# Aging in the Twin Paradox

## Recommended Posts

No, it's real. Moving clocks run slower than stationary clocks. This has been confirmed by a number of experiments and is continually tested by GPS satellite atomic clocks. (There are also effects of general relativity to consider, but the special relativity effects are well-established)

yes i accept this,the clock is affected by velocity at a miniscule level.what im trying to ask is i send the twin at a velocity in the upper atmosphere say for 10years thus GR says at his velocity he would age half the amount of time i would .He is at a height that i can observe him.when my observation of him reached 10years he would not be still circling me for another 10 years.He might land and his clock says 5 years have past but he would still land 10 years from now. From my framepoint if the universe is infinite and 14.5 billion years old thats how old it is period,something traveling at .866c from the beginning of the bigbang hits me now but if the math was correct in the twin paradox sense from the objects framepoint on its way to me has only taken what a very small fraction of the time.Thus to IT the universe wouldnt be 14.5myr which doesnt make sense.You cannot exist out of time,or be at a point in space which is measured to be 14.5myo and to the object the universe is younger.

I may be wrong but perhaps i suggest its how we measure time that creates the conflict,its only a perception an illusion we have,maybe if we actually experimented with actual people wereby they would come back 20 years from now and we all were aged by the same amount but the clock still said he had been gone only 5 we would realise our mistake in theories.

Dont flame me id appreciate someone helping me out to understand if im wrong.

Basically i feel that if my rocket does 30mpg travelling at 100mph,simply putting my foot down to increase velocity to 600mph.I still wont get more than 30mpg out of my tank of fuel.so make the velocity 70,000 mph and apart from waiting for friction to slow it down the fuel wouldnt feel like it lasted longer it would be used up in an instant,so we have a conflict surely its velocity would from its frame point make it last longer than the opposite of what we observe.(i know that my example of the velocity isnt possible with a few gallon of petrol,but its hypothetical)

##### Share on other sites

in 4-dimentional space framework...it has been said that "everying" (particle to planet) is moving at light speed in space-time. (from "the Elegant universe" by Brain Greene )

it seems impossible...but...it states that things appeared stationary are the way they are because they are moving in time dimention only and not in space dimentions..(at light speed of course...)

if you consider a photon, it is moving in space dimentions only and not in time dimention ( so they haven't aged a single atto-second or whatever since the big bang, from a single photon point of view there is no sense of time at all ...coz no one (no other photo) has struck it and tell that "hi i m here and u r there"...or "how u doing!" simply because they are moving at unifrom velocity and from their frame of reference they all agreed that they are moving at light speed.....and they will never catch each other (i would neglect the collation of two photo to simplify this line of thinking) )

so any other things moving lower than light speed are just diverting their velocity from time dimention to space dimention)

simply put....if a thing is moving at 100mph ...it's velocity in the passage of time ( is slow down the same amount ).....

(this may not be precise as an list of equations but just the idea..)

##### Share on other sites

Janus, I noticed from the past threads that you posses a lot of knowledge on this subject, and I cant tell you how grateful I am for helping me out here. Thanx pal.

Thanks to all the others who have put their inputs also.

The one which changed velocities is the one that felt the forces of acceleration. If I'm driving down the road, and I hit the brakes, I will see the car next to me seemingly accelerate forward. However, anyone can tell which of the two of us actually changed velocities by watching to see which of us is either thrown forward into his seat belt or pushed back into his seat.

Yes, everyone can tell by watching, as you say, which implies that the acceleration is viewed from a particular reference frame (i.e. the observer’s). Assuming the cars are in outer space, and there are no observers, and their relative speed changes, how can you know which one actually accelerated?

I think it’s similar like the free fall. Imagine a ball moving with constant acceleration (like free falling), while you’re standing in the air on a plane platform. I cant see a way to tell which of the two (the plane or the ball) actually does the accelerating. Isnt that why there even is a General Theory of Relativity, so that it expands the concept of relativity to accelerated movements?

This also means that he will see a different time differential, then the Earth observer would.

So the Earth and ship reference frames are not equaly valid. But you’re talking about a changing acceleration rate in your example (as one keeps moving away from Earth). Mind you, if acceleration is constant during the entire experiment, there wouldn’t be difference between the two viewpoints. Which brings us back to the previous question.

Now your twin brother could not travel at c, but he could travel at .866c. In which case, you would would see him age at half speed and only age 4 min during the trip. He on the other hand, would measure the distance between Sun and Earth as only half that that you did (length contraction) and for him the trip would then take only 4 min. Thus both of you agree that he aged only 4 min during the trip.

Are you talking about the Twin Paradox (acceleration taken into account), or just two twins moving with diff velocities with relation to each other?

Sounds to me like it’s the second example (without acceleration), in which case I must admit the explanation sounds logical, but having never considered this particular example, I find some contradicting things with my present understanding. In that case, the “travelling” twin brother would measure only 2 minutes for his brother on Earth, no? (because each observer always measures the other’s time rate as slower, in this case by half.) And the Earth twin would measure entire 8 minutes on his watch. Now, this refutes itself a bit doesn’t it?

In his frame, that deceleration looks like a force (so he would feel like he has weight in the direction of motion). The other twin (who doesn't move) feels no force.

I dont think so. The reason why we feel weight pressure is because the ground we’re standing on. Gravitational force still works on an astronaut in orbit, but he doesn’t “feel” it, exactly like if he was hypotetically outside any force field.

##### Share on other sites

I may be wrong but perhaps i suggest its how we measure time that creates the conflict' date='its only a perception an illusion we have,maybe if we actually experimented with actual people wereby they would come back 20 years from now and we all were aged by the same amount but the clock still said he had been gone only 5 we would realise our mistake in theories.

[/quote']

It's independent of the type of clock. It's an inherent change in the passage of time.

##### Share on other sites

Relativity doesn't like absolutes.

it does like absolutes. space and time may not be absolute, but space-time is.

##### Share on other sites

No, it's real. Moving clocks run slower than stationary clocks. This has been confirmed by a number of experiments and is continually tested by GPS satellite atomic clocks. (There are also effects of general relativity to consider, but the special relativity effects are well-established)

Moving relative to what? When a satellite orbits the earth, they are both moving around the sun. And, the satellite is generally moving slower than the earth wrt the sun for half of it's orbit, and faster for the other half. So when you state that moving clocks run slower, you really have to be specific as to what you're using for comparison.

##### Share on other sites

Moving relative to what? When a satellite orbits the earth, they are both moving around the sun. And, the satellite is generally moving slower than the earth wrt the sun for half of it's orbit, and faster for the other half. So when you state that moving clocks run slower, you really have to be specific as to what you're using for comparison.

In comparison to the stationary clock, i.e. the observer (when in an inertial frame)

##### Share on other sites

I may be wrong but perhaps i suggest its how we measure time that creates the conflict' date='its only a perception an illusion we have,maybe if we actually experimented with actual people wereby they would come back 20 years from now and we all were aged by the same amount but the clock still said he had been gone only 5 we would realise our mistake in theories.

Dont flame me id appreciate someone helping me out to understand if im wrong.

[/quote']It should not matter whether we use clocks or real people to test the theory. In practice it is easier to use the clocks! The results, using clocks, confirm the theory:

"During October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40+/-23 nanoseconds during the eastward trip and should have gained 275+/-21 nanoseconds during the westward trip ... Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)

##### Share on other sites

In comparison to the stationary clock, i.e. the observer (when in an inertial frame)

Since when is a stationary clock, on earth, truly inertial? There is no inertial frame. We use that term wrt the earth with the understanding that's it not true, but is convenient. Everything is moving relative to something else. The claim of relativity seems to suggest that every moving frame (whether you want to approximate it as inertial or not) has a valid claim to the statment that every other moving object is aging slower.

##### Share on other sites

Since when is a stationary clock, on earth, truly inertial? There is no inertial frame. We use that term wrt the earth with the understanding that's it not true, but is convenient. Everything is moving relative to something else. The claim of relativity seems to suggest that every moving frame (whether you want to approximate it as inertial or not) has a valid claim to the statment that every other moving object is aging slower.

I never said the earth was an inertial frame. I did in fact say there were GR effects for which you had to account.

Yes, that claim can be made. And the only way to compare the clocks side-by-side is for one of them to undergo an acceleration, so there is no contradiction involved.

##### Share on other sites

I never said the earth was an inertial frame. I did in fact say there were GR effects for which you had to account.

Yes' date=' that claim can be made. And the only way to compare the clocks side-by-side is for one of them to undergo an acceleration, so there is no contradiction involved.[/quote']

As it has been stated here earlier, the acceleration is simply a means to an end. The difference in velocity is what is supposed to account for the difference in clock rates. So the relative difference in velocities results in a real physical difference, ie the clocks rate changes? The relative difference in velocities is arbitrary. How can the subjective choice of a random reference frame cause a real physical change in anything. And, as I said earlier, that leads to the conclusion that every other reference frame out there is running slower than my own. Since that cannot be true for everyone, it cannot be a real physical change. It must simply be observed.

##### Share on other sites

Are you talking about the Twin Paradox (acceleration taken into account)' date=' or just two twins moving with diff velocities with relation to each other?

Sounds to me like it’s the second example (without acceleration), in which case I must admit the explanation sounds logical, but having never considered this particular example, I find some contradicting things with my present understanding. In that case, the “travelling” twin brother would measure only 2 minutes for his brother on Earth, no? (because each observer always measures the other’s time rate as slower, in this case by half.) And the Earth twin would measure entire 8 minutes on his watch. Now, this refutes itself a bit doesn’t it?

[/quote']

The problem here is that you are not taking into account the Relativity of Simultaneity. Imagine that each of your twins has a stop watch. The Earth twin starts his watch when he determines that the traveling twin passes the sun. He stops his watch when the traveling twin passes the Earth. If the relative velocity is .866c then this will take 9.24 mins according to his stop watch.

The traveling twin starts his stop watch as he passes the sun and stops it as he passes the Earth. since the distance between the two is 1/2 as measured by him, it will take 4.62 mins according to his stop watch.

The earth twin also sees that his brother starts his watch as he passes the sun and stops it when he passes the Earth and , due to time dilation sees his clock as running at half speed and thus it measures 4.62 mins.

This leaves what the traveling twin sees as happening to the Earth twin's clock. He will see it running at 1/2 the rate of his own, and during the time it takes to travel from sun to Earth he will indeed see the Earth clock accumulate 2.31 mins. BUT, he will not determine that the Earth twin started his watch when he passed the sun, He will in fact determine that his brother started his watch some 13.86 mins before he passes the Sun. This plus the 4.62 minutes it takes for him to travel to the sun means that by his clock his bother's clock ran for 18.48 mins, which at the 1/2 time dialtion rate means that he will expect the Earth twin's stop watch to read 9.24 mins as he passes the Earth. Both agree as to what each other's clocks read when they have stopped.

##### Share on other sites

I see Janus, but just one more thing. Shouldnt then the Earth twin observe the same Simultanity effects, since the two events (starting the earth clock, passing the sun) are also seperated by a distance? This is not in your calculations. I wonder why?

And you didnt respond to the question I asked you above about determening the acceleration. If you could please explain that too, I'll be forever grateful.

I know I'm a pain in the ass, if that helps.

##### Share on other sites

I see Janus' date=' but just one more thing. Shouldnt then the Earth twin observe the same Simultanity effects, since the two events (starting the earth clock, passing the sun) are also seperated by a distance? This is not in your calculations. I wonder why?

[/quote']

There is nothing that prevents two events that are separated by distance from being simultaneous in any given frame, it is just that the two events can not be simulataneous in both frames when the the frames have a relative velocity to each other.

All the Earth twin has to do in order to start his watch at the instant his Brother passes the Sun is to know his brother's position and speed at some time before he passes the Sun. For instance, he could spot him with a telescope while he is still two hrs away. Then by factoring in his measured distance and speed (taking into account the amount of time it took for the light to travel this distance), he can calculate exactly when his brother passes the sun by his reckoning, and start his watch accordingly.

The traveling twin waits until he sees his brother start his watch. and then "backtracks" the light carrying that info to determine exactly when his brother started his watch by the traveling twin's reckoning. Doing so causes him to determine that his brother started his watch before he passed the sun.

Thus two events: The starting of the Earth twin's watch and the traveling Twins passing of the sun are simultanteous in one frame, but not in the other.

##### Share on other sites

Yeah, I got that already, but..

Janus, you wrote earlier:

The traveling twin starts his stop watch as he passes the sun and stops it as he passes the Earth. since the distance between the two is 1/2 as measured by him, it will take 4.62 mins according to his stop watch.

The earth twin also sees that his brother starts his watch as he passes the sun and stops it when he passes the Earth and , due to time dilation sees his clock as running at half speed and thus it measures 4.62 mins.

The travelling twin starts his watch when he passes the sun, thus the two events are simultanious in his frame. However, the Earth twin cannot see his brother starting his watch as he passes the sun (as you wrote), because from his frame (which is moving at some speed relative to his brother's ref frame) the two events cannot happen at the same time. Which is what I asked you, why this effect wasnt taken into account by you.

"Assuming the cars are in outer space, and there are no observers, and their relative speed changes, how can you know which one actually accelerated?

I think it’s similar like the free fall. Imagine a ball moving with constant acceleration (like free falling), while you’re standing in the air on a plane platform. I cant see a way to tell which of the two (the plane or the ball) actually does the accelerating. Isnt that why there even is a General Theory of Relativity, so that it expands the concept of relativity to accelerated movements?"

thanx again.

##### Share on other sites

Yeah' date=' I got that already, but..

Janus, you wrote earlier:

The travelling twin starts his watch when he passes the sun, thus the two events are simultanious in his frame. However, the Earth twin cannot see his brother starting his watch as he passes the sun (as you wrote), because from his frame (which is moving at some speed relative to his brother's ref frame) the two events cannot happen at the same time. Which is what I asked you, why this effect wasnt taken into account by you.

[/quote'] But they do happen at the same time according to both frames. These two events (the starting of the traveling twin's Watch, and his passing the sun ) are not separated by distance. In fact, you could add something like a rod sticking out from the the sun which, when it hits the watch, starts it. Both observers will agree that it is the collision with the rod that starts the Watch. It is when the events involved are separated by distance from each other when you must take Relativity of Simultaneity into account, not when the events take place at the same place and the observer is some distance away.

"Assuming the cars are in outer space, and there are no observers, and their relative speed changes, how can you know which one actually accelerated?

I think it’s similar like the free fall. Imagine a ball moving with constant acceleration (like free falling), while you’re standing in the air on a plane platform. I cant see a way to tell which of the two (the plane or the ball) actually does the accelerating. Isnt that why there even is a General Theory of Relativity, so that it expands the concept of relativity to accelerated movements?"

thanx again.

Again, the one that accelerates is the one that will experiences the forces of acceleration.

SR is perfectly capable of dealing with accelerations, as long as they take place in flat space (no gravity). If you introduce gravity into the equation then you must invoke GR. With a your falling ball/airplane example, There are two effects to account for: The relative velocity between Plane and ball and the changing of gravitational potential between the two. From the plane's perpective, the ball is both gaining speed and losing gravitational potential. From the ball's point of view, the plane is gaining speed and gaining gravitational potential.

##### Share on other sites

Forgive my lack of science but ive always found the scenario of the twin paradox impossible.We have mass and we know it would take an infinite amount of energy to propel us to LS so even theoretically we cannot ever go LS

This is a common misconception that my high school physics teacher had. If you think about it, this would mean when your velocity is near LS (relative to what, btw) you would be able to measure this because you would have an increase in mass, and therefore not a equal and therefore valid frame of reference.

In reality you can accelerate as much as you want, but your time relative to others and vise a versa will change so as no observer sees you going faster than LS.

Back to the original question, the time dilation happens to the twin accelerating away, but for them to arrive back at earth they have to make the return journey and so oppisate acceleration and time dilation, making a mean 0 difference.

##### Share on other sites

What do you mean by a "mean zero difference"? if your talking in terms of total time expreinced then your dead wrong.

The noninertial twin always exprinces less time this is as in Minkowski spacetime the worldline of inertial observers are geodesics and therefore (because of the signtaure ofw the Minkowski metric) an observer whose worldine is a geodesic between two events will experince the maximal amount of time between those two events.

##### Share on other sites

Back to the original question' date=' the time dilation happens to the twin accelerating away, but for them to arrive back at earth they have to make the return journey and so oppisate acceleration and time dilation, making a mean 0 difference.[/quote']

1. time dilation always happen's to the "other guy". In other words, whch of the two time dilation 'happens to" depends on which twin you ask.

2. Acceleration does not cause time dilation to happen to the Traveling twin. The only time dilation that happens to him is that measured by his Earth twin, and that is only due to their relative velocity.

3. What acceleration does do is effect how the traveling twin measures the time rate for his brother. This effect is determined by three factors: The magnitude of the acceleration, the direction of the acceleration with resepect to the Earth twin, and the distance between the brothers as measured along the axis of the acceleration.

Thus, as far as the Earth twin is concerned, his brother's time runs slow for basically the entire trip due to his relative velocity.

As far as the Traveling twin is concerned, While he is accelerating away, his brother's time run slow for two reasons: The increasing relative velocity, and the acceleration he himself experiences.

When he is turning around and accelerating back, he also sees two effects: a slowing down due to relative velocity, and a speeding up due to his acceleration. The speeding up is due to the fact that this acceleration is towards the Earth and not away. Also, since this acceleration happens when the ship is further away from the Earth, this speeding up is greater than the slowing down that occured during the first part of the trip due to the earlier acceleration. In fact, this speeding up effect is so great that it overshadows the slowing down measured by the relative velocity also.

If you add up all the combined slowing down and speeding up of the Earth clock measured by the traveling twin, it will add up to the exact same difference in elasped time between the twins as the Earth twin measures.

For example, if the Earth twin determines that the traveling twin aged 3 yrs while he aged 6 yrs, the Traveling twin will also determine that he himself aged 3 yrs while his brother aged 6. (the Traveling twin determines that the trip took 3 years for himself because due to length contraction, the distance between himself and the Earth is shorter for him at max distance, then it is as measured fromthe Earth.)

Thus both twins agree as to who aged more and by how much, they just don't agree upon how it came about to be that way.

##### Share on other sites

You're right. How could i not notice that the two events happen on the same place.

For now, i'll suffice with understanding SR, without the accelerations and GR.

One final question, janus. (i hope i dont make a fool out of myself this time too)

in the example with the traveling twin from the sun to the earth (no acceleration), you logically concluded that in the end, the "travelinng" one would measure less time than the earth twin, for which they would both agree. Consequently, he'll be younger than his earth brother. where's the acceleration here, which we said is needed in order one of the twins to realistically age? If there's only relative motion between them (no accel), then I would expect none of them to grow older than the other.

(i thought about what's the difference that makes the two ref frames not look symetrical, and i concluded it's the fact that the distance Sun-Earth is fixed with the earth twin time frame. However, i cant incorporate this fact in the theory, and just how exactly it makes the twins age differently, if at all, or its really just another one of my brainfarts)

i admire ur willingness and persistance to work with slowminded guys like me.

##### Share on other sites

You're right. How could i not notice that the two events happen on the same place.

For now' date=' i'll suffice with understanding SR, without the accelerations and GR.

One final question, janus. (i hope i dont make a fool out of myself this time too)

in the example with the traveling twin from the sun to the earth (no acceleration), you logically concluded that in the end, the "travelinng" one would measure less time than the earth twin, for which they would both agree. Consequently, he'll be younger than his earth brother. where's the acceleration here, which we said is needed in order one of the twins to realistically age? If there's only relative motion between them (no accel), then I would expect none of them to grow older than the other.

(i thought about what's the difference that makes the two ref frames not look symetrical, and i concluded it's the fact that the distance Sun-Earth is fixed with the earth twin time frame. However, i cant incorporate this fact in the theory, and just how exactly it makes the twins age differently, if at all, or its really just another one of my brainfarts)

i admire ur willingness and persistance to work with slowminded guys like me.[/quote']

Acceleration is only a factor when you start with both physically in the same frame, and then physically return them to the same frame at the end (classic twin Paradox).

In the no-acceleration case, the twins are never in the same inertial frame. In this case, the answer lies in the Relativity of Simultaneity. Here we are measuring how much time passes between two events (the starting and stopping of each watch), and determining how much time passes for each between these events. For one twin, both watches start and stop at the same time, while for the other, his brother starts his watch long before he starts his own.

As an exercise, try this: Just as we assumed that there was a pole sticking out from the side of the sun that starts the traveling twin's watch, there is a long pole sticking out from the front of the traveling twin's ship. This pole is such a length that from the Earth twin's measurement, its length is equal to the distance from Sun to Earth. It is this pole striking the earth twin's watch that starts it.

Now, taking time dilation and length contraction into account (remembering that both see each other's clock as running slow, and that both see distances in the others frame as contracted), What is the sequence of events according to each, if they have a relative velocity of .866c.

It might help if you drew diagrams that show the relative length of the traveling twin's pole compared to the distance between Earth and Sun,as seen from Both Twin's frames.

##### Share on other sites

Janus, I drew the diagrams you suggested, sort of like a final test for you to see if I’ve completed the course in relativity. Lol. I hope they are fine. (the colour of the lines indicates the position of the traveling twin) EDIT: there seems to be a mistake in pic 1 - the pole length is obviously 20, not 40 as it's written in the parameters.

Now, the problem i had wasn’t with the diagrams, but i was wondering if some of the twins actually aged more than the other. What you have said in the first sentence, about both twins in the same frame, opened me new view. Therefore, i figured myself (could be wrong though) that for the term aging only to have sense, we have to put the twins in the same frame, because if they are in diff frames moving with relative velocity to one another, than we cannot measure aging, because events don’t happen at the same time. I tend to think in absolute terms, and that’s why i had difficulties grasping that aging can only be determined relative to one frame. I think i’m right this time, cause if i’m not, i’ll probably have to rethink my whole concept of relativity.

I beg you for one answer more. It’s short:

How do you measure a distance between two points, if one of them is static (has 0 velocity relative to you), and the other one moves with near c velocity relative to you? Is there length conraction in this case?

I hope this answer can help me a lot in the final demystification of SR.

## Create an account

Register a new account