Earth's Velocity in Space: Measuring Time Dilation

[Myslius]

Earth is rotating around it's axis, then around the sun, then around the center of the galaxy etc. But how can we know how fast it is moving in space?
Let's take two objects in space, we know that the distance between them is changing, we can determine which one moves slower, the one who's time runs faster is moving slower (time dilation). Basically we can find a frame of reference where v = 0 (where object doesn't move in space and where is no time dilation (at least it is very small).
So how fast the Earth is moving in space and what is our time dilation?

 

[my_wan]

The laws of physics says it's meaningless (impossible) to make a distinction between what is moving and what is not. However, if something is accelerating, unlike velocity, everybody in the Universe will agree that it is accelerating, but not by how much. This is the fundamentals of relativity.

 

[Rasalhague]

Forget time dilation for a moment and imagine you're in a space suit, somewhere far from any other objects--so far away, you might as well be the only thing in the universe. Are you moving, and if so how fast? With nothing to compare your speed to, you can't tell. Some people in history thought of space as a background against which you can be said to move or not move. But Galileo and Einstein, in their different ways, rejected this idea. They argued that, since there's no way to measure absolute motion (velocity relative to space itself), there's no good way to define it, and so there's no such thing. We can only define velocity relative to another object. That object can be real or imaginary. It might just be a coordinate system we've invented. But it's a free choice. There are infinitely many other coordinate systems we could have chosen to define our velocity relative to. If we chose one, such as the earth, and said "this is the still point relative to which everything else moves" it would just be an arbitrary human choice, a whim, and nothing directly to do with the real nature of motion in the universe. This is the viewpoint of Newtonian mechanics, based on Galileo's ideas, and of Einstein's relativity.

 

[Rasalhague]

Let's take two objects in space, we know that the distance between them is changing, we can determine which one moves slower, the one who's time runs faster is moving slower (time dilation). Basically we can find a frame of reference where v = 0 (where object doesn't move in space and where is no time dilation (at least it is very small).
So how fast the Earth is moving in space and what is our time dilation?

The problem with this is that we can do it at will for any object! For anything--the earth, the sun, the center of the galaxy--we can define an inertial frame of reference in which the object is (at least momentarily) at rest. So the answer to "how fast is the Earth moving?" depends on that arbitrary choice. There's no absolute movement, only relative movement.

But what about time dilation? Well, it doesn't work quite how you think. You need to read a good introduction to special relativity that explains the relationship between time, distance and simultaneity. A nice place to start might be the relativity chapter of Benjamin Crowell's Simple Nature, online here:

http://www.lightandmatter.com/html_books/0sn/

 

[Naty1]

Time dilation works likes velocity...it's relative; it depends on the observer...You can pick any frame for velocity and you can pick any frame for time dilation...each pick will give different results for both.

 

[Myslius]

Time dilation works likes velocity...it's relative; it depends on the observer...You can pick any frame for velocity and you can pick any frame for time dilation...each pick will give different results for both.

Let's take 3 atomic clocks, one on the surface of the earth, other 2 on planes, one plane moves clockwise to the Earth's rotation, other counter-clockwise (let's say v = Earth's rotation speed). By our FOR both clocks should show the same dilation? Right? Let's say now all 3 clocks are at the same position, and they manage to reach the center of the earth. Now imagine that there was fourth clock at the center of the earth. For that clock the plane who flew counter-clockwise was not traveling at all (was standing still v - v = 0), and there should be no time dilation, another clock was moving 2x Earth's rotation speed. Then how can you see time dilation and not time dilation at the same time and at the same place?
By my completely wrong understanding, time dilation can't depend on the observer.

 

[Myslius]

Another example, let's say there are only two planes, one plane starts engine, does few flips at the half speed of the light and comes back. If our FOR was one plane, then on another plane time should go slower and vice versa. Now 2 pilots meets... One says "your clock is running slower" and another answers "no, it's your clock running slower"

Time dilation when velocity is c/2
1 - sqrt(1 - (c/2c)^2) = 13%

 

[Rasalhague]

You need to distinguish between the following types of effect. The first two are covered by special relativity, the third by general relativity.

(1) Two clocks, each traveling in "flat" spacetime (that is: not under the influence of gravity) at some constant velocity relative to the other. Call an inertial reference frame in which an object is at rest the "rest frame" of that object. (Only when an object is not accelerating during the events we're interested in is there a single inertial frame of reference in which it's at rest; so we can't analyse your looping plane in the same way; see below.) According to the rest frame of each clock, the other is ticking slow. This seems paradoxical. Why should, indeed how can, they both be slow? To understand this, you need to study this most basic (by at first sight most perplexing) kind of relativistic time effect together with the related changes in spatial distance and, weirdest of all, the relativity of simultaneity. These effects are completely reciprocal like the effect of two people standing far apart who each look small to the other. In fact the formulas that describe how to get from the coordinates of events according to one inertial reference frame to the coordinates of the same events according to another are mathematically very similar to the formulas describing rotations in space. The difference between inertial reference frames differing only in velocity is analogous to a difference in spatial perspective: looking at the same events from a different angle. When two things happen in the same place at the same time, all frames agree on this. But each frame has a different way of pairing up distant events as simultaneous, this means that when events happen in different places, the amount of time between them (and in some cases even their order) depends on which reference frame you describe them in.

(2) Two clocks in flat spacetime, at least one of which accelerates, that is: changes its velocity (whether in direction or speed or both). Rule of thumb: the one that accelerates most ticks slowest. This is the kind of time effect behind the famous "twin paradox". Unlike the previous example, it's not a reciprocal effect. Your looping planes (let's imagine, for now, that they're in space away from any gravitational influence) come under this heading. The plane that loops the loop undergoes an acceleration, changing the direction of its velocity vector, so all else being equal, its clock should tick slower than that of a plane that flies at a constant speed in a straight line. If they synchronise clocks, then one flies loops, then they meet up again, less time will have passed for the looping plane.

(3) Two clocks above the surface of the earth. In curved spacetime (which is how gravity is understood in general relativity), freefall is the nearest equivalent to traveling at a constant velocity in flat spacetime. (a) For two clocks at the same height, one in freefall, the other held fixed, the one being held fixed ticks slowest. The one held in place against its natural inclination to fall is analogous to the clock in the previous example that's accelerated (against its natural inclination to move in a straight line at a constant velocity). (b) If the two clocks are both held fixed at different heights above the surface of the earth, the lower one ticks slowest, as it has to "accelerate" more to resist the stronger gravity and keep from falling.

 

[Passionflower]

The laws of physics says it's meaningless (impossible) to make a distinction between what is moving and what is not. However, if something is accelerating, unlike velocity, everybody in the Universe will agree that it is accelerating, but not by how much. This is the fundamentals of relativity.

If you mean proper acceleration then I agree but for relative acceleration it is also not determinable what is accelerating. Gravitationally bound bodies accelerate with respect to each other but there is no proper acceleration involved.

 

[Myslius]

I'm not talking about General Relativity, just Special Relativity, I'm ignoring gravitational effects, there is no need to involve it there. If time dilation depends on the observer, then every object for any FOR should have zero or higher time dilation, in other words FOR time is fastest. That does not make sense to me. I think if there was atomic clock in the center of the Earth it will tick faster compared to the clock on the surface (because Earth's rotation results in time dilation (the clock at the center of the sun will go even faster). Or let's say for any plane moving against Earth's rotation time should go faster compared to the static clock. Hafele and Keating Experiment showed that time for plane in one direction was ticking slower, and in other faster.

The problem encountered with measuring the difference between a surface clock and one on an aircraft is that neither location is really an inertial frame. If we take the center of the Earth as an approximation to an inertial frame, then we can compute the difference between a surface clock and the aircraft clock
http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/airtim.html#c5

You see, you can't take any point as inertial frame of reference.

All I'm saying that by comparing time dilation of clocks you can find inertial frame where there is no time dilation (at least it is very small - approximation)

sqrt(1 - (v/c)^2)
by taking v you're taking velocity difference between two "events". But this function isn't linear, so we can determine the exact speeds.

 

[Ken Natton]

I find a wealth of profundity in the way that Einstein quotes Newton’s first law of motion. I am not sure exactly how it is stated in the Principia Mathematica, but as I learned it at around age 14, it went like this:

‘A body will remain at rest, or move in a straight line at a constant speed unless acted upon by a force.’

When Einstein refers to this law he states it a little differently, so differently that you might not recognise it as the same law. But be assured, it is exactly the same law:

‘A body that is sufficiently removed from any other body will have uniform motion.’

The first profundity is that Einstein has recognised the pointlessness of drawing a distinction between ‘at rest’ or ‘moving in a straight line at a constant speed’. These two things are actually exactly the same thing – what Einstein calls ‘uniform motion’.

The second profundity is in the question of how, practically, one exerts a force on a body; by bringing it sufficiently proximate to another body.

So, if a body is sufficiently removed from any other body it will necessarily be in an inertial reference frame, it will have no force applied, and it will have uniform motion.

If a body is sufficiently proximate to another body, it will be in a non-inertial reference frame, it will have a force applied and it will not have uniform motion.

There is no such thing as an absolute position in space. There is no such thing as absolute velocity. All velocity is relative and that includes a velocity of zero.

 

[yossell]

When Einstein refers to this law he states it a little differently, so differently that you might not recognise it as the same law. But be assured, it is exactly the same law:

‘A body that is sufficiently removed from any other body will have uniform motion.’

Interesting - I'd love the reference for this; a quick flick through `On the Electrodynamics...' didn't bring it up, but perhaps you've another paper in mind?

 

[Ken Natton]

Hmmm yossell, trying to catch me out eh? It is not in the 1905 paper, nor indeed in any other scientific paper. I don’t know if you are aware of this yossell, but Einstein himself wrote a layman’s guide, aimed at people just like me. It was written in 1916 and revised in 1924. In my humble opinion, it beats many another layman’s guide to relativity written since. It is available for free download from the internet. I found it at Project Gutenberg. It is titled ‘Relativity: The Special and General Theory’. The quote comes from the section titled The Galileian System of Co-ordinates and Einstein actually refers to it as ‘the fundamental law of the mechanics of Galilei-Newton, which’ he says ‘is known as the law of inertia’.

 

[yossell]

Hmmm yossell, trying to catch me out eh?

Not at all!

Thanks for the reference

 

[Rasalhague]

So how fast the Earth is moving in space and what is our time dilation?

The problem with this is that we can do it at will for any object! For anything--the earth, the sun, the center of the galaxy--we can define an inertial frame of reference in which the object is (at least momentarily) at rest.

You see, you can't take any point as inertial frame of reference.

In the case of an accelerating object, including objects moving at a constant speed but changing direction, we can define an instantaneous rest frame as an inertial frame of reference as one having the velocity that the object has at a particular instant. The object will only be at rest in that frame of reference for that instant though. There's no one inertial reference frame in which an accelerating object remains at rest.

In special relativity, as in Newtonian mechanics, there's no absolute state of rest (so there's no answer to your question "how fast is the Earth moving?"), but there is an absolute state of non-acceleration. In Einstein's words, we have nicht die Bevorzugung eines bestimmtes Bewegungszustandes sondern nur die Bevorzugung eines bestimmtes Beschleunigungszustandes (not the favoring of a particular state of motion but only the favoring of a particular state of acceleration).

The kind of time effect being measured in the Hafele-Keating experiment is the kind of absolute difference that arises from differences in acceleration, as in the twin "paradox", the kind I labelled type 2. I'm guessing your unease with this comes from reading descriptions of the Hafele-Keating experiment purely in terms of a difference in velocity, which has led you to think of it as being like the symmetrical time effects of type 1. These symmetrical/reciprocal effects can be thought of as effects of perspective, analogous to the way that an object looks different when viewed from different angles. You can no more what is the velocity-induced time dilation of the Earth than what is the distortion of, say, France, due to the angle that it's at. In either case, there's no absolute answer, only relative answers, given some arbitrary position (point of view), in the case of distortion due to angle of view, or some arbitrary standard of rest ("velocity of view"), in the case of time dilation.

But the planes in the Hafele-Keating experiment are distinguished by more than relative velocity. They differed in their states of acceleration, one having a greater angular speed, and therefore a greater linear acceleration than the other, relative to the approximately inertial centre of the earth.

All I'm saying that by comparing time dilation of clocks you can find inertial frame where there is no time dilation (at least it is very small - approximation

The time dilation formula tells you how, given a time interval between two events that happen at the same place (along some spatial axis) in one inertial frame of reference, you can work out the time interval between those same events according to another inertial frame of reference moving at some velocity (along that axis) relative to the first. Inertial frames of reference where these events happen at the same place might seem like a natural choice of absolute rest, but in any such frame of reference there will be inflinitely many pairs of events which don't happen at the same place (along that axis), for which the "frame of maximum time" between them is another frame of reference. Since our choice of events, and of orientation (hence spatial axis), was arbitrary, there's nothing uniquely "rest-like / motionless-like" about that first frame of reference; we could just as well have picked another inertial frame of reference, and another pair of events by which to define "at rest".

sqrt(1 - (v/c)^2)
by taking v you're taking velocity difference between two "events". But this function isn't linear, so we can determine the exact speeds.

I don't understand this point. Nonlinear functions can have exact solutions.

http://www.quickmath.com/webMathematica3/quickmath/page.jsp?s1=equations&s2=solve&s3=basic

 

[Myslius]

Thanks for your explanation.
I was reading this (http://www.gmarts.org/index.php?go=420), another question occurred
Time dilation results in shorter distances?

Note that this distance does not just appear to be less, it really is less

Does that means that by sending telescope at the higher speed we can actually see out of observable universe by out FOR?

 

[Rasalhague]

Time dilation results in shorter distances?

Yes. To make sense of the whole theory, differences in the amount of time between two events as reckoned in different coordinate systems have to be considered together with differences in distance and differences in which sets of events are simultaneous with each other according to different coordinate systems. They're really all part of the same phenomenon.

Does that means that by sending telescope at the higher speed we can actually see out of observable universe by out FOR?

Good question! I'm afraid I don't know enough to give a good answer. Maybe someone else can help.