3 ms·

I was curious and did some rough back of the envelope math. The stadium seats about 50,000. Lets assume it's half full of 100 kg people (or entirely full of 50

I was curious and did some rough back of the envelope math. The stadium seats about 50,000. Lets assume it's half full of 100 kg people (or entirely full of 50kg people), or a total of about 2,500,000 kg. Additionally the stadium is about 300 meters from JILA. Meanwhile Earth is 6×10^24 kg at 6000 km. That's about 2x10^18 times as massive at only 20,000 times as far. Accounting for squaring the distance, that's about 5x10^9 times as much effect from Earth than from the crowd. It's plausible their instruments could pick up the effect of a difference of that much mass, though I suspect they embellished a bit the degree to which the clock went slower on game days.

wrs 6y ago
According to the article these clocks are accurate to 2 parts in 10^18, so...
ericbarrett 6y ago
Most people will drive to the stadium, so the local mass increase is a factor of ~10 higher. Assume 2 people per car and 1500kg/car (this is pretty conservative for Colorado, where SUVs and pickups are common), so each athlete, employee, and attendee would bring in ~800kg mass plus their own weight. EDIT: I was curious about the parking situation; seems to be a bunch of lots scattered around with JILA effectively in the center: https://en.parkopedia.com/parking/stadium/folsom-field-co/?arriving=202103251430&leaving=202103251630 https://en.parkopedia.com/parking/stadium/folsom-field-co/?a...
deleted 6y ago
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pdonis 6y ago
> Accounting for squaring the distance You actually don't want to square the distance, since you are not trying to compute the acceleration due to gravity, you are trying to compute the gravitational potential (since that's what affects clock rates), which goes like 1/r, not 1/r^2. So the Earth's effect should be about 10^14 larger than the effect of the people in the stadium. (Which is still several orders of magnitude larger than the sensitivity of the clocks, so it's entirely plausible that the clocks were detectably affected.)

wrs 6y ago

According to the article these clocks are accurate to 2 parts in 10^18, so...

ericbarrett 6y ago

Most people will drive to the stadium, so the local mass increase is a factor of ~10 higher. Assume 2 people per car and 1500kg/car (this is pretty conservative for Colorado, where SUVs and pickups are common), so each athlete, employee, and attendee would bring in ~800kg mass plus their own weight. EDIT: I was curious about the parking situation; seems to be a bunch of lots scattered around with JILA effectively in the center: https://en.parkopedia.com/parking/stadium/folsom-field-co/?arriving=202103251430&leaving=202103251630 https://en.parkopedia.com/parking/stadium/folsom-field-co/?a...

deleted 6y ago

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pdonis 6y ago

> Accounting for squaring the distance You actually don't want to square the distance, since you are not trying to compute the acceleration due to gravity, you are trying to compute the gravitational potential (since that's what affects clock rates), which goes like 1/r, not 1/r^2. So the Earth's effect should be about 10^14 larger than the effect of the people in the stadium. (Which is still several orders of magnitude larger than the sensitivity of the clocks, so it's entirely plausible that the clocks were detectably affected.)