A physics question

[kurokotetsu]

So, this is to do with relativity.
Apparently time slows down the faster you travel, if ive got this correct (correct me if im wrong, i failed science at school and am just into pop science so bear with me).
Would that mean that time passes slower on the equator, since the earth is spinning faster there than on one of the poles?

It is a bit harder than that, and the twin paradox is still a paradox.

Look, I'm no expert, but I'll try to explain relativity and inertianl frames of reference.

Think you are in a car. A quick question. If you are moving at a constant speed (no change in direction or velocity) in say a car, how can you be sure you are moving and not that everyone else is moving in the opposinte direction? In physics it is the same to think that you are moving a certain speed in one direction than to say the world moves in the opposite direction with the same speed. Equations work fine both ways (principle of relativity). But that is only if Newton's First Las is observed, ot in other words that you are not experiencing a force when you move. If you are experiencing a force you can be sure which one is the one movng according to the other, or you have to account for some extra forces (certrifugal force being the most famous one). When no forces are present, it is called an inertial system, and they are a very basic and important concept, where you can change the frame of reference (or the observer which is often usesd in Relativity, being where you observe the problem).

With Galileo tha change of who was moving was easy. You only added the speed and you have a new set of euqations of how is looks to you, in inertial systems. SO to now how something acted when traveling at a certain cosntant speed, for example the position of something you just go x=x0+vt (where it started plus how much it moved). But that went arwy with Maxweel's Electromagnetism, where frames of reference weren't obvious in the stated equations. A lot of problems arised and sevedral theories where put foward that there were frames of reference, ether being the main one. But Eisntein (and French matehmatician Laplace) thought that maybe things weren't so simple. The speed of light was king, in that in all frames of reference it should be constant.

THat is where time dilatation and space contraction come from. If you consider that idea that speed of light doesn't change, then the equiations aren't as easy when you change form observer to observer. If you see someone travelling, their time goes slower: But the opposite is true too. For them your time is going slower, as you travel at some speed. This is were the paradox comes. If both twins thinks that the other goes slower, how to account the idea that both twins have diferent ages.

Then we come to non-inertial frames. The travelling twin is accelerated and deaccelerated during the travel. Does that solve the paradox? Well, we aren't that sure. Non-inertial systems are hard to explain and have a lot of holes (for example how to account for radiation of a moving electron in a circle when you change the frame), even in classical mechanics. But these is a "basic" concept and explored. You can see Wikipedia for the article related to this, http://en.wikipedia.org/wiki/Relativistic_angular_momentum , in the place that talks about Lorentz transformations and angular momentum. AS you see, indeed diferent speeds do have an effect on time. Why? Because not all parts of Earth move at the smae linear speed (they have the same angular speed, that is they cover the same angle in the same time, but the distance to the rotation axis menas that to do that in the same time, the distance that they traveled is diferent)

Then comes General Relativity, where effect of gravity is acocunted for. In general relativity you have a force to recon, and it's effects on spacetime (time and space difference) Gravity is diferent fo diferent parts of Earth, accounting the non-spherical (almsot but no) nature of our planet. So the closer nature of the North Pole means that time is slower on account of this than the farthest part, the Equator. According to that the poles are the slower points.

Luckly our fellow One Catch brought the calculations for us, and those two effects cancel out. So while your idea is correct on the Special Realtivity point of view, in the whole that isn't what happens. GOod question though, and I really hope I dind't try to give to much unnecesary information.

 

[AperioContra]

With respect to what position? As mentioned before, the theory of relativity posits that velocity is different relative to respect of the observer's position. For instance, If I am traveling in the car 60 mph , and I reach over to the passenger seat and smack my friend in the back of the head with my hand going 5 mph, that does not mean I smacked him an average of ~65 mph. Since he is going the same speed, relative to me, I only smacked him at 5 mph. Now if he was on the side of the road and I smacked him from a car going 60 mph, than the speeds would add up, because he is going 60 mph less than I am at the time.

So, if you were standing at 45 degrees above the equator, where you are going 328.2 m/s, as respect to the Earth's rotation, vs a person going 136.5 m/s faster than you standing at the equator, than yes they are experiencing a time dilation. In order to find out how much, there is a simple relativistic equation. Time at stationary reference frame is equal to the time at the moving reference frame over the radical of 1 minus dividend of velocity squared and the speed of light squared. http://www.wolframalpha.com/input/?i=time+dilation+calculator that link will lead you to a site that can help you. understand if that was all gobbly-gook to you.

Factoring all of that in, the time dilation would be 0.0000000000003088 seconds slower at the equator, than at 45 degrees on the Earth, if my calculations are correct.

captcha: very nice. I think it's being condescending.

 

[Olas]

Yes, time also goes slower for you if you're at the top of a tall building than on the ground floor, however keep in mind the difference is so insignificant as to be completely undetectable with ordinary measuring equipment, much less noticeable in everyday life.

 

[2012 Wont Happen]

The difference between the speed of the poles and the equator does not come out to a relativistic speed.

 

[BurningWyvern90]

It depends on whether you're talking about special or general relativity.

Assuming one standard point of reference:

For special relativity, clocks will move more slowly the faster they're going. So, since the Equator is rotating faster, time/clocks will be moving more slowly than at the poles. But the slowing effect really is so infinitesimally small until you get to a significant fraction of the speed of light (and even then...), so for all intents and purposes it's not there.
So yes, clocks at the Equator run more slowly.

For general relativity, clocks that are deeper in a gravitational well (i.e. nearer to the source of gravity, so Earth's core in this case) will be moving more slowly. So clocks closer to the center of Earth will be running more slowly. In this case that means clocks at the poles. Because the Equator is rotating more quickly, there's a bit of a stretching effect on the Earth that makes it bulge out there. It's generally shown as kind of a football shape, but it's not nearly that significant, because the velocities aren't that different.
So no, clocks at the poles should run more slowly.

Aren't paradoxes fun?

I'm sure there are other effects there that I haven't actually learned about yet, but those numbers are negligible too. In the end, really, everything more or less balances itself out when you look at two people at separate points on the Earth, and there's not enough difference between the two amounts to actually matter. So yes, but no.

 

[AperioContra]

The difference between the speed of the poles and the equator does not come out to a relativistic speed.

You are technically correct (The best kind of correct). Generally physicists don't consider a speed relativistic until it begins to reach significant percentages of the speed of light (between 1% to 10%). However, that does not mean that relativistic time dilation does not apply in this case. Consider the International Space Station: Traveling at 18000 m/s or ~0.006% the speed of light, it does not travel at what is classically considered a relativistic speed, however it has a relativistic time dilation of ~0.007 seconds. ~0.0032 seconds of which are attributed to it's relativistic speed.

 

[Zack Alklazaris]

Yes, but its incredibly small difference. Astronauts travel much faster than we do on Earth and they still only gain about 0.007 seconds in their lifetime. Lets even take it a step further. The milky way travels at 600 kilometers per second. You only gain a day total in your lifetime (85 years assuming) compared to the galaxy being still.

 

[OneCatch]

Yes. Time goes slightly slower at the equator relative to higher latitudes, and at higher altitudes relative to lower.

This has been measured, actually, iirc.

It hasn't been measured directly because special relativity and general relativistic effects cancel out, meaning that no actual dilation occurs. But we have demonstrated both halves of relativity in other contexts - notably in GPS satellites, which would literally stop working after a few minutes if relativity wasn't accounted for.
I think they also did an experiment on one of the space stations at some point, don't hold me to that though.

Luckly our fellow One Catch brought the calculations for us, and those two effects cancel out.

*Doffs hat*