# Different time accumulated on clocks

1. Apr 20, 2013

### Matis

Greetings from Croatia :)

It may seem like a 100 times told story but it's not...

Let us imagine that we have a rocket with length 50 m when at rest. The rocket goes on a trip and accelerates to the speed near c. Observer from Earth "measure" it's length as 48m (illustrative value),that is for the observer, rocket's length is contracted. But no matter what "exhibitions" rocket preforms at speed close to c and regardless of that length contraction, when rocket returns to Earth it will be of course 50 meters long and not 48.

At the same time when length contraction occurs, observer from Earth "sees" that rocket clock is going slower than our clock and we also see all passenger's biological processes on that rocket as slowed down. Now, SR says that time for the man in that rocket goes normally and also observer's time on Earth goes normally.....so my question is, what causes different time accumulation on rocket's clock and on Earth's clock when these two clocks are compared after rocket returns on Earth ? (clocks are synchronized before the trip, and if there are any internal or external mechanical influences that can affect on process of generating seconds, they are subtracted from the result time)

Upper question also imply - What is so special in speed of light that when rocket travels at speed close to c, traveling at that speed causes different biological age of two people (observer on earth and man in the rocket born on the same date when they are reunited after rocket returns to Earth) ?

This is the point - if after rocket's return length remains the same regardless of our measurement of it's smaller length when it was traveling at speed close to c , what is the cause of different time accumulation and different biological age, that is, if the length remains the same, why the time accumulated on almost ideal clocks is also not the same but different?

For now I still believe that time dilation and length contraction are real and at the same time apparent phenomena, that is, motion is relative and every frame of reference is equal so what one observes/measure is the true value but at the same time after rocket from the upper story comes back in our frame of reference time dilation and length contraction become apparent because length is the same as before the trip and the time should also be the same on both clocks, but maybe you can explain me why I'm wrong.

I still haven't found a proper answer to these question/s. Thank you!!!

2. Apr 20, 2013

### ghwellsjr

The proper answer is very simple: pick an Inertial Reference Frame. Any object/clock/observer moving in that frame is length contracted along the direction of motion and experiences Time Dilation as a function of the speed. The faster it goes, the more the Length Contraction and the more the Time Dilation. When the object/clock/observer stops moving, the Length Contraction and Time Dilation goes away. If the traveler just had a metronome with him, it would tick slower while traveling and then come back to the same tick rate as the Earth's metronome, just like a ruler would only be contracted while traveling. The difference between a metronome and a clock is that the clock has a way to count the ticks of its built-in metronome but a ruler does not have a corresponding accumulator for any length it is marking out during the trip.

So if you pick the IRF in which the Earth remains stationary, them only the traveler's clock will suffer Time Dilation and since it is accumulating those slow ticks, when it gets back, it will have accumulated fewer ticks than the Earth's clock.

Now isn't that so very simple you could explain it to a child?

3. Apr 20, 2013

### Matis

hm....

But metronome ticks slower only for observer on Earth and not for the guy in the rocket, for him his metronome ticks normally. So traveler's clock is accumulating normal "ticks", we only see them as longer here on Earth.
And again, if regardless of the length contraction (which is also function of speed) length after arrival of the rocket doesn't change, why the time should change ?

I'm still not convinced that after this trip ideal clocks will show different time accumulated and that traveler will be younger than the observer.
As I've said in my first post - I believe that time dilation and length contraction are real and at the same time apparent phenomena, that is, motion is relative and every frame of reference is equal to other so what one observes/measure is the true value but at the same time after rocket comes back in our frame of reference time dilation and length contraction become apparent because there will be no difference in length before the trip and after the arrival and also I don't see a reason for different time accumulation if length remains the same..."

4. Apr 20, 2013

### ghwellsjr

I said you can pick any IRF. Do you realize that if you picked a different IRF where the speed of the Earth is not zero, then the Earth's clock would be subject to Time Dilation and Length Contraction. Isn't it obvious that since we can pick any IRF, observers can never be aware of Time Dilation or Length Contraction, can they? And yet you twice said that they are both apparent. They are never apparent. Think about this. If you have a ruler that is Length Contracted but your foot is also Length Contracted, then how would it be apparent? Same thing with your clock. If your clock ticks slower and your heart beats slower, how would it ever be apparent? So get the idea out of your head that Length Contraction and Time Dilation are something that anyone can see or measure, OK? Everything always seems normal to all observers, OK?

Now that you know that, isn't it also obvious that in the IRF in which the Earth is at rest, the Earth's clocks will never be Time Dilated while the traveler's clock and the traveler are Time Dilated during the entire trip? Since the traveler's clock ticks slower and the Earth clock does not, when the traveler returns, his clock will have accumulated less time than the Earth's clock. But when the traveler comes to rest, his clock will start ticking at the same rate as the Earth's clock. That doesn't make the time on his clock suddenly go to a different time, does it? Please, tell me what is so hard to understand about this?

Last edited by a moderator: Apr 23, 2013
5. Apr 20, 2013

### Fredrik

Staff Emeritus
The different times displayed by the clocks are a trivial prediction of SR. But the part of SR that's used to make this prediction is really just an assumption about the numbers displayed by a clock that should be thought of as part of the definition of SR. So it seems that what you're really asking is why SR is a good theory. The only thing that can answer that is a better theory. Unfortunately, the only better theory is GR, and its definition includes the exact same assumption, so it can't tell us why SR is right about this particular thing.

The prediction follows from this statement and the purely mathematical definition of the term "proper time".

This seems a bit illogical. It would have been weird if the clock's ticking rate had not been returned to normal when a meter stick is returned to normal. But the clock will of course display a smaller number if its ticking rate was lower during the trip.

However, the interpretation that its ticking rate was actually lower isn't the simplest one. It's kind of an old-fashioned interpretation that we don't need. The straightforward interpretation of SR is that the clock continued to work the way it always does, and that there's simply "less time" to be accumulated along the path through spacetime that describes the rocket's motion.

6. Apr 20, 2013

### Matis

Can you correct me......
When the rocket is traveling at the constant speed of 0,89c relative to the Earth, the traveler would see everything on the Earth as slowed down and observer on the Earth would see everything on the rocket as slowed down (Galilean relativity principle) ?
At the same time the traveler's clock goes normally for him and the observer's clock goes normally for him, right ?
When we apply acceleration, this Galilean symmetry goes away and than we are sure that the clock on the rocket will count less time because it needed to accelerate first and then decelerate. From GR we know that the acceleration is equal to the gravity and when the clock is influenced by gravity it will go slower, right?

I've totally overlooked this sentence from your first post : "The difference between a metronome and a clock is that the clock has a way to count the ticks of its built-in metronome but a ruler does not have a corresponding accumulator for any length it is marking out during the trip." This sentence clarifies a lot.

@Fredrik

7. Apr 20, 2013

### ghwellsjr

It depends on the relative direction. If two inertial observers are traveling towards each other, they each see the other ones clock sped up, not slowed down. When they pass, they see each others clock slowed down.
Right.
In some special cases of acceleration, you can jump to some conclusions based on symmetry but in all cases, what I described in my first post always works correctly. What if both observers accelerate? Wouldn't you like to know how to handle that situation?
There is no simple answer involving gravity like there is when we ignore gravity which is what we do in Special Relativity. You need to understand SR before you attempt GR.
Well I'm glad you went back and reread my earlier post. I read all of your posts very carefully before I respond and I assume you do the same.

8. Apr 20, 2013

### rbj

this is an unbelievably condescending and arrogant response. besides being wrong and ignoring the issue. ghwellsjr didn't explain anything and is just ignoring the whole premise of the Twin Paradox.

probably this wikipedia article will explain it better than either of us and more accurately than ghw. http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

essentially the twin that is accelerated has it different than the twin that is not accelerated. the accelerated twin changes inertial frames of reference and has to do some accounting of time each time he switches from one inertial frame to another.

9. Apr 21, 2013

### Matis

This is my perception that I've had in my mind and that was "killing" me:

Metronome ticks slower only for the observer on the Earth and not for the guy in the rocket, for him his metronome ticks normally. Traveler's clock is always accumulating normal "ticks", we only see them as longer here on the Earth but on that rocket ticks are always the same, not stretched or contracted. If the traveler's clock is always accumulating normal ticks that always have the same rate and which are only seen as longer from the Earth, from where does different accumulation of time comes if the clock on the Earth never changes it's rhythm nor does the clock on the rocket ? That is, if the traveler's clock has always been ticking normally for him and when he comes back to the Earth, observer on the Earth also sees traveler's clock ticking normally, I've asked my self how there can be different time accumulated.

Now I see that I've got it all wrong.

Last edited: Apr 21, 2013