Theory of relativity question.

[Deathcricket]

So this question came up at lunch and I cant wrap my brain around it, would like some input.

2 supersonic jets leave the earth from london traveling different directions around the earth and then land back in london. Upon landing, it's determined that the 3 atomic clocks are all at different times. There is one in london and one on each plane.

Why would the clocks on the planes be different?

So the closer you travel towards the speed of light, the slower time goes. Ok I understand that. But the part I dont understand is that the plane going against the rotation of the earth is somehow going faster? It seems to me that since the earth is rotating "underneath" the plane, the planes are traveling at the same speed but the planes travel different distances.

So even though they left from the same place and landed the same place. So did the planes go at different speeds or different distances?

Lets say they (planes) are both traveling 1000/mph and for simplicity's sake the earth is spinning at 500/mph. So plane "A" traveling with with the earth is only covering 500/mph (1000 - 500) and plane "B" has the earth rotating under it making it's speed 1500/mph. But my premise is that both planes are going the same speed, the earths rotation is making the distance longer. So one plane is spending more time going fast giving the descrepancy.

Of course I was shot down because the distance from london around the earth can be measured. And was explained that even though both planes register 1000/mph, they really are going faster based on the point of the observer.

So can anyone into physics please explain this to me? "Pretend" i'm an idiot and use small words. It is Monday.

:roflol:

[Sombeech]

It is true, the faster you go, the slower time goes.

But, did both jets land at the same time? Also true, the jet traveling West would technically be going faster against the earth, but the jet traveling East would have covered more distance (in orbit)

Let's say it took a full day to travel back to the same spot. Technically, you could just sit still (in orbit), and make the journey, because the Earth did the spinning for you. So one of the jets were making more effort, traveling further than the jet in the opposite direction.

[Sombeech]

And was explained that even though both planes register 1000/mph, they really are going faster based on the point of the observer.

This is also the point. Even though both jets have the same speedometer reading, it's the viewpoint of the observer standing in London, if it were possible.

He sees the jets traveling at two different speeds, and it's his clock that we're using as the example. The two jets will feel no different in terms of time, even if it were much more of a gap. Time is relative.

[Iceaxe]

As a side question, what's your favorite happy meal?

:lol8:

[Deathcricket]

He sees the jets traveling at two different speeds, and it's his clock that we're using as the example. The two jets will feel no different in terms of time, even if it were much more of a gap. Time is relative.

Right, I fully comprehend the jets atomic clocks not matching london's, thats cool. But what I have trouble grasping is why the jets clocks would not match each others.

I guess my thought is since they are traveling at the same speed /mph, time should be the same for them. But one technically traveled a different distance and spent a longer period at high velocity. But is it really a different distance if each plane took the same path only the opposite direction?

:ne_nau:


P.S. Iceaxe, it depends on the toy inside!

[Sombeech]

But what I have trouble grasping is why the jets clocks would not match each others.

If the earth were standing still and they both flew separate ways, their clocks would be the same. But since the earth is rotating one way, one clock will be later than the other.

They'll both cover the same earth miles, but not the same "air" miles.

Say the earth is rotating the 500 MPH, the westbound jet may actually only have to rotate 25% around the earth in orbit, because the earth does most of the work by rotating. The eastbound jet would have to fly say 175% around the orbit of earth, because it's following the spin.

The earth speed is the same, but the space speed is very different. And time & speed are all relative.

It's like picking a blade on a slow turning fan. From that blade, circle forward all the way around to that same blade. With the rotation, you'd have to go faster than the rotating fan to eventually catch up. Against the rotation, you could go slow, or not move at all until that blade caught up. So if you were using your finger to point, it would move at two different speeds on each direction.

[recinutah]

Sombeech is right, he just isn't honoring your request to speak in English.

Basically, the jet going the same direction as the Earth's rotation goes once around finds that by that time, London has moved further away and has to go a little further.

The other Jet doesn't get fully around the globe before finding London and thus has a much shorter flight.

My favorite happy meal is a thick juicy steak. That always makes me happy, unless it were actually cooked by McDonalds.

[Deathcricket]

K think I got it.

One more clarification, Just to make sure!

Plane A (following orbit direction) - Longer flight, further distance in "air miles". More discrepancy in atomic clock vrs London since they spent more time going towards the speed of light. Clock should be furthest Behind London reference point.

Plane B (going against orbit) - Shorter flight, shorter "air miles" Closer time to atomic clock in London since they spent less time traveling towards the speed of light. Also should be behind the London clock but not as far as plane A?

[sparker1]

Why would two intelligent pilots leave London and then return to London?

[Brewhaha]

Some thoughts on this:

http://www.physicsforums.com/showthread.php?t=205702

[CarpeyBiggs]

Thanks Brew. :2thumbs:

[parrothead_madness]

Now Stephen Hawking is talking in my head and wont shut up.
Damned computer voices.

[blarson]

i like somebeech's "air distance" idea, which to me makes sense. the rotation of the earth won't change the distance that one jet travels verses the other unless the actual rate at which the earth rotates changes while they are in the air, which isn't the case. for example, say that two people are standing on a 100 ft. board back to back in the middle of the board and they are going to run at the same speed away from each other to the end of the board. it won't matter if the board is standing still or moving at a constant rate, they will each reach the end at the same time. but it the rate of speed changes while they are running it will have an effect on them. so the only difference between the two jets is when you stand back from space and look at them, they are actually moving at different speeds in relation to you in space, but not in relation to the earth or each other, or london for that matter. from your point of view in space all three clocks are moving at different speeds in relation to you.

[Sombeech]

If happy meals were on each jet, the one would go stale roughly 88% faster than the other one.

OK, 2 guys on a train moving 60MPH Northbound.

One walks 3MPH to the front, one walks 3MPH to the back.

The guy going to the front is moving 63MPH Northbound, and the guy facing TOWARDS the south is still moving NORTHBOUND at 57MPH.

The 2nd guy actually has to run on the surface of the train 123MPH southbound to actually move in the opposite direction as fast as the Northbound guy is moving.

If 60MPH, he's just stationary on the earth, another 60, he's matched the train speed, and another 3 he's matched the walking speed.

None of these men have Happy Meals.

[stefan]

you guys all look like you're having fun here. interesting thread.

however, there is another element to all this which you can choose to consider or neglect.

clock on each plane is not only affected by the velocity of the plane (and how long the plane maintains the velocity) but also the elevation of the plane due to gravitation. this is one primary difference between special relativity (which neglects gravity) and general relativity (which includes it). time moves more quickly when the gravitational force is weaker (at altitude) so you get a mixed effect of slow down and speed up. in this case the effect of gravity is large relative to the effect of velocity.

[DiscGo]

It makes a lot more sense to me that the planes would arrive at different times, but have the clocks still match.

[Deathcricket]

Well the reason it is quickest isn't exactly because of the rotation, it's the winds. The jet stream goes west to east at 100-200mph, which makes a big difference flying across the US. For London to New Zeland, the winds are probably kinda complex since you are crossing the equator.



for example, say that two people are standing on a 100 ft. board back to back in the middle of the board and they are going to run at the same speed away from each other to the end of the board. it won't matter if the board is standing still or moving at a constant rate, they will each reach the end at the same time.

Crap, I thought I had it worked out in my head and now it's all fuzzy again. So because THE WINDS make the trip shorter or longer, that makes the clocks not match? It's pretty much the same thing as 2 trains (attached to the earth) traveling at different velocities, I guess. Orbit doesnt come into play since the atmosphere they travel in is spinning with the earth?

So If plane "A" has more wind resistance it would go slower and the trip would be longer, but it would not go as fast as plane "B". So even though plane "B" went faster it's trip would be shorter. Time WOULD go faster but it would spend LESS time at the high velocity. So why dont they balance out?

I liked the orbit/rotation thought better, it was easier to grasp, hehe.


It makes a lot more sense to me that the planes would arrive at different times, but have the clocks still match.

That's exactly the spot I'm stuck at, does the difference come from the planes traveling different distances, spending more time traveling at the speed of light, or both?
:ne_nau:

[Sombeech]

No, in your equation, the winds do not affect the time. You still have the same issue if there were no wind.

If the earth were not rotating, both jets would have the same atomic time reading. It's the rotation of the earth, and whether you are going with or against it that determines your relative speed.

[R]

Okay, two flying monkeys leave me butt at 4 pm...

[double moo]

Okay, two flying monkeys leave me butt at 4 pm...


What kinf of happy meals are they carrying?

[Brewhaha]

My gut feelings on this are:

1) I doubt that the jets in this scenario are flying fast enough (and for long enough time) for there to be a measurable difference in the clocks.

2) Secondly, even if there is a difference in the clocks I don't think it has anything to do with the fact that the planes are flying with or against the rotation of the earth. It seems like the rotation of the earth part of this scenario is a red herring.

[stefan]

2) Secondly, even if there is a difference in the clocks I don't think it has anything to do with the fact that the planes are flying with or against the rotation of the earth. It seems like the rotation of the earth part of this scenario is a red herring.

but rotation does play a significant role. it creates so-called coriolis effect which affect the planes both vertically and laterally. if you take into account general relativity, then clocks will be different for eastward and westward moving airplanes.

[Brewhaha]

So if the planes were flying at a constant latitude and altitude and direction (i.e. one was chasing the other around the globe) then they would be in the same reference frame, and therefore, their clocks would match?

But if you change any of the factors (i.e. different latitudes, different or changing altitudes, or different directions) then their frames of reference would be changing and their clocks would be different?

Also, here is a theory that I think is backed up quite nicely by the data: http://zapatopi.net/labs/geriatric_migration.html

[Brewhaha]

So Stefan sent me scurrying back to the library, errr, internet like an unruly student and here is what I have found. I think it does a pretty decent job addressing this type of situation (minus the pesky forces or gravity and Stefan's friend Coriolis). Enjoy:

http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm#time

Also check out this for other fun adventures in physics:

http://www.phys.unsw.edu.au/~jw/FAQ.html#twin

[stefan]

so part of the issue is that being on the surface or flying are not inertial frames due to the rotation of the earth (and earth around the sun ...), so time dilation only via special relativity becomes tricky to think about when comparing clocks on the surface to flying clocks, since the theory applies to inertial frames which neither are in. you can try to get at it by finding a suitable inertial frame and calculate the relative differences

[Gutpiler_Utahn]

YES!!! Nobody has mentioned my favorite aspect of this.

you also have to take into account the elevation of the planes. You haven't stated if they flew at the same elevation or different. Time travels faster the farther from the earth you get. The higher you are, the faster your clock will travel (I think that's right... faster, not slower...)

Anyways, here's something to wrap your brain around if you got the time. :2thumbs:

http://en.wikipedia.org/wiki/Time#Spacetime

[Brewhaha]

So does general relativity work in noninertial frames? I see it general relativeity applies when acceleration is involved, but is it also involved when there is rotation, and, therefore imaginary forces?

[greyhair biker]

...Chuck Norris was on Family Guy today....he doesnt like happy meals.

[stefan]

So does general relativity work in noninertial frames?

yes, by curving spacetime. it's locally inertial but not globally.



I see it general relativeity applies when acceleration is involved, but is it also involved when there is rotation, and, therefore imaginary forces?

yes. it includes rotating frames. rotation at constant speed still has an acceleration because the the direction of movement is constantly changing

[greyhair biker]

...speaking of relativity, Hi Fourtycal :haha: :five:

[double moo]

Looks like we are assuming that the jet's tradjectories are in latitude reference. Should they be a longitude reference, i.e. north and south, the corialis effect, rotational speed, etc... should nulify.

Can I get a large fry in that Happy Meal?

[Sombeech]

If the jets went the same speed at the same altitude, same latitude, in the same weather, their clocks would still be different.

[Brewhaha]

I think you are right Beech. All that matters (in a very simplified system) is that one object is moving relative to the other.

[denaliguide]

i always thought the theory of relativity meant that if you had a relative in the business you got it wholesale.

[James_B_Wads2000]

1) I doubt that the jets in this scenario are flying fast enough (and for long enough time) for there to be a measurable difference in the clocks.

It would seem that way but the sensitivity of the atomic clocks these days are mind boggling in and of themselves.

I saw a Nova that was about String Theory I think, but anywhoo they did this same test with two clocks. One stayed in LA and the other took a plane trip to and from NYC. And the plane clock was behind the stationary one, it was an actually positive result for testing the Theory of Relativity. :five:
http://www.bogley.com/forum/files/****u.gif "Take that Jesus!"

James

[James_B_Wads2000]

By my crude calculations that would mean the clock are at least accurate to:
0.00000000000001 seconds (1e-13 s)

That is one ten-trillionth of a second.

And if a pilot flys 8 hours a day 220 days a year for 30 years, the pilot will be one billionth of a second younger than if they had decided to become a McDonolds manager!

James

[Brewhaha]

That's very cool.

The effect is almost infinitesimal but it is there.