hlindner's "Simplest Gedanken"
From: throopw@sheol.org (Wayne Throop)
Newsgroups: sci.physics.relativity
Subject: Re: The Simplest Gedanken
Distribution: world
Organization: sheol
Message-ID: <858972597@sheol.org>
References: <332f3f73.12861055@newsserver.epix.net>
Date: Fri, 21 Mar 1997 19:29:57 GMT
: hlindner@epix.net (Henry H. Lindner)
: The simplest Gedanken to help clarify the assertion made by Wayne, Jim
: and others that clocks don't really slow in SR:
I doubt Henry has really caught on to what I asserted, or he wouldn't be
talking about "really slowing". In terms of "really slowing", what I've
been asserting all along is that clocks do really tick slower at higher
velocity. Just like fishing rods really do take up less left-right
distance if they are rotated. It's just that velocity, like direction
(eg, left-right), is coordinate-relative.
But let's examine the proposed scenario in detail.
: Out in deep intergalactic space, with no significant motion WRT the
: nearest galaxies, are two space stations 4 ly apart. They are
: stationary WRT each other. Their distance is determined periodically
: when one station sends a signal to the other which is immediately
: returned. The round trip light time is consistently 8 yrs.
( and I presume they've synchronized their clocks with these signals )
: A space ship leaves station A and goes some distance away from A and
: B. It accelerates to 0.8c and then passes near A on its way to B.
: As it passes A, it sends a message giving the time and date on its
: atomic clock, and A sends it date and time to the ship. As the ship
: flies past B, it sends a signal to B giving its date and time. B
: sends a signal to the ship giving its date and time.
:
: Will the space ship give B a date that is 3 years later than that
: given to A? Will B give the space ship a date that is 5 yrs later
: than the date given by A?. If so, this would imply that the ship's
: clock ran slow, compared to the 5 yrs time that elapsed on the atomic
: clocks at A and B.
S will give B a date 3 years later than that given to A.
B gives S a date 5 years later than that given by A.
Yes, this implies that the ship clock ran slow, in A/B coordinates.
(Of course, the A/B clocks ran slow in ship coordinates also.)
: Is this what you all would expect to happen? How do you reconcile this
: with the assumption that clocks in motion are not actually slowed?
Clocks in motion *are* actually slowed... in the "motionless" coordinates.
How is it reconciled with the fact that either can be taken "motionless"?
I've explained this many times. Two web pages, complete with diagrams, are
the bricklayers
and the football fields
The football example is especially relevant. Let's diagram the situation
that Henry describes:
Since this is a spacetime diagram, an object is represented by a line
that has a specific direction. The direction the line points (the slope
of the line) is its velocity. We have stations A and B, a ship passing
by each in turn, and nearby (compared to other things, but conveniently
out-of-the-way of the stations and the ship) galaxies.
The diagram is color coded so that things about the station frame
are in blue, and things about the ship frame are in red. In this way,
"lines of simultaneity", which depict sets of points considered simultaneous,
are also drawn through events of interest, labeled with their coordinate
times. Further, the distances between the station are given in each
frame, and the time coordinates at opposite stations when the ship is
at the opposite station are given.
: I know why relativists will answer the following questions in the
: negative, but I add them for completeness' sake. A simple "Nay" will
: suffice if that is your answer:
Henry may know the answer in yes-or-no terms, but I don't think
yes-or-no will suffice to show *why* the answer is as it is.
Therefore I'll make a detailed answer anyways.
: What if A and B themselves are co-moving at 0.8c relative to the
: nearest galaxies? Is your answer the same? Would there be any
: difference in the transmitted dates if the ship is flying in the same
: direction WRT the galaxies as AB, as compared to flying in the
: opposite direction?
Consider this drawing of the exact same events in spacetime,
with the exact same spacetime intervals between them, and again
with coordinate-specific information annoted in colorcoding.
In this case, the stations move WRT the galaxies. But nevertheless,
the times exchanged by the ship with each station remain the same,
the trip times remain the same, everything remains the same. The
only difference is, we are drawing the ship's velocity straight
up the page, and the station's velocities at an angle. When we
drop "perpendiculars" (that is, lines of simultaneity (which are
metaphhorically perpendicular (but not linterally in euclidean
space (but nevertheless.)))), we find we've got the same situation
as in the first diagram, except the galaxies "G" are still drawn
straight up the page.
In fact, it's clear that it simply doesn't matter how we draw the
galaxies in either diagram. They have no effect on who's clock
ticks fast or slow, or what clock readings are exchanged by the
ship and stations. The galaxies could be drawn in any which way,
and the direction of the Galaxy-arrow compared to the others makes
no difference whatsoever.
Consider this diagram, of two parallel walls A and B, a stone path S
at an angle between them, and two distant gravel roads G1 and G2.
Now. Surely it is totally clear here that it simply doesn't matter
which of the gravel roads G1 or G2 one takes as squarely vertical
in that diagram. It simply doesn't matter if you suppose that
the walls A and B and the road G1 are vertical and the path S
and the road G2 are crooked, or if you suppose that the path S
and the road G2 are vertical, and the walls A and B and the road G1
are crooked. Which is vertical and which slanted is irrelevant;
The walls are still 4 km long and 3 apart, and the path is still
5 km long. Doesn't matter if A and B are vertical, or S is vertical.
The matter of "vertical" simply doesn't enter into it, and
clearly the nearby gravel roads are totally irrelevant.
Just so with the space stations A and B, the ship S, and the
nearby (blue) galaxies G1, or (red) galaxies G2. Surely by now
it is totally clear that it simply doesn't matter which of the
galaxies G1 or G2 one takes as a motionless in those diagrams.
It simply doesn't matter if you suppose that the stations A and B
and the galaxy G1 are motionless, and the ship S and the galaxy G2
is moving, or if you suppose the ship S and the galaxy G2 are motionless,
and the stations A and B and the galaxy G1 is moving. Which is moving
and which motionless is irrelevant; the stations are still 4 lightyears
apart, their clocks still tick off 5 years, and the ship's clock
still ticks off 3 years. Doesn't matter if A and B are motionless,
or S is motionless. The matter of "motionless" simply doesn't enter
into it, and clearly the nearby galaxies are totally irrelevant.
And yet if you speed up or slow down that ship S WRT stations A and B, its
clocks really will tick slower or faster, when compared against station
clocks. And if you build that stone path S at a greater or lesser angle
WRT walls A and B, it really will take a greater or lesser amount of
paving stones per length of wall.
: Similarly, if A is in front of B parallel to the direction of motion,
: would the radio signals from A to B and B to A differ in travel times
: as judged by A and B?
Draw your nearby galaxies any which way you want. The relationships of
A, B, S, and the intervals between their crossings don't change a whit,
no matter which direction you face in spacetime. "Direction of motion"
simply isn't the issue. The "direction of motion" in the sense Henry
seems to be using it simply isn't a useful candidate for an objective
fact about an object's relationship to the Cosmos.
Velocity is simply a direction in spacetime. Turning a shape to
look at it from a different direction doesn't change the actual shape
(though it may change its silouette).
--
Wayne Throop throopw@sheol.org http://sheol.org/throopw
throopw@cisco.com