# B Near-light speed and time

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1. Jan 6, 2017

### Steeve Leaf

I 've waited 50 years to understand Newton.

A spaceship orbits Earth at 300,000 km distance at speed 0.5c broadcasting live images of the clock aboard, will the clocks difference will be 1 sec?

The orbit is a perfect circle.

Its moving close to the speed of light but stays at the same distance.

Is the clocks difference between the one on Earth and the images received by broadcast from the ship stay the same ?

Last edited by a moderator: Jan 6, 2017
2. Jan 6, 2017

### Janus

Staff Emeritus
For every second passing on the Earth, a person on Earth will see only 0.866 seconds worth of images from the ship. After one second, the he will see the ship clock reading 1.866 sec behind his own ( the one sec being due to light propagation delay) after two seconds it will be 2.732 sec behind his, after three seconds it will be be behind by 3.598 sec, etc.

3. Jan 7, 2017

### Steeve Leaf

Thanks, as I understand from the answer the one second delay is from the distance and 0.866 is from the speed.
No acceleration involved, or is it acceleration due to the change of direction.
If we increase the speed there will be a formula to show that 0.866 will decrease. Is it possible to explain it in words first ?

4. Jan 7, 2017

### Janus

Staff Emeritus
Yes there is acceleration due to the changing direction.
It would be the same formula as you would use for time dilation. (In this example we are ignoring the gravitational time dilation between the altitude of the rocket and the Earth clock which is very small. Now if the velocity of the rocket were small enough, like it would be if it were in non-powered orbit, then to get an accurate answer you would have to factor in gravitational time dilation)

Last edited: Jan 7, 2017
5. Jan 7, 2017

### Steeve Leaf

The reason I asked this question is because i think i understand why the clock goes faster compared to the ship who traveling away but not why it is for a ship traveling toward you. There might be two different issues here. One the doppler effect and the other I don't know/understand. I don't think you calculated allready the acceleration due to the fast orbit so I ask again to make sure .
Is the 0.866 value is due to 0.5c speed or it will change if the ship will orbit at 600,000 km distance at the same speed ( and reduce the amount of acceleration on it). ?

6. Jan 7, 2017

### Janus

Staff Emeritus
The time difference will is due to the speed alone, the radius of the circle and the acceleration experienced by the ship are not contributing factors. ( you may be interested to know that this has been verified by experiment. samples of radioisotopes have been put into high speed centrifuges and then had their decay rates measured.

So yes, for a rocket ship moving away, there are two effects that combine that result in what you see. One is the effect caused by the changing distance between the craft and observer due to the relative velocity and the the other is time dilation which is just due to the relative speed. If the spaceship is moving towards you, the decreasing distance factor due to the velocity towards you will cause you to see its clock running fast, however, if you factor this out, the spaceship clock will be ticking slow due to its relative speed with respect to you.

The Light clock is usually used to explain time dilation. It is a simply clock that counts time by a light bouncing between two mirrors.
The vital fact to keep in mind is that the speed of light is invariant. And by this we mean that everyone gets the same value for the speed of light relative to themselves regardless of relative velocity the source of the light has relative to them.

To visualize what I mean, Assume you have to observers, A and B that have some relative velocity towards each other. At the moment they pass each other, they each set off a flash of light. What does A and B measure as happening to the expanding spheres of light? Each will measure both spheres expanding outward from him at c (he will remain at, or at least very, near the center of each expanding sphere.Z)

So now let's imagine that each of them are carrying a light clock. Each will see the light from his own clock travel between the mirrors at c. If the mirrors are 150000 km apart they each measure the round trip for their own light clock to take ~1 sec( not exactly, because the speed of light is just a tad less than 300,000 km/sec)
But what happens for the other light clock? if A sees the light for it traveling at c relative to him, while B travel is also traveling at v with respect to him, he must measure B's light pulse as taking longer to make its round trip than he does for his own light pulse.
Here is an animation demonstrating this.

Each pulse of light bouncing back and forth is shown by a dot. The expanding circles show how each pulse is on an expanding front moving at c relative to the observer.
For this animation, the relative speed between the two clocks is 0.866c. Note that the clock at "rest" ticks twice ( two seconds) for every one time(1 sec) the moving clock ticks.
I put "rest" in quotes because, as far as the clock shown as moving here is concerned, he is the one at rest. So he measures his light clock as taking 1 sec per round trip. In fact, as far as he is concerned, it is the other clock that is moving to the left and is ticking slow relative to his own.

Please note that none of this involves how light travels between the two clocks, which would involve including the Doppler shift effect.

Now how does this apply to your original scenario?

In the example I just gave, both clocks are in inertial motion (not-accelerating). In your example, one of the clocks is in constant acceleration towards the other (even though due to its circular path it maintains a constant difference.) Above I mentioned that the acceleration of the ship had no affect on the time difference as measured by the Earth. However, it does have an effect on how the ship measures the time difference. The acceleration towards the Earth causes the ship to measure images coming from the Earth to run fast by a factor of 1.1547 (1/0.866) and two factors determine how fast the ship measures the Earth clock tick rate to be: The acceleration experienced by the ship and the distance between ship and Earth. Increasing the distance while maintaining the same speed decreases the acceleration, and the combination ends up giving the same answer for the difference in tick rate between the two.

Having said that, I will advise you to forgo dealing with scenarios that deal with acceleration, until you have a strong grasp of what happens in purely inertial situations. Also, there are two other aspects of Relativity that you have to grasp before you can properly deal with Relativity even in inertial motion cases. These are length contraction and the relativity of simultaneity.

The light clock example above is one of the few cases where you don't need to take the other two effects into account, but in most cases this is not true. (For example if you tried to analyze the same light clock experiment with the light clocks aligned with the line of relative motion between the clocks.)

I hope this helps.

7. Jan 8, 2017

### Steeve Leaf

Thank you.
What you are describing is an optical illusion ( the effect of speed on clock for an observer).
If the ship will broadcast an image of a digital watch on the ship to earth every time it completes orbit the difference between the clocks will stay the same 1 sec at 300000 km away.
I saw the formula that you used to get the 0.866 (√(1−(v²/c²)) and I admire it but it is still illusion because everyone will see the other clock go slower by that amount.
I 'm sorry if you think that I'm wrong (and maybe I am) but I am very thankful for you trying to explain it to me.

8. Jan 8, 2017

### Staff: Mentor

It will not. We've actually done this (with the GPS system) and the difference does not stay the same.

9. Jan 8, 2017

### Steeve Leaf

Thar is gravity effect, not speed .
I don't know why gravity affect time but it is of an interest.
Gravity is a force that can effect everything including time measuring devices.
Assume that speed don't affect time (for a moment).
The TWIN-PARADOX version with gravity/acceleration will be:
Twin A on Earth at 1g twin B accelerate at 1g for one year and then at -1g for two years then at 1g until it land on Earth.
Are they aged the same ?

10. Jan 8, 2017

### Staff: Mentor

The GPS satellites are subject to gravitational time dilation, but that makes them run faster (because they are at a higher gravitational potential), not slower. They are are also subject to time dilation caused by their speed relative to the surface of the earth, which causes them to run slower, and that's what I was referring to.

In low earth orbit the relative speed effect is greater than the gravitational effect and the orbiting clock runs slow relative to the earth-based clock. In higher orbits it's the other way around.

11. Jan 8, 2017

### Janus

Staff Emeritus
Not in the scenario with the ship circling the Earth. The equation given only applies when you are considering what the observer in an inertial frame measures (and in this case, we can consider the Earth to be an inertial frame for all practical purposes. However it can not be applied to the observer in the spaceship, who is in an accelerated frame. When you apply the rules for observers in accelerated frames, to the ship observer, you find that he sees the Earth clock running fast. Thus if you were to stop the experiment and bring the ship to a state of rest with respect to the Earth, both the Ship and Earth will agree that that less time accrued for the ship than did for the Earth.
This is an example of what I meant by jumping into scenarios with acceleration before fully grasping how to deal with inertial motion scenarios.
It not that I think you are wrong, it is the established facts that say you are wrong.

Besides the GPS example already given, there is the centrifuge experiment I mentioned in my post. You take a sample of a radioisotope and put it on a centrifuge which is spun at a high speed for a period of time. After which you compare this sample to a sample that was not spun on the centrifuge to see if there is any difference in how much the samples decayed, and if so, by how much. Now by doing this several times with centrifuges of different radii and spinning at different speeds, you can determine what effects the difference in decay rate. For example by changing the radii and rotational velocity you can have samples that travel at the same speed but experience different accelerations, or travel at different speeds and experience the same acceleration. At the end of the run for each experiment, the spun samples are again compared to a lab sample.

These experiments have actually been done with samples experiencing extremely high accelerations. In every case, the difference in decay rate for the spun sample was related to the speed it was spun in accordance to the time dilation equation and nothing else.

It makes no sense to call something an optical illusion when it has verified by real-life experiment.

Your reaction to the idea that both will measure the other clock as running slow (in inertial velocity cases) is typical for those new to Relativity. It can be hard to accept that time behaves in a manner that seems so against our intuition. And as I also mentioned, the other two effects are also needed to forma complete picture. All the apparent contradictions that arise when you just consider time dilation disappear when the other two effects are included in the analysis.

12. Jan 9, 2017

### Steeve Leaf

You manage to synchronize all the GPS satellites at different heights and speeds using formulas, that is convincing and admirable.
Thank you .

13. Jan 9, 2017

### mrspeedybob

The light clock explanation may make time dilation look like an illusion that occurs in that particular circumstance, but if you stop and think about what time actually is, in every way that matters, it is the rate at which things happen. The rate a clock ticks, the rate of radioactive decay, the rate of a chemical reaction, the rate at which we age, etc. All those processes involve interactions between subatomic particles. All those interactions involve forces acting between the particles. And all those forces propagate at the speed of light. So, if the forces have to travel further to make things happen, then the process will be slowed. It is exactly the same phenomena the light clock demonstrates, carried out between every single subatomic particle in a moving object, as opposed to just the 2 mirrors. You could pick 1 frame of reference and declare it stationary, and explain everything in terms of the increasing distances that force carriers must travel, but it's vastly simpler, both conceptually and mathematically, to call it time dilation.

14. Jan 9, 2017

### Steeve Leaf

Still on light speed and time topic but back to the basics.

Light travel at c at vacuum for every observer.

This I don't understand the above statement. The following scenario will maybe explain my misunderstanding.

A spaceship traveling at 0.5c transmitting radio signal forward at a speed of light compare to the ship.
It traveling from A to B. At the halfway point receiving a radio signal that was send from A to B. It intersect this signal and send it from its radio to B. If the radio signal travel at c compare to the ship, the signal from the ship will arrive earlier to B than the signal that was send from A.
Information can't travel faster than light speed c, what wrong with my Newtonian understanding ?

15. Jan 9, 2017

### Staff: Mentor

Both the signal from A and the retransmitted signal from the ship to B travel at speed $c$ relative to A, B, and the ship.

You are assuming that if the ship is moving at speed $u$ relative to A and B and the ship sends a signal towards B at speed $v$, that signal will be moving at speed $u+v$ relative to A. It's not - the correct formula is $(u+v)/(1+uv/c^2)$, and that leads to the conclusion that if the signal is sent at speed $c$ relative to the ship it's also moving at that speed relative to A and B.

If you compare the results of the two formulas for speeds that are small compared to the speed of light, you'll see how we could have gone for centuries without ever observing the difference between the two.... But now that we can do sensitive enough experiments, it is clear that that $u+v$ formula is not right. As a historical note, the first observations of violations of the $u+v$ formula were done in 1851 by Fizeau; these remained mysterious until 1905 when Einstein developed special relativity.

16. Jan 9, 2017

### Staff: Mentor

It might be more accurate to say that we are using formulas (that have previously been proven to work in many different situations) to correct for the observed fact that the clocks will not stay in synch without corrections.

17. Jan 10, 2017

### Steeve Leaf

So simple Math for you but I don't know how to do it.
What the values of v compare to B.
if u=0.5c
and if
u=0.75c
?
“Nothing ever exists entirely alone. Everything is in relation to everything else.” – Buddha
than 1 min on the ship is
2 min
4 min
on A or B
Respectively respectfully , where did I got lost:)

Last edited: Jan 10, 2017
18. Jan 10, 2017

### Janus

Staff Emeritus
If u is the ship's velocity with respect to A and B, then v would be the velocity of something relative to the ship as measured by the ship, and w would be the relative velocity of that something relative to A and B as measured by A or B.
Thus if the ship is moving at 0.5c relative to A and B, and fires a projectile towards B at 0.5c relative to itself, then A and B will measure the projectile as moving at
(0.5c+0.5c)/(1+0.5c(0.5c)/c^2) = 0.8c relative to themselves.

If the ship emits a radio signal towards B at c relative to itself as measured by the ship then it travels at (0.5c+c)/(1+0.5c(c)/c^2) = c relative to A and B as measured by either.

This is one of those scenarios I mentioned above where you are going to have to take all three relativistic effects, time dilation, length contraction and the relativity of simultaneity into account to form a coherent picture of what is happening.

19. Jan 10, 2017

### Steeve Leaf

Making sure that I can use this tool/formula currently.
Newton laws are good for speed that are not close to c.
If u=0.5c fires a projectile towards B at 0.5c relative to itself, then A and B will measure the projectile as moving at 0.8c
By Newton it is c.
If u=0.75c fires a projectile towards B at 0.25c relative to itself, then A and B will measure the projectile as moving at 0.8421c
By Newton it is c.
If u=0.25c fires a projectile towards B at 0.75c relative to itself, then A and B will measure the projectile as moving at 0.8421c
By Newton it is c.
I think you will agree the above statements.

1. If the ship at 0.5c time slow down by 0.866
2. If the ship at 0.75c time slow down by 0.661
Is this in min or a factor
If it is a factor then
at 0.5c , for every min A and B will see 51.96 sec pass on the ship
at 0.75c, for every min A and B will see 39.66 sec pass on the ship.

Current so far ?

20. Jan 11, 2017

### Janus

Staff Emeritus
More accurately, the relativistic formula is good for all speeds, and gives answers that are almost exactly the same as that given by Newtonian velocity addition when the velocities involved are small when compared to c. In other, the relativistic formula is correct formula for all cases, but you can get away with using the Newtonian version at low velocities without sacrificing too much accuracy. We live in a relativistic universe, not a Newtonian one.
these look okay
It's a comparison rate. The ship clock runs at this rate compared to the clocks at A and B when compared by A and B (or anyone at rest with respect to A and B). On the other hand, the Clocks at A and B run at a slower rate than the Ship clock when compared to the ship clock by the ship.