Depends on your measure for "good"ness of an analogy.
I don't think it is used in actual physics courses though - by the time someone is just starting GR, they have covered a lot of algebra and physics already so they should be ready just to go right to the basic tensor stuff and learn it directly rather than through an analogy.
In general, learning by analogy is pretty bad.
...if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels will be greater if they spin in opposite directions than in the same direction...
I don't think the student has a reason to look for it from GEM either ... and GEM will also hide facets of GR. I agree students need a guide though - that is why the student is doing a course in GR ... the whole point of doing a course is to have a guide to your study.Using the tensor equations, you can derive such an effect, but only if you have a reason to look for it. Analogies with other topics in physics can be a guide to know what to explore in a theory.
... looks like a binomial approximation - so that (v/c)<<1. afict The idea is that GEM is for that narrow range when the relative speed is not quite low enough for galilean relativity but not quite high enough to need the full Einstein treatment. The hope is, presumably, to leverage the students existing understanding of EM to get them a "feel" for some of the effects of GR sooner and less painfully than may otherwise be the case. I don't think the existence of an approximation is fatal to a theory.The GEM equivalent effectively treats the squared four-velocity ##(1 + 2\mathbf v/c + v^2/c^2)## as being roughly the same as doubling the speed to ##(1 + 2\mathbf v/c)## but completely ignores the ##v^2/c^2## term.
I thought "c" was just the (invariant) scale factor to get the units to come out how you want which is why we usually pick units so that c=1.[Another edit for clarification] For gravity, the timelike component of the coordinate four-momentum in momentum units is E/c, which varies with c. In a static field, the coordinate energy E in energy (or frequency) units is constant, so the whole equation is still valid if divided by E to remove the energy.
Physics by analogy causes more problems than it solves - do the physics by physics first, then do the analogies as temporary stepping stones where some sort of scaffolding is needed.
I agree. As long as all those things happen.I don't think that there is any problem with using analogies, as long as you remember that an analogy is at best a hint as to how something might work. You have to look at the details to see whether the analogy pans out.
I don't really know much, I'm actually reliant on you guys.I agree. As long as all those things happen.
Back to the topic:
Is GEM an effective way to introduce GR? Compared with current approaches for the same target group?
Do you know of anyone using GEM to teach "introduction to GR" courses?
Note: GEM is not an analogy itself - it's an approximate model whose motivation comes from drawing analogies between EM and GR.
GEM is where the underlying analogies take us, so maybe we should be thinking about whether the underlying analogies are a useful way to introduce GR?
I think we need to hear from OP before any further headway can be made.
I don't want to teach others (not anytime soon at least), but I'm wondering if it would make a good educational tool in general.OK so lets recap: you don't know anything... you are at introductory level with GR yourself... you want to learn more, so you can teach it to others?
Is that correct?
As I said earlier in my post, I'm using ##c## here to temporarily mean the coordinate speed of light, to make the notation more familiar and easier to compare with electromagnetism. It would be natural to use units such that the value is 1 in flat space. The concept of a single variable designating the coordinate speed of light only exists for an isotropic coordinate system when the spatial factor in the metric is the same in all directions, otherwise the coordinate speed of light is different in different directions, requiring a tensor representation.I thought "c" was just the (invariant) scale factor to get the units to come out how you want which is why we usually pick units so that c=1.
In a static gravitational field, the total energy of a test particle is constant. This is equivalent to the Newtonian way in which potential plus kinetic energy is constant. The Newtonian potential energy corresponds to the effect of time-dilation on the energy in GR.Wouldn't the coordinate E usually vary with relative speed and mass?
I don't think it's much more than a useful analogy but a very weak approximation. Gravity is somewhat like electromagnetism. The gravitational field acting on masses is somewhat like electric fields operating on charges. In gravity, moving masses induce a rotational effect which is analogous to the way in which moving charges induce a magnetic field in electromagnetism.I don't want to teach others (not anytime soon at least), but I'm wondering if it would make a good educational tool in general.
Well I asked if you were asking as a teacher or a student and you replied "both" ... it goes to the purpose of acquiring the knowledge.greswd said:I don't want to teach others (not anytime soon at least), but I'm wondering if it would make a good educational tool in general.