Re: [Phys-l] how to prove relativity

[John Denker <jsd@av8n.com>]

On 06/03/2010 11:24 AM, chuck britton wrote:

> > 	Plato said that we sometimes only can grasp appearances.

I thought Plato's point was mostly the opposite:  We 
ought to beware of the distinction between reality 
and mere appearances.  The /temptation/ is to grasp
the appearance, but we should resist the temptation.

The teacher's job is to make the reality easier to
grasp.  See below.


On 06/03/2010 10:32 AM, I wrote:

> If the clocks in the cars come back with very different 
> elapsed time readings, do you assume that one of the
> clocks was "slowed" in some spooky way, or do you consider 
> it more likely that one of them simply followed a longer 
> path, longer in the timelike direction?

I left out some references.  Sorry.  It is always better 
to give an explanation, as opposed to a bold assertion.
I had a picture clearly in mind, but I forgot to say
what it was.

We start with the idea that among all the paths from A 
to B, some of them are longer in the /time/ direction.  
This has the remarkable property that the general 
relativity contribution (gravitation) is arguably 
_easier_ to visualize and _easier_ to explain than 
the special relativity (velocity) contribution.

On the other hand, the easy GR explanation is not as
widely known.  I had a really good education, beyond 
what most people can even imagine, but I never saw a
simple explanation of this until I came up with the
following tabletop model, with help from David Bowman 
and other folks:
  http://www.av8n.com/physics/geodesics.htm#fig-darts

When you tell people about curved spacetime, they always
ask:  In what direction is it curved?  Answer:  primarily
in the time direction.  You can see from the aforementioned
figure that an object close to the planet follows a path 
that is more wiggly and therefore more lengthy in the 
timelike direction, compared to a path farther out.

The low-altitude clock is not really slowed;  it just 
follows a longer path, longer in the timelike direction.
The analogy to an odometer that follows a longer path
is direct and profound.

Trying to explain GR in terms of contraction/dilation is
a recipe for disaster.  GR is much more easily understood 
in terms of clocks that keep proper time and rulers that 
measure proper length.  (This is yet another strong reason 
for not using contraction/dilation for SR either.)

Sometimes a young student asks how I know that the tabletop
model is correct.  Surely there are innumerable incorrect 
models I could have constructed.  Well:
  a) For one thing, the blue tape behaves as it should.  
   That is, the path of the tape is a rather faithful 
   representation of the world line for an orbiting 
   particle.
  b) The model correctly explains the different behavior 
   of clocks at different heights in the gravitational 
   potential.
  c) The model is consistent with GR theory.  You (the
   young student) need to take my word on this for the 
   moment.  This gives you something to look forward to.  
   Ask the question again when you are in graduate school.

==

As for the SR contribution, the reference is:
  http://www.av8n.com/physics/twins.htm

Actually this example -- the infamous traveling twins --
straddles the boundary between SR and GR.  It invades 
the GR turf, in that it involves accelerations ... but 
it is sufficiently simple that it can be analyzed using 
the methods of SR.