# [LEAPSECS] Nit-pick: SI second

Tom Van Baak tvb at LeapSecond.com
Fri Feb 11 00:31:32 EST 2011

Magnus & Mark & Rob,

I know we're getting a bit far from the OP or from leap seconds,
so if you want to reply off-line that's ok.

>> This seems to be a common misunderstanding. Realize that

>> the relativistic dilation we're talking about would occur even if

>> the earth were not rotating: it's due to the mass of the earth.

>>

>> Actually, this shift would change if the earth was not rotating

>> as it would have a different mass distribution.

I was assuming there, for the sake of argument, that all you did
was change rotation rate; I'm not talking about earth changing
shape or temperature or climate as a result of it. But even so,
are you sure this would affect GR blueshift? The gh/c² value is
based on mass. I don't see that it matters if our 6e+24 kg planet
is perfectly sphericical or slightly oblate a hollow shell or shrinks
down to a black hole. Two clocks at roughly 6378 and 6379 km
from the center of mass will still drift apart by about 10 ns/day.

> It is the difference in gravitational level which causes an observed

> shift in frequency between two reference frames.

That's right; the h in gh/c² is difference in elevation. Sometimes
people put a delta in front of the h, but I can't type that character
in email. Neither clock has to be at sea level, of course. Note if
you get too far from MSL or want lots of decimal places then you
need something more robust than that simple formula anyway.

---

> A clock at the equator has a tangential velocity of 500m/s

> whereas for one at the pole it is 0m/s. The difference,

> This is the Sagnac effect of Special Relativity.

Something's wrong here. The Sagnac effect as applied to
clock synchronization is a time offset (a function of path
and direction), not a rate (frequency offset). Its maximum
value (for a trip around the equator) is 207 ns. Note also it
doesn't matter if that trip takes a 1/7th of a second, a day,
or 80 days, etc.

Something else is wrong here too. National UTC timing labs
are all over the world, at a variety of latitudes and altitudes.
No one corrects for latitude as far as I know; only altitude.
So I can't see why pole vs. equator would have anything to
do with the SI second. Correcting only for elevation above
the geoid I fully expect a cesium standard to keep the same
time in Fairbanks as it would in Boulder or Paris, etc. Am I
missing something? Should I start planning a new clock trip?

---

> Oooh! Google "Sagnac" and you also get lots of trendy

> pseudoscience from sites like anti-relativity.com. What fun!

Yes, there are a number of phrases related to relativity that
really spike the google hit meter.

By contrast if you want a serious article see this recent one