# Measuring pendulum period

1. Jun 6, 2012

### EmreY

I have been trying to come up with a solution for the matter but I failed, so here are my questions. I would appreciate if someone explained thoroughly.

a) There is a pendulum which has a period of 20 seconds on Earth.
If it was put on a vehicle moving at 0,6c and have its period measured on it, what would be the result?

a.1) What if the observer was on Earth and the pendulum on the vehicle?

b) This question is similiar to the first one but in reverse: The pendulum has a period of 20 seconds on the vehicle moving at 0,6c. What would be its period on Earth?

b.1) What if the observer was on the vehicle and the pendulum on Earth?

2. Jun 6, 2012

### ghwellsjr

Assuming that your vehicle traveling at 60% of the speed of light is traveling in a spaceship away from earth, then it will be weightless and pendulums don't work in a weightless environment, they need gravity or an accelerating spaceship to work. So if you want your spaceship to be circling earth at a very high speed, it will be experiencing a great deal of acceleration and the pendulum will be swinging very rapidly.

In any case, pendulums are not good time keepers except when stationary on the surface of a planet. They don't even work good in your car when you speed up or take turns.

3. Jun 6, 2012

### EmreY

Well actually I used a pendulum in the question as a method of measuring time between two events. Can you answer the question considering only the concept of time dilation?

4. Jun 6, 2012

### Mentz114

Why ? For someone who doesn't know how to calculate the time on a clock you are very picky. What is your real agenda ?

There is plenty of tutorial material available that explains special relativity so I suggest you do some studying and try to answer the question yourself.

This would be a good place to start,

http://en.wikipedia.org/wiki/Proper_time

Last edited: Jun 6, 2012
5. Jun 6, 2012

### EmreY

I have already checked the link you provided, and still couldn't figure out the exact answer, that's why I came here.
The question and its variations are on some exams I come across, and teachers haven't been able to explain it well enough as they also don't know the subject very well.

6. Jun 6, 2012

### ghwellsjr

Let me construct a scenario that I think will cover all your questions:

Assume a spaceship, far removed from earth, traveling towards earth at 60%c. On the spaceship is an observer with several different kinds of clocks, an old windup alarm clock, a new digital watch, and an atomic clock. He is wearing a device that shows that his heart beats once per second and he can count to twenty with one breath of air (it takes him twenty seconds to do this).

On earth is another observer with the same kinds of clocks and with the same heart rate and device and the same ability to count to twenty on one breath of air.

Both observers will think that time is progressing perfectly normal for himself but as they look at the other observer's clocks, heartbeat and counting, they each see the other ones timing running at twice the rate of their own. In other words, the earthling sees that it takes only 10 of his seconds for the space traveler to pass 20 seconds. And the space traveler sees that it takes 10 of his seconds for the earthling to pass 20 seconds.

After the space traveler whizzes past earth, the images of the other ones timing flip. Now the earthling sees that it takes 20 of his seconds for the space traveler to pass 10 seconds. And the space traveler also sees that it takes 20 of his seconds for the earthling to pass 10 seconds.

These effects are known as Relativistic Doppler.

But you want to know about time dilation. To get that, the observers have to take into account the time it takes for the light to travel from the other observer to himself. According to the methods of Special Relativity, when they do that, they each will determine that the other ones timing devices are running 80% of their own throughout the entire scenario, although they never actually see that happening, it's a calculation that they each can make.

7. Jun 6, 2012

### EmreY

Thanks a lot for your explanation, I have finally understood most of it. But I have one final question, which is not that related with my original question.
Does time really slow down at higher speeds, or is it just a matter of relativity-someone "seeing/thinking/observing" that the time slows down for the other one?

8. Jun 6, 2012

### ghwellsjr

I think it would help if you read the first couple sections of Einstein's 1905 paper introducing Special Relativity. In there, he points out that unless we establish a definition of remote time, we cannot answer questions such as yours. If you look at section 1, you will see that he defines all kinds of things which many people take for granted and end up with incompatible concepts that really don't make any sense. So if we want to make sense of the way the world works around us, we have to do something like what Einstein describes and then we don't worry about issues that don't have meaningful answers. Just remember, each observer is independently applying Einstein's convention for establishing a Reference Frame and so each one can say that time is running slow for the other one. What you can't do is take some definitions from one Frame and some more definitions from another Frame and try to apply them together. Stick with one Frame at a time and you won't have any problems.

9. Jun 7, 2012

### yuiop

Questions a, a.1 and b do not make sense, because a pendulum does not work in space away from a gravitational field. The answer to b.1 is that the period would be 16 seconds.

10. Jun 7, 2012

### GAsahi

You surely mean $\frac{20}{0.8}=25$, right?

11. Jun 7, 2012

### yuiop

Yes, you're right. I had the gamma factor inverted. Sorry about that!