# Problems understanding photons

#### lazarus1907

It's just too abstract for me:

A superposition of magnetic and electric fields, right; but... fields "expand" at speed of light radially, so how come photons don't "dissolve" in all directions rather than remain as particles in one direction?

If you move your arm from left to right, and then stop it, you've accelerated and decelerated lots of charges in your arm. This theoritically produces photons (electromagnetic radiation), but how many photons? What is the frequency of these photons?

Does this make sense?

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#### James R

Homework Helper
Gold Member
When you wave your arm, you're waving equal numbers of positive and negative charges, so I don't think you'll get much EM radiation.

#### dextercioby

Homework Helper
We've got photons "running" in all possible directions. Remember that a spherical light wave is produced by a pointlike source, which doesn't exist (it's one of the models physicists work with).

Daniel.

#### jtbell

Mentor
lazarus1907 said:
fields "expand" at speed of light radially, so how come photons don't "dissolve" in all directions rather than remain as particles in one direction?
In the classical picture, the magnitude of the field radiated from a source decreases inversely with distance ($1 / r$). The energy density associated with the field is proportional to the square of the magnitude of the field. Therfore, the energy density falls off as the square of the distance ($1 / r^2$). Therefore, the energy falling on a target of a given size (say 1 m^2 for simplicity) per second also decreases according to the square of the distance between the source and the target.

In the photon picture, the source emits some number of photons per second. Assume they're distributed uniformly in all directions for simplicity. Now imagine a sphere centered on the source. No matter how big the sphere is, all the photons hit its surface eventually. The total number of photons hitting the sphere per second is the same regardless of the radius. But the surface area of the sphere is proportional to the square of the radius. Therefore the number of photons per second per square meter decreases according to the square of the distance, and so does the energy per second per square meter. None of the photons "dissolve", they just spread apart as they get further from the source.

#### lazarus1907

jtbell said:
In the classical picture, the magnitude of the field radiated from a source decreases inversely with distance ($1 / r$). The energy density associated with the field is proportional to the square of the magnitude of the field. Therfore, the energy density falls off as the square of the distance ($1 / r^2$). Therefore, the energy falling on a target of a given size (say 1 m^2 for simplicity) per second also decreases according to the square of the distance between the source and the target.

In the photon picture, the source emits some number of photons per second. Assume they're distributed uniformly in all directions for simplicity. Now imagine a sphere centered on the source. No matter how big the sphere is, all the photons hit its surface eventually. The total number of photons hitting the sphere per second is the same regardless of the radius. But the surface area of the sphere is proportional to the square of the radius. Therefore the number of photons per second per square meter decreases according to the square of the distance, and so does the energy per second per square meter. None of the photons "dissolve", they just spread apart as they get further from the source.
Assume a different scenario: You have a single travelling photon, which is modelled as a point-like particle. In representing an electromagnetic wave books often give this naive picture of two perpendicular transversal waves that resemble oscillating ropes rather than EM fields. A rope clearly won't dissolve, but these EM fields won't be constrained in the same way the rope is; the effect of their fields travels at the speed of light and it's quite far reaching (of course, inversely proportional to the square of the distance). Trying to visualize this, I can't help seeing these fields "expanding" in all directions, making it almost impossible to imagine how can a photon be point-like; I'd rather expect a photon to become larger and larger... and tend to dissolve.

I know this is wrong, but I just can't see it.

By the way, another scenario: a single electron is travelling at, say 10,000 m/s, and it is brought to a halt in 0.001 seconds. How many photons do I get? What frequency do they have? Is it possible to predict its direction?

Thanks

#### jtbell

Mentor
I think the root of your conceptual problem is that you're trying to apply the classical picture of electromagnetic waves in a domain where it is not valid. If you're in a situation where you can deal with individual photons, I don't think the classical wave picture has much meaning. The electromagnetic field only gives a probabilistic description of where a photon *might* go, similar to the relationship between an electron and the quantum-mechanical wave function that describes its behavior.

To put it another way, the electromagnetic radiation field has its classical meaning only when you have lots and lots of photons, so that you can describe their effects to a very good approximation as a classical field.

#### masudr

I was gonna say all this, but it seems jtbell has gotten there first.

The photon is part of the description when the classical electromagnetic field is quantised. Electromagnetic waves are a solution of Maxwell's equations. Quantised EM fields (and it's quanta, the photon) and classical electromagnetic vector fields lines are related very indirectly at best, and certainly your visual interpretation is wrong, as you say. At a situation like this, the mathematics is all we can rely on, since the maths of field theory is overwhelming and a visual picture is not very useful.

#### cesarsvs

I have still the same doubt as lazarus1907. Imagine a electron moved from point A to point B. So the information to change the electromagnetic field vector to point to the new electron position travels through space with speed c. My first question is: Is this information travel associated with photons? If yes then wouldn't the number of photons per area decrease and the spacing between photons get bigger as the (approximate) sphere (representing the changing field) increased? If so then there would be a place far away from the moved electron that no photon would hit it and then the field vector wouldn't change? Or the photon get bigger as the sphere increase? Or the place that it would happen had to be so far away that the field magnitude there was so small that it wouldn't matter?

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