- #1
lemma28
- 18
- 1
In Brian Greene's last work (The fabric of cosmos - chapter 3) I've found an interesting approach to special relativity. It's very simple and straightforward, and I'm very surprised I've never heard of it before. But maybe it's just my fault and my ignorance. Since I'm a teacher it seems very useful to broach the themes of special relativity to young students.
It goes (more or less) like this:
All bodies have a fixed unique dynamic reserve, a velocity. Let's call it c. Every body lives in spacetime. Time always flows. So this velocity reserve can be spent totally in the time dimension. In that case the time flows with velocity c and the body is at rest in space.
But if the body moves (with respect to some frame of reference) then it spends some of the stock-velocity in the spatial dimension. The flowing of time velocity must slow down.
If the spatial velocity reach c the flowing of time velocity will come to a rest.
The relevant equation follows the simple pythagorean theorem (no need to introduce hyperbolic norm):
(propertimevelocity)^2+spatialvelocity^2=c^2.
It can be derived from the invariance of 4-velocity vector norm, just interpreting c^2 as the square of the flowing of time velocity for a body at rest and the velocity of proper time for a moving body as dtau/dt = 1/gamma.
I'm just wondering if it's possible to follow this approach to derive, starting from this simple axiom, the full frame of Lorentz transformations, and if there is some existing didactic material that goes through the same route.
What do you think?
Lemma28
It goes (more or less) like this:
All bodies have a fixed unique dynamic reserve, a velocity. Let's call it c. Every body lives in spacetime. Time always flows. So this velocity reserve can be spent totally in the time dimension. In that case the time flows with velocity c and the body is at rest in space.
But if the body moves (with respect to some frame of reference) then it spends some of the stock-velocity in the spatial dimension. The flowing of time velocity must slow down.
If the spatial velocity reach c the flowing of time velocity will come to a rest.
The relevant equation follows the simple pythagorean theorem (no need to introduce hyperbolic norm):
(propertimevelocity)^2+spatialvelocity^2=c^2.
It can be derived from the invariance of 4-velocity vector norm, just interpreting c^2 as the square of the flowing of time velocity for a body at rest and the velocity of proper time for a moving body as dtau/dt = 1/gamma.
I'm just wondering if it's possible to follow this approach to derive, starting from this simple axiom, the full frame of Lorentz transformations, and if there is some existing didactic material that goes through the same route.
What do you think?
Lemma28