Is Quantum Mechanics Coherent?

[jomoonrain]

if there are two identical systems,in quantum mechanics(or any other theorem),according to Schrödinger equation, they will evolve congruously.but from the instant of measuring,the evolution seems disobey its original principle----i mean the evolutions are not congruously any more.
is that mean quantum mechanics isn't coherent? or any other problems?

thanks

 

[Ken G]

It's not obvious what you are asking here, but without getting too deeply into the various "interpretations" of quantum mechanics, I can say that if you are measuring the two systems, then you have a lot more going on than just the systems-- you also have the measuring apparatus. You can make the two quantum systems be in identical states, but how can you do that with the measuring apparatus? Hence you will not actually be starting from two identical situations, and that may be all you need to explain the differences.

 

[jomoonrain]

It's not obvious what you are asking here, but without getting too deeply into the various "interpretations" of quantum mechanics, I can say that if you are measuring the two systems, then you have a lot more going on than just the systems-- you also have the measuring apparatus. You can make the two quantum systems be in identical states, but how can you do that with the measuring apparatus? Hence you will not actually be starting from two identical situations, and that may be all you need to explain the differences.

well,thanks

but if this is the explanation, then there will be a problem here again.

if we use the same apparatus to measure the same system(e.g.use a magnetic field to measure two identical non-zero-spin particle in succession),will the result be the same?

well, of cause, we may still cann't ensure that the apparatus can keep identical with itself of seconds ago.

 

[f95toli]

if we use the same apparatus to measure the same system(e.g.use a magnetic field to measure two identical non-zero-spin particle in succession),will the result be the same?

No, not in general. Remember that when we perform a measurement in QM we will only get a given result with a certain probability. If we e.g. measure a spin-1/2 system prepared in a superpostion we would expect to get "up" 50% of the time and "down" the other 50%.
This is of course an "extreme" situation but in real experiments we are almost always looking at probability distributions; from a practical point of view the "QM uncertainty" is essentially just another source of noise in an experiment(which is why you frequently see "quantum noise"-terms in expressions for the noise spectral density).

 

[jomoonrain]

No, not in general. Remember that when we perform a measurement in QM we will only get a given result with a certain probability. If we e.g. measure a spin-1/2 system prepared in a superpostion we would expect to get "up" 50% of the time and "down" the other 50%.
This is of course an "extreme" situation but in real experiments we are almost always looking at probability distributions; from a practical point of view the "QM uncertainty" is essentially just another source of noise in an experiment(which is why you frequently see "quantum noise"-terms in expressions for the noise spectral density).

hi
I am not quite aware of the "quantum noise". But i think if it is the apparatus' problem, the probability distributions then should also depends on the apparatus.while in fact it was determinated by the Hamiltonian which totally has no relation with the apparatus.And what is more, if the uncertainty is caused by the apparatus, it shouldn't have a certain distribution, since the apparatus cann't be determined in principle.

 

[f95toli]

No, the uncertainty (and hence the "noise") is NOT neccesarily caused by the apparatus or even the environment; it is intrinsic to the system; there is no "apparatus term" in the Hamiltonian.
There are plenty of experiments where the noise (or -to be slightly more stringent- the width of the probability distribution) is dominated by quantum effects; i.e. the "quantum noise term" I mentioned above . The other noise terms being thermal, 1/f noise and shot noise, the "experimental noise" introduced by the apparatus is usually at least approximately thermal (i.e. white).

I used to work on one such system: macroscopic quantum tunneling in Josephson junctions, the "quantum" part comes from the fact that given the right experimental conditions (very low temperatures and a many months of work in the lab) the junction will behave in a way completely dominated by quantum tunneling, in the sense that the tunneling probability and hence the shape of the probability distribution ONLY depends on the the junction potential and not on the experimental conditions (the distribution becomes independent of temperature etc). Hence, in this case the "randomness" is -at least from an experimental point of view- intrinsic, the width of the distribution does not go to zero as we lower the temperature which is what you expect for a classical system.
.
There are plenty of other examples, most notably in quantum optics.

 

[Ken G]

That's an interesting real-world example. So if one imagines two such junctions, tuned to the quantum limit, then you could have them in identical states, quantum mechanically speaking. However, the response would show the same intrinsic variation, so you would not expect identical experimental outcomes. So I think the OP is asking, how do you get different outcomes in the cases where you don't have important broadening effects due to instrumental noise? I would tend to say that the apparatus has an additional influence, which might be classified as an intrinsic noise, if that doesn't sound like an oxymoron. The intrinsic noise comes from the fact that the apparatus at some point has to couple to an instrument that does not admit an explicit wave function description. So even if the junction itself is in a pure state, whatever it is coupled to to probe that state is not. When that coupling does not enhance the statistical variation, it can still influence the actualization of the experiment over its own intrinsic quantum mechanical variation. The latter would come from untracked information, perhaps phases and so forth, in the instrument-- even when they do not enhance the variation itself.

An analogy to this might be if you have a gas in a box at a certain temperature and density, and you open a hole in the box small enough that you expect it to take, on the average, 1 ms for the first particle to emerge. You could learn to open the hole in a way that does achieve that result, so that how you are doing it doesn't matter, it's the answer intrinsic to the state of the gas. However, if you have two such boxes, and do the experiment on each, the details of how you open the hole (relative to the detailed state of the gas) would indeed alter the time it takes for the first particle to emerge-- but it would not alter the statistical distribution of that outcome. So it is with quantum measurements, I would suggest.

 

[jomoonrain]

No, the uncertainty (and hence the "noise") is NOT neccesarily caused by the apparatus or even the environment; it is intrinsic to the system; there is no "apparatus term" in the Hamiltonian.
There are plenty of experiments where the noise (or -to be slightly more stringent- the width of the probability distribution) is dominated by quantum effects; i.e. the "quantum noise term" I mentioned above . The other noise terms being thermal, 1/f noise and shot noise, the "experimental noise" introduced by the apparatus is usually at least approximately thermal (i.e. white).

I used to work on one such system: macroscopic quantum tunneling in Josephson junctions, the "quantum" part comes from the fact that given the right experimental conditions (very low temperatures and a many months of work in the lab) the junction will behave in a way completely dominated by quantum tunneling, in the sense that the tunneling probability and hence the shape of the probability distribution ONLY depends on the the junction potential and not on the experimental conditions (the distribution becomes independent of temperature etc). Hence, in this case the "randomness" is -at least from an experimental point of view- intrinsic, the width of the distribution does not go to zero as we lower the temperature which is what you expect for a classical system.
.
There are plenty of other examples, most notably in quantum optics.

thanks for you explanation
but it's totally beyond my knowledge.

 

[f95toli]

thanks for you explanation
but it's totally beyond my knowledge.

I'm afraid my explanation wasn't very good
Paraoanu has written a nice informal paper which explains it better; the title is "How do Schrödinger cats die?" and it is available on the arxiv

http://arxiv.org/abs/0806.2524

If you are really interested in this particular type of experiment I can also PM you a link to some other material.

 

[jomoonrain]

I'm afraid my explanation wasn't very good
Paraoanu has written a nice informal paper which explains it better; the title is "How do Schrödinger cats die?" and it is available on the arxiv

http://arxiv.org/abs/0806.2524

If you are really interested in this particular type of experiment I can also PM you a link to some other material.

well, I am so appreciated of your kindness.

 

[Fredrik]

if there are two identical systems,in quantum mechanics(or any other theorem),according to Schrödinger equation, they will evolve congruously.but from the instant of measuring,the evolution seems disobey its original principle----i mean the evolutions are not congruously any more.
is that mean quantum mechanics isn't coherent? or any other problems?

The two different time evolutions in quantum mechanics don't really contradict each other. Unitary time evolution holds for systems that are isolated from their environment, and a system that's being measured isn't isolated.

The fact that we don't have a contradiction doesn't mean that there's no problem. We still have to think about things like "what exactly is a measurement?" and "is the second kind of time evolution implied by the first?".

 

[jomoonrain]

The two different time evolutions in quantum mechanics don't really contradict each other. Unitary time evolution holds for systems that are isolated from their environment, and a system that's being measured isn't isolated.

The fact that we don't have a contradiction doesn't mean that there's no problem. We still have to think about things like "what exactly is a measurement?" and "is the second kind of time evolution implied by the first?".

thanks for replying.

but i cann't understand how the isolation affects the certainty.

 

[Ken G]

The two different time evolutions in quantum mechanics don't really contradict each other. Unitary time evolution holds for systems that are isolated from their environment, and a system that's being measured isn't isolated.

Right. Then the tricky part comes in when you ask, can you subsume both the measured and the measurer into a single closed system, and still treat it quantum mechanically? Or, can you only do that if you have yet something else outside that closed system to probe it and learn about it?

I maintain that the crux of the "Copenhagen Interpretation" is the statement that the way we build science, we always have to have something outside the system being modeled, to process the information. We cannot put the processor in the system on which we are doing science, and still be doing science. The crux of the "Many Worlds Interpretation" is that we can consider the rules that we establish for external systems should apply to systems that include us, so therefore the processor can participate in processing information about itself.

In my opinion, the latter may be possible, but it is far from established that it is possible, and it leads to certain absurd sounding scenarios. The former is easier to establish as valid, but leads to an incomplete description of reality so is not palatable to those who demand that quantum mechanics must be completely fundamental. Personally, I just don't see why we need to ask that of quantum mechanics, when we ask it of no other branch of scientific inquiry.

The fact that we don't have a contradiction doesn't mean that there's no problem. We still have to think about things like "what exactly is a measurement?" and "is the second kind of time evolution implied by the first?".

Exactly, those are the questions addressed by these, and other, interpretations. I've found on this forum that they lead to some spirited exchanges, but does not necessarily lead to resolution or consensus!

 

[Ken G]

but i cann't understand how the isolation affects the certainty.

It sounds like you are puzzled by what you see as an incomplete description of what is happening. I think that's very much the "devil's bargain" I referred to just above-- we are essentially choosing between incompleteness and absurdity. Choose your poison-- all there might be to understand here is our own motivations for making the choices we do, when we interpret our science.

 

[newbee]

It's difficult form me to discern whether the original question of this thread is asking about basic QM axioms or about the measurement problem. Either way I think one would do well to take a look at the Stern–Gerlach experiment to first understand what the phenomenon of interest are and how they are not consistent with classical physics. I see that Wikipedia has a page devoted to the experiment but I have not read it yet.

 

[jomoonrain]

Right. Then the tricky part comes in when you ask, can you subsume both the measured and the measurer into a single closed system, and still treat it quantum mechanically? Or, can you only do that if you have yet something else outside that closed system to probe it and learn about it?

I maintain that the crux of the "Copenhagen Interpretation" is the statement that the way we build science, we always have to have something outside the system being modeled, to process the information. We cannot put the processor in the system on which we are doing science, and still be doing science. The crux of the "Many Worlds Interpretation" is that we can consider the rules that we establish for external systems should apply to systems that include us, so therefore the processor can participate in processing information about itself.

In my opinion, the latter may be possible, but it is far from established that it is possible, and it leads to certain absurd sounding scenarios. The former is easier to establish as valid, but leads to an incomplete description of reality so is not palatable to those who demand that quantum mechanics must be completely fundamental. Personally, I just don't see why we need to ask that of quantum mechanics, when we ask it of no other branch of scientific inquiry.
Exactly, those are the questions addressed by these, and other, interpretations. I've found on this forum that they lead to some spirited exchanges, but does not necessarily lead to resolution or consensus!

thank you so much!