Interaction of two point charges

[goldbloom55]

I'm trying to get a deeper understanding of how two particles such as protons interact with each other. In high school physics, I was told that they give off a field, which is felt by the charges, and then repels them.

My first question is, if I fire two protons at each other head on (lets assume their velocity is not great enough to cause impact to simplify the situation) does their deceleration, and then acceleration away from each other produce electromagnetic radiation (from my understanding, photons)? If so, this would mean that the repulsion is a nonelastic interaction.

Also, I've read that charged particles interact with each other by exchanging photons with each other. From my understanding (somewhat of a leap from what I've read), if a proton is near another proton, they will fire photons at each other, causing them to accelerate away from each other.

 

[Bill_K]

Also, I've read that charged particles interact with each other by exchanging photons with each other. From my understanding (somewhat of a leap from what I've read), if a proton is near another proton, they will fire photons at each other, causing them to accelerate away from each other.

This description makes it sound like what charged particles do is aim little bullets at each other, and the Coulomb repulsion between them is a result of the recoil from being hit. If this were so, inevitably the next question would be, how can unlike charges attract?
Actually, the photons surrounding a charged particle are considerably different from bullets. In the first place they are virtual, meaning they do not have zero mass and do not travel at the speed of light. Secondly, they are "timelike", meaning that they are not transverse (i.e. polarization pointing in a space direction perpendicular to the momentum). Their polarization points in the t direction. And really there's an infinite number of them and they all blend together to produce a time-independent effect: a Coulomb field! An approaching particle does not get fired upon and retreat, it just senses the Coulomb field and reacts accordingly.

 

[mquirce]

By the case, i am confused:
Is the particle created by fields ?
or the fields are property of particles?
How comes that "virtual" photons have mass?
Another dilema about interaction between two electric charges:
Indeterminet integral for energy { ! e^2 / d ! ) gave different results when determine it from ingfionite to a point x and from 0 to point x .
From this dilema came that energy (or interraction) of a cuple of charges don't go further than d = C*1 / ( 2*pi / alpha) . is it right or rong?
scouse for this elementary questions that derive from doubt about " virtuals "

 

[goldbloom55]

By the case, i am confused:
Is the particle created by fields ?
or the fields are property of particles?
How comes that "virtual" photons have mass?
Another dilema about interaction between two electric charges:
Indeterminet integral for energy { ! e^2 / d ! ) gave different results when determine it from ingfionite to a point x and from 0 to point x .
From this dilema came that energy (or interraction) of a cuple of charges don't go further than d = C*1 / ( 2*pi / alpha) . is it right or rong?
scouse for this elementary questions that derive from doubt about " virtuals "

Excellent set of questions. I am interested in knowing the response to these too.

 

[goldbloom55]

My first question is, if I fire two protons at each other head on (lets assume their velocity is not great enough to cause impact to simplify the situation) does their deceleration, and then acceleration away from each other produce electromagnetic radiation (from my understanding, photons)? If so, this would mean that the repulsion is a nonelastic interaction.

I remember being taught that all accelerating charges give off electromagnetic radiation (correct me if I'm wrong). So in this case, would both protons radiate an electromagnetic field, with its strength relative to the magnitude of acceleration/deceleration at a given point?

 

[goldbloom55]

By the case, i am confused:
Is the particle created by fields ?
or the fields are property of particles?

In the https://www.physicsforums.com/showthread.php?t=43685" which helped shed some light on the questions we had.

On the page:
http://pdg.web.cern.ch/pdg/particleadventure/frameless/unseen.html

It is quoted:
"What we normally think of as "forces" are actually the effects of force carrier particles on matter particles."

So it's the exchange particles which cause the field.

I'm still curious to know why light has mass when its virtual, and what exactly it means conceptually for photons to traverse in the time direction.

 

[Bill_K]

I'm still curious to know why light has mass when its virtual

In order for a particle to travel any distance, it must be 'free', that is it must obey the equation that relates mass, energy and momentum: E² = p²c² + m²c⁴. For a particle standing still this reduces to the more familiar equation E = mc². While for m = 0 it reduces to the relationship obeyed by a free photon, E = pc. A virtual particle does not have to obey this equation, it can have any energy and momentum whatsoever. We say it is off the mass shell. But because of this, its effects can only be transmitted a very short distance before it must be absorbed again by something else.

and what exactly it means conceptually for photons to traverse in the time direction.

No, what I said was, its polarization is in the time direction. The photon is described by a vector field A_μ. Again, a free photon must obey conditions that a virtual photon is not required to. A free photon must be transverse, that is if it's traveling in the z direction, the polarization vector must point in either x or y. A virtual photon can have as well the other two polarizations: longitudinal, in the z direction, or timelike, in the t direction.