Re: Are SR effects real or not? Simplified case.
- From: stevendaryl3016@xxxxxxxxx (Daryl McCullough)
- Date: 18 Jul 2008 08:00:52 -0700
Uncle Ben says...
On Jul 18, 8:36=A0am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
Uncle Ben says...
Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
=A0If you never discussed "physical length", or "real
length", but always said "projected length" or
"measured length", I doubt very much that Einstein
(or anybody else) would object to the result.
What's wrong with being precise in terminology?
Tom Roberts
IMHO, it's not being precise. It's being wishy-washy.
How is it being wishy-washy?
It is avoiding the concept that relativity is about real things, not
just appearances. (In the Bell's Paradox, the string really does
break, doesn't it. That is as real as it can get.)
That's exactly what Tom is trying to do. If you express things
in terms of *invariants* (things that have the same value in any
coordinate system) then you are guaranteed that any predictions
made are *real* and not artifacts of a particular choice of a
coordinate system.
Of course.Length of a
moving object is perfectly well defined. You mark the coordinates of
the two ends at the same time.
And how is "at the same time" determined?
I think that you mean that if you have *already* set up
a coordinate system, then the length of an object relative
to that coordinate system is well-defined.
What you are trying to do is to preserve a pre-relativistic idea.
How in the world is he doing that? He's *rejecting* the
pre-relativistic idea of "length" as not being meaningful.
Are you sure that is what you meant? It seems to me that he is trying
to preserve the concept that the object has a real physical (proper)
length and the the "measured" lengths are just artifacts.
An object *does* have a proper length, and measured lengths
*are* artifacts. That doesn't make things Newtonian. The
difference between Special Relativity and Newtonian physics
is that they make different predictions about the results
of experiments.
I think that is a pre-relativistic view.
No, it's not. Newton never tried to cast his theory
in coordinate-independent terms. His theory was unnecessarily
tangled up in a particular choice of coordinate systems,
namely inertial Cartesian coordinates. It is possible to
recast Newtonian theory in coordinate-free terms, and you
end up with a theory that is similar in some ways to General
Relativity. But that didn't change the physical content of
Newton's theory.
Newton's theory had two different coordinate-independent
notions of the separation between two events e1 and e2:
(1) The temporal separation between the events. That is,
the time between them.
(2) In the special case in which the temporal separation is
zero, Newton had a coordinate-independent notion of the
spatial separation between the events.
If e1 and e2 are *not* simultaneous, then Newton's theory
gives no coordinate-independent notion of the spatial
distance between the events.
In contrast, Special Relativity has a single coordinate-independent
notion of separation: The spacetime interval. In an inertial
Cartesian coordinate system, this is just L^2 - c^2 T^2, where
L is the spatial separation as measured in that coordinate system,
and T is the time separation as measured in that coordinate system.
Although L and T are frame-dependent quantities, the combination
L^2 - c^2 T^2 is frame-independent.
The relativistic view is that objects
moving or not have a (real) length that is related to the proper
length through a Lorentz Transformation. And this is the view that Tom
is rejecting.
I don't agree that that's the relativistic view. That's the
coordinate-dependent relativistic view. The coordinate-dependent
view is *not* good for comparing Newtonian physics with
Einstein's physics, because it doesn't clearly show what
differences are due to different laws of physics, and what
differences are due to different choices in setting up your
coordinate system. The physical predictions made by relativity
theory don't require that you follow Einstein's conventions
for setting up a coordinate system. If the string breaks, then
it breaks in whatever coordinate system you use.
--
Daryl McCullough
Ithaca, NY
.
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