Does a charge gain energy in every frame when it is accelerated?

[kmarinas86]

In one frame, the capacitor discharges, emitting a propagating EM pulse (which carries momentum), the capacitor's momentum changes by the opposite of the momentum transferred to the pulse. The capacitor has lost energy as well. The pulse interacts with electron, transferring momentum to it; the pulse loses a little energy/momentum.

Now another inertial frame where the electron is initially moving and ends up at rest. The capacitor is moving in this frame. The capacitor discharges. The capacitor and pulse now add up to the same momentum as originally carried by just the capacitor; the pulse carries energy lost by the capacitor. The motion of the pulse in relation to the electron is such that it decelerates the electron, gaining energy and momentum from it. There is nothing mysterious about this - particle accelerators can be run to decelerate particles as easily as accelerate the; in such case, the energy and momentum of the particles is transferred to the e/m pulses, and then to whatever finally absorbs the pulses.

So is there really no difference between a:
1) Lorentz boost, where we [are] talking about looking at an electron from a different inertial frame, and
2) Physical acceleration of the electron, where we are adding momentum [of photons, each with some invariant mass ((p/c)=sqrt((E/c^2)^2-(p/c)^2)] through some external source[, and thereby adding to electron's energy content by some multiple of ((p/c)=sqrt((E/c^2)^2-(p/c)^2) as witnessed by all inertial frames.]

?

 

[PAllen]

So is there really no difference between a:
1) Lorentz boost, where we [are] talking about looking at an electron from a different inertial frame, and
2) Physical acceleration of the electron, where we are adding momentum [of photons, each with some invariant mass ((p/c)=sqrt((E/c^2)^2-(p/c)^2)] through some external source[, and thereby adding to electron's energy content by some multiple of ((p/c)=sqrt((E/c^2)^2-(p/c)^2) as witnessed by all inertial frames.]

?

No, I don't quite agree. If a charge accelerates in one inertial frame, it accelerates in all inertial frames (noting that acceleration/deceleration is just terminology for whether the acceleration is in the direction of motion or against it). Further, an actual change in the motion of charged particle produces a propagating kink in its field, a Lorentz boost does not. I don't see how any of this is related to what I said in the post you are responding to.

 

[Dale]

Two concepts:
1) Lorentz boost, where we talking about looking at an electron from a different inertial frame, and
2) Physical acceleration of the electron, where we are adding momentum to an electron through some external source.

How can these be physically identical? No proper acceleration of the electron is implied by the former, but the latter does entail such a thing.

Exactly. They are not identical. They are not even closely related.

 

[Dale]

Let's say the field that powered the electron was actually more complicated

When you don't understand a simple example it is a bad idea to move to a more complicated example. Even for an expert, it is always possible to make a system so complicated that the expert fails to analyze it correctly. Stick with very basic simple systems until you understand them, and only move on to more complicated systems then. You will almost never gain any insight by moving to a system more complicated than one you already don't understand.

Let's stick with the simplest system you can imagine that let's you understand. Fields are rather complicated since you have to integrate over all of space to get the energy, so perhaps you would want to use a mechanical example instead. But pick a simple one.

 

[kmarinas86]

So is there really no difference between a:
1) Lorentz boost, where we [are] talking about looking at an electron from a different inertial frame, and
2) Physical acceleration of the electron, where we are adding momentum [of photons, each with some invariant mass ((p/c)=sqrt((E/c^2)^2-(p/c)^2)] through some external source[, and thereby adding to electron's energy content by some multiple of ((p/c)=sqrt((E/c^2)^2-(p/c)^2) as witnessed by all inertial frames.]

?

No, I don't quite agree. If a charge accelerates in one inertial frame, it accelerates in all inertial frames (noting that acceleration/deceleration is just terminology for whether the acceleration is in the direction of motion or against it). Further, an actual change in the motion of charged particle produces a propagating kink in its field, a Lorentz boost does not.

What you thought was disagreement is actually a bit of agreement. I asked the above because I find it doubtful that the two could be equivalent.

In speaking of a "kink" in a field, it is known that photons are exchange particles for the electromagnetic force. If work were done on a charge, I would presume that means that a charge receives more energy from these exchange particles than it sends. The "rest mass" of the charge should therefore increase in that case. That bit should be invariant, even if some frames see it as "accelerating" the charge, while others see it as "decelerating", I think. Would that be correct?

When the opposite occurs, a electron literally gives off more energy via photons than it takes in. That would mean that its rest mass should decrease. Decrease of "rest mass" applies to atoms so why not stand-alone electrons?

While it had been said that energy flow can change directions with respect to a given reference frame, I'm not so sure how that could be possible if the energy flow itself were constrained to the speed of light, as it would be impossible to outpace that energy flow no matter how fast the observer is. There is no frame of reference in which you can observe the flow of a photon (with all of its energy and force content) going in the direction opposite of that seen in another reference frame. Thus, whether or not the electron gains a certain amount mass should be something that can be agreed upon by all inertial observers, correct? If so, that would make it contrary to the notion that, in a frame-dependent way, a charge may be seen to lose energy to changing electric field or the other way around.

 

[Dale]

The rest mass of an electron (or any other fundamental particle) cannot change. Therefore there are some interactions which are not possible due to conservation of mass, energy, and momentum. An isolated electron can scatter a photon, but not absorb it, afaik.

 

[kmarinas86]

The rest mass of an electron (or any other fundamental particle) cannot change.

Then how does the rest mass of an atom made of subatomic particles change without that atom emitting subatomic particles, which it clearly can?

If what you said was the case, just how many fundamental particles can make up the atom? It wouldn't be just the electrons, protons, or neutrons. There would be all kinds of photons, virtual particles, etc. that are not easily accounted for. Some of these may be even absorbed by the subatomic particles.

Therefore there are some interactions which are not possible due to conservation of mass, energy, and momentum. An isolated electron can scatter a photon, but not absorb it, afaik.

What about the photoelectric effect?

In any case, is there even such a thing as a rest mass at all? A "rest mass" could simply be the scalar sum of all the "inertial masses" of particles moving inside that so-called object "at rest", as measured relative to that object's COM frame. If that was the definition of the "rest mass", then clearly this is not preserved when energy is absorbed by it.

 

[PAllen]

What you thought was disagreement is actually a bit of agreement. I asked the above because I find it doubtful that the two could be equivalent.

In speaking of a "kink" in a field, it is known that photons are exchange particles for the electromagnetic force. If work were done on a charge, I would presume that means that a charge receives more energy from these exchange particles than it sends. The "rest mass" of the charge should therefore increase in that case. That bit should be invariant, even if some frames see it as "accelerating" the charge, while others see it as "decelerating", I think. Would that be correct?

When the opposite occurs, a electron literally gives off more energy via photons than it takes in. That would mean that its rest mass should decrease. Decrease of "rest mass" applies to atoms so why not stand-alone electrons?

While it had been said that energy flow can change directions with respect to a given reference frame, I'm not so sure how that could be possible if the energy flow itself were constrained to the speed of light, as it would be impossible to outpace that energy flow no matter how fast the observer is. There is no frame of reference in which you can observe the flow of a photon (with all of its energy and force content) going in the direction opposite of that seen in another reference frame. Thus, whether or not the electron gains a certain amount mass should be something that can be agreed upon by all inertial observers, correct? If so, that would make it contrary to the notion that, in a frame-dependent way, a charge may be seen to lose energy to changing electric field or the other way around.

Let's focus for a moment on one misunderstanding that has cropped up in several of your posts in different forms. Work done on a particle or object changes its energy. It can either *decrease* or *increase* its kinetic energy in a particular inertial frame. When you catch a baseball, you do work on it to slow it to a stop, in your frame of reference. The interaction of a particle with a field can transfer energy and momentum in either direction (depending on the circumstances). Until you understand and accept this, you will continue to confuse yourself with your various examples.

 

[Dale]

Then how does the rest mass of an atom made of subatomic particles change without that atom emitting subatomic particles, which it clearly can?

Because an atom is not a fundamental particle like an electron. An atom has internal degrees of freedom, places where it can put extra energy. Specifically, an atom can be excited to a state above the ground state. This allows the atom to absorb energy and gain mass. A free electron has no such extra internal degree of freedom and can only store energy in KE. Its rest mass is always the same.

If what you said was the case, just how many fundamental particles can make up the atom? It wouldn't be just the electrons, protons, or neutrons. There would be all kinds of photons, virtual particles, etc. that are not easily accounted for. Some of these may be even absorbed by the subatomic particles.

Protons and neutrons are not fundamental particles, quarks are. The fundamental particles which make up an atom are electrons and quarks. As you say, there are also many photons and gluons in an atom also. In fact, most of the mass of an atom is in the gluons, not the quarks or electrons.

In any case, is there even such a thing as a rest mass at all? A "rest mass" could simply be the scalar sum of all the "inertial masses" of particles moving inside that so-called object "at rest", as measured relative to that object's COM frame.

Of course there is a such thing as a rest mass. For a system or an extended object the rest mass (aka invariant mass) is the Minkowski norm of the sum of the four-momenta of the individual particles. Your description is also correct, although less general since it can only be applied in the COM frame.

 

[kmarinas86]

It is incontrovertibly true that equations as used by physics professionals work. Obviously, I am not here to try to disprove those equations.

But let me reveal my underlying problem with the current interpretation of these present equations. I have trouble accepting the idea that the energy of a particle depends on the inertial reference frame. Below I will show you what would make sense to me as an interpretation of these equations [POV 1]. After that, I will show what I currently perceive as being how the current interpretation looks at it [POV 2].

Legend
) momentum in the +z direction
( momentum in the -z direction
)) kinetic energy in the +z direction
(( kinetic energy in the -z direction
() potential energy =

• [POV 1] kinetic energy in the xy plane = sqrt(total energy^2 - kinetic energy in the z-direction^2) = rest mass according to an external observer * c^2
• [POV 2] sqrt(E/c^2 - p/c) * c^2 = invariant mass * c^2

total energy = {placeholder 1} placeholder 2 [ placeholder 3 : placeholder 4 : placeholder 5 ] placeholder 6 =

• [POV 1] invariant with respect to any observer
• [POV 2] frame-dependent

{} ground
[] ship
placeholder 1 sound -> heat
placeholder 2 photons being absorbed or emitted
placeholder 3 kinetic energy in the -z direction
placeholder 4 potential energy
placeholder 5 kinetic energy in the +z direction
placeholder 6 drag -> heat
Color code
* Red - Twin 1
* Blue - Twin 2
Outline
* [POV 1]Inelastic collision examples
* [POV 1]Elastic collision examples
* [POV 1]Difference seen between reference frames
* [POV 2]Difference seen between reference frames
* Introduce the twins
* [POV 1](t<0) Departure of Twin 2
* [POV 1](t>=0) Engine shut off of Ship 2
* [POV 1](0>t>a) Engine 1 start of Ship 1 (chemical rocket)
* [POV 1](a>t>b) Engine 1 shutdown and Engine 2 start of Ship 1 (externally-driven microwave beam propulsion)
* [POV 1](b>t>c) Engine 2 shutdown and Engine 3 start of Ship 1 (internally-driven microwave beam propulsion)
* [POV 1](c>t>d) Engine 3 shutdown and Engine 4 start of Ship 1 (lunar rover)
[POV 1]Inelastic collision examples
{()()}))))[:()()()():] // object at rest
{()()}))[:()()()()] // object accelerating and gaining energy content
{()()}[:()()()()))] // object accelerating and gaining energy content
[POV 1]Elastic collision examples
{()()}))))[:()()()():] // object at rest
{()()}))(([:()()))] // object accelerating yet not gaining energy content
{()()}(((([:))))))] // object accelerating yet not gaining energy content
[POV 1]Difference seen between reference frames
{()()()()}[:()()()():] // observer in the same inertial frame
{()()()))}[:()()()] // Lorentz boost by gamma=4/3, v/c=0.661, energy content of object remains invariant
{()()))))}[:()()))] // Lorentz boost by gamma=4/2, v/c=0.866, energy content of object remains invariant
{()))))))}[:()))))] // Lorentz boost by gamma=4/1, v/c=0.968, energy content of object remains invariant
[POV 2]Difference seen between reference frames
{()()()()}[:()()()():] // observer in the same inertial frame
{()()()()))}[:()()()()] // Lorentz boost by gamma=5/4, v/c=0.6, energy content of object is not invariant
{()()()()))))}[:()()()()))] // Lorentz boost by gamma=6/4, v/c=0.745, energy content of object is not invariant
{()()()()))))))}[:()()()()))))] // Lorentz boost by gamma=7/4, v/c=0.821, energy content of object is not invariant
Introduce the twins

• The twins will fly in separate, identical ships.
• Twin 2 will be relativistically accelerated and then will shut off the engine of Ship 2.
• Then, Twin 1 will go to the moon in Ship 1.

[POV 1](t<0) Departure of Ship 2
{()()()()()()}[:()()()()()()():]
{()()()()()()}(([:()()()()():))] // gamma=6/5, v/c=0.553
{()()()()()()}(((([:()()():))))] // gamma=5/3, v/c=0.8
[POV 1](t>=0) Engine shut off of Ship 2
{()()()()()()}(((([:()()():))))] // gamma=5/3, v/c=0.8
{()()()()()()}(((([:()()():))))] // gamma=5/3, v/c=0.8
{()()()()()()}(((([:()()():))))] // gamma=5/3, v/c=0.8
ETC.
[POV 1](0>t>a) Engine 1 start of Ship 1 (chemical rocket)
{()()()()()()}[:()()()()()()():]
{()()()()()()}(([:()()()()():))] // gamma=6/5, v/c=0.553
[POV 1](a>t>b) Engine 1 shutdown and Engine 2 start of Ship 1 (externally-driven microwave beam propulsion)
{()()()()((}(())[:()()()()():))] // gamma=6/5, v/c=0.553
{()()()()((}(((([:()()():))))))] // gamma=6/3, v/c=1.32
[POV 1](b>t>c) Engine 2 shutdown and Engine 3 start of Ship 1 (internally-driven microwave beam propulsion)
{()()()()((}(((([:()()():))))))] // gamma=6/3, v/c=1.32
{()()()((()}(((([((:():))))))])) // must cancel out the +z and -z kinetic energy
{()()()((()}(((([:()()():))))])) // gamma=5/3, v/c=0.8
{()()()((()}(((([((:():))))])))) // must cancel out the +z and -z kinetic energy
{()()((()()}(((([:()()():))])))) // gamma=4/3, v/c=0.661
{()()((()()}(((([((:():))])))))) // must cancel out the +z and -z kinetic energy
{()()((()()}(((([:()()():])))))) // gamma=3/3, v/c=0
[POV 1](c>t>d) Engine 3 shutdown and Engine 4 start of Ship 1 (lunar rover)
{()((()()()}(((([:()()():])))))) // gamma=3/3, v/c=0
{()((()()()}(((([((:():))])))))) // rotating wheels
{()((()()()}(((((([:():))])))))) // force transferred to ground
{((()()((((}))(((([:():))])))))) // force propagating through the ground

Notice that, in my interpretation, the physical energy of a physical object is not relative to an observer.

 

[Dale]

I don't follow what you are trying to say. Your notation is very non-standard and confusing. Are you familiar with the four-momentum notation? http://en.wikipedia.org/wiki/Four-momentum It is very useful.

Kinetic energy is relative to a given reference frame, even in Newtonian mechanics. I don't know how you can get a different interpretation from the equations.