Energy Levels in Hydrogen: Calculating Photon Energy & Wavelength

[bhobba]

I'm curious, what's the difference both physically and mathematically of a photon and a virtual photon?

A virtual photon is just a diagrammatic representation of something called a Dyson series - it doesn't exist - but because of an unfortunate name people who don't know the technicalities get confused. A real photon will register on things like a photomultiplier.

You will find many threads on this forum discussing it - so please don't pursue it here. It is unfortunately one of those things that leads to long threads that go nowhere.

Thanks
Bill

 

[newjerseyrunner]

A virtual photon is just a diagrammatic representation of something called a Dyson series - it doesn't exist - but because of an unfortunate name people who don't know the technicalities get confused. A real photon will register on things like a photomultiplier.

You will find many threads on this forum discussing it - so please don't pursue it here. It is unfortunately one of those things that leads to long threads that go nowhere.

Thanks
Bill

I'll look into that, but my mention of it here was simply to illustrate that mathematical entities may not always correspond to actual stuff. I asked it as a question because I wasn't totally sure I was correct. I should have phrased it to make that more obvious.

 

[Ponderer]

Let's not forget that math alone is incomplete without an interpretation. How are you going to use real life experiments without an interpretation? What interpretations are you most interested in? I find MWI to be particularly interesting.

 

[bhobba]

I'll look into that, but my mention of it here was simply to illustrate that mathematical entities may not always correspond to actual stuff.

That's true. Mathematical models can and often do contain things there are no correspondence rules for in the model. An obvious example is, say, minus numbers. You can't have a minus number of ducks for example. But you can owe someone some ducks so it can be given meaning.

The whole area of mathematical modelling in general, and physics is a mathematical model, is full of that. It's so basic its almost, but not quite because novices of a philosophical bent, in an understanding sense, can get confused by it, trivial.

Also, and this is another point those that don't have experience in mathematical modelling and applied math in general, is they read articles from pure mathematics where objects are abstract. The axioms of applied math are not like that - they can, and do, have explicit or implied correspondences with actual things. For example in QM axiomatically it mentions things like observations. Observations are a primitive and actually exist. One can develop QM in a pure math way but the resultant math is - HARD - and is not recommended for the beginner. But just for completeness here is a book that does it:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Let's not forget that math alone is incomplete without an interpretation. How are you going to use real life experiments without an interpretation? What interpretations are you most interested in? I find MWI to be particularly interesting.

The axioms of applied math explicitly or implicitly contain that correspondence. See Euclids geometric axioms compared to Hilbert's as an example. You will find a good discussion on this in Fellers classic on probability:
https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20

Thanks
Bill