B Are Schrodinger's cat and the double slit experiment the same idea?

[PeroK]

I'm trying to understand with my limited capacity of education. Yes, I get that people are people and it may not be a good example as quantum particles. My idea is that people have many different properties (age, height, girth, weight, gender, skin color, hair color, eye color, etc) just like quantum particles have many properties. If we measure one property we get one answer.

The reality is that particles have more than the single property we measure. What those properties are we don't know until we measure them, but as far as I am aware is that we can only measure one thing at a time. The uncertain principle says we can only know one thing, we can only get a binary answer to a question (yes/no) or is that not correct?

The UP (Uncertainty Principle) is subtler than that. The HUP (Heisenberg Uncertainty Principle) refers to preparation and measurement of the position and momentum of a single particle. If you have read popular sources on the HUP, they may have emphasised the "old" UP. In any case, here is a modern view. Note that the HUP is a statistical law. It puts no limitations on the accuracy with which we can measure either the position or the momentum of a particle! (I know that contradicts most popular science sources, but there you have it.)

Suppose we try to contain an electron. We have it confined to a small region - let's call it a box. We know that if we measure its position, we must get an answer that is in the box. If we repeat this many times, then we get a random spread of values - all in the box. There is a statistical measure called the variance of a set of data, denoted by $(\Delta x)^2$ in the case of position. In this case, the variance is on the scale of the width of the box.

Now, we measure the momentum of the electron in the box. What we find is a large variance in the measurements of momentum. This is denoted by $(\Delta p)^2$. Note that this excludes any experimental uncertainty in the measuring apparatus. We are assuming that we have a near perfect mechanism for measuring momentum. And, again, note that the HUP does not forbid these near perfect measurements.

What the HUP says is:$$\Delta x \Delta p \ge \frac \hbar 2$$Where $\hbar$ is the reduced Planck constant. It's about $1 \times 10^{-34}$ joule-seconds.

What does this mean? First, if the box is quite big, then the variance in position measurements will be quite large. And, that allows the measurements of momentum to have similar values. And, as the box is made progressively smaller, and the variance in position measurements gets smaller, then the variance in momentum measurements gets larger. In other words, we cannot both confine the electron to a very small space and control its momentum to a small range.

Note that we can apply this to the single-slit experiment. If we fire electrons through a wide slit at a detection screen, then we get a band related to the width of the slit. As we narrow the slit, the band narrows. All very classical. But, then, when the slit reaches a critical width where the value of $\hbar$ becomes relevant, the HUP kicks in. And by this I mean the HUP has a significant effect. At that point the the band on the detection screen begins to widen. And the narrower the slit becomes, the wider the band becomes. Moreover, the band begins to break up into sub-bands of light and dark.

Note that the HUP does not say you can only know position or momentum. You can simultaneously know both quite precisely - but only up to a point. You can't know both to arbitrary precision. And by "know" I mean predict the variance in measurements of position and momentum.

In this post I've tried to be as precise as possible. And have avoided woolly generalisations to try to explain precisely what the HUP says.

PS $\Delta x$, the square root of the variance, is also called the standard deviation.

 

[vadadagon]

If you are going to unlearn just one thing…. Unlearn this notion of wave-particle duality.

Uhmm.... OK. I thought that's the whole point of the double slit experiment. When we measure which slit it goes thru we see (or perhaps understand) light to behave as a particle and when not we see the wave pattern. Is this article then wrong and/or what should I think of light as if not a particle-wave duality?

"History of Wave-Particle Duality
Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules."

"Wave-Particle Duality - Key takeaways
Wave-particle duality is a concept that explains how both light and matter can act like both waves and particles, even though we can't observe both at the same time. When we think of light, we usually think of it a wave, but it can also be made up of tiny energy packets called photons. The properties of wave motion, like amplitude, wavelength, and frequency, can be used to measure light. Light also shows other wave properties, like reflection, refraction, diffraction, and interference. The photoelectric effect is another important concept in this area. It describes how electrons can be released from a metal's surface when it's hit by light with a certain frequency. These electrons are called photoelectrons. Finally, there's the uncertainty principle, which states that we can't accurately measure both the position and velocity of something at the same time, even in theory."https://shiken.ai/physics/wave-part...at is the wave-particle,both at the same time.

 

[vanhees71]

If you are going to unlearn just one thing…. Unlearn this notion of wave-particle duality.

Also I strongly suggest to study non-relativistic quantum mechanics first, before you start with relativistic quantum field theory, which you need to understand what photons really are. A good starting point is wave mechanics as presented in the Feynmsn lectures vol. 3. The complete 3-vol. set is legally for free online:

https://www.feynmanlectures.caltech.edu/

 

[PeroK]

Uhmm.... OK. I thought that's the whole point of the double slit experiment. When we measure which slit it goes thru we see (or perhaps understand) light to behave as a particle and when not we see the wave pattern. Is this article then wrong and/or what should I think of light as if not a particle-wave duality?

"History of Wave-Particle Duality
Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules."

"Wave-Particle Duality - Key takeaways
Wave-particle duality is a concept that explains how both light and matter can act like both waves and particles, even though we can't observe both at the same time. When we think of light, we usually think of it a wave, but it can also be made up of tiny energy packets called photons. The properties of wave motion, like amplitude, wavelength, and frequency, can be used to measure light. Light also shows other wave properties, like reflection, refraction, diffraction, and interference. The photoelectric effect is another important concept in this area. It describes how electrons can be released from a metal's surface when it's hit by light with a certain frequency. These electrons are called photoelectrons. Finally, there's the uncertainty principle, which states that we can't accurately measure both the position and velocity of something at the same time, even in theory."https://shiken.ai/physics/wave-particle-duality-of-light#:~:text=What is the wave-particle,both at the same time.

Now you have a conundrum! Who is right?

Shiken says: "The Wave Particle Duality of Light is a big deal in quantum theory".

I say: it was a big deal in the 1920's. In modern quantum theory, it's not.

Let's see what Feynman says (page 23 of QED):

You had to know which experiments you were analysing in order to tell if light was waves or particles. This state of confusion was called the "wave-particle duality". ... It is the purpose of these lectures to tell you how this puzzle was finally resolved.

I could go on. Suffice it to say, you have have to pick a reliable source and stick to it. There is nothing more to be learned from popular science sources that continue to emphaise the "state of confusion" of the 1920's as representing modern quantum theory.

My advice: ignore Shiken and all popular sources and YouTube videos, unless they have been specifically recommended. Read Cresser instead.

 

[Nugatory]

A more ambitious alternative is these notes, which are essentially at undergraduate level. If you do want to study these, then you must first forget everything you think you know about QM. I do mean that. You are already a little bogged down in imprecise generalities about QM. Anyway, you might want to take a look at this:

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

@vadadagon this is a good recommendation, any less mathematically demanding treatment of QM will be oversimplifying and cutting corners. It kind of has to be that way, because we’re dealing with things that are like nothing we’ve seen in our lifetime of experience with macroscopic objects. Without those comparisons, there’s nothing but the math on which to build our understanding.

But if you’re finding the math too much of a barrier to entry, Giancarlo Ghirardi’s book “Sneaking a look at god’s cards” is worth a try. It is no substitute for a real textbook, but it’s better than most of the pop-sci that’s out there.

 

[vanhees71]

Uhmm.... OK. I thought that's the whole point of the double slit experiment. When we measure which slit it goes thru we see (or perhaps understand) light to behave as a particle and when not we see the wave pattern. Is this article then wrong and/or what should I think of light as if not a particle-wave duality?

This is a very old misconception of the so-called "old quantum theory", which were some concepts used between Planck's black-body-radiation theory (1900) and the discovery of "modern quantum theory" (around the same time in three equivalent versions by Born, Jordan, Heisenberg (matrix mechanics), Schrödinger (wave mechanics), and Dirac (transformation theory). There the wave-particle duality is resolved by the probability interpretation by Born (1926).

"History of Wave-Particle Duality
Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules."

This is not only physically but also historically very inaccurate.

"Wave-Particle Duality - Key takeaways
Wave-particle duality is a concept that explains how both light and matter can act like both waves and particles, even though we can't observe both at the same time. When we think of light, we usually think of it a wave, but it can also be made up of tiny energy packets called photons. The properties of wave motion, like amplitude, wavelength, and frequency, can be used to measure light. Light also shows other wave properties, like reflection, refraction, diffraction, and interference. The photoelectric effect is another important concept in this area. It describes how electrons can be released from a metal's surface when it's hit by light with a certain frequency. These electrons are called photoelectrons. Finally, there's the uncertainty principle, which states that we can't accurately measure both the position and velocity of something at the same time, even in theory."

These is a great confusion, mixing many concepts together in a way that leads to misconceptions which have to be unlearned before studying the true thing, i.e., modern quantum mechanics (non-relativistic theory, not applicable to photons!) and relativistic quantum field theory (the only correct way to describe what photons really are).

https://shiken.ai/physics/wave-particle-duality-of-light#:~:text=What is the wave-particle,both at the same time.

 

[PeterDonis]

I thought that's the whole point of the double slit experiment

It isn't. Please take my advice from post #30 and stop trying to apply what you currently think you know about QM. @PeroK's advice about sources in post #34 is also good.

 

[vadadagon]

The UP (Uncertainty Principle) is subtler than that. The HUP (Heisenberg Uncertainty Principle) refers to preparation and measurement of the position and momentum of a single particle. If you have read popular sources on the HUP, they may have emphasised the "old" UP. In any case, here is a modern view. Note that the HUP is a statistical law. It puts no limitations on the accuracy with which we can measure either the position or the momentum of a particle! (I know that contradicts most popular science sources, but there you have it.)

Suppose we try to contain an electron. We have it confined to a small region - let's call it a box. We know that if we measure its position, we must get an answer that is in the box. If we repeat this many times, then we get a random spread of values - all in the box. There is a statistical measure called the variance of a set of data, denoted by $(\Delta x)^2$ in the case of position. In this case, the variance is on the scale of the width of the box.

Now, we measure the momentum of the electron in the box. What we find is a large variance in the measurements of momentum. This is denoted by $(\Delta p)^2$. Note that this excludes any experimental uncertainty in the measuring apparatus. We are assuming that we have a near perfect mechanism for measuring momentum. And, again, note that the HUP does not forbid these near perfect measurements.

What the HUP says is:$$\Delta x \Delta p \ge \frac \hbar 2$$Where $\hbar$ is the reduced Planck constant. It's about $1 \times 10^{-34}$ joule-seconds.

What does this mean? First, if the box is quite big, then the variance in position measurements will be quite large. And, that allows the measurements of momentum to have similar values. And, as the box is made progressively smaller, and the variance in position measurements gets smaller, then the variance in momentum measurements gets larger. In other words, we cannot both confine the electron to a very small space and control its momentum to a small range.

Note that we can apply this to the single-slit experiment. If we fire electrons through a wide slit at a detection screen, then we get a band related to the width of the slit. As we narrow the slit, the band narrows. All very classical. But, then, when the slit reaches a critical width where the value of $\hbar$ becomes relevant, the HUP kicks in. And by this I mean the HUP has a significant effect. At that point the the band on the detection screen begins to widen. And the narrower the slit becomes, the wider the band becomes. Moreover, the band begins to break up into sub-bands of light and dark.

Note that the HUP does not say you can only know position or momentum. You can simultaneously know both quite precisely - but only up to a point. You can't know both to arbitrary precision. And by "know" I mean predict the variance in measurements of position and momentum.

In this post I've tried to be as precise as possible. And have avoided woolly generalisations to try to explain precisely what the HUP says.

PS $\Delta x$, the square root of the variance, is also called the standard deviation.

So let me see if I understand this correctly.

In the double slit experiment the band narrows until you reach the plank constant (the shortest measurable length constant) at which point then the band begins to widen and we see the sub bands or light and dark (or the interference waves).

However, isn't that driving the point I'm making? While we can measure we get one result and as soon as we begin to reach the limit of what we can measure we see the sub-bands again as if we didn't measure it at all. Which would mean we get the results we get because we are measuring for something specific, when the measurements are so small we can no longer measure it then it returns to the wave pattern or is this entirely wrong?

It's like looking at a single atom Carbon atom and trying to figure out if that atom was extracted from a plant or an animal. All you can know it's what the atom tells you, all the relevant information about where the atom was extracted is lost because the measurements are so small it plays no relevance as to whether it came from a animal or a plant.

 

[vadadagon]

Now you have a conundrum! Who is right?

Shiken says: "The Wave Particle Duality of Light is a big deal in quantum theory".

I say: it was a big deal in the 1920's. In modern quantum theory, it's not.

Let's see what Feynman says (page 23 of QED):

You had to know which experiments you were analysing in order to tell if light was waves or particles. This state of confusion was called the "wave-particle duality". ... It is the purpose of these lectures to tell you how this puzzle was finally resolved.

I could go on. Suffice it to say, you have have to pick a reliable source and stick to it. There is nothing more to be learned from popular science sources that continue to emphaise the "state of confusion" of the 1920's as representing modern quantum theory.

My advice: ignore Shiken and all popular sources and YouTube videos, unless they have been specifically recommended. Read Cresser instead.

Well I think this is why I'm lost. By trying to do my own "research" which I could understand I come across these archaic ideas and why I'm here asking.

I'll continue to read the books recommended and if I have further questions I'll come back.
Thanks for continuing to try and explain it, I'll go back and climb up my tree where I can eat my nuts, grunt at the other apes and try to understand Feynman.

 

[PeroK]

So let me see if I understand this correctly.

In the double slit experiment

I said nothing about that. I analysed the single-slit experiment.

the band narrows until you reach the plank constant

No. Not the Planck constant. Some finite width .

(the shortest measurable length constant)

That's something else entirely.

at which point then the band begins to widen and we see the sub bands or light and dark (or the interference waves).

However, isn't that driving the point I'm making? While we can measure we get one result and as soon as we begin to reach the limit of what we can measure we see the sub-bands again as if we didn't measure it at all.

I don't know how you interpret what I said that way. We didn't really measure anything - except where each electron hit the screen. The single slit can be seen more as a preparation procedure. We only know that at some time the electron's wavefunction must have been confined to the width of the slit.

Which would mean we get the results we get because we are measuring for something specific, when the measurements are so small we can no longer measure it then it returns to the wave pattern or is this entirely wrong?

That's reading more than I would into the analysis. We fired electrons through a slit of varying width and measured where they hit a detector screen. Stick to the facts!

It's like looking at a single atom Carbon atom and trying to figure out if that atom was extracted from a plant or an animal.

I don't see that.

All you can know it's what the atom tells you, all the relevant information about where the atom was extracted is lost because the measurements are so small it plays no relevance as to whether it came from a animal or a plant.

This has nothing to do with what I wrote, as far as I can see.

 

[PeterDonis]

Which would mean we get the results we get because we are measuring for something specific, when the measurements are so small we can no longer measure it then it returns to the wave pattern or is this entirely wrong?

It's entirely wrong. I have already pointed out the underlying reason for this, that pretty much everything you currently think you know about QM is wrong. Please stop trying to reason from this wrong information. You will just keep getting the same response.

 

[PeterDonis]

Thread closed for moderation.

 

[DrClaude]

The thread will remain closed. @vadadagon, please take the time check the resources pointed to you and post any subsequent question in a new thread.