5 ms·

Magnetism, Radiation, and Relativity (1999)

37 points by cbd1984 11y ago

platz 11y ago
> electrostatic fields transform from one reference frame to another Is it true?
- GolDDranks 11y ago
  Yes, because of the Lorenz contraction.
ivan_ah 11y ago
Related: a phenomenon that can be described equivalently as due to electric or magnetic interactions, depending on the reference frame: https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_pr...
amelius 11y ago
Maxwell's equations are strange, in that there is the concept of charge (q), but also of current (density, J). If the charge starts moving by the tiniest amount, it suddenly changes "identity" by becoming a current. This is a weird kind of "discontinuity" in the theory.
- chm 11y ago
  My understanding is that current is defined as charge per unit time through a single point. The charge moving stays a charge. I don't get what you mean by it changing identity?
  - Maro 11y ago
    Maybe this helps: http://physics.stackexchange.com/questions/190259/%CE%97ow-does-a-current-density-becomes-a-charge-density http://physics.stackexchange.com/questions/190259/%CE%97ow-d...
    - reagency 11y ago
      Is there an analog to that in mass/gravity? Or no because mass doesn't have sign like charge does?
      - Maro 11y ago
        Yes. You can combine charge density and current to form a 4-vector in SR like (charge density, current vector). Other 4-vectors are (energy, momentum vector). There are also a bunch of others, the most famous/basic one being (time, position vector): https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-vectors https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-v... The reason it's a good idea to group these into 4-vectors is that the components of the vectors transform into each other under coordinate transformations in SR (see Lorentz-transformation).
- tfgg 11y ago
  Huh? A moving charge still has a charge. Imagine a charge density described by the function over space and time rho(r,t). Current is defined by the continuity equation Del[J] = - d rho(r,t) / d t (those are partial derivatives). Basically that says that the rate of increase of the charge density inside an infinitesimal box is related to the total current flowing into the box, i.e. if the charge in a box changes, it must have flowed in/out from just outside the box, i.e. continuity (assuming no sources/sinks). Both exist at the same time. In SR, you can look at the relativistic four-current. Maybe you're thinking of how a current can flow in a wire, despite the wire having no charge. This is because, on our length scales, the electric field of the positively charged atomic nuclei completely cancels the electric field of the negatively charged electrons.
- reagency 11y ago
  Is that true? If a wire has charge density, and then magically some charge starts moving, does the charge density disappear, or do you now have both charge density and current density?
- jeffwass 11y ago
  You seem to be missing the fact that current density J is for a continuously-flowing current moving through some unit of area. In your example of a single charge moving at velocity v, which passes through the origin of your coordinate system at time t, the current density at the origin is basically a Dirac delta function. In other words, there is zero current density through that point at all times other than at one instant (vt) where it would be infinite (although finite when integrated over time, basically how Dirac delta functions work). Thinking about it in this way may help you unite the gap between a moving and stationary charge. You can also think of a Dirac delta function as a finite but normalised Gaussian (or normal) distribution of charge, which gets rid of the discontinuities. When that makes intuitive sense, take the limit where the width of the distribution approaches zero (but remains normalised so the amplitude becomes infinite).
ivan_ah 11y ago
Also related: http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6 http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6
jhallenworld 11y ago
I've heard this before- that magnetism is a consequence of moving electric charges when special relativity is taken into account. But doesn't this on its own rule out magnetic monopoles?

37 points by cbd1984 11y ago

platz 11y ago

> electrostatic fields transform from one reference frame to another Is it true?

GolDDranks 11y ago
Yes, because of the Lorenz contraction.

ivan_ah 11y ago

Related: a phenomenon that can be described equivalently as due to electric or magnetic interactions, depending on the reference frame: https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_pr...

amelius 11y ago

Maxwell's equations are strange, in that there is the concept of charge (q), but also of current (density, J). If the charge starts moving by the tiniest amount, it suddenly changes "identity" by becoming a current. This is a weird kind of "discontinuity" in the theory.

chm 11y ago
My understanding is that current is defined as charge per unit time through a single point. The charge moving stays a charge. I don't get what you mean by it changing identity?
- Maro 11y ago
  Maybe this helps: http://physics.stackexchange.com/questions/190259/%CE%97ow-does-a-current-density-becomes-a-charge-density http://physics.stackexchange.com/questions/190259/%CE%97ow-d...
  - reagency 11y ago
    Is there an analog to that in mass/gravity? Or no because mass doesn't have sign like charge does?
    - Maro 11y ago
      Yes. You can combine charge density and current to form a 4-vector in SR like (charge density, current vector). Other 4-vectors are (energy, momentum vector). There are also a bunch of others, the most famous/basic one being (time, position vector): https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-vectors https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-v... The reason it's a good idea to group these into 4-vectors is that the components of the vectors transform into each other under coordinate transformations in SR (see Lorentz-transformation).
tfgg 11y ago
Huh? A moving charge still has a charge. Imagine a charge density described by the function over space and time rho(r,t). Current is defined by the continuity equation Del[J] = - d rho(r,t) / d t (those are partial derivatives). Basically that says that the rate of increase of the charge density inside an infinitesimal box is related to the total current flowing into the box, i.e. if the charge in a box changes, it must have flowed in/out from just outside the box, i.e. continuity (assuming no sources/sinks). Both exist at the same time. In SR, you can look at the relativistic four-current. Maybe you're thinking of how a current can flow in a wire, despite the wire having no charge. This is because, on our length scales, the electric field of the positively charged atomic nuclei completely cancels the electric field of the negatively charged electrons.
reagency 11y ago
Is that true? If a wire has charge density, and then magically some charge starts moving, does the charge density disappear, or do you now have both charge density and current density?
jeffwass 11y ago
You seem to be missing the fact that current density J is for a continuously-flowing current moving through some unit of area. In your example of a single charge moving at velocity v, which passes through the origin of your coordinate system at time t, the current density at the origin is basically a Dirac delta function. In other words, there is zero current density through that point at all times other than at one instant (vt) where it would be infinite (although finite when integrated over time, basically how Dirac delta functions work). Thinking about it in this way may help you unite the gap between a moving and stationary charge. You can also think of a Dirac delta function as a finite but normalised Gaussian (or normal) distribution of charge, which gets rid of the discontinuities. When that makes intuitive sense, take the limit where the width of the distribution approaches zero (but remains normalised so the amplitude becomes infinite).

ivan_ah 11y ago

Also related: http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6 http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6

jhallenworld 11y ago

I've heard this before- that magnetism is a consequence of moving electric charges when special relativity is taken into account. But doesn't this on its own rule out magnetic monopoles?