Project on pulsars/electromagnetic quantum field

[Lisastronomy]

TL;DR Summary

I am a high school student doing a project on pulsars and I would love to get into the deeper workings of a quantum electromagnetic field, but I am a bit lost.

Hello,

I am a high school student doing a project on pulsars and I would love to get into the deeper workings of a quantum electromagnetic field, but I am a bit lost. Since pulsars are neutron stars, who send out a beam of electromagnetic waves, I was quite curious about it's workings.

So, what I know by now is that because of the strong accelaration of electric charge particles, an electromagnetic wave is send out, which is in the form of a photon (This because there is this disturbance). Now, I read some things about the quantisation of an electromagnetic field and the harmonic oscillator, but since I know barely nothing about QM, it seems a bit vague to me.

Now, surely I wouldn't mind getting into these topics and putting a lot of time in it, but if they have nothing to do with pulsars and the working of the electromagnetic fields, it would be a waste of time. For now, when I read some pages on it, some words and formulas still seem to be a bit new to me and I don't really know what they mean. So my question therefore is: "Why do accelerating electric charges really produce an electromagnetic wave and how can this be in the form of a photon?"

 

[berkeman]

What math have you had so far in high school? Have you learned any Calculus yet?

 

[WernerQH]

Why do you talk about "a" photon? There are zillions of them arriving here on Earth every second, alone from the crab pulsar. We cannot really count them because they have very small energies. What is measured is just tiny currents, the motion of electrons in response to energetic processes in the pulsar's magnetosphere many centuries ago. Accelerated charges there produce (tiny) accelerations of electrons here on earth. The accelerations do not have an instantaneous effect; we describe them as electromagnetic waves, and they cannot travel faster than the speed of light.

For the radio waves from pulsars it is not necessary to think about photons any more than it is necessary to think of H2O molecules when discussing the flow of a river.

 

[vanhees71]

Pulsars are indeed among the most fascinating objects in astronomy and for physicists interested in testing the predictions of general relativity true gems, because you can observe a lot of general relativistic effects by measuring the periods of the radio pulses very accurately ("pulsar timing"), particularly when you have a pulsar in a binary star system (i.e., two stars orbiting each other due to their mutual gravitational interaction). The astronomers could measure various effects like the periastron shifts, Shapiro delay and even indirectly the emission of gravitational waves (Nobel prize for Hulse and Taylor). Quite some time ago, I've given a talk on neutron stars and pulsar timing for high school students. Maybe the presentation is still helpful:

https://itp.uni-frankfurt.de/~hees/publ/smp08.pdf

The question, how the em. fields themselves are produced, is not an easy one, but fortunately you do not need the quantum theory of electromagnetic waves, i.e., QED for it (neither photons), it's just sufficient to use classical electrodynamics. Roughly speaking, the radio emission is due to cyclotron radiation of the plasma circling around the strong magnetic field of the pulsar. Whenever charged particles are accelerated they emit electromagnetic waves, leading to the emission of radio waves in the direction of the magnetic field. We observe these as pulses on Earth if this direction of the magnetic field rotates such that the radiation hits us every time the axis is directed toward the Earth ("lighthouse effect"), which implies that the period of the pulses is the period of the pulsar's rotation.

 

[PeroK]

"Why do accelerating electric charges really produce an electromagnetic wave and how can this be in the form of a photon?"

It's worth emphasising that electromagnetic waves and photons are concepts from two different theories of light. If you want to study physics seriously, then it's important to discipline your thinking and separate these concepts.

Classical electromagnetism (EM), in which light is an electromagnetic wave, is a cornerstone of modern physics and extensively taught as an undergraduate course at universities. But, it is not a quantum mechanical (QM) theory of light and there are no such things as photons in classical EM. Instead, there are EM fields and Maxwell's equations.

The QM theory of light is QED (Quantum Electrodynamics). This theory involves photons as the quanta of the EM field. This is generally more of a graduate level subject, as is the over-arching QFT (Quantum Field Theory).

You need to decide whether you want to study the classical EM theory of light or QED, but you shouldn't mix the two together.

 

[PeterDonis]

I wouldn't mind getting into these topics and putting a lot of time in it, but if they have nothing to do with pulsars and the working of the electromagnetic fields, it would be a waste of time.

The EM radiation from pulsars does not have any significant quantum aspects; classical electromagnetism works just fine for understanding it. So I would say quantum electrodynamics has nothing to do with pulsars and you shouldn't spend time on it if what you are interested in is the EM radiation from pulsars.

 

[PeterDonis]

my question therefore is: "Why do accelerating electric charges really produce an electromagnetic wave and how can this be in the form of a photon?"

The first question is a straightforward question of classical electrodynamics; you don't need quantum electrodynamics to understand it.

The second question involves the concept of "photon", which, as has been pointed out, is a concept from quantum electrodynamics, not classical electrodynamics. But the cases where you need the concept of "photon", and quantum electrodynamics, to understand what is going on with electromagnetic phenomena do not include electromagnetic waves; those can be understood just fine with classical electrodynamics. The concept of "photon" is only necessary for phenomena that look nothing like electromagnetic waves, such as quantum optics experiments.

 

[Delta2]

Yes, as others have pointed out, I believe it is dangerous for your understanding to mix the concepts of electromagnetic waves and photons.

Classical Electrodynamics: The theory of electromagnetism as it was developed up to the late 19th century, with Maxwell's equations as its epitome. This theory, as others have pointed out, is enough to explain the EM radiation coming out from pulsars.

Quantum Electrodynamics (QED): The theory of electromagnetism as it was developed in the 20th century. This theory introduces the concept of photon. It is required for the detailed understanding of the interaction of EM radiation with electrons in atoms and matter in general.

 

[Lisastronomy]

What math have you had so far in high school? Have you learned any Calculus yet?

I have had a bit of calculus, yeah.