A physics question

[Feedmeketamine]

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?

 

[Thomas Barnsley]

Yep. A person on the equator would find time going slower relative to someone on the poles, you are right. But the amount is minuscule.

 

[Heronblade]

yes and no

Its all relative. Travel at 0.9 C compared to an observer, and time will pass approximately twice as fast for the observer than it does for you. However, if that observer hops in a ship and starts following you at the same speed, time appears to pass normally for both parties.

The relative speed of any point on the Earth's surface from the POV of any other point on the Earth's surface is zero. Therefore, from the point of view of all Earthbound beings, time passes at the same rate regardless of where you go.

Compare those same two points to something not directly associated with the Earth's movements however, such as the moon, and there will indeed be almost infinitely small changes in time dilation related to location. However, the equator won't necessarily be the slower of the two, it all depends on positioning.

 

[Esotera]

The speed that the earth orbits the sun is going to be a greater influence than the earth's rotation. Also, if time went slower at the equator, it would have to be traveling faster than the rest of the earth, which we know isn't true as the planet hasn't blown up yet.

However, for each rotation of the earth there will be a period ~12 hours where you travel faster, and a period ~12 hours where you travel slower. This is because the earth's rotation moves you forward/backward relative to where the earth is going & increases/decreases your speed, and therefore time. It would happen at everywhere apart from the magnetic poles, but the time difference is so miniscule it's not going to affect anything.

Also take all that with a pinch of salt as physics is not my area of expertise (that's what you get for posting on a gaming website). If anyone can explain it better or tell me I'm wrong that would be awesome.

 

[Heronblade]

The speed that the earth orbits the sun is going to be a greater influence than the earth's rotation. Also, if time went slower at the equator, it would have to be traveling faster than the rest of the earth, which we know isn't true as the planet hasn't blown up yet.

However, for each rotation of the earth there will be a period ~12 hours where you travel faster, and a period ~12 hours where you travel slower. This is because the earth's rotation moves you forward/backward relative to where the earth is going & increases/decreases your speed, and therefore time. It would happen at everywhere apart from the magnetic poles, but the time difference is so miniscule it's not going to affect anything.

Also take all that with a pinch of salt as physics is not my area of expertise (that's what you get for posting on a gaming website). If anyone can explain it better or tell me I'm wrong that would be awesome.

Not too far off. Time dilation is relative. From the point of view of anything moving at the exact same speed and in the same directions as the Earth, (most notably ourselves) there is no difference at all in the passage of time. Its only when you compare speed to some other datum, such as from the point of view of the sun, or the POV from the center of the universe, that a difference can be observed. And yes, in most cases, whether you move faster or slower when compared to that datum will indeed depend on timing.

 

[ClockworkPenguin]

I've only studied special relativity so far, which only deals with inertial frames. That is where the time dilation and spacial contraction effects come in.

The Earth in a non inertial frame however, as it is rotating and everything on it experiences a force due to gravity. That gets into general relativity which still has those effects, but a butload of other complicated stuff as well.

Therefore I do not know. I do know that time passes slower at higher altitudes. This I think is due to a lower gravitational field there, rather than a higher velocity however.

Engage nitpick mode

@Esotera Time dilates, but length also contracts, so velocity wouldn't have to change. Also, the actual velocity of the equator is greater than elsewhere, it's just the angular velocity is the same.

@Heronblade relative speed is meaningless; speed is a magnitude it can't be relative. The relative velocity of different points varies hugely. Ie, the relative velocity of a guy in the UK and a guy in Aus is approx twice the speed of the earth's rotation. That's why Esotera's second point is correct.

in summary angular velocity =/= velocity, and rotating frames are arseholes.

 

[Quaxar]

Uh, since the earth is actually bulging out at the equator and thus farther from the center of rotation it'd probably rotate slower there, no?

EDIT: Noooo, it wouldn't. Of course it wouldn't. Why would it. Stupid Newton!

And I'm going to go ahead and say that the faster time progression from a greater distance from mass of general relativity will probably trump any special relativity time dilation effects in this setting.

 

[Feedmeketamine]

Allright thanks for the replies, not quite sure what the consensus is but all interesting stuff nonetheless

 

[Heronblade]

@Heronblade relative speed is meaningless; speed is a magnitude it can't be relative. The relative velocity of different points varies hugely. Ie, the relative velocity of a guy in the UK and a guy in Aus is approx twice the speed of the earth's rotation. That's why Esotera's second point is correct.

Of course it is relative, velocity is a function of the change in distance over the change in time. If, due to your choice of datum, there is no change in distance, the velocity compared to that datum is zero, and the same holds true for time dilation due to velocity. This remains true even if, by picking a different datum to compare it to, the calculated velocity is 0.75 C. The fact that your results will change based on where your observations are made from should alone prove that.

That stated, I had forgotten for some reason that gravitational wells incur their own time dilation. Thank you for reminding me of that.

 

[DoPo]

Uh, since the earth is actually bulging out at the equator and thus farther from the center of rotation it'd probably rotate slower there, no?

No. The Earth does one rotation in roughly 24 hours, so at the equator, a static point would move at 1/24th the length of the equator. Since the equator is ~40 000 km long, that makes the speed of rotation there ~1670 km/h. So, because you don't get anything longer than the equator, speaking of circumference, the rest of the planet is "moving slower", so to say, as in, a full rotation would move a point less than ~40 000 km, thus the speed at which the point moves is less.

 

[FalloutJack]

Just extra twinge in the fabric of space-time from me: Anything from timezones to account for here?

 

[MysticSlayer]

Uh, since the earth is actually bulging out at the equator and thus farther from the center of rotation it'd probably rotate slower there, no?

The further away you are from the center of rotation the faster you go. The most common example is two children on a merry-go-round where one is right next to the point of rotation and the other is as far away as possible but along the same radial line being drawn from the point of rotation. Obviously, these two are going to have the same angular displacement over the same time interval (otherwise the merry go round would be ripped into two), but because the radius of the second child is greater, he had to travel at a greater speed to travel all the way around in the same time.

 

[ClockworkPenguin]

@Heronblade relative speed is meaningless; speed is a magnitude it can't be relative. The relative velocity of different points varies hugely. Ie, the relative velocity of a guy in the UK and a guy in Aus is approx twice the speed of the earth's rotation. That's why Esotera's second point is correct.

Of course it is relative, velocity is a function of the change in distance over the change in time. If, due to your choice of datum, there is no change in distance, the velocity compared to that datum is zero, and the same holds true for time dilation due to velocity. This remains true even if, by picking a different datum to compare it to, the calculated velocity is 0.75 C. The fact that your results will change based on where your observations are made from should alone prove that.

That stated, I had forgotten for some reason that gravitational wells incur their own time dilation. Thank you for reminding me of that.

Velocity is the change in position over the change in time. And that does change depending on your frame. This is important, because relative velocity is dependent on the direction of motion. Two cars travelling 15 m/s in opposite directions have a relative velocity of 30 m/s. If you take the difference in their speeds, you get zero.

That's why I said magnitudes don't really work for relativity (classical or Einstein's).

People on opposite sides of the globe are moving in opposite directions. If you where to work in the frame of guy one, and somehow the earth was invisible, the guy on the opposite side would seem to be orbiting guy one with a velocity twice the one he has relative to the centre of the earth.

If you have the game Universe Sandbox, you can see this by getting two objects to orbit something at the same rate and moving into the frame of one of those objects.

Now I have no idea how this affects time dilation, like I said, I was just nitpicking.

 

[Heronblade]

Just extra twinge in the fabric of space-time from me: Anything from timezones to account for here?

As with the rest, it depends on point of view. Any point on Earth will always have a velocity of zero compared to any other point on Earth, ergo, no difference in the passage of time from our perspective.

--1
2---4
--3

--0

However, imagine that the numbers 1-4 above are points along the equator of the Earth, and 0 is the sun. When measured from the POV of the sun, the speed and direction of each point at a particular instant is slightly different. This means that a person at point 2 with the right tools will observe a time dilation compared to the sun that is not quite the same as for someone at point 3 at the same instant.

Edit, the escapist doesn't seem to like extra spaces

 

[Quaxar]

Uh, since the earth is actually bulging out at the equator and thus farther from the center of rotation it'd probably rotate slower there, no?

The further away you are from the center of rotation the faster you go.

And this is why you don't do physics when you're sick. Now I have to go through all the trouble of recreating the Superman II ending to erase this post. Thanks, fever.

 

[Heronblade]

@Heronblade relative speed is meaningless; speed is a magnitude it can't be relative. The relative velocity of different points varies hugely. Ie, the relative velocity of a guy in the UK and a guy in Aus is approx twice the speed of the earth's rotation. That's why Esotera's second point is correct.

Of course it is relative, velocity is a function of the change in distance over the change in time. If, due to your choice of datum, there is no change in distance, the velocity compared to that datum is zero, and the same holds true for time dilation due to velocity. This remains true even if, by picking a different datum to compare it to, the calculated velocity is 0.75 C. The fact that your results will change based on where your observations are made from should alone prove that.

That stated, I had forgotten for some reason that gravitational wells incur their own time dilation. Thank you for reminding me of that.

Velocity is the change in position over the change in time. And that does change depending on your frame. This is important, because relative velocity is dependent on the direction of motion. Two cars travelling 15 m/s in opposite directions have a relative velocity of 30 m/s. If you take the difference in their speeds, you get zero.

That's why I said magnitudes don't really work for relativity (classical or Einstein's).

People on opposite sides of the globe are moving in opposite directions. If you where to work in the frame of guy one, and somehow the earth was invisible, the guy on the opposite side would seem to be orbiting guy one with a velocity twice the one he has relative to the centre of the earth.

If you have the game Universe Sandbox, you can see this by getting two objects to orbit something at the same rate and moving into the frame of one of those objects.

Now I have no idea how this affects time dilation, like I said, I was just nitpicking.

semantics, position is defined by distance from a chosen datum.

As for your two guys, you've got your frame of reference wrong. from guy one's point of view, guy two is always in the same direction and the same distance away. Guy two would only be perceived as orbiting guy one if you accounted for guy one's position, but not his rotation.

 

[OneCatch]

Just extra twinge in the fabric of space-time from me: Anything from timezones to account for here?

Nah, timeszones are just arbitrary definitions that we humans use to define the passage of time. Hence why they're so inconsistent:

Spoiler

---------------

Would that mean that time passes slower on the equator, since the earth is spinning faster there than on one of the poles?

Strictly speaking, yes, according to special relativity time will be dilated at the equator relative to the poles. General relativity also plays a significant part in practise (and actually negates the effect).

I dug this up, which does the maths of your question: http://thatsmaths.files.wordpress.com/2012/11/two-clocks1.pdf

It's late here and I'm out of practice besides, but it looks alright to my tired eyes! Anyone else feel like going through the maths to check the assumptions are ok?

---------------

@esotera - We can kind of neglect the movement around the sun unless the observer is in a completely different frame to the rest of the earth. Mathematically you can use a frame where we set the earth's 'point mass' velocity to 0, which simplifies things because then you only have to worry about the earth's rotation, and the relative velocities of various bits of the surface.
Of course, that only works if you're calculating for an observer on or near the earth - if you wanted to calculate dilation from, say, an observer at the sun, or somewhere on the earth's orbit, you'd have to (as you said) factor in the earth's orbital movement as well.

---------------

A somewhat interesting aside is that GPS satellites do actually have to account for both special and general relativity [http://en.wikipedia.org/wiki/Global_Positioning_System#Predecessors] (which to be clear are two separate phenomena) in order to stay accurate. Even though each GPS satellite has an identical nuclear clock (which is about as fundamental way of measuring time as you can get) they'd quickly get out of sync with each other because of relativistic effects. So adjustments have to be made.

 

[ClockworkPenguin]

@Heronblade relative speed is meaningless; speed is a magnitude it can't be relative. The relative velocity of different points varies hugely. Ie, the relative velocity of a guy in the UK and a guy in Aus is approx twice the speed of the earth's rotation. That's why Esotera's second point is correct.

Of course it is relative, velocity is a function of the change in distance over the change in time. If, due to your choice of datum, there is no change in distance, the velocity compared to that datum is zero, and the same holds true for time dilation due to velocity. This remains true even if, by picking a different datum to compare it to, the calculated velocity is 0.75 C. The fact that your results will change based on where your observations are made from should alone prove that.

That stated, I had forgotten for some reason that gravitational wells incur their own time dilation. Thank you for reminding me of that.

Velocity is the change in position over the change in time. And that does change depending on your frame. This is important, because relative velocity is dependent on the direction of motion. Two cars travelling 15 m/s in opposite directions have a relative velocity of 30 m/s. If you take the difference in their speeds, you get zero.

That's why I said magnitudes don't really work for relativity (classical or Einstein's).

People on opposite sides of the globe are moving in opposite directions. If you where to work in the frame of guy one, and somehow the earth was invisible, the guy on the opposite side would seem to be orbiting guy one with a velocity twice the one he has relative to the centre of the earth.

If you have the game Universe Sandbox, you can see this by getting two objects to orbit something at the same rate and moving into the frame of one of those objects.

Now I have no idea how this affects time dilation, like I said, I was just nitpicking.

semantics, position is defined by distance from a chosen datum.

As for your two guys, you've got your frame of reference wrong. from guy one's point of view, guy two is always in the same direction and the same distance away. Guy two would only be perceived as orbiting guy one if you only accounted for guy one's position, and not his rotation.

Ah, you're quite right about the rotating frames, my bad. Stupid non inertial reference frames .

(still disagree with you re: position, distance from the datum isn't enough (assuming datum means origin (yay nested bracekts)) You also need the angle from some origin line, or else you need the distance along two perpendicular axes (at least in 2D). However, on the issue that is relevant; that on the points on the earth don't move relative to each other in the earths reference frame, You are correct so it is childish of me to bang on about position vectors.)

 

[Heronblade]

snip

semantics, position is defined by distance from a chosen datum.

As for your two guys, you've got your frame of reference wrong. from guy one's point of view, guy two is always in the same direction and the same distance away. Guy two would only be perceived as orbiting guy one if you only accounted for guy one's position, and not his rotation.

Ah, you're quite right about the rotating frames, my bad. Stupid non inertial reference frames .

(still disagree with you re: position, distance from the datum isn't enough (assuming datum means origin (yay nested bracekts)))

If using straight line distance, as in polar coordinates, no that would not be sufficient alone. Typically in physics problems, I frame distance in terms of i+j+k. Vectors are built in that way. Sorry for the misunderstanding.

 

[TheYellowCellPhone]

Yes, but it's a value so close to zero it would make no difference at all. Astronauts who spend weeks in space going around 8km/s (roughly ten times faster than the initial velocity of a fired rifle bullet) don't even have one extra second added to their lives.

You probably have the same time dilation by standing on an escalator compared to that. Well, maybe the escalator is a little slower.