First let me thank you for your participation, I realize I am dealing with someone of considerable knowledge so there is much that may be gained.
vanesch said:
If you stick by the axioms of quantum theory (which you are free to do so or not, but I'm looking at the *toy world* in which these axioms are considered true), then EVERY state of the system is described by an element of a projective hilbert space. There's no distinction between "macro" and "micro" states. EVERY state.
But that's kind of ducking the issue-- I am maintaining that we have not the least experimental justification to
require that "the "axioms of quantum mechanics" must apply to macro systems! It's simply an example of taking our own physics too seriously, just like the post-Newtonians did when they grappled with a purely deterministic-seeming universe. Now, you point out that perhaps we are not
requiring this, we are
choosing it-- but if that's true, why are we choosing this is if it is not required? Where do we benefit from this choice if it is not forced on us by nature?
Now, if you assume that this is not applicable to certain kinds of systems, then you're playing with *another* toyworld. It will then follow different rules, but for sure, you cannot say that it is purely described by the axioms of quantum mechanics.
Right, I see that we are on the same page-- we are playing with "toy worlds" here, but the issue on the table is which one best describes the real world in a given situation. As I have never seen anyone meaningfully apply quantum mechanics to the state of a cat as a whole, I claim that is a clear case of using the wrong "toy world".
And then you have the difficulty of explaining what is "micro" and what is "macro" and what applies where.
As it turns out, we do not suffer much from this problem. Nevertheless, it is a real problem, and your solution will not handle it any better than mine. Indeed, even the theory of large nuclei does not follow the approach you are suggesting! The first step always looks something like "well we can't really solve quantum mechanics for this system, so here's what we do instead". That's a
nucleus, not a cat. A nucleus is complex but at least it can be coupled only weakly to its environment. A cat that is weakly coupled to its environment is not a cat for long.
So, for sake of argument, I stick to this toy world in which the axioms of quantum mechanics are strictly valid. By definition then, the physical state is given by a state vector. And from here on, we go further.
Certainly you can start somewhere, and see where it gets you, that's an excellent way to do science. But the question is, where does this get you, in regard to a cat, or in regard to wavefunction collapse? Are we trying to motivate actual new observations, or are we trying to satisfy ourselves that we in some sense understand the outcomes of impossible ones? What gets us somewhere is the mindset that says we are coupling quantum systems to macro systems expressly because we can rely on the macro system to act classically, which our brains like and we can actually call it a "measurement". What other kinds of experiments can we do? Given that, where is the gain for us in treating our macro system quantum mechanically, and why did we need a macro system involved in the first place if we were just going to treat it quantum mechanically? Let's just let the electrons measure each other if that's our perspective.
This is in a Copenhagen like view, where you have a classical world with "quantum gates" or whatever, where systems are classically prepared, then "plunge into the quantum world", and re-emerge classically when they are observed.
That does seem like a valid way to say it.
But clearly in that view, not everything is at all times described by the axioms of quantum mechanics.
True, but we already know that. Does not every experiment begin with "controls" chosen by the experimenter? Those controls do not emerge from the axioms, they are in a sense axioms of their own. They are "how we do science"-- and that's not in quantum mechanics, it is an assumption that quantum mechanics is tacked onto. It requires classical manipulation to apply those "uber-axioms", that's where we exit the self-consistent realm of quantum axioms. Electrons are lousy scientists.
To me, the exercise is to take the theory TOTALLY seriously, in its toy world.
And yes, in the toy world of classical physics, particles DO have perfectly well defined positions and momenta.
At least you are clear in what you are doing, so there is no sense to which it is "wrong", there is only a sense of "what is it good for". So I ask, what is it good for to take our theories
totally seriously? To me it sounds like we are entering into pretense in an effort to "cover our tracks", like a detective at a crime scene saying "assume I don't leave any fingerprints of my own". I think that leads to erroneous conclusions-- we do better if we say "I will be careful to not mistake my own fingerprints for that which I am trying to study". Then instead of taking our axioms too seriously, we pay close attention to what we are actually doing, and try to separate that from what the world is actually doing.
Uh, but a system with a finite lifetime doesn't violate the conservation of energy! It simply wasn't in a pure energy eigenstate - otherwise it could not evolve, and hence not have a finite lifetime.
Yes, I read your words wrong-- you said one cannot get a
violation of energy conservation, and I heard that as one has to
conserve energy. We should say it wasn't in an energy eigenstate-- but since all systems have finite lifetimes (even the whole universe), then there is no such thing as a strict energy eigenstate. So how does anything conserve energy if I cannot define its energy? The point is, these are not exact concepts, they are approximations we apply in our toy worlds but we should recognize that our "fingerprints" are all over the result. Why when should we take it
totally seriously?
That's the Copenhagen view. But it leaves you with the unsatisfied impression that there is no available description for the link between quantum theory (which is valid microscopically, and clearly not macroscopically here) and classical theory which does the opposite.
I would say that this link is very much a mysterious landscape. Would you contend that there is a theory that bridges this gap? And I don't mean expanding in powers of h, that only handles the equations not the overall axioms. You still have to prepare the system you are testing, and at some point you will always begin to be testing your own uncertainties in how you prepared it, rather than its fundamental dynamics-- like that air in your lungs. At some point you will react to that uncertainty by throwing up your hands and averaging over it, and voila, that's precisely where you enter the realm of classical physics and the pure state needs no collapsing because it already collapsed when you did that averaging. So this transition phase you speak of is not a physical change, it's a change in your analysis mode, and you will tailor it to get the best results.
It is simply by the big distance between "micro" and "macro" that we don't seem to be bothered by what actually makes nature "jump theories" in between.
I completely agree-- and a good thing too. Theories in that "middle ground" would be awful! But note the same thing can be said about classical theories like plasma physics. If you have a handful of particles, you track their positions and momenta. Add more particles and that becomes unwieldy, so you make an "awful transition" into a realm with many more particles, the kinetic level, where you recover a comfortable stance using "distribution functions". But it's still a pain to track the history of all the particles that go into the distribution function, so as you start to get more collisional "shuffling", you next make an "awful transition" into the fluid domain, and with enough collisions you again recover the comfort zone of magnetohydrodynamics. We are very lucky that these "awful transitional" regions are relatively narrow next to the full dynamical ranges we are interested in, or else, quite frankly, I wouldn't be doing physics! So this is nothing new in quantum mechanics.
In such a viewpoint, there's no need to talk about things like decoherence. At a certain point, you simply DECIDE to say that now, we switch to classical, no more superpositions.
But we don't just "decide" when a measurement has occurred in one of our experiments-- we actually have to engineer a classical system with the express purpose of decohering some quantum state. It's like eating a watermelon-- you don't just decide at some point to shove the fruit into your mouth, you have to find a way to slice it first. That involves physical interaction with the system in question, and that interaction will at some point allow us to eliminate the need to consider superpositions and instead return to the comfort zone of a purely probabilistic approach. And as we all know in quantum erasure experiments, it is very important to pay painstaking attention to what physical interaction is actually occurring before we can conclude we've "made it" to that zone.
You can do that whenever you feel like not following through the quantum interactions anymore. A photon interacting with an electron can be "classical" or "quantum" according to how much pain you want to give yourself.
That is true. But if one gets pain with no increase in predictive power, one has a bad pedagogical approach. Like the state of a cat. Perhaps you are objecting to my assertion that "a cat isn't in a pure state", when instead I should have said "it benefits us nought to imagine that a cat as a whole is in a pure state, as we have no way to control that kitten-state at the beginning of our experiment, and no way to measure it at the end". As such, I see it as an imaginary idea, an example of taking our axioms too seriously at one level but ignoring the other axioms we need to do science.
You can call a photo-electric effect a "measurement", and if you stop there, that can be good enough. You can also call it a quantum-mechanical interaction, and careful experimenting might give you some interference effects. So if you decide to study that, it is still "in the quantum world", but if you don't bother, well then it was in fact already classical.
You are saying that we tailor our descriptions to the experiment we are interested in. I totally agree! So what experiment are we interested in when we use the pure state of a whole cat?
) and also the "relational interpretation" by Rovelli.
