# Confused by time dilation

1. Sep 24, 2007

### Raul_Duke21

Confused by time dilation!!

Ok I know that the faster you travel the slower time becomes for you by outside observers, while time would seem to go by at normal speed for you.

What I dont get is that there seems to be missing time for you on the moving vehicle.

If everything for you seems to be travelling at normal speed on the outside than what happened to the time that you didnt travel.

It seems to me that if you are going near the speed of light, than the outside world would seem to speed up as well, but this would make the speed of light go faster than it should.
Since you would be seeing things at a faster rate.

So you see my problem I dont seem to grasp where this missing time goes that you cant observe. Its as if when you stop, time would jump on you.

I dont know I may be thinking to much but it seems odd to me. Sorry if I sound crazy but I just got off of work and work a night shift. Thanks for any help.

2. Sep 24, 2007

### MathematicalPhysicist

I think that what you want to say what happens when you slow your speed, i.e if you started at 0.6c speed compared to another frame and you deaccelerate upto zero speed compaerd to that frame.
well if the accleration is constnat then there's a nice term for it, if not then i think that SR doesnt answers this question.

3. Sep 24, 2007

### MathematicalPhysicist

here's the term for the time in the rest frame of the vehicle:
t'=c/a(ln(|at/c+sqrt((at/c)^2+1)|)

4. Sep 24, 2007

### MathematicalPhysicist

a is the acceleration.

5. Sep 24, 2007

### Raul_Duke21

Actually what I meant to say is, say you are traveling near the speed of light and could observe earth. Would it seem to be going faster or have the same time as you. Because either answer seems nonsensical to me.

6. Sep 24, 2007

### MathematicalPhysicist

well your question and also the answer depneds on the rest frame, in your frame if you were to compare with someone in the earth then his clock will move slower by time dilation t'=gamma*t, now if he were to measure you time he will also see your time's running slower compared to his, by the same equation (but you repalce in the gamma v with -v, which in the gamma doesnt make a difference).

7. Sep 24, 2007

### tabchouri

Although it is misleading to compare time flows at different frames especially when you take into considerations some of the "seem to be" statements.
To try to reply your question, the time flow on earth will be faster than the time flow of the traveler.

-----------------------------------------------------
Correct me if I am wrong.

8. Sep 24, 2007

### MathematicalPhysicist

compared to which frame?

9. Sep 24, 2007

### tabchouri

Compared to the time flow on earth.
I meant to say that an observer on earth would see the time flow of the traveler go slower than his time.

But, when reading this (http://en.wikipedia.org/wiki/Time_dilation): [Broken]
As well as rethinking the twin paradox, I crushed onto the same confusion.
Since an observer on an inertial object A would see the time go slower on another inertial frame B (moving at a speed v relative to A), and B observer would see also a dialation of time in A.

Say, to save some complexity, that a traveler in B travels away from A then returns to A after some period of time. During this travel, A sees the time of B go slower by relativity, then when B returns to A, A would notice that B have aged less than A.
That is the twin paradox and what is quoted from wikipedia.
BUT, during this travel, B would also see that the time of A goes slower than his time, then when B meet A again, B should notice that A aged less than B.

Now i'm really confused :S
Can someone help clarify this ?

-----------------------------------------------------
Correct me if I am wrong.

Last edited by a moderator: May 3, 2017
10. Sep 24, 2007

### Raul_Duke21

Ok I know how it works compared to your rest frame. So as the traveller I would also see earth as slowing, but that leads me to my original question. How does the missing time get involved with this?

I leave for 1 year at near the speed of light, and come back to earth. It has gone forward in time compared to my frame of reference but it seemed to be viewed as going slower? So if I viewed earth during the trip it seems that I have missed some things when I return. For ex. a war breaks out towards the end of the trip, but I cant see it because I am actually seeing in the past it seems. So when I return all hell had already broken loose. If you catch what I am saying.

No matter how I try to grasp it, it seems that light has actually traveled faster than itself compared to the time taken to view this light. I am just caught in a loop here.

11. Sep 24, 2007

### tabchouri

12. Sep 24, 2007

### pervect

Staff Emeritus
I think what probably needs to be done here is to define some operational way that you are going to use to compare "how fast" the clocks tick.

The problem lies buried in the details of how the comparison process is done. If two clocks are moving relative to one another, one must consider the question of simultaneity of distant events.

The issue here is that simultaneity is relative, so there is no single, unambiguous way of comparing the times at which distant events occur.

This ambiguity in the comparison process is path-length dependent, and because the path length is varying, it affects the rates as well.

13. Sep 24, 2007

### JesseM

The time dilation equation only applies to inertial reference frames, i.e. frames that never accelerate. If you leave Earth and fly away for a while, then turn around and come back, you accelerate during the turnaround, and are not sticking to a single frame, so you can't use the standard time dilation equation in your non-inertial frame to predict how much time will have passed on Earth. Also, even for inertial observers, the rate that things are happening in their frame is not the same as the rate they see things happening using their eyes--what they see with their eyes is affected by the Doppler effect, which has to do with the fact that if a clock is moving relative to you, light from different ticks will have a different distance to travel to reach your eyes due to the clock's motion, so the rate you see it ticking will be different from the rate it's "really" ticking in your frame (note that if you see the light from an event 5 light-years away in 2010 according to your own clock, then in your frame this event 'really' happened in 2005 in your frame). In particular, if two ships are approaching each other at relativistic velocities, each one will see the other ship's clock ticking faster than their own, even though in their frame the other ship's clock is ticking slower.

14. Sep 24, 2007

### tabchouri

The site is well written, light, simple and correct (as far as I could tell). But allow me to say:
- The doppler effect explanation would be, as stated there, more confusing than explanatory. Further, it's not the visual effect that is of interest, but the real flow of time.
- "The Spacetime Diagram Explanation" is a better formulation, but that's just SR. Furthermore, it does not solve it as the author took only one point of view. If one would take "Stella" (to paraphrase) as the rest frame (with some edge simplifications, or may be further assumptions as special cases to explain the turnaroud), one would have the symmetric diagram. And one could, to some extent get the perfect symmetry of the conclusions they get in the site : it would be Terence who would have aged less.
- Now the "GR" explanation is the most satisfying. Assuming a pseudo-gravitational field at the turnaround intuitively might solve the problem. But, I'm still bothered : if we consider the symmetric situation, which is exactly the same as before except that we consider the rest reference at Stella. Now, in the travel away and back, nothing changes except that Stella would say that the Outbound and Inbound Legs lasted 7 years each, and Terence would swear they lasted 1 year each (only by symmetry of the original situation with all its assumptions).
For the turnaround event, it's a bit tricky : in GR, we suppose that there is a huge gravitational field located at Stella, (Terence doesnt feel any gravitation), thus Terence would age more than Stella in this single event. But this difference in aging would it be in a away such that the total time trip as measured by Terence would be longer than the trip duration measured by Stella ???
Furthermore, it is so, Stella would say the total trip lasted like 14 years, but also Terence would say it lasted much more than 14 years.
This would agree with the global assessment that Stella aged less than her brother, but the durations would not agree with the situation set-up.
- "The Twin Paradox: The Time Gap Objection" may be i'm too sleepy.
but
is just too convinient thrown that way.

-----------------------------------------------------
Correct me if I am wrong.

Last edited: Sep 24, 2007
15. Sep 24, 2007

### JesseM

You can't, because Stella is the one who accelerates--in SR there can be no controversy about this, since Stella will feel real G-forces which push her back in her seat, while Terence will feel weightless throughout. SR specifically says that equations such as the time dilation equation only work in inertial frames.
Are you summarizing what they do in the "GR" explanation or proposing an alternative? Taking the rest frame of Stella is exactly what is done in the "GR" explanation. In this (non-inertial) coordinate system, there is a uniform "gravitational" field (really a sort of pseudo-gravitational field, since it doesn't involve any actual curvature of spacetime) during the acceleration phase, and Terence's clock moves forward rapidly because of gravitational time dilation. In Terence's inertial coordinate system there is no gravitational field.
No, you're confusing what happens at different spatial locations with what happens in different coordinate systems (coordinate systems which include both Stella and Terence's worldlines). In Stella's coordinate system, the pseudo-gravitational field is everywhere, including the current location of Terence. Stella would explain the fact that Terence doesn't feel any G-forces in terms of the fact that Terence is in free-fall in this field, so he feels just as weightless as a person in a falling elevator or in a space shuttle orbiting the Earth, while Stella is not in free-fall so she does feel G-forces, just like a person standing on the surface of the Earth. In Terence's coordinate system, there is no gravitational field anywhere, including at Stella's location--she feels G-forces because she accelerates.
In Stella's coordinate system, yes, Terence ages very quickly during the period when the pseudo-gravitational field appears, and this accounts for the fact that he's older when they reunite even though he was aging slower than her during the periods when there was no field. In Terence's coordinate system, nothing special happens when Stella accelerates, she's just younger because she was aging more slowly throughout the non-accelerating phase.
I don't understand what you mean by that last part in bold. Do you agree that both Terence and Stella will make the same prediction about how old each one is when they meet? If so, that's the only really physical question here, questions about how long the trip "really" lasted are meaningless in relativity.
Again, it's important to understand that if you want to use standard SR formulas like the time dilation equation, you are only allowed to use them in inertial frames, not in non-inertial frames like the one where Stella is at rest throughout the journey.

16. Sep 25, 2007

### Raul_Duke21

So there is no way to calculate an inertial frame from a non-inertial frame then. I guess the traveller would assume time is going slower for him to outside observers but could never calculate from his point of view.

Strange, that only one perspective can be used. Thanks everyone.

17. Sep 25, 2007

### Staff: Mentor

It is possible to calculate the effects of time dilation etc. in an accelerating (non-inertial) reference frame, but you have to use calculus. Loosely speaking, you consider the accelerating reference frame to be a series of many inertial reference frames, one after the other, with different velocities. You have to integrate the effects of time dilation and relativity of simultaneity over all those reference frames. The resulting equations are rather messy, and you have to be careful about interpreting them correctly.

18. Sep 25, 2007

### Raul_Duke21

Thanks jtbell. I guess the calculations arent very practical then.

What had been getting to me is in any single reference frame time and c are constants, but to outside observers time is the only variable. Its the non-inertial object that gives me the most trouble to visualize, though. I just cant understand how this point of view sees the outside world considering it is actually going faster in time yet he should see it as slowing.

19. Sep 25, 2007

### Dan.7

Sorry if it would sound stupid asking this, but when you would be travelling near the speed of light, would you not end up, as going farther and farther, end up seeing what the actual destination is like at the current time. For example, if I would travel somehow near the speed of light, to some close star, would I not see it in its CURRENT state, if light would travel instantly to earth? And If i came back would i should technically be in the future, but if i go back again, lets say the trip takes 1 year, would the star not BE 1 year older? Sorry, Im a little confused.

20. Sep 25, 2007

### JesseM

Time dilation isn't just an optical effect, if that's what you're asking. The notion of how fast a clock is ticking in a given frame is based on factoring out the fact that the light takes a little while to reach you--for example, if look through my telescope and see a star exploding 100 light years away in 2007, then in my frame I say this event "really" happened in 1907. Similarly, if I'm looking at a stopwatch moving at a velocity of 0.6c relative to me, and when my own clock reads t=20 seconds I look through my telescope and see the moving stopwatch reading t'=40 seconds at a distance of 10 light-seconds away, then when my clock reads t=36 seconds I look through my telescope and see the moving stopwatch reading t'=48 seconds at a distance of 16 light-seconds away, then factoring out the 10 seconds for the first image to reach me and the 16 seconds for the second image to reach me, I conclude the event of the moving stopwatch reading t'=40 seconds "really" happened at t=20-10=10 seconds in my frame, and the event of the moving stopwatch reading t'=48 seconds "really" happened at t=36-16=20 seconds in my frame, so that in the 10 seconds from t=10 to t=20 in my frame, the moving stopwatch only ticked forward 8 seconds from t'=40 to t'=48. So, the moving stopwatch was slowed down by a factor of 0.8, just what you'd expect if you plugged its velocity of 0.6c into the time dilation formula, $$\sqrt{1 - v^2/c^2}$$.

Also, in relativity there is no such thing as a "current state", different frames give different answers to what is going on at a distant location "now", something known as the relativity of simulataneity. For example, if we're light-years apart and in one frame your 29th birthday happens at the "same time" as my 30th birthday, there might be another frame where your 31st birthday happens at the "same time" as my 30th birthday--the two frames disagree about which birthday of yours is simultaneous with the event of my 30th.