B Project GRE^2AT - GR on Mt. Ranier

[DaveC426913]

TL;DR

Just checking his numbers. I got half his value. Did I make a mistake?

I was just verifying the number for this guy who took 3 cesium clocks and his kids on a road trip up Mt. Rainier to observe relativistic time dilation.

http://www.leapsecond.com/great2005/

I got number that's half what he got. Am I missing something?

Here's his data:

He says "the time dilation was somewhere in the 20 to 30 ns range. The number we expected was 23 ns so I'm very pleased with the result."

I ran the numbers (naively, I'm not a math whiz):

This is the formula I used:
T_h / T_0 ≈ 1 + gh/c²
where
g is acceleration due to gravity
h is the height difference
and c is ... c


So:
g=9.8m/s,
h=1332m - the difference between the base where he started (333m) and the altitude he did his tests at (1665m),
c=3x10⁸m

The fractional difference is then converted to ns per day.

When I plugged in the numbers, I got 11.6ns, which is, suspiciously, pretty much exactly half of his expected 23ns.

Just for fun, I asked a chatbot to check (twice) and it vomited the same numbers I did: 11.6ns.

Am I missing something? Where did he get 23ns from?

 

[Ibix]

I think the 23ns figure is the accumulated extra time over the two days he was up there, which is obviously twice your (correct) per-day figure.

 

[PeterDonis]

Am I missing something?

Yes: he was up there for "a full two days". Your result is ns/day, so you need to multiply by two.

 

[DaveC426913]

Yes: he was up there for "a full two days". Your result is ns/day, so you need to multiply by two.

His graph shows otherwise. His graph shows (what i believe to be) a 23ns per day increase, no?

 

[Ibix]

His graph shows otherwise. His graph shows (what i believe to be) a 23ns per day increase, no?

No. It's showing accumulated time of his clocks minus a lab clock (hence the vertical axis being "residual phase"). The comparison is only carried out in the lab - hence the two-day gap in the data when they were up the mountain. So the graph shows that during that two day gap, his clocks accumulated an extra 23ns.

Imagine starting two stop watches, A and B, simultaneously. Every time A shows exactly a whole minute elapsed, record the time on that watch in column A of a spreadsheet and the time on the other one in column B. Put B in your pocket and go up a mountain and come back, then continue logging data when you return. When you've finished, enter =B1-A1 in cell C1 and paste down. That graph is a plot of column C on the y axis and A on the x axis (for three stopwatches, of course). He's just got very precise stopwatches that show a systematic drift from relativistic effects during the gap in data logging.

 

[DaveC426913]

Thanks!

The 23ns is the cumulative gain. This is the correct interpretation of the data: