Years ago, I discovered a bizarre situation that can occur in
circular motion. At the time, I dubbed the effect
"the non-transitivity of time in special relativity".

Here's the setup:

Imagine that there is a huge circular railroad track in
space. (The track is circular and stationary, according
to some inertial observer). On the track is a train that
is so long that it occupies the entire track (i.e., the
nose of the locomotive is just touching the end of the
caboose). The train is traveling at a constant speed
of beta c (wrt the fixed track, according to the inertial
observer). There are no large masses anywhere near the
track, so that spacetime is essentially flat over the entire
region of the track.

The bizarre situation that can occur is this:

There can exist three passengers (each occupying his own
fixed seat on the train), denoted A, B, and C, who come to
the following conclusions about their corresponding
ages:

Passenger A concludes that passenger B's age
is always the same as his own age. Passenger B
agrees with that (and they both are always in agreement
about the correspondence between their two ages).

The same situation can exist between B and C: they
both agree that they always have the same age.

Passengers A and C are also always in complete agreement
about the correspondence between their ages. But they
DON'T agree that they are the same age!

I've always found this situation quite intriguing, and
I don't think that it is a widely known result.

Mike Fontenot

Mike Fontenot wrote:
Years ago, I discovered a bizarre situation that can occur in
circular motion. At the time, I dubbed the effect
"the non-transitivity of time in special relativity".
[...]

Hmmm. You are obviously thinking that each passenger imagines an
instantaneously comoving inertial frame and uses the distant
simultaneity of that frame to compare ages. That's silly -- such frames
cannot really be constructed, and don't really apply.

Instead, imagine each passenger has a clock that at every tick emits an
electromagnetic signal to the other passengers. All 3 passengers will
measure the signals from both other passengers to have the same rate as
her own clock. This is so independent of where the passengers are
located on the train. So they will all conclude they all age at the same
rate.


Tom Roberts

Mike Fontenot wrote:
Years ago, I discovered a bizarre situation that can occur in
circular motion. At the time, I dubbed the effect
"the non-transitivity of time in special relativity".

Here's the setup:

Imagine that there is a huge circular railroad track in
space. (The track is circular and stationary, according
to some inertial observer). On the track is a train that
is so long that it occupies the entire track (i.e., the
nose of the locomotive is just touching the end of the
caboose). The train is traveling at a constant speed
of beta c (wrt the fixed track, according to the inertial
observer). There are no large masses anywhere near the
track, so that spacetime is essentially flat over the entire
region of the track.

The bizarre situation that can occur is this:

There can exist three passengers (each occupying his own
fixed seat on the train), denoted A, B, and C, who come to
the following conclusions about their corresponding
ages:

Passenger A concludes that passenger B's age
is always the same as his own age. Passenger B
agrees with that (and they both are always in agreement
about the correspondence between their two ages).

The same situation can exist between B and C: they
both agree that they always have the same age.

Passengers A and C are also always in complete agreement
about the correspondence between their ages. But they
DON'T agree that they are the same age!

I've always found this situation quite intriguing, and
I don't think that it is a widely known result.

Mike Fontenot

Perhaps I'm misreading something but isn't it the Sagnac effect, only
quantified in a peculiar way?

--
Jan Bielawski

JanPB wrote:

Perhaps I'm misreading something but isn't it the Sagnac effect, only
quantified in a peculiar way?

Sorry, I can't help you there. I've heard the term, but I've
never studied it. Maybe someone knowledgeable about it can
answer your question.

Mike Fontenot

Tom Roberts wrote:

[...] So they will all conclude they all age at the same rate.

Well, my analysis does agree with that. All of the passengers
on the train agree that they are all ageing at the same rate.
But the issue of interest here is simultaneity, not the rate
of ageing.

Mike Fontenot

Mike Fontenot wrote:
Tom Roberts wrote:

[...] So they will all conclude they all age at the same rate.

Well, my analysis does agree with that. All of the passengers
on the train agree that they are all ageing at the same rate.
But the issue of interest here is simultaneity, not the rate
of ageing.

Simultaneous events are spacelike separated and therefore,
not causally related. Different observers will disagree on
which events are simultaneous for exactly the same reason that
different observers situated a differernt points on a circle
disagree over the definition of axes.

On Sat, 16 Dec 2006 13:17:45 -0700, Mike Fontenot wrote:

JanPB wrote:

Perhaps I'm misreading something but isn't it the Sagnac effect, only
quantified in a peculiar way?

Sorry, I can't help you there. I've heard the term, but I've never
studied it.

I see.

In a rotating frame, you cannot synchronize all clocks (using the usual
meaning of the term "synchronize"), due to the Sagnac effect. You end up
with a "date line" someplace and clocks on either side of the date line
are mismatched.

Suppose someone walks slowly the whole length of your train, starting at
the engine and walking back to the caboose, carrying a calendar and a
clock, and makes sure that everybody on the train agrees as to the time
and date. The two ends of the train are touching, right? So, when the
"clock checker" gets to the caboose, he just steps off the caboose onto
the nose of the locomotive and starts over.

But on his "second pass" down the train, after stepping onto the engine
from the caboose, he finds something strange: _all_ the clocks, starting
at the engine traveling all the way to the caboose, are OUT OF SYNC with
the one he's carrying -- whoops, what went wrong?

To double check, he turns around, walks up the train again to the
engine, steps from the engine back to the caboose again, and walks slowly
the whole length of the train, going the other way, tail to nose. And on
this trip, he finds all the clocks and calendars he passes _agree_ with
the one he's carrying, and when he gets back to the engine he finds that
the clock there is in sync with the one he's carrying, too, even though it
wasn't when he approached it by going "the long way around".

When he stepped from the caboose to the engine, he found the clocks on the
train were out of sync with his; when he reversed himself, and crossed
back to the caboose, everything was "right" again. All this time his
personal clock just ticked along normally.

Sounds pretty weird, doesn't it?

It's the Sagnac effect and it's for real. It's used every day in
navigation devices all over the world.


--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org

sal wrote:

In a rotating frame, you cannot synchronize all clocks (using the usual
meaning of the term "synchronize"), due to the Sagnac effect. You end up
with a "date line" someplace and clocks on either side of the date line
are mismatched.

This seems to contradict my results that say (among other things)
that all passengers agree that all passengers are ageing at the
same rate (at all times, not just on average). If that is true,
all clocks can obviously be synchronized. Perhaps the discrepancy
is in the definition of "synchronized", or, equivalently, of
simultaneity.

Mike Fontenot

"Mike Fontenot" wrote in message ...
| sal wrote:
|
| In a rotating frame, you cannot synchronize all clocks (using the usual
| meaning of the term "synchronize"), due to the Sagnac effect. You end up
| with a "date line" someplace and clocks on either side of the date line
| are mismatched.
|
| This seems to contradict my results that say (among other things)
| that all passengers agree that all passengers are ageing at the
| same rate (at all times, not just on average). If that is true,
| all clocks can obviously be synchronized. Perhaps the discrepancy
| is in the definition of "synchronized", or, equivalently, of
| simultaneity.
|
| Mike Fontenot

sal suffers from progeria.
http://www.google.co.uk/search?hl=en...Progeria&meta=

I'd like to see someone repeat Einstein's experiment where he made
lightning strike both ends of a train simultaneously and then said
it wasn't simultaneous.

http://www.bartleby.com/173/8.html

sal wrote:

[...]

I neglected to say, in my previous response to Sal, that
I appreciated his taking the time and effort to construct
that very complete and clear response. Thanks.

Mike Fontenot