Re: Das 3. Postulat der Relativitätstheorie (Clock Hypothesis)
- From: "Jürgen Rink" <juergen_arbeit@xxxxxx>
- Date: Fri, 27 Jul 2007 09:26:20 +0200
"roger" <roger@xxxxxxxxxxx> schrieb im Newsbeitrag
news:f8a9q1$bf4$1@xxxxxxxxxxx
Es ist nicht sehr bekannt, aber nach Einstein haben RTler
noch das folgende 3. Postulat der RT definiert:
"The Clock Hypothesis states that the tick rate of a clock when
measured in an inertial frame depends only upon its velocity
relative to that frame, and is independent of its acceleration
or higher derivatives. "
(Quelle: sci.physics FAQ, Don Koks und 'Erzrelativist' John Baez)
Auf Deutsch in etwa:
"Nicht von Beschleunigung sondern von der Geschwindigkeit
hängt die Länge des Zeittaktes einer Uhr ab."
Für schlaue Kritiker, die der Meinung sind dieses Postulat verletzt
das Äquivalenzprinzip (G-Feld vs. Beschleunigung) haben diese RTler
folgende billige Erklärung parat
(für mich ist diese Erklärung nicht sehr überzeugend, denn
Beschleunigung muss wie ein G-Feld behandelt werden):
"
But what about the Equivalence Principle?
Sometimes people say "But if a clock's rate isn't affected by
its acceleration, doesn't that mean the Equivalence Principle
comes out wrong?
If the Equivalence Principle says that a gravitational field is
akin to acceleration, shouldn't that imply that a clock isn't
affected by a gravitational field, even though the textbooks say it is?"
No, the Equivalence Principle is fine. Again, the confusion
here is the same sort of thing as above where we spoke about
the wind chill factor. Let's try to see what is happening.
Imagine we have a rocket with no fuel. It sits on the launch
pad with two occupants, a couple of astronauts who can't see
outside and who believe that they are accelerating
at 1 g in deep space, far from any gravity.
One of the astronauts sits at the base of the rocket, with the
other at its top, and they both send a light beam to each other.
Now, general relativity tells us that light loses energy as it
climbs up a gravitational field, so we know that the top astronaut
will see a redshifted signal. Likewise, the bottom astronaut will
see a blueshifted signal, because the light coming down has
fallen down the gravitational field and gained some energy en route.
How do the astronauts describe what is going on? They believe
they're accelerating in deep space. The top astronaut reasons
"By the time the light from the bottom astronaut reaches me,
I'll have picked up some speed, so that I'll be receding from the
light at a higher rate than previously as I receive it. So it should
be redshifted--and yes, so it is!" The bottom astronaut reasons
very similarly: "By the time the light from the top astronaut reaches me,
I'll have picked up some speed, so that I'll be approaching the
light at a higher rate than previously as I receive it. So it should be
blueshifted--and yes, so it is!"
As you can see, they both got the right answer, care of the
Equivalence Principle. But their analysis only used their speed,
not their acceleration as such. So just like our wind chill factor above,
applying the Equivalence Principle to the case of the rocket doesn't
depend on acceleration per se, but it does depend on the
result of acceleration: changing speeds!
"
(Quelle: sci.physics FAQ, Don Koks und 'Erzrelativist' John Baez)
Hallo roger,
zu Deiner Information. Koks sagte auch:
"So the clock postulate says that the rate of an accelerated clock doesn't
depend on its acceleration. But note: the clock postulate does not say that
the rate of timing of a moving clock is unaffected by its acceleration. The
timing rate will certainly be affected if the acceleration changes the
clock's speed of movement, because its speed determines how fast it counts
out its time (i.e. by the factor ?). (The clock rate won't be affected by
circular motion at constant speed.) If that all seems confusing, think of
an everyday analogy. If you ride your bicycle on an icy morning, you get
very cold due to the wind chill factor. The faster you go, the colder your
hands get. This wind chill is a function of your speed, but not your
acceleration. Nevertheless, it is affected by your acceleration when your
acceleration changes your speed. But regardless of whether you have a low
or a high acceleration, the only thing that matters as far as your cold
hands are concerned is what your current speed is. And for circular motion,
two cyclists who follow different-diameter circles at the same speed will
feel the same wind chill, even though they have different accelerations. So
the wind chill factor does not depend on your acceleration, but it certainly
can be affected by your acceleration.
The clock postulate also implies that the amount of shortening of a moving
rod is independent of its acceleration. And also, that the relativistic
mass of a moving object also doesn't depend on its acceleration.
The clock postulate is not meant to be obvious, and it can't be proved.
It's not merely some kind of trivial result obtained by writing special
relativity using non-cartesian coordinates. Rather, it's a statement about
the physical world. But we don't know if it's true; it's just a postulate.
For instance, we can't magically verify it by noting that the Lorentz
transform is only a function of speed, because the Lorentz transform is
something that's built before the clock postulate enters the picture. Also,
we cannot simply wave our arms and maintain that an acceleration can be
treated as a sequence of constant velocities that each exist only for an
infinitesimal time interval, for the simple reason that an accelerating body
(away from gravity) feels a force, while a constant-velocity body does not.
Although the clock postulate does speak in terms of constant velocities and
infinitesimal time intervals, there's no a priori reason why that should be
meaningful or correct. It's just a postulate! This is just like the fact
that even though a 1000-sided polygon looks pretty much like a circle, a
small piece of a circle can't always be treated as an infinitesimal straight
line: after all, no matter how small the circular arc is, it will always
have the same radius of curvature, whereas a straight line has an infinite
radius of curvature. It also won't do to simply define a clock to be a
device whose timing is unaffected by its acceleration, because it's not
clear what such a device has got to do with the real world: that is, how
well it approximates the thing we wear on our wrist.
Although the clock postulate is just that, a postulate, it has been verified
experimentally up to extraordinarily high accelerations, as much as 1018 g
in fact. Of course, the postulate also speaks of more than acceleration, it
speaks of all derivatives of v with respect to time. But still it can be
shown to be a reasonable thing to assume, because it leads to something that
has been tested in other ways, as we'll see in the next section."
[Quelle: http://www.math.ucr.edu/home/baez/physics/Relativity/SR/clock.html]
MfG,
Jürgen Rink
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42
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