yeah I agree I garbled up the transverse/perpendicular thing, I shouldn’t have added that bit to what was otherwise a good statement (there being zero magnetic effects for a frame in which the two charges are stationary). I said it more eloquently in my earlier post:
For two parallel-moving electrons, there is no extra deflection or attraction from if they were stationary: the magnetic field exactly compensates for relativistic length-contraction of the electric field.
Due to the zero relative velocity (at t=0, which is what I assume we are interested in) I don’t think time-dilation is relevant in this circumstance, just the geometry of the field. The point is that in the reference frame in which the two charges are stationary there is only the static E and the force qE. This force transforms relativistically, sure, but the B-field that is in the different RF is exactly compensated by the E-field transformation so that E just effectively transforms to qE times a gamma factor, as it would if there were no such thing as a magnetic field. Magnetic fields arise due to relative motion of charged particles, and there is no lorentz transformation that takes stationary charges into relatively moving charges.
Oh I think I see what you meant by time-dilation here, you were just pointing out why F–>F/gamma. Yeah, agree, there is no disagreement about that. Just some confusion about what MikeS meant when saying the force went to zero. I think we are on the same page now. Might be my fault, I’m tired. In my last post I started saying “field” when I meant “force” and vice-versa. Going to sleepy-beddy-bye.
It’s not that the magnetic force is compensated for by the relativistic change in the electric force; rather, the magnetic force is the relativistic change in the electric force. If you have two electrons moving parallel to each other at high speed in the lab frame, then in that frame, you will measure a very small net force on each of those electrons. You can describe this as “there’s a repulsive electric force and an attractive magnetic force that’s nearly as strong”, or you can describe it as “there is only an electromagnetic force, but it’s decreased due to the Lorentz transformation”, but either way, it’s the same thing happening.
It’s the other way around! In his setup he considers the rotational electric field produced by moving loop of wire with electric current and then goes on with the claim that this rotational electric field can be transformed away by choosing a proper reference frame, which is perfectly right, but somewhat misleading because the nature of rotational fields is a quite different issue, almost irrelevant to the topic of this discussion, which concerns static electric and magnetic fields.
Here is a link for you for better understanding of the nature of magnetism. http://newton.umsl.edu/run//magnets.html
And thanks for the link you provided, regarding hypothetical magnetic monopoles.
But i believe it’d be more useful to start with things that are much better understood before going into subtle theories.
If you take out the rotational part of the electric field (i.e., that part which has a nonzero curl), then all that’s left is the part with nonzero divergence. In other words, you’re saying that the divergence of the electric field is frame-invariant. But the divergence of the electric field is just charge (possibly with some proportionality constant, depending on the units you’re using), which we all already know is frame invariant. So yes, saying that that portion of the electric field is invariant is true, but that’s not the entire electric field. One might as well say that total energy is frame-invariant, because mass is a portion of the energy, and mass is frame-invariant.
There is repulsion between two electrons due to the like electrical charges, but the magnetic fields of two electrons result in attraction (his image correction model accounted for both forces). I’m not sure how the relativistic correction factors into things.
The same Lorentz transformation applies to non-electrically-charged objects that are attracted through other forces. I guess the question is: does a pair of oppositely-charged electrons under lorentz-boost behave the same way as a pair of neutral gravitationally-attracting bodies (ignoring gravitomagnetic effects here). If they do, then my thinking about this is correct (though my articulation garbled). If not, then I’m wrong and confused. I may very well be wrong and confused.
Depends on the distance. Since the bright parts of the image were pinched, there was clearly some (original) electron flux at which magnetic attraction exceeded charge-based repulsion. But the bright parts of the images were never reduced to singular points, presumably because at some close range (i.e. high electron flux), the charge-based repulsion had increased to the point where it exactly offset the magnetic attraction.
This sounds like a problem commonly encountered in imaging devices using magnetic deflection of an electron beam. It’s been [del]years[/del] decades since I’ve worked with video electronics, but there were a variety of techniques to deal with this at normal video rates. It must be a much bigger problem with the frame rate you’re talking about. We used digital correction to deal with this, but it was CGI, and imaging wasn’t happening in real time, much less a 10 million FPS rate.
Any kind of force would undergo the same transformations, and if we wanted to, we could describe the change in the force as being due to a “new” force. In the case of gravity, that “new” force is what’s referred to as gravitomagnetic effects. You can’t ignore them, because they’re precisely what you’re asking about.
No; gravitomagnetic effects are many orders of magnitude smaller due to the vastly different field strengths. The electrons would need to be very massive indeed for the gravitomagnetic effect to compete with the corresponding magnetic effect for +1/-1 electrically charged objects.
I (and assumedly Chronos) thought you were talking about the ratio of gravitomagnetic to gravitoelectric forces. And roughly speaking, the ratio of gravitomagnetic forces to gravitoelectric forces is of the same order of magnitude as the ratio of magnetic to electric forces. (In fact, the gravitomagnetic:gravitoelectric ratio is four times larger than the magnetic:electric ratio in an analogous situation.) Take a gander at the equations here. But if you’re comparing gravitomagnetic forces to magnetic forces instead, then yes, they’ll be much much smaller.
Well, I’m not sure what you mean by “a stationary electron”, but magnetic dipole moment is usually explained as follows:
“The electron possesses the intrinsic property of spin angular momentum (rotational motion about an axis), in addition to the intrinsic properties of charge and mass.”
There’s no such thing as “entire” electric field. Static and rotational fields have absolutely different nature, you just can’t mix them together and treat as a single entity. They are not parts of one thing, they both should be explained individually. And by the way, the point is not about “invariance”, it’s about the underlying nature and interpretation of electromagnetism. We might conveniently use the notions of electric and magnetic fields as parameters that enter the Maxwell equations, but it doesn’t necessarily mean that all of them exist as physical entities, it’s just extremely convenient for the sake of elegance of the theory to use some coined notions in mathematical interpretations of observed phenomena. In the same way we can think of gravity where, even though the observed phenomena create a powerful illusion that there exists some entity, a “gravitational field”, which exerts a force on anything in it, the underlying nature of the interactions is best explained by curvature of space-time.
I’m sure you remember what Occam’s Razor is about - “Whenever possible, substitute constructions out of known entities for inferences to unknown entities.”
This principle if applied to the explanation of dynamics of moving charges and currents makes creation of a new entity - a magnetic field - redundant.
This is messed up. What mass are you talking about? And how is this related to the topic at hand?
It sounds like you’re arguing that there are really two types of electric fields: “static”, created by charges, and “rotational”, created by changing magnetic fields. Experimentally, though, there’s not any way to tell the difference between a “static” and a “rotational” field if all you have access to is the field. As an example of this: suppose I’m in a room with a test charge, but no other charges, currents, or magnetic fields present in the room. Somewhere outside of the room, there’s something that is creating an electric field extending into the room; it could be an electric charge distribution, or a toroidal solenoid with a changing current in it (which creates no magnetic field outside of it, but does create a rotational electric field circulating around it.) What experiment can I do with my test charge to figure out what the source of the field is? The answer: I can’t. Inside the room, the divergence and the curl of the electric field are both zero; no matter how carefully I map out the electric field, I can’t tell the difference between an electric field created by some charge distribution outside the room and one created by a changing magnetic field outside the room.
Apologies for the pun, but Occam’s razor cuts both ways: you can either postulate one field that has both non-zero divergence and non-zero curl, or you can postulate two different types of fields, one of which has non-zero divergence and the other of which has non-zero curl, and which just happen to exert forces on charges in exactly the same way. I would argue that postulating one field is inherently simpler than postulating two.