Why is Schrodinger's Cat only a thought experiment?

[DaveC426913]

The explanation I've heard is that quantum superposition is an atomic-scale phenomenon, that it makes no sense to apply it to a macro-scale object such as a cat.

But that's not what the experiment is doing. The radioactive isotope is subject to quantum effects, and it seems to follow that the result can be detected (and thus acted upon) at a macro-level.

So, why would the cat not exist in two states?

 

[peter0302]

Well, it would according to the many-worlds interpretation. The worlds would split as soon as the cat interacted with anything else in a theremodynamically irreversible way.

In any other interpretation, you'd have to define what it means for the cat to "exist" in two states. The cat certainly knows whether it's alive or not, so from his perspective there's only one state. From the outside world's perspective, the state is one of ignorance. Mathematically, it's in superposition, and so the wave function as calculated by the outside observer would indeed reflect both states. So in a sense, the cat *does* exist in both states as far as the outside world is concerned. But are there literally two cats, or is the superposition of states nothing more than a fancy way of saying that we don't know the cat's state? It's a matter of interpretation.

 

[turbo]

Schrodinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour. Penrose uses this example in his popular lectures on the possibility of unifying quantum physics with classical physics.

 

[DaveC426913]

Schrodinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour.

I know, but why does it not work? Where does it fall apart?

Does it indicate that the isotope particle is not really in a superpsoed state?

 

[peter0302]

I know, but why does it not work? Where does it fall apart?

It falls apart when you try to assign physical meaning to the wave function. Only then do you have to ask the question whether the cat is "really" alive or dead. The wave function tells you the probability amplitudes of the cat's various possible states, and works perfectly well as long as you don't try to use it for anything other than calculating probabilities.

And again, if you believe in MWI, then there literally ARE two cats, with the universes splitting as the cats interact with the rest of the world.

Does it indicate that the isotope particle is not really in a superpsoed state?

The isotope is absolutely in a superposed state as far as the ignorant observer is concerned. As far as the cat is concerned, it's not. Now, you can start getting really philosophical and ask if the cat is intelligent enough to be considered an observer - that's really stretching the bounds of meaningful science if you ask me. Again, as long as you treat the wavefunction as nothing more than probability amplitudes, there is no paradox. If you try to assign deeper meaning to it, then you run into trouble, and I believe MWI is the only thing you can use to make any sense of it.

 

[DaveC426913]

Now, you can start getting really philosophical and ask if the cat is intelligent enough to be considered an observer

Well, observation has a specific meaning in this context, and it has nothing to do with intelligence. A camera could be an observer.

 

[jostpuur]

Schrodinger was posing what he considered an absurdity to point out what he felt was a disconnect between deterministic classical physics and quantum theory. Clearly a cat cannot be both alive and dead at the same time, and opening the box after an hour to observe whether the cat is dead or alive does not collapse the wave-form of the cat (a macroscopic being), it simply tells us that the radioactive material either did or did not decay during the previous hour. Penrose uses this example in his popular lectures on the possibility of unifying quantum physics with classical physics.

Clearly, according to the quantum mechanics, the cat will be in superposition of being alive and dead at the same time. Combining this with your claim, we arrive at the source of the paradox. Two claims, both clearly true, both contradictory. That's why we call it a paradox! IMO ignoring the paradox only tells about lack of understanding of quantum mechanics.

Why is Schrodinger's Cat only a thought experiment?

I believe I can answer this: Because a physical experiment would be useless. There is no interferences for a macroscopic objects, so you cannot prove the existence of the superposition.

Classical theory: The cat will be either dead or alive in the closed box. When you open the box, you see the cat being dead or alive.

Quantum theory: The cat will be in superposition of being dead and alive in the closed box. When you open the box, the cat's wave function collapses, and you see the cat being dead or alive.

The experimental result: When you open the box, the cat is dead or alive.

An actual experiment wouldn't tell us anything. That is why this is a thought experiment. Somebody might claim that the Occam's razor instructs us to abandon the hypothesis of cat being in superposition, since it is so complicated idea, and cannot be checked by experiment, but IMO this is invalid use of Occam's razor. This is a fact: Whenever the predictions of classical and quantum theory differ, the experimental result is that quantum theory is right. So IMO it seems simplest to assume, that the quantum theory is right also when it cannot be checked.

In any other interpretation, you'd have to define what it means for the cat to "exist" in two states. The cat certainly knows whether it's alive or not, so from his perspective there's only one state. From the outside world's perspective, the state is one of ignorance. Mathematically, it's in superposition, and so the wave function as calculated by the outside observer would indeed reflect both states. So in a sense, the cat *does* exist in both states as far as the outside world is concerned. But are there literally two cats, or is the superposition of states nothing more than a fancy way of saying that we don't know the cat's state? It's a matter of interpretation.

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

 

[lbrits]

I know, but why does it not work? Where does it fall apart?

Does it indicate that the isotope particle is not really in a superpsoed state?

One particular modern viewpoint is that the cat will be both alive or dead, but will unitarily evolve into a definite state because superimposed states tend to be unstable. Read up on Einselection ( http://en.wikipedia.org/wiki/Einselection ) and if you are familiar with density matrices, I invite you to take a look here: http://www.physics.thetangentbundle.net/wiki/Quantum_mechanics/einselection

 

[peter0302]

Well, observation has a specific meaning in this context, and it has nothing to do with intelligence. A camera could be an observer.

That's not exactly right. The pure form of the Copenhagen Interpretation is agnostic as to what qualifies as observation and what doesn't. Some people believe that intelligent observatoin is actually required for wave function collapse. I once accidentally offended someone on here quite seriously by calling those people nuts, but apparently it's not without its supporters.

 

[belliott4488]

The subject line of this thread made me think you were asking what's wrong with putting a cat in a box with a vial of cyanide with a random trigger ...

 

[DaveC426913]

An actual experiment wouldn't tell us anything.

I hadn't thought of it that way. The test is not falsifiable.

Although I think that's not the real reason why this is only a thought experiment.

 

[DaveC426913]

That's not exactly right. The pure form of the Copenhagen Interpretation is agnostic as to what qualifies as observation and what doesn't. Some people believe that intelligent observatoin is actually required for wave function collapse. I once accidentally offended someone on here quite seriously by calling those people nuts, but apparently it's not without its supporters.

I am of the pure camp.

 

[nanobug]

So, why would the cat not exist in two states?

Decoherence! The isotope needs to interact with the mechanism that breaks the vial. This mechanism is macroscopic. Entanglement with the particles of this mechanism will eliminate superposition, resulting in classical probabilities for the outcome.

 

[jostpuur]

Decoherence! The isotope needs to interact with the mechanism that breaks the vial. This mechanism is macroscopic. Entanglement with the particles of this mechanism will eliminate superposition, resulting in classical probabilities for the outcome.

Decoherence eliminates interference, not superposition.

 

[lbrits]

Decoherence eliminates interference, not superposition.

Well... actually... you can eliminate superposition by changing basis... so decoherence can also eliminate it, for what it's worth.

 

[vanesch]

So, why would the cat not exist in two states?

I think the obvious answer is that we all like cats, and we are not going to do cruel things to them

Seriously, MWI-people claim that the cat DOES exist in two states, of which we are only aware of one of them (and other "we's" are aware of the other state).

 

[Hurkyl]

To my knowledge, only three options are offered by all of the main interpretations of quantum mechanics are:

(1) You see a cat that's dead, or you see a cat that's alive.
(2) You are actually in a superposition of states, some of which see a dead cat, some of which see a live cat, and none of which see any sort of ambiguity.
(3) Both (1) and (2) are valid analyses.

 

[LURCH]

I hadn't thought of it that way. The test is not falsifiable.

Although I think that's not the real reason why this is only a thought experiment.

I notice that you posted this last night. Having had a chance to sleep on it, do you still have the same opinion? I myself am quite convinced that this is exactly the reason this test is not performed in reality (using something other than a live cat, of course).

 

[lbrits]

The test is very falsifiable... Take a beam splitter and shine one part of the beam on the alive/dead cat and allow the other to pass straight through. Recombine the beams onto a detector. I believe you should get a different interference pattern based on whether the cat is alive/dead/superposition.

I didn't say the test was practical, though.

 

[jostpuur]

The subject line of this thread made me think you were asking what's wrong with putting a cat in a box with a vial of cyanide with a random trigger ...

I think the obvious answer is that we all like cats, and we are not going to do cruel things to them

this is exactly the reason this test is not performed in reality (using something other than a live cat, of course).

You are so excessively ethical! The medical industry already uses animal experiments for scientific purposes. Why not theoretical physics too!?

 

[jostpuur]

Well... actually... you can eliminate superposition by changing basis...

Like instead of using basis

<br /> |\psi\rangle_{\textrm{cat is alive}},\;|\psi\rangle_{\textrm{cat is dead}}<br />

we choose a new basis

<br /> |\psi\rangle_1 = |\psi\rangle_{\textrm{cat is alive}} + |\psi\rangle_{\textrm{cat is dead}}<br />

<br /> |\psi\rangle_2 = |\psi\rangle_{\textrm{cat is alive}} - |\psi\rangle_{\textrm{cat is dead}}?<br />

Now the cat won't be in superposition of two basis vectors, but this is not a very convincing trick if you wanted to solve the Schrödinger's paradox!

so decoherence can also eliminate it, for what it's worth.

You put the word "so" there, as if the previous comment somehow explained how decoherence removes superposition

The test is very falsifiable... Take a beam splitter and shine one part of the beam on the alive/dead cat and allow the other to pass straight through. Recombine the beams onto a detector. I believe you should get a different interference pattern based on whether the cat is alive/dead/superposition.

This is only a complicated way of opening the box.

 

[lbrits]

Like instead of using basis

<br /> |\psi\rangle_{\textrm{cat is alive}},\;|\psi\rangle_{\textrm{cat is dead}}<br />

we choose a new basis

<br /> |\psi\rangle_1 = |\psi\rangle_{\textrm{cat is alive}} + |\psi\rangle_{\textrm{cat is dead}}<br />

<br /> |\psi\rangle_2 = |\psi\rangle_{\textrm{cat is alive}} - |\psi\rangle_{\textrm{cat is dead}}?<br />

Now the cat won't be in superposition of two basis vectors, but this is not a very convincing trick if you wanted to solve the Schrödinger's paradox!



You put the word "so" there, as if the previous comment somehow explained how decoherence removes superposition



This is only a complicated way of opening the box.

My first statement elucidates the fact that it isn't the superposition that gets people in knots, but the direction the state is pointing in. So either all states are equally good, and detractors should just shut up, or that some states seem "preferred", and we should figure out why. (Said differently, if you buy the whole wavefunction collapse argument, why can't we simply collapse it into \left|\psi\right\rangle_1 etc.?) Personally I believe that environmental eigenstate selection gives a decent explanation.

My second statement, a "complicated way of opening the box", eliminates the possibility that the act of measurement will cause a) collapse or b) decoherence, e,g, by a macroscopic observer. Of course, the cat could still observe itself (thereby violating linearity/unitarity of QM), but I digress... See statement 1.

 

[Manchot]

I regularly use http://www.randomnumbers.info/ as a type of "quantum coin flip." In other words, I am a type of living Schrodinger's cat. :-D

 

[minimal]

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

Doesn't the many worlds interpretation SERIOUSLY violate the first law of thermodynamics though? The only way I think you can get around that is to argue that time doesn't exist (as the common conception) and all possible states ever exist simultaneously.

 

[Ken G]

Clearly, according to the quantum mechanics, the cat will be in superposition of being alive and dead at the same time.

Quantum mechanics does not say that because a combined cat/apparatus state does not have to project onto a pure (or "superposition") state for the cat alone. This is a common misconception you see in a lot of places. But as Hurkyl said, the real issue is whether or not the entire system (including you, importantly), can be in a superposition state or not. That is not at all the same as asking if the cat can be.

Combining this with your claim, we arrive at the source of the paradox. Two claims, both clearly true, both contradictory. That's why we call it a paradox!

But it isn't a paradox, there is no difficulty in resolving it-- the real problem is we have multiple choices of how to do it! (Again see Hurkyl's post.)

Quantum theory: The cat will be in superposition of being dead and alive in the closed box. When you open the box, the cat's wave function collapses, and you see the cat being dead or alive.

Again, this is not what quantum theory says. Quantum theory says that "opening the box" means projecting the cat onto a state you can label "alive" or "dead", that's just what you mean by opening the box, however you do it. For simple systems, that involves "collapsing the wave function", but a cat doesn't have a wave function. Even for quantum systems, however (which are "systems usefully treated using wave functions"), collapse occurs for a particular reason-- you intentionally forced them to project onto a certain basis. You collapsed it on purpose, in other words, it wasn't anything mysterious. What is mysterious is why all we can get is a statistical prediction of how that collapse will play out, but there may not be any resolution of that problem-- it may be all we can do (it certainly is so far).

Somebody might claim that the Occam's razor instructs us to abandon the hypothesis of cat being in superposition, since it is so complicated idea, and cannot be checked by experiment, but IMO this is invalid use of Occam's razor.

It can be checked. If the alive cat is standing, and the dead cat is lying down, then you can easily check for interference between the two states. The beamsplitter approach has already been mentioned by lbrits.

This is a fact: Whenever the predictions of classical and quantum theory differ, the experimental result is that quantum theory is right. So IMO it seems simplest to assume, that the quantum theory is right also when it cannot be checked.

But a standing/lying cat that you could send a light beam through is not the prediction of quantum mechanics. To use that language, you would have to be talking about the projected state of the cat, and any such projection will destroy the superposition you are claiming to exist.

Wise words! IMO the solution to the paradox lies in the many worlds interpretation, and not in restricting the quantum theory to the microscopic objects only.

I would go the opposite direction-- restrict quantum theory to the realm of wherever wave functions are actually useful, which excludes the realm of the experimenter and suggests Hurkyl solution #1. Anything else just seems like semi-magical philosophical baggage to me.

 

[Hurkyl]

Anything else just seems like semi-magical philosophical baggage to me.

Actually, #1 is the one with extra baggage. #1 postulates that, in addition to the framework that QM requires to describe reality, there is an ill-defined and essentially untestable process that magically transitions the universe out of a generic quantum state and into one that more closely resembles certain pre-conceived philosophical notions about how the universe should behave.

If you like sticking to pre-conceived notions, or simply believe that quantum mechanics has not yet stood the test of time, then #1 is good. But, alas, it's the least desirable if you believe that scientific theories should be the primary motivator of natural philosophy.

 

[Ken G]

Actually, #1 is the one with extra baggage. #1 postulates that, in addition to the framework that QM requires to describe reality, there is an ill-defined and essentially untestable process that magically transitions the universe out of a generic quantum state and into one that more closely resembles certain pre-conceived philosophical notions about how the universe should behave.

I don't agree there. That process is neither ill-defined nor magical-- it is the process of science. If you look at how quantum mechanics is actually tested, absent of all philosophical baggage, you find that it involves the setup of an apparatus that ignores, neglects, or averages over all information that is not deemed important for the experiment at hand (we, for example, might use light from the Sun, or a laser, never worrying about the history of that light or its entanglements-- we pretend our apparatus is a closed system with known inputs, which it is not). This very setup of the apparatus means we do not have a "total pure state" on which we are carrying out our observations, but we don't care-- we only wish to treat what we are testing, so we may, for example pretend that our initial state is a statistically mixed state (like a cat).

Then, if that wasn't untrue enough to the axioms of quantum mechanics, the next thing we do (after time evolving the initial conditions, that part we might expect to unfold quantum mechanically) is to intentionally couple the quantum system to something we can rely on to behave classically-- the detection apparatus. What is "ill-defined" or "magical" about that? We chose to do it, and then get all bothered when the results appear paradoxical when viewed quantum mechanically! If you can name an experiment that tests quantum mechanics that never invokes the use of a classical apparatus that is chosen expressly to behave classically, then I can agree with your stance.

Physically, what is happening when we choose such a "classical apparatus" is that we are coupling in all kinds of untraceable noise modes that intentionally decohere the quantum system we are testing, and project it onto a statistically mixed array of possible outcomes. But the point is, we very intentionally decided to do that, and we always do-- because science is at its heart a classical endeavor. A quantum scientist might do things very differently, but we don't know how such a scientist could be intelligent...

 

[Hurkyl]

That process is neither ill-defined nor magica

The unitary part of quantum mechanics predicts:
(1) Classical apparatuses cannot exist
(2) Quantum apparatuses can simulate classical ones
(3) Thermodynamics can make the simulation's flaws essentially undetectable

The Copenhagen interpretation postulates that the actual, physical state of the universe undergoes an effectively undetectable 'collapse', which violates both the unitary and relativistic parts of quantum mechanics. To the best of my knowledge, the CI does not give any hints about the mechanism of collapse, nor any theoretical indication about where and when a collapse should occur. If there has been progress in these respects, please share.


In my opinion, the primary mistake in the CI is the insistence upon using unconditional probabilities. Consider the classical setup where Alice and Bob each have half of an entangled pair of qubits. If Bob measures his qubit and gets a |1>, then it is impossible, even in principle, for the experiment to give any information about

P(Alice gets a |0>, given that Bob gets a |0>),

from which it follows that it is impossible for this experiment to give any empirical evidence regarding

P(Alice gets a |0>).

However, this is precisely the probability that the CI insists is being tested when it concludes that wavefunction collapse must occur! This is based upon an assumption of statistical independence, which the CI prefers to retain, even at the cost of sacrificing the best tested laws of nature in the history of mankind.

 

[Ken G]

The unitary part of quantum mechanics predicts:
(1) Classical apparatuses cannot exist
(2) Quantum apparatuses can simulate classical ones
(3) Thermodynamics can make the simulation's flaws essentially undetectable

I would say that this argument inverts the process of how science is done. Science is not done by asserting axioms and seeing how their ramifications connect to reality, monkeying with our understanding of reality as necessary. Instead, it starts with real phenomena, like the way we interact with our measuring devices and how we rely on those devices to behave when we formulate the meaning of "objective observation". Then we take that interaction as the fundamental reality that we wish to understand, and we form axiomatic structures to attempt to simulate it. So prediction (1) is ascientific, and prediction (2) is the purpose of quantum mechanics, so it is not a prediction of quantum mechanics. You will need to cite an experiment done with a "quantum apparatus" to show the logic in the direction you are applying it (the main problem being, the human mind has built science around classical behavior). I don't know what you mean by prediction (3), perhaps elucidating that would help.

The Copenhagen interpretation postulates that the actual, physical state of the universe undergoes an effectively undetectable 'collapse', which violates both the unitary and relativistic parts of quantum mechanics.

I would call that the "Heisenberg skew" to the Copenhagen interpretation, but Heisenberg was engaging in philosophy-- I much prefer the approach Bohr finally settled on, which to me is that we were never talking about the "physical state of the universe", for all we have access to is science. The scientific approach is to engage in behaviors that intentionally accomplish the "collapses" you refer to, but these are not collapses in the "state of the universe", they are simply collapses in the information that we have chosen to track. The fingerprints of the physicist is all over the result, as is always the case in science-- treating it like an abstract event happening to the "state of the universe" is to turn science into philosophical baggage, forgetting along the way what defines science in the first place (i.e., Galileo not Plato).

As for "nonunitariness", the unitarity applies only to the complete system, which includes us, as you yourself pointed out. As we have no way to step outside that system to test its unitariness, we find that unitariness is actually only an effective concept-- a concept that applies imperfectly to subsets only to the extent that they are treatable as closed systems. Measurement violates that closure requirement, so we do not expect measurement to be unitary, when projected onto the state of the system being measured (which is what science does). That holds unless we subsume our apparatus into a larger one that includes us-- betraying the entire point of objective science as something to be distinguished from untestable philosophy.

To the best of my knowledge, the CI does not give any hints about the mechanism of collapse, nor any theoretical indication about where and when a collapse should occur. If there has been progress in these respects, please share.

It is nothing new in science to note that we cannot access the details of a process that we are treating statistically. It is no less true in classical physics than quantum mechanics-- we never had any idea that wasn't purely statistical about how to predict the weather next January. So I don't see why we should be bothered that quantum mechanics yields inherently statistical results when we project our predictions onto real or hypothetical observations in the future. No one ever promised we could predict everything-- I find it much more amazing that we do so well, than am I bothered by our need to resort to statistical predictions in quantum mechanics. Who said reality was deterministic? Even in classical mechanics, that was always just a philosophical pretense-- it never came from science, again because that would be inverting the proper logic of how we choose axioms to describe reality, not interpreting reality to fit our axioms.

In my opinion, the primary mistake in the CI is the insistence upon using unconditional probabilities. Consider the classical setup where Alice and Bob each have half of an entangled pair of qubits. If Bob measures his qubit and gets a |1>, then it is impossible, even in principle, for the experiment to give any information about

P(Alice gets a |0>, given that Bob gets a |0>),

from which it follows that it is impossible for this experiment to give any empirical evidence regarding

P(Alice gets a |0>).

I don't understand your point here-- the CI allows for joint wave functions, and joint wave functions successfully pass every experimental test you can name in regard to Alice and Bob-- even ones where Alice and Bob are using different wave functions to reflect different information. The desire to make the wave function "something real" that has a unique existence outside of how Alice or Bob is using theirs is pure philosophical baggage, quantum mechanics works fine without that.

However, this is precisely the probability that the CI insists is being tested when it concludes that wavefunction collapse must occur! This is based upon an assumption of statistical independence, which the CI prefers to retain, even at the cost of sacrificing the best tested laws of nature in the history of mankind.

The CI does not make any incorrect predictions in any known experiments, I think you are misinterpreting what a wave function collapse is. It is a reflection of the change in information in some physicists head-- that's what it is, anything more is something you may choose to add if you have a philosopical bent, but the science doesn't care, in regard to testing predictions. I'm saying that if you look at what science is, rather than philosophize about what reality is, the problems vanish and the CI works swimmingly (the minimal Bohr version).

 

[Hurkyl]

Science is not done by asserting axioms and seeing how their ramifications connect to reality, monkeying with our understanding of reality as necessary.

To further our understanding of reality is one of the primary reasons we have the natural sciences, is it not? The bulk of your post appears to insist the opposite -- we force science to conform with some a priori notion of how reality is supposed to behave. I suppose attitudes like that are why we have the famous quote, "Science progresses one death at a time."

 

[vanesch]

I would go the opposite direction-- restrict quantum theory to the realm of wherever wave functions are actually useful, which excludes the realm of the experimenter and suggests Hurkyl solution #1. Anything else just seems like semi-magical philosophical baggage to me.

Although it is of course the practical way of doing quantum mechanics, it has a problem of principle. It would mean that the laws of physics change according to whether we deem them useful or not. One might prefer a more universal concept of "law of nature", which goes beyond "where they are useful". Do we consider that two marbles don't have a gravitational attraction, just because that's most of the time not useful ? Is for instance, Newton's law of gravity not "valid" for marbles, unless we are using them in a kind of http://en.wikipedia.org/wiki/Cavendish_experiment" ?
In other words, does a pair of marbles exert a gravitational force one on the other always, or only when it is useful ?

Are systems describable by quantum theory, always, or only when it is useful ?

 

[vanesch]

I would say that this argument inverts the process of how science is done. Science is not done by asserting axioms and seeing how their ramifications connect to reality, monkeying with our understanding of reality as necessary. Instead, it starts with real phenomena, like the way we interact with our measuring devices and how we rely on those devices to behave when we formulate the meaning of "objective observation".

Well, before relativity, we could say the same thing about absolute time. Maybe the concept of "objective observation" is simply too naive an idea, in the same way as "absolute time" was too naive an idea. It starts with certain preconceptions, which are certainly very useful up to a certain point, but what gives us the right to think that they are absolutely inviolable ?

In my understanding, quantum mechanics puts in relativity the concept of "observation" in a similar way in which relativity put into relativity the concept of "time".

 

[Ken G]

To further our understanding of reality is one of the primary reasons we have the natural sciences, is it not?

Absolutely yes, to further that understanding-- not to impose it. The key is to start with reality not the axioms, because it is pure pipe dream that axioms are what reality "is" anyway. We are trying to retrofit the axioms to the experiments, and thereby gain that understanding-- but all too often we then mistake the understanding for the reality, inverting our priorities.

The bulk of your post appears to insist the opposite -- we force science to conform with some a priori notion of how reality is supposed to behave.

That is what I am saying the axiomatic approach does. Your "prediction (1)" above is doing that, when you try to use the axioms to model the experiment. The way we conduct the experiment is what is real, the axioms are the idealization-- doing it the other way around is forcing science to conform to the notions of your axioms.

I suppose attitudes like that are why we have the famous quote, "Science progresses one death at a time."

Well, Bohr is dead, last I checked, and his approach to QM is alive and well, and still predominantly used, with no signs of ever being any different outside of philosophical over-extrapolations of the meaning of quantum mechanics (like MWI). So I'd say it is a very foolish maxim in this case.

 

[vanesch]

Well, Bohr is dead, last I checked, and his approach to QM is still what makes the field advance. So I'd say it is a very foolish maxim in this case.

Point is, it was Bohr's

 

[Ken G]

Ah, good point-- though I doubt he meant it to be applied to him! Still, as I said, the evidence so far is that it won't be. I'd say he had an acute sense of what science really is, which is being somewhat lost amid today's grumblings about "many worlds", "multiverses", and "universal wave functions", not one of which has demonstrated a shred of predictive power. The best thing physics ever did was separate from natural philosophy, and "just when we thought we were out, they pull us back in."

 

[reilly]

Let's talk about cats. Barring a few exceptions- accidents, disease,…-, a cat alive now will be alive for some time. So, assuming continuity of state's temporal development, outside or inside the cat will be and remain alive until an unfortunate radioactive decay occurs.

Yes, with a real cat there is quantum superposition -- how could it be otherwise? And we know cats and other live things follow a dynamical path of quantum states. But, the alive states clearly have millions of individual state-amplitudes in very small range; the noise states have virtually no amplitudes at all. Thus the quantum superposition , for all practical purposes, is among alive-states. That is, the cat is alive, according to quantum mechanics and to a common sense interpretion of direct evidence..
Regards, Reilly Atkinson

 

[Ken G]

Although it is of course the practical way of doing quantum mechanics, it has a problem of principle. It would mean that the laws of physics change according to whether we deem them useful or not.

In other words, it is absent of unnecessary philosophical baggage? Because your statement is just the way we do science. This is really my point, that "believing in axioms" is to forget what science is, and invert the normal logic reality --> choosing appropriate axioms, instead making it: choosing universal axioms --> reality. The latter is what I would call natural philosophy, and look where it got Aristotle. The former is science.

Do we consider that two marbles don't have a gravitational attraction, just because that's most of the time not useful ?

We predict that an experiment sensitive enough to detect that will indeed show it, because we have no reason to doubt the presence of gravity in such a system. But we do not include it in any experiment that is not sensitive enough. The point is, the axioms of gravity are expected to apply to marbles because we have not found that they don't, but if we did an experiment that found they don't, we would just say "oh yeah, we're doing science, not philosophy, now let's figure out why marbles don't have mutual gravity".

In other words, does a pair of marbles exert a gravitational force one on the other always, or only when it is useful ?

The definition of "useful" is "predictive". So your question is internally inconsistent, even within the confines of science as science rather than science as philosophy.

Are systems describable by quantum theory, always, or only when it is useful ?

Again you invert the question-- the real question is, when is it useful to apply quantum theory? What other question do you think is a scientifically posable question?

 

[Ken G]

Well, before relativity, we could say the same thing about absolute time.

Exactly, a perfect example of the flaw of asking reality to conform to our axioms. We always think "ah, but this time we got it right". When do we learn?

Maybe the concept of "objective observation" is simply too naive an idea, in the same way as "absolute time" was too naive an idea.

But there is a very important difference here. "Absolute time" was just a tool of science, to be discarded where it is not useful (and maintained where it is, as we do all the time). But "objective observation" is not a tool of science, it is part of the modern definition of science. Absolute time was not in the instructions for doing science, but objective observation is. Perhaps you are suggesting that science needs to evolve into something different, more akin to natural philosophy, but my whole point is that science only made its breakthrough when it evolved away from natural philosophy, so I see that suggestion as a terrible step backward. Maybe it will just be a pendulum, back and forth over time, but I think the breakthroughs will come during what I might think of as the forward swings, not the backward ones.

In my understanding, quantum mechanics puts in relativity the concept of "observation" in a similar way in which relativity put into relativity the concept of "time".

I'm saying it's not "quantum mechanics" that does that-- it's science.

 

[Ken G]

Let's talk about cats.

Yes, this debate is quite reminiscent of the cat paradox issues, and I was hoping you might see this thread (as I know you are thinking along similar lines to what I'm advocating above). If one adopts an axiomatic approach, then there is a "universal wave function" that might be in a pure state (we don't even know that, by the way). If so, it will still not project even approximately onto a pure state of a cat, projections onto substates don't work that way. However, we the physicist may choose to average over everything we don't care to trace in that projection, and doing that will yield a mixed state for the cat subspace. We may know the cat is alive, and further project that mixed state onto the alive substates that conform to whatever knowledge we have about the cat (Siamese, female, what have you). So there's no way we are starting any quantum explorations of a cat where we are not starting in a mixed state for that object, but we can know the mixed state has essentially zero projection onto dead-cat mixed states.

Then we attach the cat to the decay device, and for some strange reason, we expect the pure state of the nucleus to imprint itself onto the cat. What quantum mechanics gives us that? If we analyze the cat as a mixture of alive-cat states, and couple it to the device, then reformulate the mixture, the reformulation itself will destroy any coherences that could have allowed the pure state of the nucleus to imprint on the cat. Also, noise in any device capable of killing a cat will also do that. So the "cat paradox" is simply wrong quantum mechanics, it's not even an issue for interpretation of quantum mechanics.

 

[Hurkyl]

Absolutely yes, to further that understanding-- not to impose it.

Then I am confused. Not only have you implied that quantum mechanics doesn't actually say anything about reality, but you have insisted there are facets of reality that science itself is not allowed to question.

We are trying to retrofit the axioms to the experiments, and thereby gain that understanding

That's a bad idea. Statistical learning has demonstrated retrofitting data is very prone to the problem of overfitting -- developing 'theories' that are capable of explaining past data, and little else.

Even conventional wisdom in science is that for a theory to be scientific, not only does it have to agree with past data, but it must make new predictions that can be tested by experiment! At the very least, predictions are one of the most important applications of scientific understanding.

-- but all too often we then mistake the understanding for the reality, inverting our priorities.

Yes. In fact you have made that mistake at least once in this very thread -- you have taken your understanding that measuring devices are classical, and have so thoroughly confused that with reality that you insist questioning that understanding would be ascientific!

That is what I am saying the axiomatic approach does.

The axiomatic method has nothing (directly) to do with reality -- it is an effective tool for studying theories. And, for the record, you are the only one in this thread talking about axioms.

 

[Ken G]

Then I am confused. Not only have you implied that quantum mechanics doesn't actually say anything about reality, but you have insisted there are facets of reality that science itself is not allowed to question.

Where on Earth did I say that quantum mechanics doesn't "say anything" about reality? It predicts reality, in the appropriate situations where we can use it. What else has it been demonstrated to do, I'm curious. Also, I regret that you read in the idea that I was saying what science was "allowed" to question, when in fact I was trying to point out what science is effective at questioning. We must watch the scientific process carefully or all kinds of mystical additions get piled on its back, weighing it down unnecessarily and reducing its separation from other non-evidence based pursuits.

That's a bad idea. Statistical learning has demonstrated retrofitting data is very prone to the problem of overfitting -- developing 'theories' that are capable of explaining past data, and little else.

If you think it is a bad idea, then I am curious how you imagine science occurs, other than by retrofitting axioms to existing data. I know, you will cite the axioms of relativity on the grounds of their symmetry and elegance, but I will point out we came up with them after we knew the speed of light was the same in all frames experimentally. You will cite the existence of the neutrino, but I will point out that this particle was suggested because of energy missing from an experiment, not because someone wanted it to be there. You will ask "but how did we know energy would be conserved", and I will say "we didn't-- we had to throw out countless theories that would have seemed brilliant and prescient had energy not been conserved". You will mention Dirac's positron, and I will cite this interesting Wiki (http://en.wikipedia.org/wiki/Dirac_sea) snippet:

"Initially, Dirac identified this hole as a proton. However, Robert Oppenheimer pointed out that an electron and its hole would be able to annihilate each other, releasing energy on the order of the electron's rest energy in the form of energetic photons; if holes were protons, stable atoms would not exist. Hermann Weyl also noted that a hole should act as though it has the same mass as an electron, whereas the proton is about two thousand times heavier. The issue was finally resolved in 1932 when the positron was discovered by Carl Anderson, with all the physical properties predicted for the Dirac hole."

Funny how the winners write the history, isn't it? We see that in reality, experiments played a huge role in understanding what positrons are. In virtually all cases, useful science has retrofit its axioms to the observations-- exactly what you are saying we should not do. Yes we sometimes advance when we extrapolate theories, and sometimes we do not-- without the ultimate authority of observations of reality, we would have no way to tell the difference, even if we pretend that we could.

Even conventional wisdom in science is that for a theory to be scientific, not only does it have to agree with past data, but it must make new predictions that can be tested by experiment! At the very least, predictions are one of the most important applications of scientific understanding.

I certainly would not dispute that science must predict, and it must lead to unification of familiarities. These are its two goals. The way it achieves both these goals is making observations, then approximating those observations using a retrofit axiomatic structure. The axiomatic structure then allows us to chart the unifications of familiarities (which we call "explanations"), and also to make quantitative predictions, which are then tested by the new observations the theory suggests we make. When the tests work, we say we have "good axioms for those kinds of situations", and we extrapolate those axioms as far as we can get away with, never being surprised when we hit a regime where we can't get away with it. Is this not a perfectly accurate description of the last five centuries of physics, since Galileo ripped it from the suffocating busom of natural philosophy? Why would we want to go back now?

Yes. In fact you have made that mistake at least once in this very thread -- you have taken your understanding that measuring devices are classical, and have so thoroughly confused that with reality that you insist questioning that understanding would be ascientific!

That is simply false. It is not my understanding that treats measuring systems as classical, it is scientists that do that. Need I list every experimental Nobel prize in the last century and cite the way the apparatus was treated classically, or will you instead provide a counterexample? That seems a normal thing to ask of you if you will claim that it is a "mistake" to say that scientists treat their apparatus classically, or that classical thinking is not built right into the very fabric of science. There will be some commotion, I imagine, when the first paper is ever published where the observed result is a superposition state of a measuring apparatus. No need to cite the SQUID at Stony Brook, I will simply tease out the places where its behavior was probed by classically-treated measuring devices-- i.e., where it made contact with science.

The axiomatic method has nothing (directly) to do with reality -- it is an effective tool for studying theories. And, for the record, you are the only one in this thread talking about axioms.

How is the axiomatic method a means for studying theories? I see it as what the theories are. And how can I be the only one talking about axioms, I thought we were discussing your claims about the ramifications of the "unitary part of quantum mechanics". That isn't about axioms? You don't seem to understand what I'm saying at all, I'm not sure where the disconnect is here-- I'm trying to be pretty clear (even direct, you might say, not one to mince words!).

 

[Hurkyl]

Where on Earth did I say that quantum mechanics doesn't "say anything" about reality?

I seems the obvious implication from your argument where you insisted that quantum mechanics is about "the information that we have chosen to track", and "we were never talking about the 'physical state of the universe'".

While this allows for the possibility that QM can predict the results of some experiments, your post looks like an explicit denial that the primitive notions of QM correspond to facets of "reality".

Also, I regret that you read in the idea that I was saying what science was "allowed" to question, when in fact I was trying to point out what science is effective at questioning.

And I am entirely unconvinced that science is ineffective at studying the nature of our measuring devices and how they behave.

If you think it is a bad idea, then I am curious how you imagine science occurs, other than by retrofitting axioms to existing data.

My next paragraph should have answered your question: progress happens when theories are developed capable of making predictions beyond the data upon which it was retrofitted.

I know, you will cite the axioms of relativity on the grounds of their symmetry and elegance,

Why would I do that? I don't see how such a citation, or those grounds, would be relevant to discussion.

In virtually all cases, useful science has retrofit its axioms to the observations-- exactly what you are saying we should not do.

That is not what I said -- my point is that retrofitting is not enough.

The way it achieves both these goals is making observations, then approximating those observations using a retrofit axiomatic structure. ... make quantitative predictions, which are then tested by the new observations ... we extrapolate those axioms as far as we can get away with ... Why would we want to go back now?

We shouldn't -- in particular, we should not turn our backs on this process when faced with a century of experimental confirmation that the universe is not classical.

Need I list every experimental Nobel prize in the last century and cite the way the apparatus was treated classically, or will you instead provide a counterexample?

That wouldn't be useful. The point of "predictions (2) and (3)" that I listed are that such behavior is consistent with quantum theory. This exercise wouldn't support your position that reality is classical unless you could find such an example where you could demonstrate that its behavior is inconsistent with quantum mechanics. Only then would you have empirical support for your assertions that measuring apparatuses are classical objects.

Until you do that exercise, your assertions are philosophical baggage -- they are unverified claims that the laws of quantum mechanics are suspended at unspecified places and times for no apparent reason.

How is the axiomatic method a means for studying theories?

The role of a set of axioms for a theory is very similar to the role of a basis for a vector space; e.g. the use of formal proofs from axioms to indicate assertions of a theory is very similar to the use of linear combinations of basis vectors to indicate elements of a vector space.

 

[DaveC426913]

Ok. I have decided to unask the question. You can all stop discussing it now.

 

[Ken G]

I seems the obvious implication from your argument where you insisted that quantum mechanics is about "the information that we have chosen to track", and "we were never talking about the 'physical state of the universe'".

Then I hope I have clarified that things which impart information, without specifying the "state of the universe", do not obviously imply that they have nothing to say about reality.

While this allows for the possibility that QM can predict the results of some experiments, your post looks like an explicit denial that the primitive notions of QM correspond to facets of "reality".

That all depends on what you mean by "correspond". If you mean "have something to do with", then obviously if they can predict reality under specialized conditions, they have something to do with the facets of reality. If you mean that the primitive notions "are real", then obviously that violates the definition of reality ("notion" = "reality"?). Unless you have an usual definition of that term?

And I am entirely unconvinced that science is ineffective at studying the nature of our measuring devices and how they behave.

You are dodging my question-- please cite an example of a measuring device that we do not treat classically in the process of doing science. Or, explain why the failure to come up with such an example is consistent with a claim that it is a "mistake" to think that science relies on treating its measuring devices classically, and in that sense is built on the back of classical thinking.

My next paragraph should have answered your question: progress happens when theories are developed capable of making predictions beyond the data upon which it was retrofitted.

Obviously. The issue is at what point those theories become so authoritative that their predictions can stand in for observational tests. In science, that answer is "never". However, we make the default assumption that we can use a good theory if we have no evidence to the contrary. Whether or not we can rely on them is up to the individual's risk assessment (imagine a transporter based on axioms of quantum mechanics that have never been used to build a transporter before. Are you the first to try it out?). The point I'm making, in regard to the CI, is that the ultimate authority is always experiment. The CI says that we use quantum mechanics to make predictions that are in a form suitable for comparison with experiment, i.e., confrontation with a classically-behaving instrument chosen for that express purpose. That's exactly what science is. Pretending that it is an axiomatic system for deciding what reality is "really doing" is pure philosophical baggage that at no point enters into any concrete scientific result. Or can you cite a place where it does? I'm not making this up, this is just the truth about how science works.

Why would I do that? I don't see how such a citation, or those grounds, would be relevant to discussion.

I was just saving you the trouble of that particular citation. Do you plan to cite anything at all to support your view?

That is not what I said -- my point is that retrofitting is not enough.

I never said it was enough, I said that is how we get the axioms we use in science. So saying "retrofitting is not enough" is just saying "choosing axioms is not enough". I realize that, the next step is testing them in various situations of interest, not asserting their reality-- the latter is simply not a step in science. So why is the CI so wrong for simply noticing that, in regard to quantum axioms? How does that deny that quantum mechanics has anything to do with reality?

We shouldn't -- in particular, we should not turn our backs on this process when faced with a century of experimental confirmation that the universe is not classical.

Obviously the universe is not classical, I never said it was! I said that our instruments for probing the universe must be treated classically, because we haven't the vaguest idea how to do anything else with them. I further pointed out that this decision on our part is what creates the tension with interpreting quantum mechanics, concepts like "wave function collapse", not the CI. The CI merely notices that that tension was put there by the way we always do science, which is, by the way, the only way that can give demonstrable results. MWI approaches, on the other hand, try to avoid this tension, but they are not demonstrable expressly because their implications cannot be tested with classical devices. Or will you cite a situation where a MWI prediction is demonstrable, or argue that science does not need to be objectively demonstrable, as floated by vanesch in recognition of this problem?

The point of "predictions (2) and (3)" that I listed are that such behavior is consistent with quantum theory. This exercise wouldn't support your position that reality is classical unless you could find such an example where you could demonstrate that its behavior is inconsistent with quantum mechanics.

My goodness, you think I'm arguing that "reality is classical"? You think I'm a quantum mechanics denier of some kind? Once more: reality is obviously not classical, but our ways of interfacing with it, to do science, are. Every quantum mechanical equation ever used to make a prediction did so by converting a quantum result into a classical response of a measuring device, no exceptions. If you don't think that statement is true, why do you keep dodging the need to cite evidence? I would love to be proven wrong, imagine what I could learn from a single counterexample.

Only then would you have empirical support for your assertions that measuring apparatuses are classical objects.

I need support for that? When you detect a photon in a photomultiplier tube, we need to discuss whether or not my interpretation of the charge I pull off my CCD is being treated classically? How do you read CCDs?

Until you do that exercise, your assertions are philosophical baggage -- they are unverified claims that the laws of quantum mechanics are suspended at unspecified places and times for no apparent reason.

I do that "exercise", every single day. Every time I see anything with my eyes, I am detecting photons in an optic nerve that responds classically. If I am looking at a dark room, and see a flash, do I say "look, a flash", or do I say "aha, I detect a superposition state over there"? How is the former not treating my eyes as classical detectors? My brain has no idea what else to do with that information. There's your "collapse of the wave function", we do it on purpose because we have no concept of anything else. Science is built on collapsing wave functions, because decohering complex correlations is how we think about the world. It is not reality that is classical-- we are.

 

[DaveC426913]

Damn.

 

[Ken G]

What's wrong with intellectually probing how the CI describes quantum mechanics as a science? Too argumentative? Sometimes the important things are worth a little argumentation, and your question is just the one to open that box. No personal aspersions are implied or intended, I wouldn't waste time on a debate unless with someone with a worthy opinion. The goal is to get to the truth-- that process doesn't always look like a Q&A, thank goodness.

 

[vanesch]

This is really my point, that "believing in axioms" is to forget what science is, and invert the normal logic reality --> choosing appropriate axioms, instead making it: choosing universal axioms --> reality. The latter is what I would call natural philosophy, and look where it got Aristotle. The former is science.

It is not about believing in universal axioms, it is exploring what a set of axioms would imply if it were rigorously valid.

We predict that an experiment sensitive enough to detect that will indeed show it, because we have no reason to doubt the presence of gravity in such a system. But we do not include it in any experiment that is not sensitive enough. The point is, the axioms of gravity are expected to apply to marbles because we have not found that they don't, but if we did an experiment that found they don't, we would just say "oh yeah, we're doing science, not philosophy, now let's figure out why marbles don't have mutual gravity".

We are now a bit confused. Imagine that we can, with a lot of pain, empirically show that there is a tiny gravitational attraction between two marbles. Now, the question is: is this because it are the *atoms* in the marbles that attract each other ? Or does the gravitational force only appear when there are enough atoms together to form a marble ? Now, you can then pull out your calculator, and show that we will have a lot of experimental difficulties to do the same experiment with atoms. In fact, you can even conclude that it will be experimentally *impossible* to ever find out whether two atoms, 1 cm one from the other, attract each other. However, nevertheless, Newtonian gravity gives you the *theoretical picture* that they do. But it is in the limit a non-scientific question, as it will be in practice undoable. It will never be possible to do the experiment where we put 2 atoms 1 cm one from the other, and measure their gravitational attraction. 1000 atoms, maybe, but not 2 atoms. So the question as of whether individual atoms undergo Newtonian gravity belongs to the realm of natural philosophy according to you. Nevertheless, the theoretical picture is crystal-clear. It would make the whole business more consistent *in principle* to assume that Newtonian gravity is *also* working in between two individual atoms, even though this is not open to experiment. The extrapolation to the two marbles attracting each-other then makes "axiomatic sense". It is a simple extrapolation of the theoretical concepts that were measurable at more macroscopic scales to the "whole of the world", even in those domains where it is impossible to measure it. It makes the whole story much more coherent. Otherwise we would have to invoke strange principles of non-attracting atoms that, when put together, at a certain point suddenly "wake up their gravitational holism". And we would run in all kinds of paradoxes, like things such as conservation of momentum and all that, if we tried to pin down exactly WHEN the gravitational interaction was "switched on". So it would be simply a much "cleaner" picture to ASSUME that, although it is unmeasurable, individual atoms do attract one another.

Well, the same applies to quantum theory. We predict that experiments, sensitive enough to do "cat interference experiments" (these are complicated EPR-style experiments, where we measure the high-order correlation function of all things the cat interacted with), if cats are in an entangled superposition, will give different results than if the cats are NOT in such situation. Unfortunately, as with the two atoms, such experiments are impossible to perform. Nevertheless, they are simply the extrapolation of the principles we've seen at work in more microscopic situations. We've never encountered a situation where this principle of superposition was NOT valid (just as we've never encountered a situation where two tiny masses did clearly NOT attract one another) ; but we've encountered situations in which we could predictably tell that we wouldn't see any difference (in the same way as we could predictably tell that we wouldn't observe any effect of attraction between small clusters of atoms). We run in a whole bunch of paradoxes when we try to pinpoint exactly WHEN the superposition principle stops working. We would have to explain by new principles how it comes that superposition is "switched off" and no matter how we do it, we always run into problems of one kind or another.

So the "natural extrapolation" is to assume that the superposition principle applies to everything, even there where we can't observe it - in the same way as we assume that individual atoms do obey Newtonian gravity, even though we can't observe it. It makes the whole picture much more consistent. Now, concerning observation, it was Einstein who said that it was *the theory* that had to tell you what was observable. Well, lo and behold, *keeping superposition* doesn't alter the consistency of observations! The conditional links that happen to exist between different "memory states" of the observer in every term of these superpositions are consistent. The "projection" on the "internal inconsistency" states is zero. The only thing we now find, conceptually, is that observation histories also exist in superpositions. But in the same time, we also find that there's no way to find this out (to find a measurable quantity which indicates "yes there are superpositions of consistent histories"). All these observables that would indicate such a superposition (except the empirically unavailable ones, of high correlation order) indicate that there is none. This is what decoherence learns us.

In other words, *if we assume* that there is superposition everywhere, then from that hypothesis follows that we should see them for microscopic systems, and that they become impossible to measure for macroscopic systems. Exactly as we observe.

This looks a lot like *if we assume* that individual atoms have gravitational attraction, then from that hypothesis follows that we can observe gravitational attraction at "marble" level, but not at "atomic" level. Exactly as we observe.

Again you invert the question-- the real question is, when is it useful to apply quantum theory? What other question do you think is a scientifically posable question?

So, in the end, do you think that individual atoms undergo gravitational attraction, 1 cm one from the other, or not ? And given that this is, according to you, not a scientific question, don't you find it a pity that many textbooks make students calculate such kinds of quantities which, according to you, have no physical meaning, just to show that we should expect the effect to be unobservable ?

What's the most scientific approach ? *Assume* that two atoms attract, plug the quantities in Newton's equation, and find out that the effect is so tiny that you won't be able to observe it (and if we do, be surprised and try to find out why), OR
postulate that, given that we can't observe the attraction of two atoms 1 cm one from the other, Newton's equation is NOT VALID ?

 

[Hurkyl]

because we haven't the vaguest idea how to do anything else with them.

Yes, we do -- we can, for example, invoke decoherence to suggest, with high probability, the <measuring device, experiment> system transitions into a purely mixed state. Invoke past experience that it does so in a consistent manner. Use conditional probabilities, rather than collapses.

If we do this, the observed behavior of measuring devices is, as far as we know, consistent with unitary evolution.

My goodness, you think I'm arguing that "reality is classical"?

Yes -- at least, I thought that you were arguing certain parts of reality assumed a priori to be classical, and that science cannot be used to question that assumption.

Now, it looks like it might be that you understand certain parts of reality as classical simply because you have not yet formulated any other understanding -- and you are asserting that everybody in the world currently suffers this limitation, and that it is insurmountable.

Once more: reality is obviously not classical, but our ways of interfacing with it, to do science, are.

Our interface with reality is real, isn't it? Shouldn't it follow that the interface is also nonclassical?

I do that "exercise", every single day. Every time I see anything with my eyes, I am detecting photons in an optic nerve that responds classically.

You only did half of the exercise. You apply your classical viewpoint in a domain where it is known to be consistent with reality -- but you have not also shown that reality is inconsistent with a quantum viewpoint!

For comparison, I will point out that architects often assume the Earth is flat when they design buildings, and when the building is built, it works out exactly as the architect foresaw. Is this exercise a demonstration that the Earth really is flat? No -- because the building is small, the results are also consistent with the round Earth hypothesis, and so this exercise is of no use in distinguishing the two.

In order for this exercise to distinguish the flat and round Earth hypotheses, we would need a situation where they make different predictions, such as a very large building. (And, as expected, very large buildings are consistent with the round Earth hypothesis, and inconsistent with the flat Earth hypothesis)

The exercises you propose are the same -- they are situations where classical and quantum physics are not known to be observably different, and so they shed no light on the issue!

There's your "collapse of the wave function", we do it on purpose because we have no concept of anything else.

I do, and I'm pretty sure I'm not the only one.

 

[reilly]

Overfitting

That's a bad idea. Statistical learning has demonstrated retrofitting data is very prone to the problem of overfitting -- developing 'theories' that are capable of explaining past data, and little else./
............
RA(Although I'm talking statistics here, my colleagues and I used the approaches and sensibilities of physics for business and government problems -- KISS, be empirically driven. Further there is no body of theoretical research that does a decent job of providing real insight into the behaviors in the marketplace. So, in fact, underlying what I discuss is my physics persona.)

Several things --I spent many years of doing business analytics and market research dealing with issues like forecasting daily news stand sales, stand-by-stand for the Boston Globe, or determining who is likely to purchase a GM vehicle after visiting the GM Pavillion in Disney Wrold -- based on seven different intercept interviews. Oh, and I've taught statistics and business research as well. So, I like to think I know a bit about issues like overfitting. In fact, more than a few corporate clients know about overfitting, and will hammer the consultant who tries to offer the same.

So, yes overfitting can be a problem, but a solvable one. And beware of the analyst who disregards overfitting, or collinearity or claims great success with an R^^2 of .2 or .3. Statistical learning theory is fairly new, while the problem of overfitting goes back hundreds of years -- something about Occam and his razor.

There's much more -- neural networks for example -- but suffice it to say that there are many techniques and approaches to conquering overfitting and it's cousin collinearity. So, overfitting is only a problem for beginners or lazy consultants. Pros whose work might be contaminated by overfitting, fix the prtoblem, often in the early stages of work.

Finally, if you do your statistics right, forecasting can be remarkably accurate -- my colleagues and I, some years ago, did monthly sales forecasting for all Ocean Spray juices. Over several years, we were consistently within 5-10 percent of actual sales. Again, if you do it right, you can indeed forecast the future, at least in many business environments.

Physics, market research -- it's all about models.

Regards, Reilly

 

[Ken G]

It is not about believing in universal axioms, it is exploring what a set of axioms would imply if it were rigorously valid.

Yes, that is so, but what you must remember when you are doing that is that your goal is to confront the result with observational data, because that was the point of postulating the axioms. What I instead see, in things like the MWI, is "reasoning from the axioms" in the sense that the axioms describe the reality to us, even in situations where there will be no intended confrontation with data. That is what I mean by natural philosophy sneaking back into science by the back door. The point of the CI (ultimate Bohr version, essentially the same as the "ensemble interpretation") is to keep the way we confront axioms with data right there in the "loop" of our reasoning process, so that it does not require that we add philosophical baggage.

We are now a bit confused. Imagine that we can, with a lot of pain, empirically show that there is a tiny gravitational attraction between two marbles. Now, the question is: is this because it are the *atoms* in the marbles that attract each other ? Or does the gravitational force only appear when there are enough atoms together to form a marble ?

You are just asking the same question again on a smaller scale. This is very straightforward: we have a theory of gravity, which holds as an axiom that mass generates gravity. We test that theory in certain situations, and it works. We therefore like our axiom, it has unified our familiarities. To gain predictive power, we then extend the expectation to other situations involving mass. In the absence of any contrary evidence, we may "believe" that mass creates gravity at all levels, but where do we need that in our science? We adopt the axiom, we don't believe it, science is not a faith-based endeavor.

Our goal was unification of familiarities, and predictive power, and if we adopt the axiom that all mass generates a proportionate gravity, we get those without "believing" anything. And that holds right up to the point where it doesn't work. No experiment has been done on the gravity of an atom, and no experiment needed to assume anything about the gravity of a single atom. Perhaps when we do such an experiment, we find that Einstein's law of gravity doesn't work there. It sounds like that would rock your belief system, but I would just shrug and say "what did you expect"? We're doing science, not religion.

However, nevertheless, Newtonian gravity gives you the *theoretical picture* that they do.

Yes it does. So what? What do we do with theoretical pictures but confront them with observations, and are they therefore not scientifically meaningless if we have no such intention? This is the key issue. How do you define "scientific meaning": that which is demonstrable, or that which gives you a "warm fuzzy feeling about reality"? This is a serious question, because I believe I see an awful lot of the latter these days, and to me, it simply breaks down the distinctions between science and nonscience.

It will never be possible to do the experiment where we put 2 atoms 1 cm one from the other, and measure their gravitational attraction.

In that case, science has absolutely nothing to say on the matter. What else could be true? Let me sum up this position with three serious questions for you:
1) If it had never been possible to do observations of light interactions with individual atoms, say Planck's constant was a trillion times smaller than it is, why wouldn't Newton and company simply ask the very same question you asking now? Does not classical mechanics provide a crystal-clear picture of the action of an atom, and would it not be completely wrong for an atom, but still work fine for all our experiments?
2) Let's say a technological breakthrough became possible at some point, and we could study the interaction of light with a single atom for the first time. Would a "follower of Newton" stake their life on the idea that the atom would behave classically?
3) If a technological breakthrough allowed us now to measure the gravitational interaction of two atoms at 1 cm distance, would you, as a "follower of the axioms of relativity", stake your life that GR would work? If not, then why are you asking me if individual atoms make gravity in the normal way? I have no idea!

So the question as of whether individual atoms undergo Newtonian gravity belongs to the realm of natural philosophy according to you.

No, not according to me, according to the definitions of science. I'm saving us from constantly having egg in our faces, we never seem to learn.

It would make the whole business more consistent *in principle* to assume that Newtonian gravity is *also* working in between two individual atoms, even though this is not open to experiment.

But what need do we have for such a meaningless extrapolation? It's exactly what I mean by "philosophical baggage". Occam's razor is not intended to replace observations, it is indended to seek the cleanest organization of actual observations. What part of classical mechanics required that we imagine that atoms behave classically? Luckily, no part, and we can still use classical mechanics when it serves. Why couldn't general relativity simply conform to some "correspondence principle" applied to the ways atoms act gravitationally, and if it did, how would that make the theory any "clunkier" a la Occam? It wouldn't.

The extrapolation to the two marbles attracting each-other then makes "axiomatic sense".

But don't you see how that is imposing our axioms onto the reality in exactly the way I am criticizing? This is the history of science: 1) observe, 2) make axioms that unify the observations, 3) extend the axioms to inspire new observations, 4) test the axioms, 5) find they work, 6) get all philosophical about the axioms as being what is "really happening", 7) get shocked when we hit the place where they don't work, 8) modify the axioms. Are we not ready to just dispense with step #6 so that step #7 can simply be "modify the axioms as required by observation"? What part of the scientific method is step #6 anyway? We achieve the unification of our familiarites, i.e. "understanding", entirely without it, as soon as we realize that understanding is something that happens in our heads, and so is science. There's simply no MWI in that prescription of what is going on here.

It makes the whole story much more coherent.

Exactly, that's the lure. That's the reason we leave science, to achieve that "warm fuzzy feeling" that we "know what's really happening". This is precisely the same lure of using different modes of inquiry to get to that place, be they art, music, or religion. But we are doing science, and have a special definition which we use to claim a different kind of result-- one that is demonstrable by experiment. I would be loathe to part with that, and let science become "just another way to arrive at untestable ideas about what is real"-- like the MWI.

Otherwise we would have to invoke strange principles of non-attracting atoms that, when put together, at a certain point suddenly "wake up their gravitational holism".

Or, we'd have to invoke quantized units of angular momentum to explain atoms-- think how terrible that would be.

And we would run in all kinds of paradoxes, like things such as conservation of momentum and all that, if we tried to pin down exactly WHEN the gravitational interaction was "switched on".

If we chose a cartoon version of such a theory, yes. We would simply need a correspondence principle.

So it would be simply a much "cleaner" picture to ASSUME that, although it is unmeasurable, individual atoms do attract one another.

There is no scientific need for that assumption, and history is dotted with the flaws of that mentality. Don't get me wrong here: I have nothing against saying that "although I cannot test it, I use this pedagogical picture because it works for me when I extend it to situations that are testable." We do that all the time, "you can picture it this way if you want to, or like this other way if you prefer, but the science just says this". I also have no objection to the MWI as such a pedagogical option, a kind of crutch to help you visualize the equations you are solving. Keep in mind, that is precisely how I view the wave function itself, so I'd have no issues with extending that to MWI. The issue comes in when people start saying "my theory says that many worlds are spawned by quantum interactions" because "the universal wave function must evolve unitarily, so the subspace I am living in cannot be the whole reality". The latter is not a pedagogical picture, it is a nonscientific approach to knowledge about reality-- it is neither objective nor demonstrable. It is religion in the guise of science, an aberration that serves neither.

We run in a whole bunch of paradoxes when we try to pinpoint exactly WHEN the superposition principle stops working.

No, I know exactly when the superposition principle stops working. It is the instant we purposefully take a projection from a closed state to an open substate, i.e., "the cat". We did it, not "reality", it is in how we choose to analyze the situation. Reality doesn't know a cat from a hole in the wall, but it knows the difference between a closed and an open system. Open systems are a problem for us, we lose information when we deal with them, and the way we deal with that lost information is exactly what "collapses the superposition"-- we average over what we can't know, like a card player who can't see all the hands. There's no mystery at all, we did it on purpose. It's in how we "open the box" to look at the cat-- we do it in such a way that decoheres the coherences, on purpose, because our brains haven't the vaguest idea how to treat those coherences. We had to eliminate them, it's why we shuffle the deck of cards, and it's all part of doing science. If I did something that did not decohere the coherences, you would notice that I have not looked in the box, because that's what "looking in the box" means.

We would have to explain by new principles how it comes that superposition is "switched off" and no matter how we do it, we always run into problems of one kind or another.

No new principles, the CI covers it without specifying the details of how it occurs, and we see easily enough what the upshot was. That's the part we can test, as we cannot trace the lost information.

So the "natural extrapolation" is to assume that the superposition principle applies to everything, even there where we can't observe it - in the same way as we assume that individual atoms do obey Newtonian gravity, even though we can't observe it.

Again, we don't assume that, but we do build it into a pedagogical picture because it helps us picture why large masses have gravity. Let me give you a clearer example of the problem here-- real gravity is nonlinear, so it is not the simple sum of the gravity of all the atoms. Furthermore, the gravitational mass of a neutron star is not the sum of the rest masses of the particles within it. So your pedagogical picture fails you, but you can kind of fix it up by including the gravitational potential energy, and say "it's still from the individual atoms but we also have to keep track of their interactions". A crack in the pedagogy, but it's hanging in there. Now spin the system-- and lose that pedagogy completely. My knowledge of GR is not sufficiently profound, but I do not believe that you can view the gravity of a spinning neutron star as somehow directly emergent from the gravities of all those particles, you need to start from the "holistic" view you rejected above or you just can't do it-- the animal you are modeling is an inherently holistic one. So the example here is not even hypothetical.

Now, concerning observation, it was Einstein who said that it was *the theory* that had to tell you what was observable.

What does MWI tell us is observable that CI does not?

Well, lo and behold, *keeping superposition* doesn't alter the consistency of observations! The conditional links that happen to exist between different "memory states" of the observer in every term of these superpositions are consistent. The "projection" on the "internal inconsistency" states is zero.

You are saying that MWI does not make wrong predictions. I think that is a weak standard for science-- what right predictions does it make? The main problem with MWI is not that it is wrong, it is that it "is not even wrong". It's projection onto the scientific method is the CI.

In other words, *if we assume* that there is superposition everywhere, then from that hypothesis follows that we should see them for microscopic systems, and that they become impossible to measure for macroscopic systems. Exactly as we observe.

The issue isn't really "microscopic" or "macroscopic", it is "closed" or "open", where by "open" I mean that either there are interactions outside of what we are treating in detail, or that there is information present that we are not tracking but are instead averaging over. In other words, a pure state versus a projected state. Microscopic systems can be projected states too, they are not always treatable as pure states, and in some situations macroscopic systems (SQUIDs) can be treated as being in a pure state.

What matters is, the way you will treat it all depends on what our goals are, and what information you are choosing to track, but we may be sure that if you are doing science, then at some point you will confront the system with a device that can be relied on to behave classically. You will thus introduce decohering influences involving information you are not tracking but are averaging over-- you will collapse the wavefunction on purpose. The "collapse" is not some mysterious entity the CI has to "tack on", it is very much part of how we do science, the CI merely recognizes that. You may imagine there are an infinite copies of you doing that, even pray to them if you like, but it will never show up in any experiment. That's not a strength of thinking that why-- it is why its projection onto science is null.

This looks a lot like *if we assume* that individual atoms have gravitational attraction, then from that hypothesis follows that we can observe gravitational attraction at "marble" level, but not at "atomic" level. Exactly as we observe.

But is it science? If I like to picture that invisible elves are responsible for conserving energy, and sure enough energy is conserved, have I established my elves? How would I establish them?

So, in the end, do you think that individual atoms undergo gravitational attraction, 1 cm one from the other, or not ?

As I said, I have not the foggiest idea what the gravity between two atoms is like. It would be hard to imagine there was none at all, as that would require a whole new explanation, but I see no reason at all to expect Newton/GR to work. I think we already know that you cannot build up the gravity of a rotating neutron star as a sum of gravities of its particles.

And given that this is, according to you, not a scientific question, don't you find it a pity that many textbooks make students calculate such kinds of quantities which, according to you, have no physical meaning, just to show that we should expect the effect to be unobservable ?

Well, I certainly never said that establishing whether or not a certain test is possible is "not a scientific question". What I said was not a scientific question, once you have established that you will never be able to test Newton's law of gravitational interaction between two atoms, is "what is the gravitational interaction between two atoms". How do you define a scientific question, I'm curious? Anything we think our science can answer, even if it is untestable? Does that sound like science, or something else we see a lot of?

What's the most scientific approach ? *Assume* that two atoms attract, plug the quantities in Newton's equation, and find out that the effect is so tiny that you won't be able to observe it (and if we do, be surprised and try to find out why), OR
postulate that, given that we can't observe the attraction of two atoms 1 cm one from the other, Newton's equation is NOT VALID ?

Neither-- there is no reason to make that "assumption" just to do the tentative calculation, and there is even less reason to assume the inverse.