Re: [Phys-l] Relativity Question (corrected)

[John Denker <jsd@av8n.com>]

On 05/06/2009 12:28 PM, Eric Lane, Lane wrote in part:

> As far as we can determine so far, our deductions from this approach
> give the accepted results of space-time SR, with some additional
> insights. One is that the gamma in the SR version of p belongs to the
> v. 

This is not a "new" insight.

The underlying issue is important in a practical sense, if
only because it is widely misunderstood.  OTOH there is almost 
no physics in it;  it's just a matter of keeping the definitions 
straight.

The four-velocity u is defined as d/d(tau) of the 4-position.
In contrast, the three-velocity v is conventionally defined
as d/d(t) of the 3-position.  Given that the three-position is
the spatial part of the four-position, the three velocity is
*not* the spatial part of the four-velocity!  There is a factor
of gamma i.e. d(t)/d(tau) on the loose.

This is a huge trap for the unwary, because it deviates from the
nice pattern:
 ++ three-momentum is the spacelike part of the 4-momentum
 ++ three-position is the spacelike part of the four-position
 -- three-velocity is *not* the spacelike part of the four-velocity

You could argue that the three-velocity is misdefined, but the
conventional (mis)definition is well established and is occasionally
useful ... so I reckon it is not going to change anytime soon.

The corresponding problem with the momentum does not arise because
conservation of momentum dictates the right answer.

This concept is super-easy to teach: d/d(tau) is different from d/d(t).
It is also super-easy to test for.