# So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick less

1. Aug 29, 2009

### jinksys

I'm reading Concepts of Modern Physics by Beiser, and the chapter example says:

A spacecraft is moving relative to earth. An observer finds that in one hour, according to her clock 3601s elapse on the spacecraft's clock. What is the craft's velocity relative to earth? (This is not a homework question, I can get the correct answer.)

So is this saying that for every 3600 seconds on earth, the spacecraft's clock moves 3601 seconds? Wouldn't this mean that time runs faster on the craft and not slower?

2. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Seems like an ambiguously worded example. Are you quoting it exactly, word for word?

In any case, moving clocks are observed to run slow. So if she is observing a moving clock, then when she sees 1 hour pass on the observed clock, her clock may show 3601 seconds having passed.

3. Aug 29, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Here is the example, verbatim:

A spacecraft is moving relative to the earth. An observer on the earth finds that, between 1 and 2 pm according to her clock, 3601s elapse on the spacecraft's clock. What is the space craft's speed relative to the earth?

Solving for v, I have:

$v = c \sqrt{1-\frac{t_0^2}{t^2}}$

Where t0 is the clock at rest, and t is the clock in motion.

t0 has to be more than t or else the square produces an imaginary number. So from this it seems like the clock in motion always has to read faster than the stationary one.

Furthormore, here is the solution it gives:

Here, t0 = 3600s is the proper time interval on the earth and t = 3601 s is the time interval in the moving frame as measured from the earth. From here they provide the math solution which is 7.1 x 10^6 m/s.

Last edited: Aug 29, 2009
4. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

This is Example 1.1 in Beiser, right? (I just looked it up on amazon.com preview.) In any case, Beiser has it backwards. (Someone should tell him!)

5. Aug 29, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Yep, the first example :( not a good start to a book I have to use all semester!

6. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

7. Aug 29, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Luckily I was able to get an international version for $20, I feel for those who bought it from the bookstore for$176. I have another question...

This is the author's formula and explanation of time dilation...

$t = \frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$

t0 = rest clock
t = moving clock
c = speed of light
v = speed of clock in motion

An Amazon review says that he has definitions of t and t_0 backwards, is this true?

8. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

I'd say so. That formula is OK if t0 means the time elapsed on the moving clock and t means the time elapsed on the "rest" clocks. Better read that book critically! (Get another book as a backup.)

9. Aug 29, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

I am definitely going to Borders or Barnes and Noble and getting a backup. Do you have any recommendations?

10. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

I suggest you post something in the Science Book discussion forum asking for opinions. We have quite a few active instructors who might be able to recommend a good one. (Someone who's taught from a book would be able to give a useful opinion.)

11. Aug 29, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Ok, well now that I have that sorted out, I actually do have other questions regarding time dilation.

Suppose there are two GIANT clocks, one perched upon the earth and one perched upon a spacecraft. The clocks can be seen by both observers, one on earth and one in the craft.

Are the following true?

To an observer on earth and spaceship's clock ticks slower than the earth's clock.
To the observer in the ship, the earth's clock moves slower than his. (assuming he is at a constant speed).

12. Aug 29, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Yes, both "see" the other's clock as running slow. I put "see" in quotes since relativistic effects like time dilation are what's observed after taking light travel time into account. (In order to make sense of what you see, you must factor in the time it takes for the light to reach you. You don't just go by raw observations--what you literally see.)

13. Aug 29, 2009

### Naty1

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Yes each observer sees the other fellows time as running slow. A good way to visualize this is via a "mirror reflecting photon clock"....a simple example which reflec the longer path taken by a photon in relative motion...maybe someone can post an online diagram source....

14. Aug 29, 2009

### atyy

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

I learnt from an old edition of Beiser - it's very good. But typos are indeed irritating and make things hard, so it's good to also have eg. AP French's Special Relativity, and French and Taylor's An Introduction to Quantum Mechanics, Schroeder's An Introduction to Thermal Physics. Schaum's series is usually very reliable.

15. Sep 3, 2009

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

I asked my physics adviser about the time dilation equation and she said that T should be larger than T0 because the moving clock moves slower. She said the larger number represents the amount of local time it will take for moving clock to show T0.

16. Sep 3, 2009

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Huh? Slower that what?
Huh? The number shown on the clock itself is the local time (in the clock's frame)!

Ask her this question: A rocket travels past earth (point A) to planet X (point B). During that trip, the rocket clock shows a time t0. Will earth clocks show a larger or smaller time for that rocket to go from A to B?

17. Aug 29, 2010

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

So, for the problem to be correct with Special Relativity the 'proper time' should be t0=3600, and t should be 3601, since it was stated that the ship was moving relative to earth and the observer was at rest on earth. It looks like they set up the problem correct, since they get the correct answer, but in the problem and setup they have the times reversed.

Is this right?

Last edited: Aug 29, 2010
18. Aug 29, 2010

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Yes. It's not just a typo, though, it's more of a sloppily constructed problem. What they meant to say was something like: "Earth observers find that from 1:00:00 pm to 2:00:01pm on their clocks only 3600 seconds have passed on the ship's clock."

They compound the confusion with the first sentence of the solution: "Here t0 is the proper time interval on the earth...." huh? They should have said, "Here t0 is the proper time interval as recorded by the ship's clock..."

19. Aug 29, 2010

### jinksys

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Again, thanks for the all the help.

Here is an email I sent out to my classmates regarding this example. Was I correct in my statements?

If you were one of the lucky ones who've been able to acquire a textbook, I would like you to take a look at example 1.1 in the text.

Example 1.1 is set-up incorrectly. It should read:

A spacecraft is moving relative to the earth. An observer on the earth finds that between 1:00:00 PM and 2:00:01 PM, according to her clock, 3600 seconds elapse on the spacecraft's clock. What is the spacecraft's speed relative to earth?

Here t0 = 3600s is the proper time interval on the spacecraft and t=3601s as measured by a clock at rest with the observer.

Since it was stated that the spaceship was moving relative to earth, a clock in the ship's frame of reference measures the 'proper time'.

The plugging-in of numbers and solving for v part of the example is correct, however.

20. Aug 29, 2010

### Staff: Mentor

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Sounds good to me (and much improved over the original).

21. May 12, 2012

### avalanchesj

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Not to stray too far from the origional post, but i have a question. Please keep in mind that I am a computer geek not a physics major, professor, or any other large brained person sporting a white coat. Does time itself slow down or just our relitive perception of time?

lets try this scenerio:

If i'm looking at my watch and it is syncronized with a clock aboard a spaceship before it departs from earth and travles thru space at close to the speed of light, and the ship is transmitting it's clock time to me. When the ship returns will my watch read a different time then the ships clock? or does it only depend on the time it takes the signal to travel to me from it's location? in other words does time actually change for something travleing at at or near the speed of light or does time just APPEAR to change to an observer?

I hope I didnt confuse anyone. lol

22. May 12, 2012

### yuiop

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

This is the famous "Twin's paradox" of which there a thousand threads here. In a nutshell, your watch will show more time elapsed than the clock on the ship. If the journey is long enough and the ship travels fast enough then you will have aged noticeably more than the ship pilot. All physical processes (chemical, nuclear, biological etc) are affected equally by time dilation. The twin's paradox requires one of the twins to turn around and so that traveller experiences proper acceleration and cannot be considered an inertial observer. This breaks the symmetrical time dilation relationship observed in purely inertial reference frames, where each observer considers the other observer's clock to be running slower than their own.

It is only when clocks are brought back together and compared side by side that you can give a definitive definition of which clock was ticking slower.

I hope I haven't confused you now ;)

23. May 12, 2012

### avalanchesj

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Pardon my ignorance, but you used a lot of complicated phrasing (for me at least) but i think i got the jist of what you were saying, let me reitterate in my own words so i can be sure i understand.

When traveling at or near the speed of light, an observer from a relitivly stationary object (such as Earth), would notice that the ships clock seems to be running slower than his own. So time does change, not just our perception of time.

Is this because Space and Time are one in the same (Spacetime) and since the space between the Earth and the ship is growing more and more as the ship moves further away, the differance in time is also growing more and more? or did i miss the mark entirely? If so, could you explain it in a more dumbed down context? Ppossibly a pop-up book? lol jk

Because if that is the case then why do objects in orbit also show signs of time dialation? The space between the objects doesnt change, just the speed of the orbiting object. Is speed the only factor in time dialation?

I guess I'm just trying to wrap my head around WHY time seems to dialate when an object is moving at high speeds now lol.

24. May 12, 2012

### yuiop

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

This is slightly different than the example in the last post, because the clocks have not been brought back alongside each other and compared side by side. While clocks moving relative to each other are spatially separated there is a symmetrical relationship. The pilot on the ship thinks the Earth clock is ticking slower than the ship clock. Remember I said "It is only when clocks are brought back together and compared side by side that you can give a definitive definition of which clock was ticking slower"?
It is not about the space or distance between the observer and the observed clock growing. (See below).
You are right about orbiting object showing time dilation relative to a clock at the centre, despite the distance from the central clock not growing. It is more about motion relative to a "grid" or reference frame rather than relative to an individual observer. If you are at the centre of that orbit, (and sticking to 2 spatial dimensions for now) you can imagine a grid of synchronised clocks spread out at regular intervals along x and y lines forming a map with coordinates. The orbiting object is a bit like a race car on circular track on this map. Its velocity is relative to the track (or grid or map) rather than to you standing at the centre and it is that "grid" velocity that determines its relative time dilation. If you are interested in learning more about the "grid" I might elaborate at a later time ;)
There is no real explanation for "why". Nature just does what it does and we puzzle over it. Time dilation does however seem to be one the required ingredients for a universe where all the laws of physics are the same in any inertial reference frame. On the other hand, I am not sure why a universe has to have that property, but our universe seems to have it.

Last edited: May 12, 2012
25. May 12, 2012

### avalanchesj

Re: So clocks in motion are 'slower' to observers in rest, shouldn't the clocks tick

Ahhhh... the gears in my head are still smoking but i'm starting to get the picture. so it's all relitive. it all depends on witch frame of reference you're are observing, from my point of view his clock is running slow, and from his point of view mine is running slow, it's not untill we are both moving at the same speed (relitive to eachother) that we can determine which clock was running slow. so a satalite's velocity is relitive to space, not to me on the planet?