Teaching about electromagnetic radiation & struggling

[flintstones]

Summary:: I teach high school (grade 12) and have always struggled with teaching about electromagnetic radiation. I'm looking for resources aimed at laypeople about EMR that may give me some ideas on how to teach it more clearly.

I teach high school (grade 12). We have just finished a unit about electric and magnetic fields. For example we talk about how charges make electric fields, and how moving charges make magnetic fields. Students sort of grasp this idea, though I'd say they struggle with it. Note that we don't discuss flux in high school here.

Next, we're starting to learn about light and electromagnetic radiation. But I am having problems teaching it because I actually never studied it myself in university. Here are the issues I'm having:

• The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles. How do I explain this? In the past I've said that an accelerating charged particle, because it's moving, makes a magnetic field. Since it's accelerating, that magnetic field is changing. Changing magnetic fields make changing electric fields, and these sustain each other as EMR. Is this even true? It feels unsatisfying for some reason.
• If the above explanation is true, then how do I explain why a changing magnetic field makes a changing electric field? Maybe it's not necessary to explain this, and that's just the way the world works. What do you think? I think the issue is the link between this and our last unit isn't quite clear. In the last unit, we just say that moving charges induce magnetic fields, and that changing magnetic fields induce currents. But now we are saying that changing magnetic fields actually make changing electric fields, and I feel like the link there is not entirely clear.
• I tried to read up on this online but am having trouble finding a resource that's at the right level. Does anyone know of a good resource? Maybe something aimed at laypeople? I did take ~10 undergraduate physics courses, so I could probably understand something written for 2nd year physics students, if necessary. Ideally though it would be a resource that I could share with my students.

 

[vanhees71]

I'm not familiar with the level of math your high school students have. When I went to high school we had a basic knowledge of calculus and in E&M we learned in a semiquantitative way to understand line-, volume-, and surface integrals. Here are some old lecture notes I used in an introductory E&M-physics lecture for engineering students (though in my handwriting only) using just that prerequisites:

https://itp.uni-frankfurt.de/~hees/physics208/phys208-notes-IV.pdf

The complete material of this lecture can be found here:

https://itp.uni-frankfurt.de/~hees/physics208.html

 

[flintstones]

I'm not familiar with the level of math your high school students have. When I went to high school we had a basic knowledge of calculus and in E&M we learned in a semiquantitative way to understand line-, volume-, and surface integrals. Here are some old lecture notes I used in an introductory E&M-physics lecture for engineering students (though in my handwriting only) using just that prerequisites:

https://itp.uni-frankfurt.de/~hees/physics208/phys208-notes-IV.pdf

The complete material of this lecture can be found here:

https://itp.uni-frankfurt.de/~hees/physics208.html

Thank you! Most of my students have not learned any calculus yet, so we mostly stick to discussing things on a qualitative level. But I will have a look at your notes, since if I understand the concepts better myself, I will be able to figure out how to explain them more clearly.

 

[vanhees71]

Then it's really difficult. I think the most difficult task in teaching physics is if you are not allowed to use math. In fact I only learned some years ago that there's indeed some didactical opinion that one should have "calculus free physics" at the university. I guess, there are textbooks for such courses. I only had to substitute one of my colleagues for 2 weeks in a mechanics lecture. So I don't know, how they handle electromagnetism in a calculus-free way. I think the best you can do in calculus-free physics is to discuss experiments. In the ideal case I would do some in class and, if there's enough hardware around, let the students do experiments themselves.

In connection with em. waves I remember an experiment our physics teacher did in class with an old vacuum tube and a wire loop with an AC inducing a vortex field within the tube leading to beautiful colored vortices of charged particles. I cannot remember the details, but in a way it was a demonstration of Faraday's Law which made it really a quite direct experience of this particular law.

 

[kuruman]

I am a fan of PhET simulations. Try this one for a visualization of what's going on. I suggest that you use the button controls on the right to show how the static field propagates in space and what it's like in the near and far zones. One has to imagine the magnetic field perpendicular to the shown electric field but that's the price to pay when you reduce three mutually perpendicular dimensions into two.

https://phet.colorado.edu/en/simulation/radio-waves

 

[A.T.]

The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles. How do I explain this?

On the fundamental level:
https://phet.colorado.edu/en/simulation/radiating-charge

 

[Andy Resnick]

Summary:: I teach high school (grade 12) and have always struggled with teaching about electromagnetic radiation. I'm looking for resources aimed at laypeople about EMR that may give me some ideas on how to teach it more clearly.

I teach high school (grade 12). We have just finished a unit about electric and magnetic fields. For example we talk about how charges make electric fields, and how moving charges make magnetic fields. Students sort of grasp this idea, though I'd say they struggle with it. Note that we don't discuss flux in high school here.

Next, we're starting to learn about light and electromagnetic radiation. But I am having problems teaching it because I actually never studied it myself in university. Here are the issues I'm having:

I think this is a tricky problem, mostly because trying to teach the underlying theory is so abstract (for the students). I don't know how much autonomy you have in this situation, but perhaps a more useful approach would be to teach the students "How is it (based on what evidence) that we came to understand that light is composed of both a changing electric and changing magnetic field combined in a highly specific and particular way?" Remember, the electric and magnetic fields are not independent entities here; there is but a single field: the electromagentic field.

I do want to caution you that "The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles." is problematic. For example, when an excited atom emits visible light, that emission is not due to acceleration of charged particles.

This article may provide some insight, by discussing Hertz's experiments:

https://www.britannica.com/science/light/Light-as-electromagnetic-radiation

 

[flintstones]

Then it's really difficult. I think the most difficult task in teaching physics is if you are not allowed to use math. In fact I only learned some years ago that there's indeed some didactical opinion that one should have "calculus free physics" at the university. I guess, there are textbooks for such courses. I only had to substitute one of my colleagues for 2 weeks in a mechanics lecture. So I don't know, how they handle electromagnetism in a calculus-free way. I think the best you can do in calculus-free physics is to discuss experiments. In the ideal case I would do some in class and, if there's enough hardware around, let the students do experiments themselves.

In connection with em. waves I remember an experiment our physics teacher did in class with an old vacuum tube and a wire loop with an AC inducing a vortex field within the tube leading to beautiful colored vortices of charged particles. I cannot remember the details, but in a way it was a demonstration of Faraday's Law which made it really a quite direct experience of this particular law.

Yes, it's been quite challenging to teach for that reason! Especially once we start getting into wave particle duality and it's super hard to explain, possibly even impossible, without any math. Thanks for the experiment idea - I will check with the lab tech at the university here and see if he has heard of this demo!

 

[flintstones]

I am a fan of PhET simulations. Try this one for a visualization of what's going on. I suggest that you use the button controls on the right to show how the static field propagates in space and what it's like in the near and far zones. One has to imagine the magnetic field perpendicular to the shown electric field but that's the price to pay when you reduce three mutually perpendicular dimensions into two.

https://phet.colorado.edu/en/simulation/radio-waves

Oh, that will be excellent! Thanks so much!

 

[anorlunda]

But I will have a look at your notes, since if I understand the concepts better myself, I will be able to figure out how to explain them more clearly.

If you look at Maxwell's equations, there are terms for electric charge and for current flow. But if you set the values of charge to zero and current to zero, there remains a set of equations that describe radiation, i.e. radio and light. If you see that, maybe you could find a way to teach it.

I do not see any wisdom in teaching physics without math. That's like study of literature without language.

 

[flintstones]

I think this is a tricky problem, mostly because trying to teach the underlying theory is so abstract (for the students). I don't know how much autonomy you have in this situation, but perhaps a more useful approach would be to teach the students "How is it (based on what evidence) that we came to understand that light is composed of both a changing electric and changing magnetic field combined in a highly specific and particular way?" Remember, the electric and magnetic fields are not independent entities here; there is but a single field: the electromagentic field.

I do want to caution you that "The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles." is problematic. For example, when an excited atom emits visible light, that emission is not due to acceleration of charged particles.

This article may provide some insight, by discussing Hertz's experiments:

https://www.britannica.com/science/light/Light-as-electromagnetic-radiation

I do have quite a bit of autonomy, and I think your suggestion is great. I will try that.

Thanks for the caution. It prompted me to look at the curriculum again and it actually says "understand that all accelerating charges produce EMR", so that's good. However, I can see one of my students asking why a charge moving at a constant velocity doesn't produce EMR, and I'm not feeling confident about explaining that part yet.

I read through the article and I think that'll be a good resource - thank you!

 

[Ibix]

However, I can see one of my students asking why a charge moving at a constant velocity doesn't produce EMR, and I'm not feeling confident about explaining that part yet.

The easy answer to that is that anything moving inertially can regard itself as at rest (and regard you as moving if you would say it was moving - this is the principle of relativity). So if an inertially moving charge radiates, so must a stationary one, and we know it doesn't.

Whether that's as easy an answer for your students as it is for a physics nerd, I don't know.

 

[Dale]

I think the best you can do in calculus-free physics is to discuss experiments.

I second that. It wouldn’t be too difficult to run a constant current or constant voltage and show no EM wave and then run a sinusoidal voltage or current and show a wave.

 

[A.T.]

I can see one of my students asking why a charge moving at a constant velocity doesn't produce EMR, and I'm not feeling confident about explaining that part yet.

In this applet you can choose "linear" to show a charge at constant velocity. :

https://phet.colorado.edu/en/simulation/radiating-charge

The mechanism is roughly: The field lines emanating from the charge "inherit" its velocity. So if the charge maintains a constant velocity, they will remain straight and radial around the charge. If the charge velocity changes, the field lines just at the charge "inherit" the new velocity, but this disturbance in the pattern propagates at the finite speed c, resulting in "waves".

 

[Delta2]

Summary:: I teach high school (grade 12) and have always struggled with teaching about electromagnetic radiation. I'm looking for resources aimed at laypeople about EMR that may give me some ideas on how to teach it more clearly.

• The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles. How do I explain this? In the past I've said that an accelerating charged particle, because it's moving, makes a magnetic field. Since it's accelerating, that magnetic field is changing. Changing magnetic fields make changing electric fields, and these sustain each other as EMR. Is this even true? It feels unsatisfying for some reason.

I find this explanation good enough for high school purposes. Only thing you should add is that a changing electric field creates a changing magnetic field so that the "cycle" would be complete that is "changing magnetic field"->"changing electric field"->"changing magnetic field" and so on.

• If the above explanation is true, then how do I explain why a changing magnetic field makes a changing electric field? Maybe it's not necessary to explain this, and that's just the way the world works. What do you think? I think the issue is the link between this and our last unit isn't quite clear. In the last unit, we just say that moving charges induce magnetic fields, and that changing magnetic fields induce currents. But now we are saying that changing magnetic fields actually make changing electric fields, and I feel like the link there is not entirely clear.

One way to do the connection is to tell the students of the above cycle. Then to argue that the induced current (by a changing magnetic field) is because it creates a changing electric field which in turn puts the free electrons of a conductor in motion, and that's how we have a current as an end result.

 

[vela]

• If the above explanation is true, then how do I explain why a changing magnetic field makes a changing electric field? Maybe it's not necessary to explain this, and that's just the way the world works. What do you think? I think the issue is the link between this and our last unit isn't quite clear. In the last unit, we just say that moving charges induce magnetic fields, and that changing magnetic fields induce currents. But now we are saying that changing magnetic fields actually make changing electric fields, and I feel like the link there is not entirely clear.

Ask the students to consider what gets the charges moving to produce the induced current. There has to be some sort of force on them. If they're at rest or there is no magnetic field where the charges are, it can't be a magnetic force, so it has to be an electric force, which implies there must be an electric field.

I don't think it's unreasonable to let your students know that some questions about radiation are outside the scope of the course and that they won't really be able to understand radiation until they study physics with the appropriate mathematics. I figure there are many potential questions you'll probably need to gloss over, like how we know E and B are perpendicular to each other and to the direction of propagation, how we know the field oscillate in phase, etc. I wouldn't worry too much about being able to justify all the details and encourage curious students to see if they can find the answers to their questions themselves.

 

[BvU]

In the Maxwells laws Physics Videos by Eugene Khutoryansky, a fairy tale setting is used, but no formulas.

I wonder if they are useful, but I sure find then entrancing !

 

[alan123hk]

The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles. How do I explain this? In the past I've said that an accelerating charged particle, because it's moving, makes a magnetic field. Since it's accelerating, that magnetic field is changing. Changing magnetic fields make changing electric fields, and these sustain each other as EMR. Is this even true? It feels unsatisfying for some reason

I find this https://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf very interesting and useful.

For an accelerated charge, we can only use Coulomb's law and simple algebra to get the radiation field, then apply the Poynting vector to get the radiation power, and finally apply a little calculus to get the total radiation power.

The advantage is that for those who are not very good at math, they can avoid using advanced vector calculus.

 

[Delta2]

I find this https://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf very interesting and useful.

For an accelerated charge, we can only use Coulomb's law and simple algebra to get the radiation field, then apply the Poynting vector to get the radiation power, and finally apply a little calculus to get the total radiation power.

The advantage is that for those who are not very good at math, they can avoid using advanced vector calculus.

That paper is quite good, it avoids the use of advanced math as you say. However one might find the "little crucial" gap that the paper has: It introduces the field component $E_{\perp}$ out of thin air and also assumes that we have a wave traveling at speed c. One needs the full Maxwell's equations (and not only Coulomb's law/Gauss's Law) to prove those two facts.

 

[alan123hk]

That paper is quite good, it avoids the use of advanced math as you say. However one might find the "little crucial" gap that the paper has: It introduces the field component E⊥ out of thin air and also assumes that we have a wave traveling at speed c. One needs the full Maxwell's equations (and not only Coulomb's law/Gauss's Law) to prove those two facts.

I totally agree with you. If we do not use the full Maxwell equation to derive the speed of light, then we can only use experimental methods to measure the speed of light. As for Coulomb's law, it is easy to use experimental methods to verify it.

Another disadvantage of this method is that it does not provide near-field information.

 

[snorkack]

• Changing magnetic fields make changing electric fields, and these sustain each other as EMR. Is this even true? It feels unsatisfying for some reason.
• If the above explanation is true, then how do I explain why a changing magnetic field makes a changing electric field? Maybe it's not necessary to explain this, and that's just the way the world works. What do you think? I think the issue is the link between this and our last unit isn't quite clear. In the last unit, we just say that moving charges induce magnetic fields, and that changing magnetic fields induce currents. But now we are saying that changing magnetic fields actually make changing electric fields, and I feel like the link there is not entirely clear.

On the most trivial mathematical level, changing magnetic fields actually make electric fields, period.
But here is quite easy, and qualitatively explainable, mathematical reason why it needs to make changing electric fields.
Compare the cases of a transformer.

• Put direct current in the input coil of transformer - and the direct current will not pass into output coil of the transformer. A constant current in primary coil produces constant magnetic field, which induces neither electric fields nor currents.
• Switch the direct current in input coil off and on. When input current changes, magnetic field changes and therefore induces currents. Result: a transformer with direct current in input gives electric impulses when input is switched, but no current when input switches are left steady.
• How might you get direct current in transformer output? You would need steadily changing magnetic field. But that would have to mean steadily changing input current - input current that steadily racks up to infinitely strong input current. Which is impossible. This is why a changing magnetic field has to make changing electric fields, and why transformer cannot have direct output.
• Put alternating current in input, and then put a voltmeter as the load of the output coil. A voltmeter has a high resistance and let's hardly any current through. But when the transformer output is blocked by voltmeter, the voltmeter would make voltage. The reason is that the changing magnetic field first of all induces electric field. If the current is blocked by resistor/insulator, the electric field exists all the same
• Now, consider the law called Maxwell correction to Ampere´ s Law. What is it? Well, consider experiment: use the output alternating current to charge a capacitor. Consider the magnetic field around a wire entering the capacitor: under Ampere´ s law the total magnetic field over a loop around the wire is proportional to the current through the loop. But now consider a loop drawn around the capacitor itself. There is no actual current through capacitor (it would be leakage). Is there any magnetic field around a capacitor? Maxwell correction says that there is: changing electric field, such as due to charging capacitor, but also for any other reason, induces a magnetic field exactly as if the current continued through the capacitor. This does not mean that the magnetic field is the same as it would be if the capacitor were short-circuited - the voltage of the capacitor resists loading current, so the loading current is weaker than shortcircuit current would have been, and so is its magnetic field - but the magnetic field does not disappear completely.
• Now, remove the secondary coil altogether. The electric field in vacuum that would have induced voltage in secondary coil if secondary coil were there is changing, and therefore behaves as a "displacement current". It therefore induces magnetic field of its own. And so on, propagating to free space. Transformers have some radiative losses.

 

[alan123hk]

The illustration and text explanation of this https://pulsar.sternwarte.uni-erlangen.de/wilms/teach/astrospace/spacechap5.pdf seems to be easier to understand, so I want to share it with those who are interested.

 

[VEReade]

Summary:: I teach high school (grade 12) and have always struggled with teaching about electromagnetic radiation. I'm looking for resources aimed at laypeople about EMR that may give me some ideas on how to teach it more clearly.

I teach high school (grade 12). We have just finished a unit about electric and magnetic fields. For example we talk about how charges make electric fields, and how moving charges make magnetic fields. Students sort of grasp this idea, though I'd say they struggle with it. Note that we don't discuss flux in high school here.

Next, we're starting to learn about light and electromagnetic radiation. But I am having problems teaching it because I actually never studied it myself in university. Here are the issues I'm having:

• The curriculum says students are supposed to understand that the source of all EMR is accelerating charged particles. How do I explain this? In the past I've said that an accelerating charged particle, because it's moving, makes a magnetic field. Since it's accelerating, that magnetic field is changing. Changing magnetic fields make changing electric fields, and these sustain each other as EMR. Is this even true? It feels unsatisfying for some reason.
• If the above explanation is true, then how do I explain why a changing magnetic field makes a changing electric field? Maybe it's not necessary to explain this, and that's just the way the world works. What do you think? I think the issue is the link between this and our last unit isn't quite clear. In the last unit, we just say that moving charges induce magnetic fields, and that changing magnetic fields induce currents. But now we are saying that changing magnetic fields actually make changing electric fields, and I feel like the link there is not entirely clear.
• I tried to read up on this online but am having trouble finding a resource that's at the right level. Does anyone know of a good resource? Maybe something aimed at laypeople? I did take ~10 undergraduate physics courses, so I could probably understand something written for 2nd year physics students, if necessary. Ideally though it would be a resource that I could share with my students.

In UK, Year 12/13 students don’t have to actually understand how EM waves are generated by accelerating charges. They just need to know (without understanding) that the phenomenon occurs. I used to teach it in passing by discussing radio transmitter aerials and how X-rays are produced. In my experience of 30 years of teaching year 12/13 physics in UK, students in general will find Faraday’s law of EM induction hard enough. (Ofcourse - always worth understanding it yourself when you’re in front of a class - there’s always a student who will ask!)

 

[John Kovach]

Not sure if you can acquire signal generator and an oscilloscope. EMR is normally generated by an AC current/voltage flowing through a wire (antenna). You could visibly demonstrate the presence of EMR even w/o signal generator as 60Hz is virtually. everywhere. It's nice to see things instead of just talking about them. To demonstrate the presence of EMR, you can take cell phone, put it in a metal grounded box and show you cannot call the phone. It's similar to losing bars. The idea is to relate EMR to something the students can appreciate. Then you can launch into electromagnetic fields. The one does not exist w/o the other.

 

[John Kovach]

I'm wondering if the perceived problem is how to teach EMR rather than classical EMF. I have never seen a photon, but i have seen electronic waves on a scope. I never could picture photons in a standing wave or bouncing down a waveguide. Even Maxwell's equations are not written for photons. Not criticizing, just wondering if the effort to be "right on"(why do we have to be?) is making it difficult. In a typical class maybe 1 in a 1000 will ever learn QFT. Whether a student knows what a photon is may not be as important as appreciating radio waves so he or she is not brain dead while making a radio or TV purchase. I bought a telescope for my grandson because he was fascinated by one he used at school. He never used it. To me the most important aspect of education is to find ways to hit that hot button in each child. It's the excitement that motivates further learning, sometimes, that is if you can compete with Bat Man.

 

[vanhees71]

It's of course nonsense to teach a calculus-free E&M course using photons. Photons cannot be understood without using the language of mathematics. In my opinion this also holds to some extend for classical physics too, but in the case of quantum theory and particularly photons it's better not to tell students anything about it than to teach them old-fashioned concepts which have to be unlearnt later anyway. To picture a photon as a point-like particle is the most errorneous picture you can teach them!

 

[John Kovach]

It's of course nonsense to teach a calculus-free E&M course using photons. Photons cannot be understood without using the language of mathematics. In my opinion this also holds to some extend for classical physics too, but in the case of quantum theory and particularly photons it's better not to tell students anything about it than to teach them old-fashioned concepts which have to be unlearnt later anyway. To picture a photon as a point-like particle is the most errorneous picture you can teach them!

OMG. After reflecting on my days in high school, I remembered that public schools are not just sources for education, but entertainment as well. We had pet names for teachers based on their physical features and body language. The first rule in teaching is control. If the sharper students detect the slightest uncertainty in what or how you teach, they will entertain the class at your expense.

At some point in basic electronics (E&M) I had to move on from electrons to current flow and the right and left hand rules. I could handle discussions of electron flow in DC circuits, but not for electrons running all the way from Niagara Falls to school and back.

 

[vanhees71]

I'm a bit puzzled by the statement that one loses control in a physics class only when using the one adequate language to express the content of physics and to communicate about it: math. To the contrary, in my high school days the math-illiterate science teachers (and already then there was some percentage of such "teachers") had a very hard time, because nothing exposes the incompentence of a science teacher more than not knowing the fundamentals. On the other hand, there's no problem to admit as a teacher that you don't know everything. It's much more competent to admit, not to know the answer to some question than to pretend to be able to answer it. Rather one should tell the students that you don't know the answer right now, but that you'll try to figure it out till the next lesson.

 

[John Kovach]

I agree. I was surprised to find QM introduced in my grand daughters chem text. Historically we argued for centuries about whether light is a wave or particle which we now relate to proprties of rather than nomenclature. I still have trouble shifting gears between optics, EM and QM. I believe students would have similar issues because of the way we learn for infancy. It's like Aristotle's teaching about the properties of things. An infant puts things in his or her mouth because he or she is testing the properties of objects. What is this thing used for. The investigations into the nature of things is rudimentary. The ihfant observes how people interact and models his or her own behavior accordingly. Acquisition of data is through the senses. It's the foundation for learning other stuff: how to hit a baseball, cut with a knife. Mathematics except for unique individuals does not contribute to one's understanding.how many of us can look at the structure of a flower and say,"I know that equation."

What i believe the average student looks for is a sort of hands on approach to understanding the principles of E and M. That is why I suggested using an oscilloscope to show behavior that cannot be seen optically. It's funny how the human brain works, but i did not really "believe" two small spheres could attract each other until i saw it with my own eyes. It was not part of my everyday experience. I didn't express my doubts to anyone. I highly value hands on approaches to education (labs, research). I don't think we learn effectively until we get our hands dirty and metaphorically put things in our mouths.

 

[John Kovach]

The comment about control holds. As I think about my hs teachers, they were all dedicated and wonderful, but some commanded respect more than others. Even adults can be cruel to each other. It's in our nature. I don't turn my back to barking dog regardless of any training I've had.

I substituted for one HS physics class. Right away some students started testing me. I ignored them and stuck to their assigned work. The testing continued until one girl spoke up telling the clowns in the class not to harass me because I might be testing them to see if teaching HS physics was worth it. The harassment ended. Recognizing what is honest query and what is not can be more difficult than the subject matter.

 

[flintstones]

Ask the students to consider what gets the charges moving to produce the induced current. There has to be some sort of force on them. If they're at rest or there is no magnetic field where the charges are, it can't be a magnetic force, so it has to be an electric force, which implies there must be an electric field.

Thanks! I'll give that a try. I think it'll work well.

 

[bob012345]

To picture a photon as a point-like particle is the most errorneous picture you can teach them!

I assume it's the 'point-like' you object to since every definition I've seen uses the word particle?

 

[vanhees71]

A photon cannot be localized. It's the least particle-like quantum you treat in introductory quantum mechanics. I always emphasize that photons are not like miniature billiard balls and the meaning of the single-photon states as detection probabilities.

 

[bob012345]

A photon cannot be localized. It's the least particle-like quantum you treat in introductory quantum mechanics. I always emphasize that photons are not like miniature billiard balls and the meaning of the single-photon states as detection probabilities.

Ok. Thanks. Could you elaborate a little what you mean by emphasizing the meaning of the single-photon states as detection probabilities. Is it about writing a wave function for the photon state that allows computation of the probability it will be detected in one state as a function of all possible states? Does that imply it is meaningless to talk about a photon apart from a detector unless one knows from a previous experiment what state the photon is in?

 

[Frodo]

Without wading through the thread ...

... my advice would be to get or read a copy of Feynman's Lectures in Physics and all will be revealed. The lectures are mainly written prose as Feynman was a most brilliant teacher who always explained the physics before going on to develop the equations.

I see that some of the lectures themselves are now on line Now, You Can Watch the Feynman Lectures Online For Free so you can see how he explained things.

Also check out Richard Feynman - Science Videos for his lectures on QED - they are breathtaking.