Beginner question about combined waves

[Jo-Jo]

I am new to this forum and forums in general. Please let me know if I am not following the rules, or have posted to an incorrect topic. I did search before posting, but please let me know if I missed a thread that answers this.

I have done a little bit of reading about the ideas behind Quantum Physics, but am definitely A BEGINNER and do not understand the formulas behind them at this time (I am not yet sure how to start tackling that part). I am looking to get the basics of the ideas involved. It is likely that I will use terms incorrectly, and I welcome polite explanations of my mistakes. I will also ask questions in different ways, so please know I am not being argumentative or trying debunk answers or think I know better. I can get caught in incorrect ideas and confuse myself and sometimes need to slash them from multiple angles so I can move on to the next step of learning.

I recently searched on youtube to see if what I thought I had learnt in the past about quantum theories was correct, and maybe learn about more recent developments. I watched a few videos with Brian Greene, his approach seems good for a beginner like myself. In the video "Chasing Quantum Realities -- Brian Greene" https://www.youtube.com/watch?v=GXdSktsE8pY about 27 minutes in he talks about how waves can be combined...and I hit a snag and I know I am fundamentally misunderstanding something.

Question: If the locations of two electrons are known, and you combine their wave shapes, why is it surprising that the the detector would flip back and forth between the two locations? Are they not still two separate electrons with two locations?

Edited September 3, 2020 by Jo-Jo

[studiot]

9 hours ago, Jo-Jo said:

Question: If the locations of two electrons are known, and you combine their wave shapes, why is it surprising that the the detector would flip back and forth between the two locations? Are they not still two separate electrons with two locations?

I really don't like the (double) slit experiment as it is so often used to present a slick 'Look how clever and tricky I am'  point of view of the combination of waves.

(Yes it does also have legitimate significance)

 

Here is a simple sine wave

 

Do you understand

1) What is being measured along both axes 

2) The difference between a travelling wave and a standing wave.

 

This is very important when it comes to combining waves.

[joigus]

10 hours ago, Jo-Jo said:

Question: If the locations of two electrons are known, and you combine their wave shapes, why is it surprising that the the detector would flip back and forth between the two locations? Are they not still two separate electrons with two locations?

The double slit experiment is about measuring the position of electrons one at a time. But all of the electrons respond to the same preparation (the same quantum state). So it's never two electrons at the same time.

So the wave is the same, it represents a situation, reproduced exactly as before. But the electrons are one electron, and then another, and then another.

Although in a way, you can think of it as the same electron doing different things under the same initial conditions.

I hope that helps. It's the most common source of confusion in relation to this experiment.

The first 2 chapters of Feynman's Lectures on Physics, Vol III are a classic.

[Jo-Jo]

6 hours ago, studiot said:

Do you understand

1) What is being measured along both axes 

2) The difference between a travelling wave and a standing wave.

1) Above the solid line (vertical axis) is the peak of the wave. Where the waves are largest are the places where the electrons are most likely to be, and below less likely, and not at all at the lowest point (or does that only apply to interference, not a single wave?). The horizontal axis shows the width of the wave. If you have a certain amount of the locations (x and y) you can graph the wave (show/determine it's curvature)? One can also see the wave cycle.

2) Based on the snippet I have just read, a traveling wave is moving (along the horizontal axis), like the ripples we see in water. A standing wave is created when two waves of equal height travel in opposite directions. Do they need to be traveling at the same speed too for this occur? I do not yet understand how the medium can cause interference.

4 hours ago, joigus said:

I hope that helps. It's the most common source of confusion in relation to this experiment.

Yes, thank you. I will try to see if I can get a copy of that book through my library. I now need to learn more about what happens when waves are combined.

Edited September 3, 2020 by Jo-Jo

[swansont]

16 hours ago, Jo-Jo said:

 I recently searched on youtube to see if what I thought I had learnt in the past about quantum theories was correct, and maybe learn about more recent developments. I watched a few videos with Brian Greene, his approach seems good for a beginner like myself. In the video "Chasing Quantum Realities -- Brian Greene" https://www.youtube.com/watch?v=GXdSktsE8pY about 27 minutes in he talks about how waves can be combined...and I hit a snag and I know I am fundamentally misunderstanding something.

This is probably not the best way to learn QM, but it is a reasonable way to learn a little bit about QM. You will miss a lot by skipping over fundamental concepts.

16 hours ago, Jo-Jo said:

Question: If the locations of two electrons are known, and you combine their wave shapes, why is it surprising that the the detector would flip back and forth between the two locations? Are they not still two separate electrons with two locations?

If the waves overlap, you can't say that they are in two locations. (and in this case it doesn't matter if you are talking about the deBroglie waves or the wave functions, which are two separate concepts) The electron is not a tiny ball. 

(I don't get the comment about the detector flipping back and forth; I assume that's from a specific example, and if it is, it may be true only for that example.)

 

[Jo-Jo]

1 hour ago, swansont said:

This is probably not the best way to learn QM, but it is a reasonable way to learn a little bit about QM. You will miss a lot by skipping over fundamental concepts.

A while back I read 30‑Second Quantum Theory and 30-Second Einstein published by Propero Books. Why these books? My fiance found them on sale after I had asked for books on string theory. I am egged on to learn about string theory not only because it fascinated me from the very first time it was described to me (that definition has since evolved a bit), but also by the fact that I have a "doppelganger" with the same first and last name as me who teaches string theory where I used to live. This is hilarious and crazy, is the professor proof that I can exist in two places? I dropped out of high school physics and chose to pursue visual art in university only because the physics teacher's idea of teaching was to point at the equation he had written on the board or to the text book. I learn by asking questions. This "other me" that did pursue physics intrigues me. I did try contacting them to see if we were somehow related, but they did not respond, if it were me I would be freaked out or think it was a joke. Since we might both cease to exist (they do not look like me to be clear) I decided to drop it and have it remain mysterious 😉. I don't have the prerequisite to take their class, and if I did what would they think!

Back to the books, I understand anywhere from %50 to %80 of what I am reading if it has a lot of terms I am not familiar with. So I thought I would try another medium, the one I am apt at, the visual mediums, to brush up. But some parts of the videos seem to challenge what I thought I had gleaned from the books. So now I am trying discussion here on this forum to try and clarify what has become muddled. Suggested reading, particularly about the fundamentals as you mentioned are very much welcome. I still enjoy reading about it even if I have no idea if I am actually getting it.

1 hour ago, swansont said:

(I don't get the comment about the detector flipping back and forth; I assume that's from a specific example, and if it is, it may be true only for that example.)

In the video for which I shared a link, it is stated (not word for word) that in an imaginary example the location of two electrons can be known, using an instrument to detect them. Brian then goes on to say that the waves of those two electrons can be combined. When this is done, he says something confusing happens, that the instrument becomes confused switching back and forth between the two locations.

 

1 hour ago, swansont said:

If the waves overlap, you can't say that they are in two locations.

This is what I do not understand, I am hoping studiot will continue working with me so I can fully understand what happens when waves are combined. I apologize to all in advance, I am a slow learner.

Edited September 3, 2020 by Jo-Jo

[joigus]

3 minutes ago, Jo-Jo said:

This what I do not understand, I am hoping studiot will continue working with me so I can fully understand what happens when waves are combined. I apologize to all in advance, I am a slow learner.

You're not. The nature of the problem is difficult.

In order to show the effects of interference you need the wave to come together again so to speak.

OTOH, the "electron in two different places" is a kind of language developed to try to express puzzling nature of the situation but it's not correct, actually, it's plain wrong, and it refers to the immediate past. While the wave was going through the slits, the wave must have split. But upon arrival and detection, the electron always appears as a particle. Here's the apparent paradox:

Classical thinking makes you think "either the wave went through slit 1 or through slit 2". Not true! No matter how compelling it sounds.

It's not "the electron went through slit 1 and 2 at the same time" either. This is nonsense. The conclusion is weaker (weaker assertions are safer):

"Neither the electron went through slit 1, nor it went through slit 2 as long as no interaction was set to detect which slit the electron went through".

It's about what you cannot say, not about what you can say. You must read Feynman chapters 1 and 2. Nobody has explained this as illuminatingly.

Weaker assumptions are much more solid, much less likely to be incorrect.

[swansont]

15 hours ago, Jo-Jo said:

In the video for which I shared a link, it is stated (not word for word) that in an imaginary example the location of two electrons can be known, using an instrument to detect them. Brian then goes on to say that the waves of those two electrons can be combined. When this is done, he says something confusing happens, that the instrument becomes confused switching back and forth between the two locations.

No, that’s not what he said. He’s talking about one electron.

He’s also overselling the situation. Nobody* says the detector would be confused, or that we would (or should) detect an electron in two places. At best he’s trying to convince people that this isn’t the right way to interpret the wave function, but IMO it’s a poor way to do it, and you’re confused, so...

 

*Rhetorical. I’m sure if you did an exhaustive search you could find one or two confused people claiming this. It’s not a mainstream, widespread claim/explanation 

[studiot]

2 hours ago, Jo-Jo said:

In the video for which I shared a link, it is stated (not word for word) that in an imaginary example the location of two electrons can be known, using an instrument to detect them. Brian then goes on to say that the waves of those two electrons can be combined. When this is done, he says something confusing happens, that the instrument becomes confused switching back and forth between the two locations.

 

3 hours ago, swansont said:

If the waves overlap, you can't say that they are in two locations.

This is what I do not understand, I am hoping studiot will continue working with me so I can fully understand what happens when waves are combined. I apologize to all in advance, I am a slow learner.

Thank you for your confidence.

That is entirely possible for an instrument to be switching and for it to be confused if it is not properly set up.

The technique is used extensively in electronics and is called multiplexing.
There are quite a few variations.

The old fashioned FM radio broacasts as well as TV used what was called frequency or phase division multiplexing.

More recently the Internet runs on something called time division multiplexing.
It also employs route division (space) multiplexing

The idea is best illustrated by a diagram.

Basically signals from more than one source are connected through a switch which cycles through each signal source for a fixed period then moves on to the next and so on round the cycle.
So the instrument sends or displays or measures or whatever, the signal from each source in turn and then moves on to the next until it has read them all. Then it starts again round the cycle.
 

That is shown diagramtically in fig1.

But enough of this digression  -  back to waves.

Good on you for looking up travelling and standing waves.
The sine wave I posted is a travelling wave, but there is a twist to the story.
A wave connects time and space.
I won't post the 'wave equation' for now but let us put some flesh on the bones of my sine wave.
I didn't label the axes for a particular reason, I will now explain.
A wave shows the variation of some property or quantity in time and/or space.
This variation is periodic in nature which means it repeats over and over again indefinitely.
The quantity always remains finite   - do you understand this  ?

So if we plot a graph of this quantity as the vertical y axis, it is often called the amplitude against either time or space as the horizontal axis
we will see the sine wave I posted.
The shape of the wave is called the wave function, in this case a sine curve but it could be a different repetitive curve that always remains finite.

So now we have two plots

Amplitude against space (distance)
Amplitude against time.

These appear in figs 2 and 3

And waddaya know ?

They are both the same.
An observer looking out over the wave crest cannot tell if he is looking out over time or space.

This is a most remarkable characteristic.

Next time we will combine some waves to produce some interference and standing waves.

[swansont]

12 hours ago, studiot said:

Thank you for your confidence.

That is entirely possible for an instrument to be switching and for it to be confused if it is not properly set up.

The technique is used extensively in electronics and is called multiplexing.
There are quite a few variations.

 

Faulty setup is simply not an issue for a QM concept. 

The question asked also has no obvious (to me) connection to multiplexing, or necessarily to interference (while it's one way to get to a scenario like what was described, it's not the only one, and such details are moot)

[Sensei]

On 9/3/2020 at 2:38 AM, Jo-Jo said:

and I hit a snag and I know I am fundamentally misunderstanding something.

You can send one electron (in electrons double slit experiment), or one photon (in photons double slit experiment) per second (or fraction of second).. after a while you will get interference pattern on the screen anyway.

Screen/detector detects one particle hitting it at a time and counts them (or reflects them in photons double slit experiment performed at home). Pattern area where more particles hit screen/detector is brighter.

In the case of photons double slit experiment, wavelength of photon is given by formula [math]\lambda=hc/E[/math]

In the case of electrons double slit experiment, wavelength of electron is de Broglie wavelength. Read article from Wikipedia, if you're not familiar with it:

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

 

What you should start with is getting equipment allowing you to perform double slit experiment at home for photons.

Search net for "double slit experiment ebay" or "double slit experiment amazon", "alibaba", "aliexpress" or so.

You will need filter like this:

https://www.amazon.com/Diaphragm-Double-Slits-Different-Spacings/dp/B00KWZ5WQ0

and laser (preferably multiple colors, red, green and blue, to see difference between them).

 

Pattern changes with different color light source.

Pattern changes with different space between slits.

Pattern changes with different width of slits.

 

Once you have equipment at home, tested various colors, various widths of slits, various spaces between slits, you can figure out equation which will satisfy the all cases.

 

[swansont]

15 hours ago, joigus said:

You're not. The nature of the problem is difficult.

In order to show the effects of interference you need the wave to come together again so to speak.

OTOH, the "electron in two different places" is a kind of language developed to try to express puzzling nature of the situation but it's not correct, actually, it's plain wrong, and it refers to the immediate past. While the wave was going through the slits, the wave must have split. But upon arrival and detection, the electron always appears as a particle. Here's the apparent paradox:

Classical thinking makes you think "either the wave went through slit 1 or through slit 2". Not true! No matter how compelling it sounds.

It's not "the electron went through slit 1 and 2 at the same time" either. This is nonsense. The conclusion is weaker (weaker assertions are safer):

"Neither the electron went through slit 1, nor it went through slit 2 as long as no interaction was set to detect which slit the electron went through".

It's about what you cannot say, not about what you can say. You must read Feynman chapters 1 and 2. Nobody has explained this as illuminatingly.

Weaker assumptions are much more solid, much less likely to be incorrect.

The issue isn't the double-slit experiment. The video merely states that the electron's wave function has two peaks. Explaining the double-slit is getting bogged down in irrelevant (for now) detail, IMO.

A wave function that has two sharp peaks basically describes a situation where the electron, if detected, will be found in one of two locations. In this case, the probability is equal, as the wave function has the same amplitude.

However, it is not wrong to say that the electron is at both locations before detection. There are experiments other than the double-slit where you have superposition of locations (Kasevich did this with launched atoms into a superposition of states, where the two states would have a physical separation) and the result is not consistent with atoms at one location or the other. (see also: entanglement) The experiments that show this are typically interference experiments, because that's where the results manifest themselves - classical physics can't account for the results.

So, both states are occupied before detection. But detection is in one state or the other. How this happens is a matter of what physics interpretation is discussed - that's what was meant by "physicists don't know how this happens." One interpretation is that the wave function "collapses" as a result of the measurement, but that's just a way of understanding the result, not a description of some physical process.

 

[joigus]

36 minutes ago, swansont said:

The issue isn't the double-slit experiment. The video merely states that the electron's wave function has two peaks. Explaining the double-slit is getting bogged down in irrelevant (for now) detail, IMO.

I haven't watched the video yet.  

Thanks for the clarification. I'll follow your pointers ASAP.

[swansont]

1 hour ago, joigus said:

I haven't watched the video yet.  

Thanks for the clarification. I'll follow your pointers ASAP.

It'd be better if one didn't have to, but when the video gives a (IMO) poor explanation and the OP is a physics neophyte, it's the only way to figure out what's going on, and try and see what the misconception is.

But in that section of video (starts at about 28:00) he just has a wave function, first with one spike and then with two. He's using two locations in Manhattan, NYC, as examples, which drives home the spatially-separated aspect of it.   

 

[studiot]

2 hours ago, swansont said:

Faulty setup is simply not an issue for a QM concept. 

The question asked also has no obvious (to me) connection to multiplexing, or necessarily to interference (while it's one way to get to a scenario like what was described, it's not the only one, and such details are moot)

The title says nothing about QM, and as I already noted, there are legitimate and worthwhile  implementations/uses of the single, double and multiple slit experiments.

It is clear that the OP would like to learn and get straightened out some misconceptions, not least that he has mixed up classical wave theory and QM, which is very common.

It is also clear to me that a poor presentation of much more difficult material has been partly responsible for this, along with a shaky foundation of the whole subject.

I was simply trying to shore up this foundation at an acceptable level, so I am sorry you clearly think I have failed, particularly in my attempt to build up the background material.

 

So I will leave you to to explain the finer details of QM to a beginner who is clearly aware that he hasn't yet appreciated what constitutes a wave, let alone a wave function which is something else again.

 

I apologise for my intrusion in this thread.

[joigus]

8 hours ago, swansont said:

It'd be better if one didn't have to, but when the video gives a (IMO) poor explanation and the OP is a physics neophyte, it's the only way to figure out what's going on, and try and see what the misconception is.

I really want to take a look at the Kasevich experiment that you mentioned. Does it have to do with gravitation? He's got some experiments that involved gravitation...

10 hours ago, swansont said:

However, it is not wrong to say that the electron is at both locations before detection.

Well. Maybe there are good reasons to say that as a way of wording the very surprising fact that the energy-momentum of the whole thing really is split. Maybe even the charge density. I wouldn't be shocked if that were so. Detection is a different matter, though. I'm afraid. About that we seem to agree.

Thank you for the really valuable info. I'm done for the day, I'm afraid. At least with difficult topics.

[swansont]

24 minutes ago, joigus said:

I really want to take a look at the Kasevich experiment that you mentioned. Does it have to do with gravitation? He's got some experiments that involved gravitation...

Well. Maybe there are good reasons to say that as a way of wording the very surprising fact that the energy-momentum of the whole thing really is split. Maybe even the charge density. I wouldn't be shocked if that were so. Detection is a different matter, though. I'm afraid. About that we seem to agree.

Thank you for the really valuable info. I'm done for the day, I'm afraid. At least with difficult topics.

https://www.nature.com/articles/nature16155

Paywalled, unfortunately 

[Jo-Jo]

On 9/3/2020 at 3:36 PM, studiot said:

This variation is periodic in nature which means it repeats over and over again indefinitely.
The quantity always remains finite   - do you understand this  ?

I have not been to find an answer to why a traveling repeats indefinitely and why the quantity remain finite. For the purposes of this explanation is it enough that I I simply accept this as the definition of a traveling wave?

This is what I have used to try and get a better understanding of waves (I have not yet completed the unit): https://www.khanacademy.org/science/physics/mechanical-waves-and-sound

 

On 9/4/2020 at 7:21 AM, studiot said:

The question asked also has no obvious (to me) connection to multiplexing, or necessarily to interference (while it's one way to get to a scenario like what was described, it's not the only one, and such details are moot)

It does illuminate things a bit for me, because I did not find it surprising that an instrument could react this way. It is interesting that this can be used practically. However you are correct that my question was assuming that instrument was working correctly. It is understandable that my question was not entirely clear since I was confused.

 

On 9/4/2020 at 5:11 AM, swansont said:

The issue isn't the double-slit experiment. The video merely states that the electron's wave function has two peaks.

Yes my question was not about the double slit experiment although Brain in the video does say that waves can be combined as in the double slit experiment. So a comparison may be drawn (?), but to be specific I was struggling with the example of what I mistakenly thought was describing the measurement two separate electrons in central park (minutes 28 - 30 into the video). I am so sorry and embarrassed! But it is one electron in the example, not two, my bad.

I still would like to learn what happens when the waves combine, if some of you have not lost patience with me already!

On 9/4/2020 at 7:21 AM, studiot said:

I apologise for my intrusion in this thread.

I did not find it intrusive, and would like to continue wherever it is that you may be going with the lesson. I have personally found everyone's input to be helpful.

Edited September 6, 2020 by Jo-Jo

[swansont]

2 hours ago, Jo-Jo said:

Yes my question was not about the double slit experiment although Brain in the video does say that waves can be combined as in the double slit experiment. So a comparison may be drawn (?), but to be specific I was struggling with the example of what I mistakenly thought was describing the measurement two separate electrons in central park (minutes 28 - 30 into the video). I am so sorry and embarrassed! But it is one electron in the example, not two, my bad.

I still would like to learn what happens when the waves combine, if some of you have not lost patience with me already!

The question of what happens when waves combine us a general one; there are multiple kinds of waves. The example in the video is more specific, as it has to do with the waves of the Schrödinger equation, which describe the probability of finding the electron at a particular place (and other things)

[joigus]

On 9/3/2020 at 2:38 AM, Jo-Jo said:

Question: If the locations of two electrons are known, and you combine their wave shapes, why is it surprising that the the detector would flip back and forth between the two locations? Are they not still two separate electrons with two locations?

OK. I've watched the video, and it's definitely here where you're getting confused: The described situation of two peaks is about one electron, not about two electrons. 

You can add two, three, etc. waves each representing the probability amplitude for one among two, three, etc., different incompatible outcomes of an experiment for one particle.

[studiot]

16 hours ago, Jo-Jo said:

I have not been to find an answer to why a traveling repeats indefinitely and why the quantity remain finite. For the purposes of this explanation is it enough that I I simply accept this as the definition of a traveling wave?

This is what I have used to try and get a better understanding of waves (I have not yet completed the unit): https://www.khanacademy.org/science/physics/mechanical-waves-and-sound

+1 for trying to bring yourself up to speed on waves and or asking questions where you are not sure of something. The Khan Academy has a good reputation.

It also fits well with what I was trying to say. Notably that it is a good idea to at least look at, if not study deeply, classical waves before trying for Quantum waves, which are more difficult.
This is not least because many of the classical ideas are directly transferable, although there are some stark differences.
Although the combination of quantum waves is one of the most common processes on Earth, if not in the Universe, it is purely abstract in that we can't directly grab hold of it like we can with classical waves in a wave tank or on a string . Another word for combination of quantum waves is chemical reactions. That is the main situation where you have the quantum waves of two electrons involved.

To answer your questions about travelling waves, which are good ones that show you have read carefully what I wrote, yes it is important to understand why.
These are one of several 'wrinkles' to get clear as they are amongst the things that transfer (in some way) from classical to quantum, but the ideas are easier to introduce in a classical setting.
Luckily they are easy to elucidate, but I will need to draw some more diagrams.

Do you understand what a sine a cosine and a tangent are in trigonometry or anything else ?
(The blue curve I originally posted is part of a sine wave),