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Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
Hi...
I just want to check if I'm right or wrong about one thing:
Analogy is made between gravity and electromagnetism by comparing the frame dragging and Maxwellian magnetic field.
As moving charge produces magnetic field, moving mass produces gravitomagnetic field.
Massive objects rotating relative to each other will attract more than if they are still. (but can't repel since we have only one type of 'charge' and like attract). These forces are in reality very weak and hardly measurable, but now;
Magnetic field in a coil inherently resists it's change by electric current.
Something we know from very long ago, the mass has inertia, and also inherently resists change in momentum. Through analogy it could be described as gravitomagnetic field resisting it's own change, making acceleration of mass (dv/dt) direct analogy to rate in change of current, dI/dt?
This implies that in reality, inertia and inductance are very same phenomena happenong on two different interactions.
I could imagine a lump of mass and a lump of charge behaving exactly the same way, each having ''inertia'' in ''their own spacetimes''.
Kinetic energy of everything is actually stored in GM field, as well as magnetic energy is stored in a magnetic field.
But what keeps confusing me, gravitomagnetism is such a weak force that it's barely detectable. Could it really be something that big or I'm completely wrong in everything I just said?
Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
I'll try one more time;
Any moving charge produces magnetic field, and resists to change in that field. So even if mass is negligible it still possesses sort of ''inertia'' from this field because it stores energy.
I'm embarrassed because I couldn't figure out relation of a velocity of a single lump of charge to it's energy and magnetic field. That's where my teenage math capabilities end.
Moving massive object has analogous gravitomagnetic field.
I couldn't figure out how is it related to object mass and velocity either, all I found is a faraday's law analogy + relation to 1/c which makes it very weak.
Now, all massive object resist acceleration too, and store energy by 1/2mv^2.
Question is, does this have anything with the analogy from the above?
Can it be that the thing we call kinetic energy is actually energy stored within Bg of an object; but for some reason the field is very poorly couplable and overwhelmed by static gravity and other interactions.
To simplify that further I tried to compare a spinning flywheel to a toroidal superconductor carrying current. But I don't know how much can I tell from that apart from large similarity of equations.
PS. If I need to add, left I is moment of inertia, right is electric current
Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
Hi Marko, I don't know about gravitomagnetic fields, but in electromagnetism, the electric and magnetic fields are manifestations of the same thing. Different inertial frames will see different E and H fields depending on the relative velocity between the charge and observer. The same goes for accelerated frames.
Your question about field energy and velocity is not a trivial one. It has been a long time since I have done the math to prove it, but the energy in the field of a charge moving at a constant velocity is more than when it is "standing still" (with respect to a "stationary" observer. The fields (and hence the energy) can be calculated using the "Lienard-Weichert" potentials... This would be consistent with special relativity because the field energy also represents mass. If memory serves me, about 2/3 of the electron's rest mass is due to the energy in its electric field.
Accelerated charges are not so simple, because you then need to include radiation fields in the solution... A reference frame attached to a rotating system is an accelerated frame...this makes things far more difficult.
I hate to say it, but without sufficient mathematical tools, it is very difficult to visualise what is going on because the field (energy) solution to accelerated charge problems is not at all obvious using simple circuit or mechanical analogies. This is why electromagnetism is not a very popular part of EE curricula.... :(
Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
I don't know about gravitomagnetic fields, but in electromagnetism, the electric and magnetic fields are manifestations of the same thing. Different inertial frames will see different E and H fields depending on the relative velocity between the charge and observer. The same goes for accelerated frames.
That's exactly the point of frame dragging. GM field is just a formal analogy; it's nothing but gravitational field in different inertial frame.
That's where gravitational radiation hype arised from - change in gravitational field changes GM field which in turn induces another gravitational displacement field and so endlessly, carrying away energy as a wave perfectly analogous to EM radiation... but that's another story.
Your question about field energy and velocity is not a trivial one. It has been a long time since I have done the math to prove it, but the energy in the field of a charge moving at a constant velocity is more than when it is "standing still" (with respect to a "stationary" observer. The fields (and hence the energy) can be calculated using the "Lienard-Weichert" potentials... This would be consistent with special relativity because the field energy also represents mass. If memory serves me, about 2/3 of the electron's rest mass is due to the energy in its electric field.
I thought it's simple enought?
Energy of moving charge in conductor is 1/2LI^2, so it would be sort of like we chopped out a small portion of it.
Would it work if I just took into account only the inductance of that small part?
That's why I went for much simpler flywheel analogy:
Spinning mass produces GM field pretty much the same way as spinning current produces magnetic field in a closed loop.
Mass brought over that flywheel would indeed attract more to it than if it was still relative to it. But effect is minuscule for anything less than planet scale.
All these nice analogies made me think that GM field must absolutely be storing energy too, having some sort of resistance to change like real magnetic field does. Do I need to tell again what it looks like?
But I couldn't find any amthematical or canonical proof for that.
And another problem is that there are some forms of energy, like EM radiation, which are affected by gravity but don't have inertial mass in common sense. That's the other thing.
Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
Energy of moving charge in conductor is 1/2LI^2, so it would be sort of like we chopped out a small portion of it.
No. For charges moving at appreciable speeds, this is _not_ true. Not to mention that inductance is a circuit, not a field concept...and consequently is not the whole story. In a conductor, average charge carrier speeds are very small.
While the particle field is inseparable from its energy/mass properties, a full relativistic treatment requires including models of subatomic particles.
But what keeps confusing me, gravitomagnetism is such a weak force that it's barely detectable. Could it really be something that big or I'm completely wrong in everything I just said?
This is getting beyond my expertise to explain, but I do know that in the General Relativistic framework, gravity is not a force in the usual sense (it is a fictitious force). In the Newtonian sense, the gravitational potential is represented by a scalar field. Nothing like the classical electromagnetic field....but then I am ignorant of theories that represent gravity as a tensor field (like the electromagnetic one...)
Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
I'll shut up now...........
Hey, don't go, don't...
I really lack knowledge of some of much more fundamental things here.
What I don't understand is general difference/similarity of mass and energy.
What is really mass, and what is energy? It is generally talked about objects ''with'' and ''without'' mass. I thought of mass as
Things with mass are bound to velocities <c. Massless particles, like EM radiation carry energy and momentum, still interact with gravity but don't feel inertia?
Gravitational mass was always told to be equal to inertial mass.
What really makes a particle (boson) massless/inertia-less while it still owns energy?
But why do some other forms of energy, like kinetic, appear to increase mass of a body to more than it's inertial mass?
No. For charges moving at appreciable speeds, this is _not_ true. Not to mention that inductance is a circuit, not a field concept...and consequently is not the whole story. In a conductor, average charge carrier speeds are very small.
While the particle field is inseparable from its energy/mass properties, a full relativistic treatment requires including models of subatomic particles.
I always imagined current as sort of fluid pushing on itself and having constant charge movement speed because they are oppressed by R same way as air drag limits speed of a falling object.
As I think it shouldn't be too difficult to relate current with charge velocity.. if I know Q = I*t, elementary charge and number of charges in conductor volume, hmm...
Now as I think their acceleration should be proportional to dI/dt, right?
And when they are in conductor and relatively slow, energy storage of magnetic field represents major energy storage and inertia can be ignored; if they are fired through vacuum they accelerate grossly and their kinetic energy outweighs magnetic energy by far.. is that right?
Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
Hey, don't go, don't...
Ok...I won't!
What is really mass, and what is energy?
This is a really tough question that I don't know how to answer in its deepest sense. On the surface, and this may seem silly, but:
1. Mass feels heavy when you push on it (inertia...Inertial and gravitational mass can be shown to be equivalent, IIRC)
2. Energy is the act of doing work (kinetic) or the potential to do work on a system (potential)
Sorry...at this hour, that's the best I can do! Maybe someone else lurking in the background can offer a better, more elucidating definition....
Things with mass are bound to velocities <c. Massless particles, like EM radiation carry energy and momentum, still interact with gravity but don't feel inertia?
But EM radiation can be made to "look like" it has inertial mass... Imagine photons (or EM fields) in a box. These fields exert pressure on the walls of the box. If the box is is accelerating, more pressure is exerted on the bottom than on the top of the box (just like a gas would). You can show this is linked both to Doppler-shift in the box waves as well as its length contraction as a result of its velocity and will contribute to an apparent increase in mass as its speed increases in accordance with the Einstein's relativity.
As I think it shouldn't be too difficult to relate current with charge velocity.. if I know Q = I*t, elementary charge and number of charges in conductor volume, hmm...
Now as I think their acceleration should be proportional to dI/dt, right?
The problem with this is that inside of a conductor, charges undergo collisions with "stationary" particles that make up the conductor material. The charges in copper, for example, look like a gas interacting with a porous material. In fact, in solid materials at room temperature, the velocity of charges obey a drift-diffusion relationship like that found in hydrology, for example (google Darcy's Law). Compare this to the Drude Model of conduction (using electric field derived from scalar electric potential). Charge acceleration is indeed proportional to electric field E.....in a vacuum! In a conductor, this is not so because of collisions with stationary ions.
And when they are in conductor and relatively slow, energy storage of magnetic field represents major energy storage and inertia can be ignored; if they are fired through vacuum they accelerate grossly and their kinetic energy outweighs magnetic energy by far.. is that right?
The problem is that "kinetic energy" becomes more difficult to define. You must consider the energy of the entire system: electromagnetic coupled with mechanical... Unfortunately, the best descriptions of what happens are mathematically based... However, even the mathematics in the end amounts to bookkeeping of all the contributions to energy .....
Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
Don't think I forgot about this.. I'm just so..overloaded.. last weeks, and I can spend days just thinking about these things
But EM radiation can be made to "look like" it has inertial mass... Imagine photons (or EM fields) in a box. These fields exert pressure on the walls of the box. If the box is is accelerating, more pressure is exerted on the bottom than on the top of the box (just like a gas would). You can show this is linked both to Doppler-shift in the box waves as well as its length contraction as a result of its velocity and will contribute to an apparent increase in mass as its speed increases in accordance with the Einstein's relativity.
That's what is paradoxical to me - something that has inertial mass can't move at speed of light. So there must be some intristic difference.
What do physicists mean when they say ''massless particle'', what that is, apart from being a boson (although there are massive bosons too).
The problem is that "kinetic energy" becomes more difficult to define. You must consider the energy of the entire system: electromagnetic coupled with mechanical... Unfortunately, the best descriptions of what happens are mathematically based... However, even the mathematics in the end amounts to bookkeeping of all the contributions to energy .....
Yes! You hit exactly what I wanted to point out.
I want to understand how does magnetic field of a charge moving in free space store energy;
So would it manifest simply like another kind of inertia, i.m. accelerating charge would store both kinetic and magnetic energy?
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Relativity and Maxwellian analogies; frame dragging
What was the question again?
