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Theory Of Time


freenrg

Hi rvalkass,

 

This topic is great. I am glad I found it. You seem to know quite a bit about this.

 

Here are some questions for you:

 

QUESTION 1.

How do we determine that an object is in motion?

 

QUESTION 2.

Newton used space as an absolute frame of reference?

Einstein said this was incorrect. Does Einstein use space-time as a frame of reference?

 

QUESTION 3.

As an object accelerates (I am assuming we have answered the previous questions) , time measured on that object slows down with respect to time measure on an object that is at rest.

Is this correct?

 

Let me know if you think I must rephrase my questions.

Thanks


rvalkass

QUESTION 1.

How do we determine that an object is in motion?


Mainly you detect its change in position relative to another object. So, if the distance between two cars decreases you can be confident there is some motion involved. How do we know which is moving? Use other reference points. If you can see one car is not moving relative to a nearby tree, you can say the other car is in motion relative to the first one.

 

The difficulty comes when there are no other reference points. If you've ever been in a traffic jam, especially next to a truck, and the truck pulls away, you can appear to be moving backwards. As you have no other reference, this is one option. The other, of course, is that the truck has moved forwards. Until you look round and see you are still relative to other cars, trees, etc. it is impossible to tell.

 

QUESTION 2.

Newton used space as an absolute frame of reference?

Einstein said this was incorrect. Does Einstein use space-time as a frame of reference?


An absolute frame of reference is generally considered to be one where Newton's laws of motion are valid. The problem was with Newton's original definition. He assumed that the stars were stationary and therefore could be used to create a stationary reference frame. This is not true, as we now know. Einstein extended this to say an inertial reference frame was one where light travelled at the speed of light in all directions, irrespective of wavelength.

 

However, Einstein also suggested we can't have an overarching inertial reference frame as it is impossible to tell if one exists. It is impossible to tell if a dropped object accelerates downwards due to gravity, or if everything else is moving upwards. As odd as that may sound, it is the same as the traffic jam analogy above.

 

QUESTION 3.

As an object accelerates (I am assuming we have answered the previous questions) , time measured on that object slows down with respect to time measure on an object that is at rest.

Is this correct?


More generally than that. Time slows down on an object in motion relative to another. Generally the effect is only noticeable at near-light speed, but you can see it using an atomic clock and flying around the world. Comparing the clock to one that stayed on the ground during the flight, you will find they have measured a different elapsed time period.

freenrg

More generally than that. Time slows down on an object in motion relative to another. Generally the effect is only noticeable at near-light speed, but you can see it using an atomic clock and flying around the world. Comparing the clock to one that stayed on the ground during the flight, you will find they have measured a different elapsed time period.

This is where I feel confused.

I had read about the atomic clocks and the difference in measured time.

You wrote that there is no absolute frame of reference. Then, as far as the plane is concerned, the earth could be the object moving, while the plane is at rest. Why does the clock on the plane slow down and not the clock on the earth?

What is special about the earth?
If there is no absolute frame of reference, why are the clocks acting as if the earth is at rest and the planes are moving?

freenrg

rvalkass,

 

These equations describe the differences in time measured by the clocks on the planes and on earth, am I right?

 

where

 

So how do we calculate v?

 

example...

v of earth = 0

v of plane = 2,000 mph

 

how do we reach these values?

why is v of earth 0 and v of plane 2,000 mph and not the other way around?


rvalkass

These equations describe the differences in time measured by the clocks on the planes and on earth, am I right?

 

where


Yes. They're known as the Lorentz transforms and are used to change both time and position to account for relativistic effects.

 

So how do we calculate v?

 

example...

v of earth = 0

v of plane = 2,000 mph

 

how do we reach these values?

why is v of earth 0 and v of plane 2,000 mph and not the other way around?


If you did take a view of the Earth from a distance, you would see the plane was moving faster than the Earth. Therefore the plane is travelling at a speed v relative to the Earth.

freenrg

Yes. They're known as the Lorentz transforms and are used to change both time and position to account for relativistic effects.

 

 

 

If you did take a view of the Earth from a distance, you would see the plane was moving faster than the Earth. Therefore the plane is travelling at a speed v relative to the Earth.

So does this observer watching both the earth and the plane from a distance constitute an inertial frame of reference?

rvalkass

So does this observer watching both the earth and the plane from a distance constitute an inertial frame of reference?

Not necessarily. An inertial reference frame is one where the observer's speed is 0 and every physical law obeys its standard form. In the example of the Earth and the plane, by standing on the Earth as an observer, you make it your inertial reference frame and define its speed as 0 (which makes sense, the Earth's speed relative to the Earth would be 0). This then means the plane is moving relative to you, and hence the value of v in the equation.

freenrg

Not necessarily. An inertial reference frame is one where the observer's speed is 0 and every physical law obeys its standard form. In the example of the Earth and the plane, by standing on the Earth as an observer, you make it your inertial reference frame and define its speed as 0 (which makes sense, the Earth's speed relative to the Earth would be 0). This then means the plane is moving relative to you, and hence the value of v in the equation.

OK.
So, if I am standing in the plane looking at the plane's clock, then for me (and for that clock) the plane is an inertial frame of reference and the earth is moving at speed v, in the opposite direction?

freenrg

wait a minute...I was swimming this morning and thinking about this (yes, I am that weird).The apparent lack of symmetry between the earth and the plane kept me puzzled. Why does the plane clock slow down with respect to the one on earth and not the other way around?You (rvalkass) mentioned that a distant observer could tell which one was moving and which one was not. But how do the clocks "know"?Then I thought...The clocks have to be synchronized at some point. ... So, the clocks are synchronized when the plane is still on the earth, right?. Then the plane takes off and moves around, and finally lands on the earth again and we check the clocks and find the difference.Does this synchronization and the fact that is takes place on the earth break the symmetry? I think it may, but I am not sure why.Does it?Why?


rvalkass

Then I thought...The clocks have to be synchronized at some point. ... So, the clocks are synchronized when the plane is still on the earth, right?. Then the plane takes off and moves around, and finally lands on the earth again and we check the clocks and find the difference.
Does this synchronization and the fact that is takes place on the earth break the symmetry?
I think it may, but I am not sure why.

Does it?
Why?


You are correct that the fact the synchronisation occurs on Earth is an issue. What you have stumbled across in a round about way is known as the "Twins Paradox". You have also managed to reach the solution to it The paradox is normally explained with spaceshuttles as the effect is more obvious, but planes work just as well.

Consider two twins: Laura and Emily. Emily stays on Earth while her twin, Laura, is put in the space shuttle and fired off into the distant reaches of space. Because of the speed of the shuttle, Emily observes time as proceeding more slowly in the space shuttle than on Earth. So, when Laura returns she will be younger than Emily.

However, to Laura the space shuttle is an inertial reference frame. As the Earth moves relative to her, she thinks Emily is ageing slower than her. When she returns, Laura thinks Emily is younger. So, who's right?

Laura's space shuttle has had to accelerate relative to the Earth to take off. Then again as it turns round to return. However, Emily has remained fairly inertial throughout the entire process. Laura's frame of reference (the space ship) therefore cannot be considered inertial, and her calculations are incorrect. Emily's are right, and Laura is the younger of the twins when she gets back.

The same can be said of planes. As they need to accelerate away from the Earth, and then back towards it, they can't be considered inertial.

freenrg

You are correct that the fact the synchronisation occurs on Earth is an issue. What you have stumbled across in a round about way is known as the "Twins Paradox". You have also managed to reach the solution to it The paradox is normally explained with spaceshuttles as the effect is more obvious, but planes work just as well.
Consider two twins: Laura and Emily. Emily stays on Earth while her twin, Laura, is put in the space shuttle and fired off into the distant reaches of space. Because of the speed of the shuttle, Emily observes time as proceeding more slowly in the space shuttle than on Earth. So, when Laura returns she will be younger than Emily.

However, to Laura the space shuttle is an inertial reference frame. As the Earth moves relative to her, she thinks Emily is ageing slower than her. When she returns, Laura thinks Emily is younger. So, who's right?

Laura's space shuttle has had to accelerate relative to the Earth to take off. Then again as it turns round to return. However, Emily has remained fairly inertial throughout the entire process. Laura's frame of reference (the space ship) therefore cannot be considered inertial, and her calculations are incorrect. Emily's are right, and Laura is the younger of the twins when she gets back.

The same can be said of planes. As they need to accelerate away from the Earth, and then back towards it, they can't be considered inertial.

I understand it now!
Thanks

This is great.


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