tag:blogger.com,1999:blog-11295132.post8305461568159682840..comments2019-01-08T20:18:02.133-08:00Comments on A Neighborhood of Infinity: What is a photon?Dan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-11295132.post-34841191100765126942017-12-12T08:09:30.941-08:002017-12-12T08:09:30.941-08:00@oij
> What's oscillating? The direction a...@oij<br /><br />> What's oscillating? The direction and strength of the electromagnetic field at a point?<br /><br />Exactly. The electric and magnetic field vectors.<br /><br />> but you should have also mentioned position, right?<br /><br />Actually, no! :-)<br /><br />You can measure the electric and magnetic fields at a point, but you can view these fields as being built up from plane waves - ie. sinusoidal waves that extend across space. So they aren't in any particular position. They do have a direction though. Just like with ocean waves, electromagnetic waves have amplitude, frequency and direction.<br /><br />So I'd rewrite<br /><br />"when we say that there are 3 photons of some frequency f in some position p, we mean that the amplitude of the oscillation of the electromagnetic field at some frequency f at position p is 3 quanta"<br /><br />as<br /><br />"when we say that there are 3 photons of some frequency f in some direction k, we mean that the amplitude of the oscillation of the electromagnetic field at some frequency f and direction k is 3 quanta"<br /><br />The Heisenberg uncertainty principle tells us that if we know the exact momentum of a particle, we don't know its position. It turns out that knowing the frequency and direction of a photon also tells us its momentum and therefore we can't assign a position. But even though we can't give the position of a photon in this sense, we can still talk about the value of the field at some point.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-14545623551343498122017-12-12T06:58:11.627-08:002017-12-12T06:58:11.627-08:00Hi Dan. Thanks. Do you mind if I summarise what yo...Hi Dan. Thanks. Do you mind if I summarise what you wrote for my own understanding?<br /><br />There is an electromagnetic field. It's oscillating at every point. The oscillation at any point can be broken down into waves with independent frequencies and polarisations. The amplitudes are discrete. (You said the amplitude is a function of direction and frequency, but you should have also mentioned position, right?). **So**, when we say that there are 3 photons of some frequency f in some position p, we mean that the amplitude of the oscillation of the electromagnetic field at some frequency f at position p is 3 quanta.<br /><br />Question: What's oscillating? The direction and strength of the electromagnetic field at a point?<br /><br />Thanks again.oijhttps://www.blogger.com/profile/11425391970388005796noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-55766935305459396542017-10-18T20:56:39.646-07:002017-10-18T20:56:39.646-07:00Leaning toward logic and generally limited to 3 di...Leaning toward logic and generally limited to 3 dimensions, human thinking does not lend itself well to the quantum world. Nearly all aspects of physics and thermodynamics lose coherence -- and contradictions turn everything upside down. For the sake of discussion, if there is a God and he designed the systems that make up everything, everywhere, he was not only a master mathematician -- but the greatest magician imaginable.ScaryTruthhttps://www.blogger.com/profile/10631602368172512888noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-71619084463222325002017-10-14T10:37:29.514-07:002017-10-14T10:37:29.514-07:00"For the electromagnetic field the quanta are..."For the electromagnetic field the quanta are called photons"<br /><br />thanks for the great analogies, can you extend these analogies to single photons [ or i see your comment to Sundar's question now but I'm still having trouble getting rid of the billiard-ballness view of that wavefunction when it comes to single photons], say single photons being emitted from these oscillating systems and how it takes time for the single photon to travel from the source of emission to a detector and then after that single photon is detected no other photon is detected? <br /><br />How do you reconcile conceptually the single quanta of energy(spectrum or frequency domain) of a photon to a single photon in space or time domain that has a high probability(thru the wavefunction) in a local region of space? Classically a single short pulse in time with a well defined location in space (not continuous wave) is broad in spectrum(energy or wavelength) through its fourier transform, is it right to say that this single short pulse is not *a* photon, but *many* photons? What about a continuous wave at an extremely precise single quanta/energy/frequency- is it right to say this is not *a* photon but *still* *many* photons in this continuous wave, since incident on a detector there are very many photons but still just one electromagnetic field at one energy/wavelength(one quantum)? Then what about when you attenuate that single energy continuous wave down to a very low power so that in one minute there is only 1 photon at one quantum(1 energy), isn't there some billiard-ballness in that those can be counted? A single photon's probabilistic location in space/time versus it's probabilistic quanta in energy/wavelength is related through the uncertainty principle relating k/wave-vector space to momentum space- how do we reconcile all this conceptually without any billiard-ballness?Jeaniehttps://www.blogger.com/profile/15718694362618476340noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-81328392541372391452017-10-14T10:37:15.690-07:002017-10-14T10:37:15.690-07:00"For the electromagnetic field the quanta are..."For the electromagnetic field the quanta are called photons"<br /><br />thanks for the great analogies, can you extend these analogies to single photons [ or i see your comment to Sundar's question now but I'm still having trouble getting rid of the billiard-ballness view of that wavefunction when it comes to single photons], say single photons being emitted from these oscillating systems and how it takes time for the single photon to travel from the source of emission to a detector and then after that single photon is detected no other photon is detected? <br /><br />How do you reconcile conceptually the single quanta of energy(spectrum or frequency domain) of a photon to a single photon in space or time domain that has a high probability(thru the wavefunction) in a local region of space? Classically a single short pulse in time with a well defined location in space (not continuous wave) is broad in spectrum(energy or wavelength) through its fourier transform, is it right to say that this single short pulse is not *a* photon, but *many* photons? What about a continuous wave at an extremely precise single quanta/energy/frequency- is it right to say this is not *a* photon but *still* *many* photons in this continuous wave, since incident on a detector there are very many photons but still just one electromagnetic field at one energy/wavelength(one quantum)? Then what about when you attenuate that single energy continuous wave down to a very low power so that in one minute there is only 1 photon at one quantum(1 energy), isn't there some billiard-ballness in that those can be counted? A single photon's probabilistic location in space/time versus it's probabilistic quanta in energy/wavelength is related through the uncertainty principle relating k/wave-vector space to momentum space- how do we reconcile all this conceptually without any billiard-ballness?Jeaniehttps://www.blogger.com/profile/15718694362618476340noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-57641744145491526712017-10-13T18:10:20.656-07:002017-10-13T18:10:20.656-07:00Great article, thanks! What happens to a normal mo...Great article, thanks! What happens to a normal mode represented by a sine wave when its energy is quantized? Does its amplitude become quantized too? Jean-Philippe Cournoyerhttps://www.blogger.com/profile/04575406288400193497noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-14766169731487148992017-10-13T17:58:46.033-07:002017-10-13T17:58:46.033-07:00This comment has been removed by the author.Unknownhttps://www.blogger.com/profile/04575406288400193497noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-31718214604552362712017-10-11T06:41:00.880-07:002017-10-11T06:41:00.880-07:00I'm a lawyer with no concept of "higher&q...I'm a lawyer with no concept of "higher" math, but I'm nonetheless keenly interested in physics, light, astronomy, etc. This article about photons is the best, most well-explained I've ever read in this area. Great job, and thank you!Unknownhttps://www.blogger.com/profile/01219190272371453537noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-8034023549409864692017-10-08T17:08:43.867-07:002017-10-08T17:08:43.867-07:00Good job!
Good job!<br />Adriano Mehttps://www.blogger.com/profile/03007179115792821735noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-14805792184429373722017-08-29T07:04:34.754-07:002017-08-29T07:04:34.754-07:00@Sundar: Sorry, long answer.
When a physicist set...@Sundar: Sorry, long answer.<br /><br />When a physicist sets out to solve a problem using quantum field theory, at no point do they say "we'll use wave-particle" duality. There is no such principle in physics. It's a made up thing stated after the fact by philosophers and pop science writers (and by science writers when forced to write introductions to textbooks).<br /><br />Still, I'll try to point out where the "duality" it is in what I described. The tricky thing here is that there are two waves. I don't even know which should be the wave in the duality. There's the EM wave. And then there's the quantization of how much energy there is in each harmonic wave which I've just described. So you have a wave-particle duality of a sort right there.<br /><br />But there's another wave buried in here. The idea is that when you have a harmonic oscillator that is a particle swinging back and forth in space there is a wave function associated with it. That wave function gives a probability to find a particle at any given position - the places where the wave function takes a larger value are places where you're more likely to find the particle if you measure its position.<br /><br />But for the EM wave the corresponding wave function is an abstract thing that says how likely the electric field or the magnetic field is to take a value at any particular point. So it's a wave on the very large (in fact, infinite-dimensional) space of all possible EM waves - not a wave in spacetime. Think of it as like a probability density function on the space of all EM waves. In this case, I think that's the correct wave when talking about wave-particle duality. But most popular accounts talk about the EM wave, not this abstract wave.<br /><br />I personally think that once you know the details, you can dispense with talking about wave-particle duality.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-49672852472730794342017-08-29T00:56:50.637-07:002017-08-29T00:56:50.637-07:00I'd always been confused when Harmonic Oscilla...I'd always been confused when Harmonic Oscillators made an appearance in quantum mechanics questions in, for eg., r/askscience, so thanks for this simple from-the-scratch explanation. <br /><br />How do wave-particle duality and things like the double slit experiment with photons fit into this explanation though, what the best way to think of them knowing this? <br /><br />Sundarhttps://www.blogger.com/profile/00415039983973239001noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-61135715136153258422017-08-22T08:36:03.419-07:002017-08-22T08:36:03.419-07:00@Francisco Albani This *is* the story behind E=hf....@Francisco Albani This *is* the story behind E=hf. The only thing missing is that I didn't say what the spacing is between energy levels. Quantum mechanics predicts that if you have a harmonic oscillator of frequency f, then the spacing between energy levels is hf..<br /><br />So that leaves having to explain why harmonic oscillators have energy levels with spacing hf. I deliberately left that out because I don't know an easy argument as it's a fundamentally quantum mechanical argument. I could probably say something about why you might expect a discrete set of energy levels but it would still require talking about wave functions or some such thing.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-11615642330762520672017-08-22T00:27:44.207-07:002017-08-22T00:27:44.207-07:00Many thanks for this! It really helped me to come ...Many thanks for this! It really helped me to come closer to solving the "E = h·f" (personal) mystery. Don't you want to make an article about that? I will be grateful.<br /><br />Having an Electronic Engineering background (classic EM for RF and a little of QM for semiconductors) I have never been able to understand why the photons of a macroscopic EM wave causing electrons in a conductor move with certain frequency f, have each one h·f joules.<br /><br />I always hope to find a nice equivalence similar in spirit to the one between macroscopic pressure and microscopic momentum of atoms in a gas.<br /><br />Thanks to this article I started reading more about QFT and I'm starting to see "the light" at the end of the tunnel.Francisco Albanihttps://www.blogger.com/profile/12722364785259927270noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-87783532194595579592017-08-17T12:11:12.463-07:002017-08-17T12:11:12.463-07:00Typo: if you move the mass on the left to the righ...Typo: if you move the mass on the left to the right, the mass on the right will feel a force pushing it to the *right*, not the left.Mike Stayhttps://www.blogger.com/profile/03408641732412584050noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-48817452573465350102017-08-12T11:57:35.465-07:002017-08-12T11:57:35.465-07:00Wonderful article, thanks!Wonderful article, thanks!Sevcsikhttps://www.blogger.com/profile/00446714600407385810noreply@blogger.com