Re: Are SR effects real or not? Simplified case.
- From: stevendaryl3016@xxxxxxxxx (Daryl McCullough)
- Date: 18 Jul 2008 05:36:14 -0700
Uncle Ben says...
Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
If 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?
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.
That's attractive and comforting. The thing is, relativity is
uncomfortable to common sense. But we need to get used to it, not to
dodge it.
Once again, this has to do with two different ways of understanding
special relativity. One way is to focus on relative quantities that
have different values in different coordinate systems, and the other
way is to focus on covariant quantities that have the same meaning
in any coordinate system. The latter is really the more modern
approach, and is more convenient to use for General Relativity.
If you want to concentrate on the *real* differences between
Newton's physics and Einstein's physics, I think that the
coordinate-dependent approach is *not* the best way. People
always argue about whether coordinate-dependent effects are
"real" or just an artifact of using a weird coordinate system.
(For instance, you have the various cranks complaining about
Einstein's synchronization procedure.) The real differences
between Newton's physics and Einstein's physics is in terms
of experiments: If you do X, then Y will happen, according
to Einstein, while Newton predicts Z will happen. The Bell
paradox is a good example.
People, even physicists, may have a hard time with it, but as far as
we can tell, moving objects do shrink; moving clocks run slow, but
only w.r.t. the frame of reference in which they are moving.
I don't believe that is the best way to think about it. The
problem with the statement "moving objects shrink" or
"moving clocks run slow" is that they are *only* true if
you set up your coordinate system in a particular way.
Yes, the conventions used by Einstein are particularly
convenient for Special Relativity (but *not* General
Relativity), but they are still just conventions. The
beauty of expressing the laws of physics in covariant
form is that then the predicted results are completely
independent of what conventions you use to set up a
coordinate system.
There are four intertwined concepts that *cannot* be
untangled without adopting a convention, and those are:
(1) clock synchronization, (2) the rate of a moving clock,
(3) the velocity of moving objects, and (4) the length of
moving objects.
To measure the length of an object, you
can do two things: (A) You can note the location
of the two ends of the object at a specific time,
but that requires clock synchronization. (B) You
can time how long it takes for the object to pass
a single point (that is, how long between the time
the front passes and the time the rear passes), but
that requires that you can measure velocities
accurately.
So how do you measure velocities? Well, you can
use radar, and measure the Doppler shift, but that
assumes that you already know the velocity of the
radar signal. You can note the time that it takes
for the object to pass between two points, but
that assumes that you already have a means to
synchronize clocks.
So how do you synchronize clocks? You can bring
the clocks together, set them to the same value,
and then bring them back to their original locations,
but that assumes that the act of transporting the
clock doesn't affect its synchronization. Alternatively,
you can use light signals (or any other communication
mechanism relying on a known velocity) to synchronize
distant clocks, but that assumes that you already know
the velocity of light (or whatever synchronization
signal you are using).
The four different concepts are inherently circular
in their definitions. To break out of the circularity,
something has to be true "by definition". Einstein
boldly proposed that light always has the same
constant speed, which simplified his analysis, but
it is still just a *definition*. The physical content
of Special Relativity does not depend on that definition.
The rate of a clock is defined relative to a frame of reference,
no matter what your intuition tells you. Try to get used to it.
More precisely, it is defined relative to a convention for
how clocks are synchronized and how velocities are measured,
etc.
--
Daryl McCullough
Ithaca, NY
.
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