Stupid Google Tricks

November 30, 2004 7:33 PM

Does relativity have any practical significance? In fact, relativity had to be taken into account by the designers of the Global Positioning System. The GPS satellites are affected both by special relativity (since the satellites are moving, clocks aboard them appear to run slower as seen from the ground), and by general relativity (since the satellites are farther away from the mass of the earth, clocks appear to run faster as seen from the ground). The net effect of both is that clocks aboard GPS satellites would gain 38 microseconds per day relative to the ground, if relativistic effects were not corrected for--a figure which can be confirmed by using Google calculator.
posted by DevilsAdvocate (26 comments total)

If you think spelling everything out in that last link was silly, you might prefer this one.
posted by DevilsAdvocate at 7:33 PM on November 30, 2004

Nice! thanks.

It's interesting to think that if GPS had arrived before the theory of relativity, we'd be worrying about the really strange time lag demonstrated by satellites.

The offhand (and true) explanation that they are traveling through Time at a different rate than we are still sounds like something out of science fiction.
posted by vacapinta at 7:47 PM on November 30, 2004

I really like that little google trick. I wonder if it has a nesting limitation?
posted by odinsdream at 8:16 PM on November 30, 2004

This can only be a hoax - as everyone know the earth is flat, space and time are absolute - and never relativ - unless you watch soap operas and love creationism.
posted by homodigitalis at 8:46 PM on November 30, 2004

RE: Nesting limitation. apparently not. However, as you will find out if you try to double up on that "equation," Google does have a character limit as to what you can send their search engine before they default with a, "Bad Request: Your client has issued a malformed or illegal request."
posted by reflection at 8:49 PM on November 30, 2004

This can only be a hoax

Agreed. Remember: relativity is a *theory.* Like gravity.
posted by Ayn Marx at 8:53 PM on November 30, 2004

I should add, the next limitation will be their 32 bit processors. As an example, try this link, and take note of the number at the end of the URL. Then try this link. You will notice it peaks at 2,147,483,647. Don't be deceived by that number on the front page (8,058,044,651), or by this search returning 8,000,000,000 results.
posted by reflection at 8:57 PM on November 30, 2004

And were it not for this incredibly sophisticated technology, precision bombing, like we saw in Fallujah, would not be possible. It's saving tens of thousands of innocent lives.
posted by weapons-grade pandemonium at 9:10 PM on November 30, 2004

Einstein was right--everything is relative.
posted by weapons-grade pandemonium at 9:12 PM on November 30, 2004

Meanwhile, if you were riding aboard a GPS satellite, a clock on the ground would appear to lose 53 microseconds per day. An observer on the ground and an observer on the satellite "agree" that the clock on the ground runs slower due to gravitational time dilation, but the time dilation due to velocity is, for each observer, perceived as making the other clock run slower. The two effects partially cancel for the observer on the ground looking at the satellite (the satellite clock runs faster due to gravity and slower due to velocity), but act with the same sign for the observer on the satellite looking at the ground (the clock on the ground runs slower due to gravity, and slower due to velocity).

everything is relative

Not quite...the speed of light in a vacuum, among other things, is constant.
posted by DevilsAdvocate at 9:43 PM on November 30, 2004

How about irony?
posted by weapons-grade pandemonium at 9:51 PM on November 30, 2004

Not quite...the speed of light in a vacuum, among other things, is constant.

Maybe not. I believe I read another article about how a new super-accurate clock was accurate enough to witness the slew of the cosmological constants over a period of a few years.
posted by breath at 10:14 PM on November 30, 2004

Shit, it's late at night and I'm drunk. But, I appreciate this post. I will check your calculation in the morning. Thank you, this is interesting. Nighty night.
posted by jefbla at 10:25 PM on November 30, 2004

Special relativity by itself is enough to give you the permanent kind of headache. But I love it anyway. C'mere, you big, crazy universe, you! HUGS
posted by jenovus at 10:56 PM on November 30, 2004

Nah! Relativity is relatively easy to understand.
posted by weapons-grade pandemonium at 11:19 PM on November 30, 2004

Nice. I don't want to use a word too huge, but nice. I am in your debt.
posted by jenovus at 11:22 PM on November 30, 2004

MeFi University.
posted by No Explanation at 11:35 PM on November 30, 2004

No tinyurl's please! Google (and MeFi) are likely to be around long after tinyurl is gone, and people reading this in the archive won't be able to get the links. And anyway, you're putting the URLs in HTML links, so nobody's going to be bothered by the links being rather long (but it is nice to be able to mouseover links, even if they don't fit in your status bar in their entirety).

DevilsAdvocate's first link and his second. Apart from that, excellent post!
posted by fvw at 1:10 AM on December 1, 2004

Nice, Devil'sAdvocate. But I think this guy has the right idea.
posted by fatllama at 1:30 AM on December 1, 2004

Agreed. Remember: relativity is a *theory.* Like gravity.

i'd be careful with saying things like that. i guess you're trying to make a comparison with evolution, using the assumption that gravity is obviously correct. in fact, classical gravity was superceded by general relativity, so in this context, you're arguing against yourself.

and maybe it's just me, but i'd prefer scientific debates to be won by argument, rather that trite slogans that snigger at the "the other side". isn't the whole point that there is a correct answer, whatever the soundbites are?
posted by andrew cooke at 2:18 AM on December 1, 2004

the speed of light in a vaccum is constant--- thats why everything is relative.
posted by buddhanarchist at 4:54 AM on December 1, 2004

...using the assumption that gravity is obviously correct. in fact, classical gravity was superceded by general relativity...

The effects of gravity are readily observable, regardless of the current theory to explain their cause. Those arguing against evolution deny not only the cause, but the effects as well.

Not to mention, that a theory like intelligent grappling would not gain much traction in a public debate.
posted by bashos_frog at 7:09 AM on December 1, 2004

Does relativity have practical significance? Pah! IC designers have to worry about quantum mechanical effects
posted by Capn at 8:09 AM on December 1, 2004

the speed of light in a vaccum is constant
...which means you can't double c in a vacuum.
posted by weapons-grade pandemonium at 10:41 AM on December 1, 2004

fvw: point taken.

I didn't want to bog down the thread with this earlier, but now that it's more or less died down, here's all the gory details on the math I used to build up that expression:

G = gravitational constant
m = mass of earth
c = speed of light
t = orbital period = 1/2 sidereal day A sidereal day is the time it takes for stars to reappear in the same position as seen from earth, about 4 minutes shorter than a standard (solar) day.
r_E = radius of earth

The really neat thing about Google calculator is that you don't have to actually look these values up or worry about units; Google takes care of all that.

Oh, and this: p is a pi; sorry that it looks a little funky in the default font.

r_s = distance of satellite from the center of the earth = [Gmt²/(2p)²]^1/3

v = velocity of satellite = 2pr_s/t = (2pGm/t)^1/3

Convention: Throughout this, I'll define time dilation factors (f) to be the time which appears to elapse on a clock in a different frame from an observer, divided by the time which elapses as measured by a clock with the observer. Thus, f>1 indicates the distant clock appears to run faster than ours, while f<1 indicates that it appears to run slower.

Gravitational time dilation:

To an observer an infinite distance from a mass, a clock near the mass appears to run slow:

f_8->r = 1 - (Gm/c²r)

Thus, an observer at an infinite distance from earth sees a clock at the surface of the earth run with

f_8->E = 1 - (Gm/c²r_E)

While for the same infinite observer, the clock aboard the GPS satellite runs with:

f_8->s = 1 - (Gm/c²r_s)

To an observer on earth, therefore, the clock aboard the GPS runs faster due to gravitational time dilation with:

f_E->s = f_8->s/f_8->E

Velocity time dilation

There is also a time dilation effect due to the fact that the satellite is moving relative to the earth; this factor is given by:

f_v = [1-(v/c)²]^1/2

(This is constant for an observer at the poles; for anyone else, the velocity will vary over the course of a day due to rotation of the earth, but to a first-order approximation the effect of the rotation will cancel out over the course of a day.)

The clock aboard the satellite appears to run slower due to velocity time dilation, so this is less than 1.

Finishing up

The overall factor for how the clock aboard the satellite appears to run from the ground is the product of the gravitational and velocity factors:

f = f_vf_E->s

The time which appears to elapse on a clock on the satellite for a given time at the surface of the earth is given by

T_s = fT_E

Set T_E = 1 day, and ever so slightly more than one day elapses on the satellite. Subtract 1 day from T_s to find just how much more.
posted by DevilsAdvocate at 1:51 PM on December 2, 2004

Gah, all my π's got changed to p's between the preview and the post. Sorry about that.
posted by DevilsAdvocate at 1:53 PM on December 2, 2004