Op-ediots

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Aresen
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Re: Op-ediots

Post by Aresen » 18 Nov 2018, 15:34

Painboy wrote:
18 Nov 2018, 15:13
More curious than anything, but is knowledge of relativity absolutely necessary for GPS? Is it possible they could have used a hack of some kind that would work about as well. I know throughout history there were lots of "good enough" calculations used where the underlying mechanism was still unknown.
GPS and Relativity:
Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.
Last edited by Aresen on 18 Nov 2018, 15:35, edited 1 time in total.
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thoreau
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Re: Op-ediots

Post by thoreau » 18 Nov 2018, 15:35

Painboy wrote:More curious than anything, but is knowledge of relativity absolutely necessary for GPS? Is it possible they could have used a hack of some kind that would work about as well. I know throughout history there were lots of "good enough" calculations used where the underlying mechanism was still unknown.
Relativistic corrections go into the calculations. Without them the data rapidly loses accuracy. My understanding is that the Air Force requested two versions of the software, one with and one without the relativistic corrections. Some people mock them for not trusting Einstein, but GPS was/is the largest test of relativity ever conducted. It was smart to be prepared for more than one outcome.
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Re: Op-ediots

Post by Jennifer » 18 Nov 2018, 16:42

If only college-age Warren had majored in a STEM field, he'd have known that GPS uses relativity. Even my ex-English-major self knew that much. [/ducks]
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Re: Op-ediots

Post by Jadagul » 18 Nov 2018, 17:42

thoreau wrote:
18 Nov 2018, 15:35
Painboy wrote:More curious than anything, but is knowledge of relativity absolutely necessary for GPS? Is it possible they could have used a hack of some kind that would work about as well. I know throughout history there were lots of "good enough" calculations used where the underlying mechanism was still unknown.
Relativistic corrections go into the calculations. Without them the data rapidly loses accuracy. My understanding is that the Air Force requested two versions of the software, one with and one without the relativistic corrections. Some people mock them for not trusting Einstein, but GPS was/is the largest test of relativity ever conducted. It was smart to be prepared for more than one outcome.
The question I think is how constant the drift is; if the relative time drift is constant then you could probably correct for it by trial and error. Wikipedia suggests that it would be relatively constant if the orbits were circular, but they're elliptical so the error is much less constant. No idea if they're right, or if I'm interpreting them right.

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Re: Op-ediots

Post by thoreau » 18 Nov 2018, 18:26

If the orbits were circular then you might be able to make it work by subtracting off some quantity that's linear in time. But, (1) that's a wild non-expert guess (there may be other complications) and (2) you'd probably need elevation corrections. And I guess that by taking enough data and figuring out what you need to subtract to make it all work you could figure out what the elevation corrections are, but in the end, there's no getting around that all of this stuff deviates massively from what relativity predicts. You turn on the machine and you're immediately confronted with the fact that Newtonian mechanics isn't enough.

You can probably curve-fit your way out of this and most other problems without understanding the underlying physics, but without the underlying physics you'll be left with a question of "OK, what if we try to do this in some situation that we haven't checked yet? Will our extrapolations [which is what curve fits ultimately are] still work?" You need the physics to have some informed basis for trying new things and improving.

I don't think that the ability to curve-fit your way out of a problem changes the fact that GPS really is an application of relativity. It's a technology that you can make work with much greater ease if you know relativity. A few pages of relativistic calculations saves you a year or more of additional testing and calibration, and immediately points out what will/won't matter in the next-generation design.
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Re: Op-ediots

Post by thoreau » 18 Nov 2018, 18:27

Put it this way: In principle, with pure trial and error, you could figure out which substances are or aren't useful drugs. But you save a hell of a lot of time if you know some chemistry and physiology. Our knowledge of those fields is far from perfect, but it's enough to massively reduce the amount of trial-and-error. So I'm comfortable saying that pharmaceuticals are applications of chemistry and physiology, even if we don't, technically, need to know anything about mechanisms to learn things by trial-and-error.
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Re: Op-ediots

Post by Jadagul » 18 Nov 2018, 18:35

I don't think either I or Painboy was disagreeing with that. But it's a separate mildly interesting question of whether you could have found the corrections by trial and error without yet knowing the theory.

(I suspect if we'd invented GPS before developing relativity, the GPS would have led to figuring out relativity pretty quickly as people tried to figure out what was driving the inconsistency. But I could imagine someone curve-fitting the inconsistency and then looking for theories that match it).

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Re: Op-ediots

Post by thoreau » 18 Nov 2018, 18:41

Jadagul wrote:
18 Nov 2018, 18:35
(But I could imagine someone curve-fitting the inconsistency and then looking for theories that match it).
In some sense, that's what more than a thousand years of planetary astronomy was all about. Epicycles are basically a form of curve-fitting.

Anyway, GPS is one reason why I have very deep trust in relativity. It may be that relativity will someday be replaced or upgraded, but it passes precision tests again and again on a daily basis. That puts some pretty big constraints on what sorts of deviations we might see from relativity.
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Re: Op-ediots

Post by Aresen » 18 Nov 2018, 21:34

Jadagul wrote:
18 Nov 2018, 18:35
(I suspect if we'd invented GPS before developing relativity, the GPS would have led to figuring out relativity pretty quickly as people tried to figure out what was driving the inconsistency. But I could imagine someone curve-fitting the inconsistency and then looking for theories that match it).
I have a hunch satellites could not have been developed prior to general or special relativity. I won't assert this absolutely, but I suspect the technologies that led to satellites either depended on a knowledge of relativity or were closely related to technologies that required relativity. (Transistors come to mind.)
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Re: Op-ediots

Post by thoreau » 18 Nov 2018, 21:55

Transistors don't require relativity. They require quantum mechanics.

Magnets only require quantum mechanics and relativity at the very deep "But why...?" level.

However, a society that has mastered the tech required for radio transmission to/from satellites probably knows Maxwell's equations, and they strongly imply relativity.

So satellites are possible w/o relativity, but if your scientific enterprise is capable of walking and chewing gum at the same time then they probably have figured out relativity before satellites anyway.
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Re: Op-ediots

Post by Jasper » 19 Nov 2018, 14:33

Weird tangent / "thing i saw on the series of tubes": I saw a claim that the Earth's core is actually younger than surface/crust because of relativity. True?
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Re: Op-ediots

Post by Jennifer » 19 Nov 2018, 14:56

Jasper wrote:
19 Nov 2018, 14:33
Weird tangent / "thing i saw on the series of tubes": I saw a claim that the Earth's core is actually younger than surface/crust because of relativity. True?
Yeah, but not enough to be noticeable on a human timescale. I saw a "science for non-scientists" documentary about it: the closer you are to a center of gravity/mass,the slower time moves, so if you are on the top floor of the Empire State Building, say, you will age faster than someone in the basement, though the actual difference would be measured in fractions of a nanosecond.
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Re: Op-ediots

Post by Jennifer » 19 Nov 2018, 14:58

And THAT, dear friends, is why Mom's-basement-dwellers never grow up!

/not really
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Re: Op-ediots

Post by Jasper » 19 Nov 2018, 15:29

Hmm. See, I thought it was the other way 'round. The farther and faster you are from the center of gravity, the slower time goes for you. Which is why the trope in "hard" scifi is explorers returning to Earth after relativistic speeds come home to their cohort being dead & buried for oh so many years.

So if the crust is moving faster due to planetary rotation than at any point 'beneath' it along a line to the core, it's aging slower than any of those points, so the core ought to be older, not younger.

The only way it could be younger is if it was spinning faster than the crust's rotation.

...

Google says this is the case. But only by about 1 degree every megayear.

Hmm.
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Re: Op-ediots

Post by Jennifer » 19 Nov 2018, 16:37

Jasper wrote:
19 Nov 2018, 15:29
Hmm. See, I thought it was the other way 'round.
FWIW, so did I until I looked it up, because I'd confused it with another documentary I'd seen: astronauts in orbit who carried hyper-sensitive timepieces with them confirmed relativity: the astronauts in orbit aged very slightly less than people on Earth. (More precisely, their clocks moved very slightly slower than identical clocks on Earth.) But in the case of the astronauts, the time slowdown was due to their fast speed relative to the earthbound clocks. If somehow it were possible for astronauts to merely hover motionless -- stay up and be immobile relative to the earth below, as opposed to the current system of "technically the orbiting astronauts are always falling downward, but they are also moving forward fast enough that the earth curves away below them at the same rate" -- then those astronauts would age slightly faster than earthbound people (though again, not enough for anyone with merely human senses to actually notice).
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Re: Op-ediots

Post by Mo » 21 Nov 2018, 18:55

So this is doubly funny. David French is so Christian that he's upset that Thanksgiving is no longer the most important holiday to Americans, but insufficiently Christian to believe that Easter is the most important Christian holiday. Granted, I'm married to a weekly churchgoing Catholic and went to ND, but even raised Muslim, atheist/agnostic me knows that.
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Re: Op-ediots

Post by Aresen » 21 Nov 2018, 19:10

Mo wrote:
21 Nov 2018, 18:55
So this is doubly funny. David French is so Christian that he's upset that Thanksgiving is no longer the most important holiday to Americans, but insufficiently Christian to believe that Easter is the most important Christian holiday. Granted, I'm married to a weekly churchgoing Catholic and went to ND, but even raised Muslim, atheist/agnostic me knows that.
Huh? :?: :?: :?: :?: :?: :?:

I thought the most important religious holiday in 'Murica was Super Bowl Sunday! ;)
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Re: Op-ediots

Post by Hugh Akston » 21 Nov 2018, 21:04

Mo wrote:
21 Nov 2018, 18:55
So this is doubly funny. David French is so Christian that he's upset that Thanksgiving is no longer the most important holiday to Americans, but insufficiently Christian to believe that Easter is the most important Christian holiday. Granted, I'm married to a weekly churchgoing Catholic and went to ND, but even raised Muslim, atheist/agnostic me knows that.
I mean
David French wrote:As a fundamental idea, celebrating the birth of the Savior of humanity, of the Word made flesh, the “light of all mankind,” is an event rivaled only by the celebration of His triumph over death in Resurrection weekend.
"rivaled only by" reads to me as "of approximately equal value". And even if they do value Easter over Christmas, papists are not representative of Xtians generally.

Also, apropos of nothing, every use of the phrase "civic religion" makes me that much more anarchist.
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Re: Op-ediots

Post by lunchstealer » 21 Nov 2018, 21:49

Aresen wrote:
21 Nov 2018, 19:10
Mo wrote:
21 Nov 2018, 18:55
So this is doubly funny. David French is so Christian that he's upset that Thanksgiving is no longer the most important holiday to Americans, but insufficiently Christian to believe that Easter is the most important Christian holiday. Granted, I'm married to a weekly churchgoing Catholic and went to ND, but even raised Muslim, atheist/agnostic me knows that.
Huh? :?: :?: :?: :?: :?: :?:

I thought the most important religious holiday in 'Murica was Super Bowl Sunday! ;)
That was the before times. Now football man no stand up.
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Re: Op-ediots

Post by Pham Nuwen » 21 Nov 2018, 22:00

lunchstealer wrote:
21 Nov 2018, 21:49
Now football man no stand up.
Freedom cloth no make freedom if football man no stand up!
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Re: Op-ediots

Post by nicole » 21 Nov 2018, 22:13

Who’s not into Christmas? The idea that people are over Christmas seems like something he made up.
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Re: Op-ediots

Post by Aresen » 21 Nov 2018, 22:41

nicole wrote:
21 Nov 2018, 22:13
Who’s not into Christmas? The idea that people are over Christmas seems like something he made up.
I like Christmas. For about 10 days running from December 22 to January 1. Beyond that, I can tolerate it from December 15 to January 6.

Outside of that period, it's like fingernails on a chalkboard.
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Re: Op-ediots

Post by Aresen » 21 Nov 2018, 22:42

Pham Nuwen wrote:
21 Nov 2018, 22:00
lunchstealer wrote:
21 Nov 2018, 21:49
Now football man no stand up.
Freedom cloth no make freedom if football man no stand up!
Trump smash.

[Orange is the new green.]
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Re: Op-ediots

Post by Mo » 30 Nov 2018, 06:02

The fact that this frightening and authoritarian impulse ridden story was the cover story of National Review, is more horrifying than Donald Trump in the White House.

Google is sitting on cash and selling to the Chinese. Break them up!
The governor of California is cozy with one of the largest industries in his state. Attack him!
Colleges are liberal. Take away their tax exemptions and redistribute the money to organizations I like!
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Re: Op-ediots

Post by JasonL » 30 Nov 2018, 09:11

*shudder*
.
.
.

*drink*

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