Wow! That quote goes back to page one when we were still actively discussing the abstract that edbarx brought up as the subject of the thread!
As I said then, a proton occasionally appears to be a quantum mixture of the usual three quarks, but with a small amount of additional momentum which appears to come from another quark and antiquark.
As I said then, a proton occasionally appears to be a quantum mixture of the usual three quarks, but with a small amount of additional momentum which appears to come from another quark and antiquark.
@gulu You’re too smart for me.
Well, I just had to give you a like for that! 😀
P.S. It's Galu.
"Through rain and wind and weather, Hell-bent for leather ..."
A bloke in the pub thinks I am a cowboy.
He keeps calling me a Clint.
Perhaps this thread should restart at post 314, 666 and 1235?
Make it non deterministic!
Make it easy!
Give the page numbers.
It definitely not oscillatory in any sense we consider normally where there is phase shift taking place. But it does beg the question as to what is going on when the two waves are 'self sustaining'.I have not come across any suggestion that energy is transferred between the oscillating electric field and the oscillating magnetic field.
The stock explanation is that an oscillating charged particle at the source will cause the electric field surrounding it to oscillate as well.
The oscillating electric field, in turn, causes an oscillating magnetic field, as predicted by Maxwell’s equations.
A self-sustaining electromagnetic wave can carry energy through empty space as the electric field component and magnetic field component each continually change and each perpetuate the other.
As an apparent correction to an earlier statement, the oscillating electric field and an oscillating magnetic field oscillate perpendicularly to and in phase with one another as shown in the attached gif.
That's all I can offer with the help of some confirmatory googling - without atttempting to delve into mathematics that I would be unable to follow!
Nice post Steve! (Daniel Fleisch has a nice book on Schrodinger's equation BTW). I have a book on Linear Algebra . . . so many things to look intoYou got me thinking there, Bonsai!
The point of similarity between Maxwell's Equations (which is about electromagnetism, and not a quantum idea, i.e. there is no h(bar) explicitly involved) and Schrodinger's Wave Mechanics (which is about matter waves and h(bar) is crucial, it is the quantum...) is they both use a wave equation.
Wave equations work rather nicely with exponential functions:
View attachment 1240099
Anyway, lot of handwaving here. What does a quantum point particle like an electron look like as a wave? This is Scrodinger's wave idea, rather than Heisenberg's matrix interpretation:
https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics
View attachment 1240100
You add a sum of kinetic and potential energy Hamiltonian (H = T+V) to the workings:
View attachment 1240101
View attachment 1240102
Differentiation becomes an operator. Anyway, with a Hamiltonian and the right boundary conditions, some simple but powerful solutions exist. Here he quantum harmonic oscillator: You can do this fairly rapidly on half a page:
View attachment 1240103
Quantum Mechanics in one post! 😎
Of course, it gets worse... but lovely maths that also applies to loudspeakers and information theory and Fourier and Laplace transform.... 🙂
But it does beg the question as to what is going on when the two waves are 'self sustaining'.
Yeah, the term is a big fudge 'cos nobody knows what keeps an electromagnetic wave going.
Just like we don't know what keeps a photon going.
Just like we don't know much of how the universe works!

I stuck through it. But then I have bravery.
https://en.wikipedia.org/wiki/Apollo_8
https://www.bbc.co.uk/sounds/play/m0001lw3
The Moon is an awful place. I have no wish to go there.
Looks like grey Pumice. Actually is.
I will stick to Home:
We must look after our Planet. There is no finer place to Live. 🙂
https://en.wikipedia.org/wiki/Apollo_8
https://www.bbc.co.uk/sounds/play/m0001lw3
The Moon is an awful place. I have no wish to go there.
Looks like grey Pumice. Actually is.
I will stick to Home:
We must look after our Planet. There is no finer place to Live. 🙂
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Some audio like terms crop up in that pdf when it gets to baryonic oscillations. Used to try and establish a ruler. 😉You might think a rather odd yardstick.This thread is not audio related.
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe,
I wonder if Plank made empirical constants popular.
How many posts per page do You use? 😉Make it easy!
Give the page numbers.
//
I find Leonard Suskind’s ‘ephemeral fermions’ as a photon propagation medium as hard to believe as the now debunked ‘luminiferous aether’ explanation 😊Yeah, the term is a big fudge 'cos nobody knows what keeps an electromagnetic wave going.
Just like we don't know what keeps a photon going.
Just like we don't know much of how the universe works!![]()
‘ephemeral fermions’ as a photon propagation medium
I see that we discussed that hypothetical method of photon propagation earlier in the thread. Here's a quick reminder:
Photons propagate by making instantaneous leaps between ephemeral fermion-antifermion pairs which pop up in the quantum vacuum.
One for the mumbo jumbo lovers perhaps?
If electrons (or other atomic level particles) have wave functions, you have to wonder why we can’t unify that (which is quantum in nature) with photon or EM radiation without invoking the strange stuff you mentioned above. The fact that photons collapse from wavelike properties to particle like properties when interacting with matter seems very similar to Schroedinger’s wave function. Or am I totally off beam here?
The question you are really asking is: "For a travelling particle such as an electron or a photon, 'what' is waving?"
The Schrödinger equation introduced the wave function (Ψ).
The square of Ψ represents the probability of an electron being found within a certain area or the probability of where a photon would be found were it to be detected.
What's waving can therefore be said to be a mathematical function used to determine where the particle is likely to be when a position measurement is performed.
Mathematics - it's all mathematics!
Just ask Steve! 😉
The Schrödinger equation introduced the wave function (Ψ).
The square of Ψ represents the probability of an electron being found within a certain area or the probability of where a photon would be found were it to be detected.
What's waving can therefore be said to be a mathematical function used to determine where the particle is likely to be when a position measurement is performed.
Mathematics - it's all mathematics!
Just ask Steve! 😉
Looking back through my 'Diary of Cosmology', I see this written down:
"In the 1930s, physicists realised that the wave functions of many individual photons collectively behave like a single wave propagating through conjoined electric and magnetic fields - exactly the classical picture of light discovered in the 19th century by James Clerk Maxwell."
This realisation led to the quantisation of classical field theory.
"In the 1930s, physicists realised that the wave functions of many individual photons collectively behave like a single wave propagating through conjoined electric and magnetic fields - exactly the classical picture of light discovered in the 19th century by James Clerk Maxwell."
This realisation led to the quantisation of classical field theory.
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