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 relative 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.
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.
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. 🙂
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.
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.
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?
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?
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?
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?
In the below sense I am talking about how perception is shifted from what we had always understood. 🙂
A Fifth Force?
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).
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.
“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? 🙂
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.
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.
And another, I had read the wiki for many world interpretation. It was very hard for me to grasp the concept…
I mean “physical questions”–>technical questions for experiment.
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?
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??
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.
PS: uh, I want to change the word “entangled” to some other word.
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.
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?
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
Here’s a fast forward from Bell.
WE should, still worry? 🙂
“it’s generic probability theory.”
I got it. How slow I am…