Relativity: Energy in AC Circuits & Mass Momentum

[marlowgs]

Is it correct to say that the energy in resistance and reactance components of a LR or RC series A.C. circuit are the same thing as the momentum energy and rest energy of a moving mass in special relativity?

 

[Nugatory]

No, not correct. They are totally unrelated.

 

[ZapperZ]

Is it correct to say that the energy in resistance and reactance components of a LR or RC series A.C. circuit are the same thing as the momentum energy and rest energy of a moving mass in special relativity?

Nugatory has already answered this question.

I, however, want to point out something, and this needs to be made very clear to many new members, because I've seen this type of posting way too frequently lately.

You simply should consider posting a more substantial and thoughtful question than this. For example, in this case, you simply shouldn't ask if such-and-such is true without offering any kind of justification. Why would you think the "energy" in the impedence/reactance of those components be "the same thing" as momentum and energy of a relativistic mass? There must be a reason or an impetus for you to think that. It just can't come to you in a dream!

In other words, try and offer some "rational" explanation on why you think that way, or what made you think of it. for many of us, it tells us exactly what you had understood (or misunderstood), and in some way, reveal the level that you might be able to comprehend. This is especially important for new members since we usually do not know much of your backgrounds and what you have already comprehended. Otherwise, it will also be appropriate for us to simply respond, as Nugatory did, by saying "no, it isn't!" and leave it at that. If that kind of a response is frustrating or unsatisfactory to you, then that's the same type of reaction I get when I read a question like this.

Zz.

 

[marlowgs]

I’m reaching this conclusion because that the magnetic field is the relativistic effect of a changing electric field and visa versa. The phase of electric and magnetic fields in pure momentum energy (photons) is in-phase as it is for the resistor. The energy is radiated away from the resistor but it stays with the moving mass. The energy in an inductor or capacitor is stored energy as it is for rest energy. Total energy is the vector sum of momentum energy and rest energy. Total energy for the resistor and inductor or capacitor is also the vector sum of the two.

 

[ZapperZ]

I’m reaching this conclusion because that the magnetic field is the relativistic effect of a changing electric field and visa versa.

Where did you get this from?

The CONCEPT of magnetic field being generated by a changing electric field came out of classical E&M's Maxwell equation. Granted, there is a relativistic, covariant form of it, but it did NOT require any relativistic effects for there to be the connection between the two. So it is false that ".. the magnetic field is the relativistic effect of a changing electric field..."

The phase of electric and magnetic fields in pure momentum energy (photons) is in-phase as it is for the resistor. The energy is radiated away from the resistor but it stays with the moving mass. The energy in an inductor or capacitor is stored energy as it is for rest energy. Total energy is the vector sum of momentum energy and rest energy. Total energy for the resistor and inductor or capacitor is also the vector sum of the two.

I find this part very difficult to understand. Remember, you simply cannot equate something just via qualitative means. There must be a quantitative agreement between the two for you to be able to reasonably conclude that they are the same. This, you haven't done.

In any case, you have received the definitive answer to your question. Are you not satisfied with the answer you received?

Zz.

 

[rumborak]

Where did you get this from?

I don't think you can fault him for that one. I remember hearing it during my college days (this was before the age of internet, so I couldn't just google it), but now there's pages like this: http://en.wikipedia.org/wiki/Relativistic_electromagnetism

I must admit that I find that formulation to be mesmerizing too. I always felt that the E and B duality (one produces the other when changing) indicated that they're just the same thing really. Which they are of course (the EM field), but that the separation of two aspects of it into E and B was more a historical and computation happenstance.

 

[marlowgs]

A changing electric or magnetic field in LRC components comes down to relative movement of electrons in the components. The relativistic effect is more apparent because of the great number of electrons and their high velocity in the components.

 

[ZapperZ]

I don't think you can fault him for that one. I remember hearing it during my college days (this was before the age of internet, so I couldn't just google it), but now there's pages like this: http://en.wikipedia.org/wiki/Relativistic_electromagnetism

I must admit that I find that formulation to be mesmerizing too. I always felt that the E and B duality (one produces the other when changing) indicated that they're just the same thing really.

But like I said, while there is a covariant form of Maxwell equation, one needs to remember that the relationship between E and B does NOT require any knowledge of relativity. Relativity came later, much later, than classical E&M. And in fact, even today, we design stuff such as antenna without bothering about any relativistic effects.

Zz.

 

[ZapperZ]

A changing electric or magnetic field in LRC components comes down to relative movement of electrons in the components. The relativistic effect is more apparent because of the great number of electrons and their high velocity in the components.

No. Read up a bit on solid state physics. The electron speed in metals is VERY SLOW when compared to c. We do no relativistic corrections on charge transport in metals at all!

Zz.

 

[rumborak]

No. Read up a bit on solid state physics. The electron speed in metals is VERY SLOW when compared to c. We do no relativistic corrections on charge transport in metals at all!

Zz.

Even at the speeds observed in a conductor, the point is that you can describe the magnetic force as a relativistic effect on the electric field of the moving particle.
I hate linking to Wikipedia articles, but see here: http://en.wikipedia.org/wiki/Relativistic_electromagnetism#The_origin_of_magnetic_forces

 

[marlowgs]

My mistake - electron velocity is very slow. But the great number of electrons makes the relativistic effect more apparent.

 

[ZapperZ]

My mistake - electron velocity is very slow. But the great number of electrons makes the relativistic effect more apparent.

This makes no sense. A lot of very slow electrons somehow increases the relativistic effects? Would you care to calculate this and show me how?

I can show you the Drude model. Purely classical. It can derive Ohm's law that we all know and love. Can you show me how that model actually works when we are dealing with HUGE number of electrons in metals without ever considering any relativistic effects? After all, you claim that this should be apparent when we deal with Avogadro's scale numbers.

Zz.

 

[ZapperZ]

Even at the speeds observed in a conductor, the point is that you can describe the magnetic force as a relativistic effect on the electric field of the moving particle.
I hate linking to Wikipedia articles, but see here: http://en.wikipedia.org/wiki/Relativistic_electromagnetism#The_origin_of_magnetic_forces

You should be.

The fields are relativistic. The electrons are not. The relativistic form of Maxwell equation deals with the fields, not the charge transport in metals! However, how would this Wiki entry somehow explain the OP's initial premise? I don't see the connection.

I feel as if I'm battling two different battles here. I'd rather address one issue at a time, because you have a completely separate problem.

Zz.

 

[rumborak]

Sorry, I'll step away from this discussion for now to keep it at the OP topic. I felt you were coming down rather hard on him for associating electromagnetic forces with relativity; I simply stepped into say that there *is* such a connection.

 

[marlowgs]

It doesn't increase the relativistic effect - just makes it more apparent. The relativistic effect is very small at low velocities (and ignored) but it still exists.

 

[ZapperZ]

It doesn't increase the relativistic effect - just makes it more apparent. The relativistic effect is very small at low velocities (and ignored) but it still exists.

The gravity from Alpha Centauri is very small, but it still exists. But realistically, how many of the designs of our buildings and dynamics have taken into account of that effects? Just because it exists, in principal, it doesn't mean it has any noticeable or significant presence that affects the things we do! Think of how hard structural engineers will laugh at you when you insist that they consider relativity when they design a building!

Look at your original question. You are attributing a LARGE part of the phenomenon to relativity. You have been told that this is incorrect and what you are describing has nothing to do with what you think. Every single "physics" that you tried to invoke was either wrong, or not applicable or not realistic. If you are still not satisfied with the answer so far, there's nothing else I can do because it appears that you've already made up your mind.

Zz.