Heisenberg uncertainty principle -- Questions about a practical experiment

[L Drago]

TL;DR

The Heisenberg uncertainty principle states that position and momentum cannot be determined at the same time.

There is an experiment to demonstrate it :

A laser light is fixed and there are two razor blades we are bringing slowly together. We are predicting positions of photons on screen but after moving it more it changes shape and momentum changes. Hence, we cannot predict position and momentum at the same time.

Please review this experiment I watched from a video in YouTube and I think is correct. If there are flaws or there is a better experiment of proving this principle, kindly tell me.

 

[Nugatory]

The Heisenberg uncertainty principle states that position and momentum cannot be determined at the same time.

That's an OK English language description, but there's a lot more to it and the principle can be generalized to observables other than just position and momentum. But with that said, yes, the experiment that you describe is a demonstration (not a proof, that's in the math) of the how the uncertainty principle works with position and momentum.

We start with a particle's wave function, from which we can calculate the probability of getting a particular result out of a position measurement or a out of a momentum measurement. Suppose t wave function says that the position probabilities are tightly clustered around a particular position; this will be the case for those photons that pass between the razor blades because they're so close together. Then we go to calculate the probability that the momentum values will be clustered around some particular value; we find that the narrower the range of probable positions, the wider the range of possible momenta.

Please view this experiment I watched from a video in YouTube and I think is correct.

Be very cautious about online videos (unless they happen to be the Feynman lectures). Some are good, many are garbage, and there's no easy way of picking the occasional good ones out of the junk.

Although there are no really good texts accessible to a seventh-grader (understanding QM requires a lot of math) you might try working through Giancarlo Ghirardi's book "Sneaking a look at God's cards". You won't find it an easy read, but I don't think QM can be made any easier.

 

[L Drago]

That's an OK English language description, but there's a lot more to it and the principle can be generalized to observables other than just position and momentum. But with that said, yes, the experiment that you describe is a demonstration (not a proof, that's in the math) of the how the uncertainty principle works with position and momentum.

We start with a particle's wave function, from which we can calculate the probability of getting a particular result out of a position measurement or a out of a momentum measurement. Suppose t wave function says that the position probabilities are tightly clustered around a particular position; this will be the case for those photons that pass between the razor blades because they're so close together. Then we go to calculate the probability that the momentum values will be clustered around some particular value; we find that the narrower the range of probable positions, the wider the range of possible momenta.

Be very cautious about online videos (unless they happen to be the Feynman lectures). Some are good, many are garbage, and there's no easy way of picking the occasional good ones out of the junk.

Although there are no really good texts accessible to a seventh-grader (understanding QM requires a lot of math) you might try working through

Are there any more experiments which are better and more precise to demonstrate and Thanks for the information @Nugatory.

 

[phinds]

In addition to @Nugatory 's excellent explanation let me add this, in more colloquial terms. The (HUGE) difference between classical mechanics and Quantum Mechanics, is that in classical mechanics, if you can exactly, and I mean EXACTLY, replicate the starting conditions of an experiment,, the results will always be the same because that is the deterministic characteristic of classical mechanics. In Quantum Mechanics, on the other had, if you can EXACTLY replicate the starting conditions of an experiment, you will NOT get the same results because that is the non-deterministic characteristic of Quantum Mechanics (exemplified by the HUP)

 

[Nugatory]

In Quantum Mechanics, on the other had, if you can EXACTLY replicate the starting conditions of an experiment, you will NOT get the same results because that is the non-deterministic characteristic of Quantum Mechanics (exemplified by the HUP)

On the other hand, EXACT replication of the initial conditions is only possible in a thought experiment. This is true even in classical physics - we can write down hypothetical initial conditions as precisely as we like but there's no way of setting up a physical system that exactly matches that specification.

Note also that QM does offer a thought experiment in which we will get the same result every time: If the initial conditions are that the wave function is an eigenstate of an observable that commutes with the Hamiltonian then it won't change. This is not possible, even in principle, with position and momentum - they don't come in well behaved eigenstates.

 

[PeroK]

TL;DR Summary: The Heisenberg uncertainty principle states that position and momentum cannot be determined at the same time.

There is an experiment to demonstrate it :

A laser light is fixed and there are two razor blades we are bringing slowly together. We are predicting positions of photons on screen but after moving it more it changes shape and momentum changes. Hence, we cannot predict position and momentum at the same time.

Please review this experiment I watched from a video in YouTube and I think is correct. If there are flaws or there is a better experiment of proving this principle, kindly tell me.

We don't usually recommend popular science videos here, but this one on the HUP (Heisenberg Uncertainty Principle) is better than most.



If you really want to learn QM (which is significantly harder than SR), then these notes are perhaps the most accessible serious introduction to the subject. Even if you don't follow all the mathematics, the insights are invaluable:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

 

[L Drago]

We don't usually recommend popular science videos here, but this one on the HUP (Heisenberg Uncertainty Principle) is better than most.



If you really want to learn QM (which is significantly harder than SR), then these notes are perhaps the most accessible serious introduction to the subject. Even if you don't follow all the mathematics, the insights are invaluable:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

Thanks a lot @PeroK for giving me the authentic sources to read from.

 

[L Drago]

In addition to @Nugatory 's excellent explanation let me add this, in more colloquial terms. The (HUGE) difference between classical mechanics and Quantum Mechanics, is that in classical mechanics, if you can exactly, and I mean EXACTLY, replicate the starting conditions of an experiment,, the results will always be the same because that is the deterministic characteristic of classical mechanics. In Quantum Mechanics, on the other had, if you can EXACTLY replicate the starting conditions of an experiment, you will NOT get the same results because that is the non-deterministic characteristic of Quantum Mechanics (exemplified by the HUP)

QM is actually weird though true. For example, in Schrödinger cat experiment, the cat is in a state of quantum superposition. It means it is both alive and dead at the same state as there is 50 percent chance of emitting radiation and the Geiger counter doing its job and spilling poison. Hence, the cat is both alive and dead at the same time before we open the box.



That means QM is very weird but interesting at the same time

 

[PeroK]

QM is actually weird though true. For example, in Schrödinger cat experiment, the cat is in a state of quantum superposition. It means it is both alive and dead at the same state as there is 50 percent chance of emitting radiation and spilling poison. Hence, the cat is both alive and dead at the same time before we open the box.

The point of the Schrödinger's cat thought experiment is that we know that the cat is not alive and dead at the same time. That makes no sense from our knowledge of macroscopic objects. But, QM appears to suggest that it should be. The experiment asks where do we go wrong when we apply QM to this scenario?

 

[phinds]

in Schrödinger cat experiment, the cat is in a state of quantum superposition. It means it is both alive and dead at the same

No, that is not only not correct, it is EXACTLY the misunderstanding that Schrödinger was pointing out --- the absurdity of taking the Copenhagen Interpretation of QM too literally. The moon, after all, IS still there whether anyone is looking at it or not (this is another misconception), and the cat is NOT simultaneously alive and dead, it is always just one or the other. It is not the cat that is in superposition, it is a quantum object (subatomic particle).

EDIT: I see @PeroK beat me to it.

 

[L Drago]

The point of the Schrödinger's cat thought experiment is that we know that the cat is not alive and dead at the same time. That makes no sense from our knowledge of macroscopic objects. But, QM appears to suggest that it should be. The experiment asks where do we go wrong when we apply QM to this scenario?

But in the internet, I found this Schrödinger cat experiment and his theory. Now I think I realize that Schrödinger was wrong. Even the great scientist Albert Einstein regarded this as absurd.

 

[L Drago]

No, that is not only not correct, it is EXACTLY the misunderstanding that Schrödinger was pointing out --- the absurdity of taking the Copenhagen Interpretation of QM too literally. The moon, after all, IS still there whether anyone is looking at it or not (this is another misconception), and the cat is NOT simultaneously alive and dead, it is always just one or the other. It is not the cat that is in superposition, it is a quantum object (subatomic particle).

EDIT: I see @PeroK beat me to it.

Yes, Einstein regarded it as absurd but Niels Bohr confronted that

'Automobiles aren' t subatomic particles '

But the laws of physics which work only to subatomic particles and not to real life objects seem absurd and weird.

 

[Nugatory]

For example, in Schrödinger cat experiment, the cat is in a state of quantum superposition. It means it is both alive and dead at the same state as there is 50 percent chance of emitting radiation and spilling poison. Hence, the cat is both alive and dead at the same time before we open the box.

That is a common misconception, something you think you’ve learned that you’ll have to unlearn, and an example of why you should be cautious about online videos and other pop-sci sources.

Schrödinger proposed his cat thought experiment to show that something was bad wrong in the then-current (close to a hundred years ago now) understanding of QM: it’s absurd to suggest that the cat is in that superposed state (and later paradoxes such as “Wigner’s Friend” put a sharper edge on this point) but that’s still what the math seemed to be saying.

Since then this problem has been resolved with the discovery of quantum decoherence: the cat inside the box is either dead or alive, the same way that a tossed coin is either heads-up or tails-up whether we look or not.
You might give David Lindley’s book “Where did the weirdness go?” a try. It’s pop- sci, but at least not misleading pop-sci. For the real thing, Google for “quantum decoherence” but be warned that this will take you into some mathematical deep water pretty quickly.

 

[Nugatory]

Yes, Einstein regarded it as absurd but Niels Bohr confronted that

'Automobiles aren' t subatomic particles '

But the laws of physics which work only to subatomic particles and not to real life objects seem absurd and weird.

You are now very deep in “It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so” territory.

 

[phinds]

Now I think I realize that Schrödinger was wrong.

NO. He was not wrong, he was exactly right in pointing out the absurdity of the "alive/dead" statement.

 

[L Drago]

That is a common misconception, something you think you’ve learned that you’ll have to unlearn, and an example of why you should be cautious about online videos and other pop-sci sources.

Schrödinger proposed his cat thought experiment to show that something was bad wrong in the then-current (close to a hundred years ago now) understanding of QM: it’s absurd to suggest that the cat is in that superposed state (and later paradoxes such as “Wigner’s Friend” put a sharper edge on this point) but that’s still what the math seemed to be saying.

Since then this problem has been resolved with the discovery of quantum decoherence: the cat inside the box is either dead or alive, the same way that a tossed coin is either heads-up or tails-up whether we look or not.
You might give David Lindley’s book “Where did the weirdness go?” a try. It’s pop- sci, but not at least not misleading pop-sci. For the real thing, Google for “quantum decoherence” but be warned that this will take you into some mathematical deep water pretty quickly.

I now realize that the YouTube videos I thought were preety authentic and I regarded as reliable are not authentic except a few.

 

[phinds]

But the laws of physics which work only to subatomic particles and not to real life objects seem absurd and weird.

Again, you are overextending your knowledge and making statements that don't actually make sense. QM IS, technically, completely valid for "real life objects", even if in practice most of the "weirdness" evens out due to the presence of huge #s of particles. There are even special circumstances (e.g. superconductivity) where QM is directly applicable.

 

[L Drago]

Again, you are overextending your knowledge and making statements that don't actually make sense. QM IS, technically, completely valid for "real life objects", even if in practice most of the "weirdness" evens out due to the presence of huge #s of particles. There are even special circumstances (e.g. superconductivity) where QM is directly applicable.

OK, now I understand is this the correct statement kindly check

Cat is either dead or alive until we open the box and is in a state of quantum superposition according to QM and Schrödinger's cat experiment which was correct.

 

[Nugatory]

But the laws of physics which work only to subatomic particles and not to real life objects seem absurd and weird.

The same quantum mechanical laws of physics that work for subatomic particles apply just as well to macroscopic objects. We use the methods of classical physics to analyze the behavior of automobiles because for car-sized objects classical physics is a really excellent approximation (an approximation that is accurate far far beyond the error of any imaginable measurement) and because it’s way less work (the difference between computationally possible and computationally hopeless).

There’s an analogy with the way that we use concepts of pressure, volume, temperature, density, flow and turbulence to analyze the behavior of macroscopic quantities of gases. All of these properties are results of Newton’s laws describing the behavior of each gas molecule. But we don’t solve Newton’s laws for the trajectory of each individual molecule to calculate the behavior of the gas, because we know that (for example) pressure is a really good approximation for the collective force of all these molecules bouncing off the side of the container. And we’d rather work with $PV=nRT$ then try to derive that force by calculating the constantly changing positions and speeds of $10^{25}$ individual molecules from Newton’s laws.

 

[phinds]

OK, now I understand is this the correct statement kindly check

Cat is either dead or alive until we open the box and is in a state of quantum superposition according to QM and Schrödinger's cat experiment which was correct.

NO. The cat is ALWAYS either alive or dead and is never in a state of superposition. That is the POINT of the (thought) experiment. Reread post #10. You don't seem to be paying close attention to what we keep telling you.

 

[L Drago]

NO. The cat is ALWAYS either alive or dead and is never in a state of superposition. That is the POINT of the (thought) experiment. Reread post #10. You don't seem to be paying close attention to what we keep telling you.

Okay thank you for clearing my misunderstanding.

 

[PeroK]

But cats aren't subatomic particles and QM is all about them.I don't want to say that he was completely wrong or something but I think there is a flaw in this experiment and his theory.

What Schrödinger did was link fundamental QM behaviour and macroscopic behaviour in one thought experiment. It was up to the proponents of QM. (I.e. Bohr and Heisenberg) to explain this. Which at the time they were unable to do satisfactorily.

 

[L Drago]

NO. The cat is ALWAYS either alive or dead and is never in a state of superposition. That is the POINT of the (thought) experiment. Reread post #10. You don't seem to be paying close attention to what we keep telling you.

That means -
the cat is either alive or dead but never in the state of quantum superposition.

Kindly verify is this correct

I think I need to start learning from authentic sources instead of following videos of YouTube.

 

[Nugatory]

But cats aren't subatomic particles and QM is all about them.I don't want to say that he was completely wrong or something but I think there is a flaw in this experiment and his theory.

Stop posting until you’ve had time to read the replies already posted to this thread.

Pretty much everything you think you know about this particular topic is wrong. That’s not your fault, you’ve been misled by badly oversimplified pop-sci stuff on the internet, but that’s why we tell you to be cautious about trusting the pop-sci.

 

[PeterDonis]

I think I need to start learning from authentic sources instead of following videos of YouTube.

Yes, definitely. @Nugatory gave you a reference to a good book to start with. It's not a textbook, but it's a good book for a lay person.

To really understand QM you will need to learn the required math at some point. Normally that means at the college undergraduate level.

 

[L Drago]

Stop posting until you’ve had time to read the replies already posted to this thread.

Pretty much everything you think you know about this particular topic is wrong. That’s not your fault, you’ve been misled by badly oversimplified pop-sci stuff on the internet, but that’s why we tell you to be cautious about trusting the pop-sci.

Thank you @Nugatory . I have deleted that post to avoid misunderstanding and now I will start following some authentic sources instead of those videos.

 

[L Drago]

@PeroK , @phinds, @Nugatory Now please check whether I am correct or not.

In Schrödinger cat experiment, the cat is either alive or dead is not in a state of quantum superposition.

 

[PeroK]

Now please check whether I am correct or not.

In Schrödinger cat experiment, the cat is either alive or dead until we open the box and is not in a state of quantum superposition.

Schrödinger's cat is not a good place to start learning about QM. You can only really start to analyse the problem properly once you have a firm grasp of how QM works. One issue is that alive/dead is not obviously a well-defined QM state for the cat. If you have a live cat, then the overall state of the $10^{25}$ molecules that make up the cat are in a continual state of change. You lose the coherence of the simple QM state associated with a single radioactive atom.

Moreover, QM superposition applies to complex probability amplitudes. Not to classical probabilities. This is a mistake that is often made and many popular science sources talk about the superposition of states as though these represented actual probabilities.

Until you understand QM states, superposition, coherence and interference, you end up thinking about a cat in classical terms and trying to add some sort of quantum/classical uncertainty. Which is a dead end.

Look at it this way: the cat is essentially as much of a macroscopic measuring device as the scientists in the lab looking into the box. Whatever happens when the box is opened has already happened before the box is open. The cat effectively measures whether the sample has decayed or not. And QM at the level of an individual atom has somehow transformed into the definiteness of the macroscopic world: either the sample decayed or it didn't. Either tha cat died or it didn't.

This raises the question, which is the measurement problem, of what constitutes a measurement? The only answer that Niels Bohr had was that we know what a measurement is when we see one.

https://en.wikipedia.org/wiki/Measurement_problem

You may have to leave thinking about the resolution of the measurement problem until you have a firm grasp of the basics of QM.

In many ways the simpelst explanation of Schrödinger's cat is the MWI interpretation. Although resolving the measurement problem, MWI opens up other problems (such as why do experience a single world and how do probabilities that are not 50-50 arise?). Personally, there is nothing fundamentally wrong with the MWI, but it only shifts the measurement problem onto something else.

You can read more about this through some reputable popular science sources. I think @Nugatory has already mentioned these. But, my advice would be to try the notes by James Cresser. If you can understand those notes, they will give you so much more insight into what QM is really all about. You will, however, have to be patient, as Cresser won't cover Schrödinger's cat. He does, however, tackle Stern-Gerlach in wonderfully illuminating detail.

 

[L Drago]

Schrödinger's cat is not a good place to start learning about QM. You can only really start to analyse the problem properly once you have a firm grasp of how QM works. One issue is that alive/dead is not obviously a well-defined QM state for the cat. If you have a live cat, then the overall state of the $10^{25}$ molecules that make up the cat are in a continual state of change. You lose the coherence of the simple QM state associated with a single radioactive atom.

Moreover, QM superposition applies to complex probability amplitudes. Not to classical probabilities. This is a mistake that is often made and many popular science sources talk about the superposition of states as though these represented actual probabilities.

Until you understand QM states, superposition, coherence and interference, you end up thinking about a cat in classical terms and trying to add some sort of quantum/classical uncertainty. Which is a dead end.

Look at it this way: the cat is essentially as much of a macroscopic measuring device as the scientists in the lab looking into the box. Whatever happens when the box is opened has already happened before the box is open. The cat effectively measures whether the sample has decayed or not. And QM at the level of an individual atom has somehow transformed into the definiteness of the macroscopic world: either the sample decayed or it didn't. Either tha cat died or it didn't.

This raises the question, which is the measurement problem, of what constitutes a measurement? The only answer that Niels Bohr had was that we know what a measurement is when we see one.

https://en.wikipedia.org/wiki/Measurement_problem

You may have to leave thinking about the resolution of the measurement problem until you have a firm grasp of the basics of QM.

In many ways the simpelst explanation of Schrödinger's cat is the MWI interpretation. Although resolving the measurement problem, MWI opens up other problems (such as why do experience a single world and how do probabilities that are not 50-50 arise?). Personally, there is nothing fundamentally wrong with the MWI, but it only shifts the measurement problem onto something else.

You can read more about this through some reputable popular science sources. I think @Nugatory has already mentioned these. But, my advice would be to try the notes by James Cresser. If you can understand those notes, they will give you so much more insight into what QM is really all about. You will, however, have to be patient, as Cresser won't cover Schrödinger's cat. He does, however, tackle Stern-Gerlach in wonderfully illuminating detail.

Thank you

 

[Lord Jestocost]

NO. He was not wrong, he was exactly right in pointing out the absurdity of the "alive/dead" statement.

In chapter 9 “The problem of the interpretation of quantum theory” in his book “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker), Carl Friedrich von Weizsäcker writes in section 9.3.2 “Schrödinger's cat: The meaning of the wave function”:

“Schrödinger had to admit, after the discussions described above, that a wave theory was not suitable for describing particle phenomena. For this reason he remained ever since of the opinion that quantum theory in its present form is not an adequate theory of reality, despite all its successes. He no longer participated in its development, and turned to Einsteinian-type of problems of a unified classical field theory.

In an article from 1935 (see Jammer 1974, pp. 215—218) he treats with irony the Copenhagen point of view by means a thought experiment. Let a living cat be locked up in a box and with it a deadly poison which can be released by a single radioactive atom inside the box. After one half-life of the atom the probability is $1/2$ for the cat being still alive, and $1/2$ for being dead. Schrödinger describes the $\psi$-function of the system at this time with the words: ‘The half-alive and the half-dead cat are smeared out over the entire box.’

The answer is trivial: the $\psi$-function is the list of all possible predictions. A probability $1/2$ for the two alternative possibilities (here: "living or dead") means that the two incompatible situations must now be considered equally possible at the instant of time meant by the prediction. There is no trace of a paradox.

Schrödinger's reason to consider the situation as paradoxical lay in his hope to interpret the $\psi$-function as an ‘objective’ wave field. In the implied deterministic description, he saw no reason to take seriously the difference between the present and the future. I have seen from a letter he once wrote to me (after the war) how foreign the idea was to him, as well as to many other physicists, that this difference was something to be taken seriously physically, and not merely ‘subjectively’……….”