you mean the decay event isn’t QM property?
I remember that the reason for nucleus decay probability is from time-energy uncertainty.
What if I use an electron with spin, instead of the unstable nucleus. And then measure spin up/down.
The trigger will act as soon as the electron passes the detector.
What if I use an excited atom and a photon detector. The experiment is still valid?
What is the operator for the eigenstates {|dead>,|alive>}? Uh…I need some device and description of acting. What is operator for {|decay>,|not decayed>}?
I guess the wavefuction for {neucleus and environment) is very different in each cases. The case when I include a detector or not. When I put the neucleus in a small containment or not, to prevent the cat detecting the radiation. And even the size of containment matters when gamma particle(photon) is emitted.
I guess my these questions can be answered without any interpretation. Very physical questions(?)… Hmm…Are they nonsense questions?
December 29th, 2005 at 2:47 pm
Tom– I think the wavefunction has a completely different status than the Hamiltonian or the partition function. In any theory of physics, you have certain objects that obey certain dynamical equations; those objects are “what the world is made of” according to that theory. In quantum mechanics, the objects are the wavefunctions (or state vectors, to be slightly more precise). The wavefunction is as real as the laptop on which I’m typing; according to QM, the laptop is a wavefunction of certain degrees of freedom in a certain state. I’m not one of those people who would say that the evolution equations “exist,” although I know that plenty of people to think that; if Schrodinger’s equation exists, it certainly doesn’t exist in the same way that the wavefunction does.
December 29th, 2005 at 3:24 pm
Thanks, Sean — that helps. Never thought of my computer (nor myself, for that matter) as actually being a state vector in some Hilbert space.
E and B fields would be considered “real” and “existing” according to classical EM because they are objects of dynamical (Maxwell’s) equations. So, these fields are partially what the world is made of according to this theory. Doesn’t sound too bad.
Could we extend this viewpoint all the way back to classical mechanics? For example, suppose a particle is moving in one dimension (x-axis) under the influence of a known force. It’s trajectory x(t) would be an “object” that obeys a dynamical equation (Newton’s 2nd law). And so this function x(t) would “exist” and x(t) would be part of what the world is made of? x(t) would be just as “real” as the particle itself? I can use x(t) to predict where the particle will be a some instant of time – similar to using the wavefunction to determine the probability of finding the particle in a region of the x-axis at some time.
OK, I’m being a nuisance so I’ll quit. But I do find all of this interesting to ponder and thanks in advance for any further comments.
December 29th, 2005 at 3:41 pm
And another, I had read the wiki for many world interpretation. It was very hard for me to grasp the concept…
December 29th, 2005 at 5:51 pm
I mean “physical questions”–>technical questions for experiment.
December 29th, 2005 at 11:09 pm
What occurs in QM and in GR, is that the probability of observing an ‘event’, decreases with the number of Photons. Being that photons are the energy needed for observation by ‘observers’, what happens to a system when the limit of observation is at a minimum ie single photons?
December 30th, 2005 at 1:11 am
Maybe the question above can be put in context of “Which way“?
Is the histories of the path taken, still intact? The screen becomes “something else” then would it not if given some new way in which to look at this??
December 30th, 2005 at 2:59 am
Paul Valletta:”that the probability of observing an ‘event’, decreases with the number of Photons.” In a little bit easy words or with example…?
Dissident:”Knowing the probability of an event is not the same as knowing when or even that it will occur within a certain amount of time.” What does this mean?
1.If I measure a nucleus, the nucleus goes to either |decay> or |undecayed>.
2.”The probability that a nucleus would decay within 1 hour is 1/2.”
Does that mean these two are different? But the experiment uses nucleus…, with a detector waiting for emitted particle.
The reason that I want to replace an unstable nucleus with an excited atom is that: Physicists are more familiar with an atom emitting a photon. Right? At least to me:-)
If Schroedinger really wanted to entangle nucleus with a big cat, I guess detector must not be included. If there’s detector, what are entangled are a nucleus and a microscopic detector, not a cat. If he’d say “detector and cat are also entangled.”…
What if the state of the nucleus is this?:
|unstable nucleus> = |decay(ground)> + |not decayed1(first excited)> + |not decayed2(second excited)> +…
Then the situation becomes different, right? I hope I’m not starting to become nuisance.
December 30th, 2005 at 3:41 am
PS: uh, I want to change the word “entangled” to some other word.
December 30th, 2005 at 5:28 am
One problem with the interpretation of QM is that the formalism implicitly assumes a macroscopic classical observer. Namely, the Hamiltonian formalism assumes a foliation of spacetime, i.e. an immutable time function. But to observe a system we need to interact with it. This interaction will transfer momentum to the observer, making her undergo a Lorentz transformation, and change the definition of time (if we define time as the ticks of the observer´s clock). By assuming that time is independent of observation we ignore this effect, which seems to me a serious flaw in principle, although unimportant in practice.
December 30th, 2005 at 1:17 pm
Maybe the examples are then in how we use the math models for apprehension of what is taking place in our universe?
AS a “observer” you need a place from which to do that? Is it really outside of the 3+1 that we know and love?
While one talks about a “decay process” you might be engaging in mathematical realms that seem very far away, yet are really under our nose?
It’s a way of how we look at our surroundings?
It seems so easy in a visual sense, yet it has move to asbtract mathematical thinking? Would we say that these people who have these same questions in this thread have been removed from reality?
December 30th, 2005 at 10:11 pm
I used to worry a lot about what QM means. I finally came to the conclusion that the only “reasonable” interpretation resolving the reality vs. locality question was to define “reality” in information theoretic terms. I can then preserve the “common sense” definition of locality while redefining reality as such:
Here is an example regarding the position of a particle:
Traditional realistic viewpoint – Things are where they are regardless of any measurment or measuring device.
Copenhagen (standard) Interpretation of QM – Things are where we measure them to be.
Information Theoretic version of Reality – Things are where they “tell us” they are. QM effects are due to the fact that reality does not have infinite bandwidth to give us information about itself. If it did it would require infinite energy. So reality is bandwidth limited.
I could be wrong. But I don’t worry about it anymore
Elliot
December 31st, 2005 at 9:55 am
Here’s a fast forward from Bell.
WE should, still worry?
January 3rd, 2006 at 12:19 am
“it’s generic probability theory.”
I got it. How slow I am…
January 4th, 2006 at 4:15 pm
I would like to ask a question that someone reading this blog is likely to be able to answer: In the case of the double-slit experiment, in the one photon-at-a-time mode, why doesn’t the space between the slits cause the wave function to collapse at the slotted barrier? If the slotted barrier consists of photographic film, then the wave function of all photons impacting it should collapse to some point on the slotted-barrier and be recorded, and, since some of these points will be located at the slits, the photon impacting at that point will not be absorbed by the emulsion when the wave function collapses. However, the collapsed wave function must then re-expand, when the photon emerges from the slit, right? But how can that happen?
On the other hand, if the wave function doesn’t collapse at the slotted-barrier, so that it can go through both slits simultaneously (as inexplicably shown on most diagrams of the experiment,) it should also reflect from the surface area between the slits and thus continue in the reverse direction back toward the source. If this reflected wave is a probability wave as well and is a continuation of the original wave, if a rear barrier-detector exists at the source, and is located at less distance from the slits than the forward barrier-detector on the other side of the slits, will the first wave function collapse at the rear detector prevent any photons from being recorded on the forward detector?
Doug