B Any good lay explanation of the Schrödinger cat duality?

[Quandry]

On the subject of QM, here's what my serious QM textbook has to say about the uncertainty principle (UP). Rather than talk about the infamous cat he says:

"You might wonder how the UP is enforced in the lab - why can't you determine the position and momentum of a particle? Niels Bohr was at pains to track down the mechanism by which the measurement of position destroys the previous value of momentum. The crux of the matter is that in order to determine the position of a particle, you have to poke it with something - shine light on it, say. But these photons impart to the particle a momentum you cannot control. His famous debates with Einstein include many delightful examples, showing in detail how experimental constraints enforce the UP."

So, it's not so weird as a cat that's alive and dead at the same time, after all!

It seems to me that this is a very simple issue. To determine position you need a single measurement. To determine momentum you need two. There is no way to determine what has happened between the first and second measurement.

 

[PeroK]

It seems to me that this is a very simple issue. To determine position you need a single measurement. To determine momentum you need two. There is no way to determine what has happened between the first and second measurement.

If it were that simple, Bohr and Einstein would not have found so much to debate.

In any case, you can measure momentum of a bullet, say, by firing it into a block and measuring the displacement of the block. You would never need to measure the bullet directly.

 

[Nick Levinson]

I've read the SciAm article (@Nugatory) and it makes sense, especially when considering an observer as anything that can affect or be affected by the observable. The observer as human is metaphorical and for laity, but it's more metaphorical than I thought and it's too constraining. The abstraction helps me, since I tend to take wordings more literally. Perhaps an author for laity should combine both.

I'm getting to other sources (@Nugatory and @Simon Bridge).

On whether something unobserved should count as existing (@Simon Bridge, comment 7, end): I distinguish the unknown from the metaphysical (I'm not saying you don't). The scientific basis for the metaphysical is approximately zero. Once a scientific point is accepted, conflicting metaphysics moves over to another place, e.g., when the world was created has theologically moved from 4,004 B.P. or B.C.E. (I forgot which) to 13.8 billion B.P. (around the Big Bang). But not knowing is different. If there's ground to believe that generally in given circumstances neutrinos may come into existence and then leave existence but in a particular case having those circumstances neutrinos weren't detected, I'm not prepared to say they didn't exist. I can find that there is no omnipresent deity that is physically distinct from whatever else is physically present but I cannot find that there were no neutrinos in the given case. Even with instrumentation of the kind available today and assuming proper training, I just wouldn't know. By specifying it as unknown, I leave more room for investigation. There's less motivation to investigate what's supposedly known even if incorrectly. Declaring something unknown has the conversational hazard of getting misapplied Socratic method thrown back at me (as in, "c'mon, you know the answer . . .") but better that than being both certain and wrong.

 

[Nugatory]

I've read the SciAm article...
On whether something unobserved should count as existing ...If there's ground to believe that generally in given circumstances neutrinos may come into existence and then leave existence but in a particular case having those circumstances neutrinos weren't detected, I'm not prepared to say they didn't exist.

You may not have made all the connections yet.

If you've made it through earlier posts in this thread and the Scientific American article, you see how the unmeasured superposition does not have a definite value: when a particle is in the state "superposition of spin-up and spin-down" the only thing that we can say about its spin is that it will take on various values with various probabilities when and if we do make a measurement. That's superposition.

But now let's look at what it means to say "a neutrino has come into existence". In quantum field theory, particles are not little solid objects like tiny bullets. They are excitations of a quantum field. The state of that quantum field is itself a a superposition. For example the state of the neutrino field at a particular time and place (which is to say, at a particular point in spacetime) will be a superposition of the states "there are zero neutrinos here now", "there is one neutrino here now", "there are two neutrinos here now", and so forth. As with the superpositions discussed earlier this in thread, this means that until we put a detector there to interact with the field and collapse the superposition there is no number of neutrinos present - not zero, not one, not two, nor any other number either. Thus, asserting that the undetected neutrino is definitely there just because we would have detected one if we had a detector there is analogous to the assertion that the superposed spin has definite value even when we don't measure it - and we've already seen that doesn't work.

(I mentioned above that the use of the word "observation" in quantum mechanics is an unfortunate historical accident - the word doesn;t mean what it means in ordinary English usage. The same is true of the word "particle", and fewer people would form the wrong mental model of quantum objects if we had called them "quantized excitations of a quantum field" instead of "particles").

 

[Quandry]

If it were that simple, Bohr and Einstein would not have found so much to debate.

In any case, you can measure momentum of a bullet, say, by firing it into a block and measuring the displacement of the block. You would never need to measure the bullet directly.

No, but you would have to measure the position of the block twice and you would never know whether the momentum was as a result of mass or velocity without measuring the bullet.
But all that is neither here nor there. We still don't know where the bullet came from, what its trajectory was or what other forces acted on it during its travels and you can't know that based on your example.

 

[PeroK]

No, but you would have to measure the position of the block twice and you would never know whether the momentum was as a result of mass or velocity without measuring the bullet.
But all that is neither here nor there. We still don't know where the bullet came from, what its trajectory was or what other forces acted on it during its travels and you can't know that based on your example.

You CAN measure the position and momentum of a bullet simultaneously to a very high level of accuracy. The uncertainty principle does apply to a macro object like a bullet, but the uncertainty is negligible. There is no practical issue measuring the momentum and position of a bullet simultaneously. A high-speed camera would do it. The camera does not affect the bullet to any measurable degree.

But, the uncertainty for a quantum object like an electron is not negligible. You cannot simply use a high-speed camera to follow an electron.

The question that Niels Bohr analysed (which is clearly not as simple as you would like to believe) is what happens practically when you carry out measurements on an electron. And how and why the uncertainty principle is enforced by experimental constraints.

 

[Quandry]

You CAN measure the position and momentum of a bullet simultaneously to a very high level of accuracy. The uncertainty principle does apply to a macro object like a bullet, but the uncertainty is negligible. There is no practical issue measuring the momentum and position of a bullet simultaneously. A high-speed camera would do it. The camera does not affect the bullet to any measurable degree.

But, the uncertainty for a quantum object like an electron is not negligible. You cannot simply use a high-speed camera to follow an electron.

The question that Niels Bohr analysed (which is clearly not as simple as you would like to believe) is what happens practically when you carry out measurements on an electron. And how and why the uncertainty principle is enforced by experimental constraints.

My purpose in continuing with your macro example was to illustrate that, in any terms your example was incorrect.
To continue with your example, no high speed camera can capture the position of the bullet at every instance of time and therefore you cannot have certainty of momentum between two frames.
But uncertainty is not about measurement.
"Historically, the uncertainty principle has been confused with a somewhat similar effect in physics called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems, that is, without changing something in a system"
Heisenbergs uncertainty principle is independent of measurement, it says that there is a fundamental limit to the precision with which complimentary variables, such as position and momentum Can Be Known.

 

[PeroK]

My purpose in continuing with your macro example was to illustrate that, in any terms your example was incorrect.
To continue with your example, no high speed camera can capture the position of the bullet at every instance of time and therefore you cannot have certainty of momentum between two frames.
But uncertainty is not about measurement.
"Historically, the uncertainty principle has been confused with a somewhat similar effect in physics called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems, that is, without changing something in a system"
Heisenbergs uncertainty principle is independent of measurement, it says that there is a fundamental limit to the precision with which complimentary variables, such as position and momentum Can Be Known.

You are misunderstanding the point. If the HUP is independent of measurement, then what stops someone simply carrying out an experiment to a degree of accuracy less than the HUP predicts?

You could argue that other uncertainties in experimental measurements must always be greater than the theoretical HUP uncertainty. Okay, but why? What if you simply get better and better at experimentation: eventually you should get in under the HUP.

Also, the HUP predicts uncertainty only in certain so-called "incompatible" observables. For example, even for an electron, there is no HUP for the position in the x-direction and the momentum in the y-direction.

So, in theory, you COULD measure these quantities with unlimited accuracy.

So, if you measure the x-position and y-momentum to a certain accuracy, why can't you measure the x-position and x-momentum to the same degree of accuracy? Something must stop you. And, it's not non-commuting Hermitian operators - as they are not physically present in the lab.

A theory alone cannot stop you doing anything - there must be a physical manifestation of the theory. That's what Bohr was looking for.

For example, it's not the theory of relativity that stops you going faster than light. There must be a physical manifestation of the theory.

 

[PeroK]

But uncertainty is not about measurement.
.

If uncertainty is not about measurement, then what it is about?

 

[vanhees71]

The uncertainty is about preparation. You cannot prepare a particle to have accurate momentum and position at the same time due to the uncertainty relation
$\Delta x_j \Delta p_k \geq \delta_{jk}/2.$
You can measure momentum and position as accurately as you want. In fact, to verify the uncertainty relation you must measure both quantities with a much higher accuracy than the given standard deviations in the uncertainty relation. Of course, you cannot measure position and momentum at a single particle but you can measure either of these quantities on an ensemble of identically prepared particles with arbitrary accuracy, and in this sense the uncertainty relation is understood in quantum theory.

 

[Nick Levinson]

I read the Weirdness book despite it being 20 years old; the author is well-credentialled. It appears that the empirical evidence and the math should be taken as good and not as following the narrative but as the authority for the narrative, so that major defects belong to the major narratives as explanations of the evidence and math. And three major narratives differ and yet dominate. It was helpful to read the narratives as separate, not unified, which may have been my error in understanding other literature.

The many-worlds narrative is an infinitely-many-worlds narrative, which means measurements of the spatial dimensions of our universe (a universe of matter and energy, not of emptiness beyond) must be infinitely long, which scientists in cosmology fields reject by their finite measurements.

The hidden-variables approach makes sense. Every time we identify a new "smallest" atomic particle it's said to have no known internal structure until the day it's agreeably theorized to have a structure, thus a variable, thus a variable that's hidden till revealed, leaving some other particle to enclose its own hidden variable/s. If some seemingly-indivisible particles spin, some motivator must cause or continue the spinning, and if the motivator is not always external to the particle then at least sometimes it's internal, implying the particle has a hidden structure, thus a hidden variable.

But I don't want to trash the other approaches. They may contribute to a theoretical synthesis.

I had to return the book so I can't quote for its lacunae, but I think the assertion that what is unobserved therefore doesn't exist (Copenhagen) appears still as a faith-based statement, of a kind that lurks in various forms in various sciences until the existence is proven (e.g., biology's concept of "junk DNA" that now has acknowledged existing purpose (https://www.scientificamerican.com/article/hidden-treasures-in-junk-dna/ & http://healthland.time.com/2012/09/06/junk-dna-not-so-useless-after-all/ both as accessed Oct. 16, 2016)).

One problem with the unobserved being nonexistent: Suppose I, Nick, in a space suit with oxygen, am rocketed into outer space, ejected, and, becoming a complete system, momentarily unobserved. Through that moment, I think, feel, and talk to myself. From the standpoint of people on Earth, do I not exist? Am I thereafter, when re-observed, born an adult (at any arbitrary age not less than when being observed was lost plus the duration of nonobservation)? I don't think so. If not, then at least history is part of observationalism, since observation at one point in time would deny the ability to say that the observed could not have existed when unobserved.

If war and a natural calamity combine to wipe out all of Earth's telescopes except hand-held optical models and to lower our food supply so no more generations of people are very intelligent, the partial loss of humans' ability to observe and the passage of time sufficient for natural destruction of the formerly observed would, I think, not degrade the larger universe through progressive nonobservation by former particles of remaining particles until the universe's contents are much reduced to far less than we catalogue today.

Perhaps the math assigns the same value (e.g., 0) to a thing's nonacknowledgment and to its nonexistence, but, if so, that could be a convention, and perhaps not a solid donor to a pending narrative.

Maybe I'll look for Bohr's paper.

Einstein's objectivist view that we just may not understand what underlies the empirical findings and the math may be dated but right, I think. We may have to keep analyzing until one theory explains all that's known, and that need not be classical mechanics but likely will be quantum. I'll assume we even today have experimental results that are solid, replicated with variants, and yet not wholly explained ("weird"), maybe not the experiments that David Lindley wrote of but maybe newer results. Subjectivity is not without a role but maybe we're pushing objectivity too far away.

It won't be the first time a partial explanation was replaced.

 

[Avinash Arrah]

Hi Everyone,

One question that boggle my mind , now that they have been able to photograph light behaving as wave and particle at the same time , does the theory of multi universe still stands good?

 

[vanhees71]

Hi Everyone,

One question that boggle my mind , now that they have been able to photograph light behaving as wave and particle at the same time , does the theory of multi universe still stands good?

Can you give a reference in a scientific journal, where it is detailed, what's meant by "photograph light behaving as wave and particle at the same time" (which in my opinion is never the case since there is no wave-particle dualism since 1925 in our contemporary quantum theory anymore). I'm also not aware that any theory of "multi universe" has a particularly good standing anywhere in the science community.

 

[Avinash Arrah]

thanks Vanhees for the reply.

I was referring to following link
https://phys.org/news/2015-03-particle.html (light behaving as wave and particle)

And for the mutli universe :
http://science.howstuffworks.com/innovation/science-questions/quantum-suicide4.htm

I am really a newbie in quantum physics but i like to read a lot on that. What i may have ask may be totally irrelevant. But please be kind enough to go through it and give me your thought.

 

[vanhees71]

Well, the photoelectric effect does NOT demonstrate wave-particle duality in any sense. At the level described by Einstein, it shows the quantum nature of the electrons but not the quantum nature of the em. field. I highly recommend to read good no-nonsense textbooks on the subject. As a first starter, I recommend Susskinds "Theoretical Minimum" book.

Concerning the many-worlds interpretation, it's just up to you what you like to follow. It's irrelevant for quantum theory as a physical theory. All you need is the minimal statistical interpretation to relate the formalism of the theory to real-world experiments and observations, and that's all that counts in science. Interpretations are, to a large extent, just philosophical speculation and is rather hindering an understanding of QT instead of helping to understand it.

 

[Quandry]

If uncertainty is not about measurement, then what it is about?

Been away, so I guess there was some uncertainty about whether or not I would answer. How long did that uncertainty last? When did you conclude I would not answer? You had no way of knowing, and were probably wrong if you made an assumption.

Uncertainty is about ability to know. No matter how good your measurement system is you cannot know a particles absolute position and its velocity at the same time because velocity is a measure dependent on time change. You can't know two things at the same time if time is a factor in determining one of them.

 

[Nugatory]

You can't know two things at the same time if time is a factor in determining one of them.

That's not where the uncertainty principle comes from. For example, time is in no way a factor in determining the spin of a particle along either of two different axes, but the uncertainty principle still applies and prevents us from determining both at the same time.

 

[Quandry]

That's not where the uncertainty principle comes from. For example, time is in no way a factor in determining the spin of a particle along either of two different axes, but the uncertainty principle still applies and prevents us from determining both at the same time.

Heisenbergs Uncertainty Theory was based on measuring the conjugate variables, principally position and momentum. Originally he argued that determining the position by measurement affected the momentum. He later argued that if you knew the velocity, then measured the position, the uncertainty principal did not apply, i.e. there was no uncertainty in the past.
Therefore it seems fairly clear that the uncertainty principle 'comes from' consideration of a particles position and momentum. Which was the topic being discussed.
Certainly, it is only one example of a great many including your example.
As to whether or not time is a factor you state that the UP "prevents us from determining both at the same time" So time is a factor.
More specifically, if one of the variables is velocity, time is a critical factor because velocity cannot be determined at one point in time. It takes at least two.

 

[vanhees71]

The uncertainty is not about measurement but about preparation. It's important to understand that. It says that in any (pure or mixed) state the standard deviations of two observables $A$ and $B$ obey
$$\Delta A \Delta B \geq \frac{1}{2} |\langle [\hat{A},\hat{B}] \rangle|.$$
This implies that, if the observables are incompatible, i.e., the operators do not commute, you cannot prepare the system to be in a state, where both variables are determined, and the more determined you make one of them the less determined the other one gets.

This does not limit the accuracy with which you can measure the observables $A$ and $B$. According to the Born rule, i.e., the statistical meaning of quantum states, you measure an observable by preparing a lot of quantum systems in the same way (avoiding any correlations between these preparation procedures) and measure either $A$ or $B$. To verify the uncertainty relation for the given state, you must perform the measurements such that the accuracy of each measurement is much better than the standard deviations in order to verify these standard deviations by collecting "enough statistics", i.e., by repeating the preparation and measurement procedure often enough to be able to determine the statistical properties of the ensemble, defined by the state you prepare it in, with sufficient confidence (in particle physics for a discovery you need at least $5 \sigma$ significance level).

 

[Quandry]

The uncertainty is not about measurement but about preparation.

Measurement and preparation both imply that uncertainty would change if we could prepare and measure. However, it is no more dependent on our ability to prepare than it is on our ability to measure. The point is that it is not possible to determine with exactness two conjugate variables at a single point in time. No matter how short the time is between the two determinations, assumptions have to be made about what has happened in the intervening interval.
The Born rule (sometimes called the Born Law - but Law it is not) is a matter of probabilities. It is possible, with sufficient information, to determine to a high degree of accuracy the probability of A and B having specific states. But this has nothing to do with determining a single particles position and momentum. Born's rule implies that so long as the standard deviation is other than zero, we have uncertainty.

 

[Nugatory]

Measurement and preparation both imply that uncertainty would change if we could prepare and measure. However, it is no more dependent on our ability to prepare than it is on our ability to measure. The point is that it is not possible to determine with exactness two conjugate variables at a single point in time. No matter how short the time is between the two determinations, assumptions have to be made about what has happened in the intervening interval.
The Born rule (sometimes called the Born Law - but Law it is not) is a matter of probabilities. It is possible, with sufficient information, to determine to a high degree of accuracy the probability of A and B having specific states. But this has nothing to do with determining a single particles position and momentum. Born's rule implies that so long as the standard deviation is other than zero, we have uncertainty.

Can you cite a source for this claim?

 

[Quandry]

Can you cite a source for this claim?

Not sure which of the claims you mean.
Para 1 - I am sure you know many sources for the claim, but it may be that there is something in the way I have expressed it that makes it uncertain.
ΔaΔp ≥ h/ 4π supports the claim but I have chosen not to express it in terms of particle wavelengths.

Para 2 - Once again, I know that you know more about Borns Rule that I do. My claim is that if you do only one measurement Born's rule does not apply, and if you do a statistically meaningful number of measurements resulting in an SD of zero uncertainty does not exist for the case.

 

[vanhees71]

Born's rule applies. It tells you the probability for the outcome of a measurement given the (pure or mixed) state of the system. A single measurement, of course, doesn't tell much about whether these probabilities are correct predictions of not. For that you need an ensemble to get "enough statistics". That's why I think that the minimal statistical interpretation is the only interpretation of QT which makes sense of the formalism as a physical theory. You may add philosophical twists to it (or even to the very "meaning" of probabilities), but in the lab to test a probabilistic prediction you need to repeat an experiment often, i.e., you have to use (large) ensembles.

 

[Quandry]

A single measurement, of course, doesn't tell much about whether these probabilities are correct predictions of not.

You're right of course. My statement was a course way of saying that without sufficient input Borns rule could not provide useful output.

 

[bhobba]

But the real problem - that of measurement in QM (which many will also say is a 'solved' problem - or not even a problem) - hasn't gone away - we've just shifted it about a bit.

Exactly.

Although beyond the level of this thread THE book that explains it is a standard text:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

For the OP start with Feynman:
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

Once you have done that tell us how you went and we can make further suggestions.

Thanks
Bill