Calculating the speed of the earth

[hmvince]

Hey guys,
Lately I've been thinking (and I know it would take a lot of other variables like the orbit around the sun (circular motion etc.)), but as we can see, the graph of [Time dilation] vs [velocity as a fraction of the speed of light] is NOT linear, as shown here: http://www.thebigview.com/spacetime/timedilation.html"
Because of this, wouldn't we be able to put a clock on an aeroplane (or something extremely fast), and measure time dilation between our time and the time on the plane, then rearrange the formula for v, and solve for how fast we, on earth, are traveling through space?
Of course this would have to be EXTREMELY accurate, and depending on what stage the Earth is rotating around the Sun and what direction the plane flies in is all important, but isn't there just that little possibility that this could be done?

Using this information couldn't we also find how long the Universe has been around, and where the centre of the Universe is (using another galaxy as a guide)?

 

[Polyrhythmic]

Because of this, wouldn't we be able to put a clock on an aeroplane (or something extremely fast), and measure time dilation between our time and the time on the plane, then rearrange the formula for v, and solve for how fast we, on earth, are traveling through space?

The only v appearing in that calculation would be the velocity of the aeroplane with respect to the earth. How do you want to gain information about the Earth's state of movement with respect to the sun?

 

[Janus]

Hey guys,
Lately I've been thinking (and I know it would take a lot of other variables like the orbit around the sun (circular motion etc.)), but as we can see, the graph of [Time dilation] vs [velocity as a fraction of the speed of light] is NOT linear, as shown here: http://www.thebigview.com/spacetime/timedilation.html"
Because of this, wouldn't we be able to put a clock on an aeroplane (or something extremely fast), and measure time dilation between our time and the time on the plane, then rearrange the formula for v, and solve for how fast we, on earth, are traveling through space?
Of course this would have to be EXTREMELY accurate, and depending on what stage the Earth is rotating around the Sun and what direction the plane flies in is all important, but isn't there just that little possibility that this could be done?

Using this information couldn't we also find how long the Universe has been around, and where the centre of the Universe is (using another galaxy as a guide)?

You are making the mistake of assuming that there is such a thing as absolute motion; that the idea of the Earth traveling "through space" has meaning. one of the basic tenets of Relativity, from where we get the time dilation concept from is that there is no absolute motion, only relative motion.

In the time dilation formula the v is the relative velocity between the object whose time dilation is being measured and the reference from which it is being measured. In your example, this reference would be the Earth. It doesn't matter how fast the Earth is moving relative to some other reference (like the Sun), it will get the same answer for the time dilation for the plane( as compared to its own clock).

The short answer is that your experiment would only give you the relative speed between plane and Earth and nothing else.

 

[hmvince]

Appreciate the replies,
but I don't think you understand what I am saying, as shown here http://www.thebigview.com/spacetime/timedilation.html" the graph is not linear (if the graph was linear my experiment would not work).

I am saying that we fly the plane and then compare the two clocks, obviously there is going to be a minute difference in time, but this difference, since the graph is NOT LINEAR, will depend on HOW FAST THE EARTH IS MOVING relative to a STATIONARY POINT IN SPACE. So what I'm saying is

If the Earth is moving 3/4 of the speed of light
Then the time dilation between the two clocks will be much more than
If the Earth was moving only 1/4 the speed of light

Because of this change in dilation we would be able to plot the speeds on the graph and as stated in my previous post could use this to find how fast the Earth is moving relative to a stationary point in space

Am I missing something (sorry bout caps)?

 

[bcrowell]

If the Earth is moving 3/4 of the speed of light
Then the time dilation between the two clocks will be much more than
If the Earth was moving only 1/4 the speed of light.

Nope, not true.

 

[yuiop]

Am I missing something (sorry bout caps)?

Probably missing the relativistic velocity addition law http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

 

[hmvince]

I think I'm getting over my head here, but I don't really understand relativistic velocity and how it affects how we see things. Could someone please explain?

 

[bcrowell]

I think I'm getting over my head here, but I don't really understand relativistic velocity and how it affects how we see things. Could someone please explain?

Here's how velocity addition works in relativity: http://en.wikipedia.org/wiki/Velocity_addition#Special_theory_of_relativity If you want to learn some SR, a good place to start is An Illustrated Guide to Relativity by Takeuchi.

 

[hmvince]

Here's how velocity addition works in relativity: http://en.wikipedia.org/wiki/Velocity_addition#Special_theory_of_relativity If you want to learn some SR, a good place to start is An Illustrated Guide to Relativity by Takeuchi.

Will definitely check them out, thanks so much for the replies!

Just curious, is there any way to calculate the speed of the Earth relative to a stationary point "in space"?

 

[yuiop]

I think I'm getting over my head here, but I don't really understand relativistic velocity and how it affects how we see things. Could someone please explain?

1) Start with a test clock that is moving at say 0.8c relative to the Earth from the point of view of an observer at rest with the Earth. The time dilation of the clock is 0.6 relative to the Earth clock.

2) Now use the addition law to calculate the velocity of the test clock from the point of view of an observer that sees the Earth moving at say 0.6c and then calculate the time dilation of the Earth clock and the test clock.

3) Now use the addition law to calculate the velocity of the test clock from the point of view of an observer that sees the Earth moving at say 0.9c and then calculate the time dilation of the Earth clock and the test clock.

In each case you find the time dilation of the test clock relative to the Earth clock is 0.6 no matter what the velocity of the observer relative to the Earth is, so no preferred frame can be discovered using this method.

 

[yuiop]

Just curious, is there any way to calculate the speed of the Earth relative to a stationary point "in space"?

The trouble is that there is no way to define a stationary point in space in relativity in an absolute way. If two inertial observers are moving at 0.75c relative to each other in empty space, each can consider themselves as stationary as the other as moving.

 

[hmvince]

The trouble is that there is no way to define a stationary point in space in relativity in an absolute way. If two inertial observers are moving at 0.75c relative to each other in empty space, each can consider themselves as stationary as the other as moving.

I see, so even if we on Earth are moving (around the sun of course) we can think of ourselves as a stationary point in space. But then doesn't then that contradict the fact that light is constant and we are in fact succumbing to time dilation?

 

[ZikZak]

No, there is no contradiction. Two observers moving relative to one another have no way of determining which one is "in fact" at rest, and which is in motion. Each observes the other's clock to run slow, and each observes all light rays to travel at c, relative to himself. Neither is "in fact succumbing" to time dilation in any absolute sense. Which clock runs normally and which runs slow entirely depends on the reference frame of the observer. There is no observational difference whatsoever between motion and rest. That is what "Relativity" means.

In SR, the observer *never* measures time dilation on his own clock. Time dilation only ever happens to other things: all those clocks which move relative to him. The speed "v" in the equation you're looking at is speed relative to the observer.

 

[hmvince]

No, there is no contradiction. Two observers moving relative to one another have no way of determining which one is "in fact" at rest, and which is in motion. Each observes the other's clock to run slow, and each observes all light rays to travel at c, relative to himself. Neither is "in fact succumbing" to time dilation in any absolute sense. Which clock runs normally and which runs slow entirely depends on the reference frame of the observer. There is no observational difference whatsoever between motion and rest. That is what "Relativity" means.

In SR, the observer *never* measures time dilation on his own clock. Time dilation only ever happens to other things: all those clocks which move relative to him. The speed "v" in the equation you're looking at is speed relative to the observer.

thanks for the reply, everyone, thanks for the replies.
I do understand now, It all makes sense!