# Is age relative?

We well know that time is relative according to the Special Theory of Relativity. So, a person on a spaceship close to the speed of light (~c) could go on a trip for some years, return and find out that he is still young, while his friends or relatives are already very old or gone. This happens because the observers on earth see the clockticks on the spaceship go slower. Now, speed is relative, so the observer on the spaceship sees the earth frame of reference move away with the same speed. So he reaches a similar conclusion, that clocks on earth go slower so that he would expect to find his relatives younger than usual. Now this is the contradiction or paradox as we may say: time is relative, ok, but is grey hair relative? Certainly not. Only one of them could be younger than usual.
When I was discussing this paradox in 33rd IPHO, Indonesia, some said that the two frames of reference are not equivalent. One accelerates, while the other stays at constant velocity. So the laws of physics are not valid for the observer on the spaceship while it accelerates. I agree. But what happens when the spaceship ceases to accelerate and is in constant velocity? It is an inertial frame of reference as good as the earth is, the physical laws hold. So the observations of the guy on the spaceship are correct and the observations of the persons on the earth are correct as well. Both parties observe that the clocks on the other frame of reference run slower. Isn't this now a paradox? I've thought long about it. If somenone has any idea, I would appreciate their opinion.

Time is relative, the speed of time is not. Every observer is traveling to the future at 1 second per second, each one with its second lenght depending on the speed.

ramollari - You're initial analysis of the situation is correct, the fact that at some point in the journey the twin in the rocket has to undergo an acceleration to change direction to come back allows us to determine that with respect to us here on earth, he is the one really moving, so it's his clock that actually runs slow.

Another interesting discussion of this paradox which uses the relativity of simultaneity can be found in "A First Course in General Relativity" By Bernard Shutz. To paraphrase: If you draw a two dimensional space-time diagram, with one axis being time, the other being space, you notice that on the outward journey the rocket twin's line of simultaneity includes the the departure event and so you can't say whose clock is really running slowly. But, once the rocket twin changes direction, she changes inertial frames and her line of simultaneity shifts to the return event, and she sees the earth twin age incredibly quickly.

geometer said:
ramollari - You're initial analysis of the situation is correct, the fact that at some point in the journey the twin in the rocket has to undergo an acceleration to change direction to come back allows us to determine that with respect to us here on earth, he is the one really moving, so it's his clock that actually runs slow.

Another interesting discussion of this paradox which uses the relativity of simultaneity can be found in "A First Course in General Relativity" By Bernard Shutz. To paraphrase: If you draw a two dimensional space-time diagram, with one axis being time, the other being space, you notice that on the outward journey the rocket twin's line of simultaneity includes the the departure event and so you can't say whose clock is really running slowly. But, once the rocket twin changes direction, she changes inertial frames and her line of simultaneity shifts to the return event, and she sees the earth twin age incredibly quickly.

I don't quite understand your second argument, i'd need to consider it more closely. Regarding the first argument, I think that you're correct in that we can make a difference between the two frames of reference: they are not equivalent. Maybe there's some more detailed theory behind this paradox. But the the way time dilation is generally explained is too simplistic. It doesn't take any factors like acceleration into consideration.

ramollari said:
I don't quite understand your second argument, i'd need to consider it more closely. Regarding the first argument, I think that you're correct in that we can make a difference between the two frames of reference: they are not equivalent. Maybe there's some more detailed theory behind this paradox. But the the way time dilation is generally explained is too simplistic. It doesn't take any factors like acceleration into consideration.

The relativity of simultaneity resolution of the twin's paradox is much easier to understand graphically. It basically uses the fact that relativity did away with the idea of absolute simultaneity also.

The equation for time dilation falls right out of the definition of proper time if you differentiate proper time with respect to coordinate time.

The relativity of simultaneity resolution of the twin's paradox is much easier to understand graphically. It basically uses the fact that relativity did away with the idea of absolute simultaneity also.

Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous. The simultaneous condition of the source may be established by synchronizing the two sources at the observer then moving them away each in the same manner to points that are equal distance.

You now have established a circle or sphere of simultaneity. If the observer moves the two sources are not influenced by his change of position and therefore remain simultaneous. The observer however no longer sees the flashes of light simultaneously but will see all points that are now equal distance from his position as simultaneous, thus establishing another circle or sphere of simultaneity. It must follow then that if the two simultaneous circles intersect both circles must be simultaneous.

Since an infinite number of circles may be simultaneous in both cases then all possible points in the universe must be simultaneous. You may also move the observer to an infinite number of positions with also the same results.

Einstein’s theory not only does not disprove simultaneity but it requires it. Einstein’s theory is a theory of relative observation not reality.

Einstein’s theory using simultaneity resolves the problem of time travel. If all things in the universe occur at the same time, then it is impossible to arrive before an action takes place even if you exceed the speed of light.

Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous.

OK if your observer is at rest, in relation to the light sources one in front of him/her and one behind, but travelling a say 90% of the speed of light. how do you get the idea that the light from both arrives at the observer at the same time???

Twistedseer

4newton said:
Einstein’s theory not only does not disprove simultaneity but it requires it. Einstein’s theory is a theory of relative observation not reality.

The failure of simultaneity is an inescapable aspect of Relativity. Consider two space-time coordinate systems A and B. We'll condense the space axes down to one, the x-axis. And, we will call the speed of light 1 just to make things simpler. Now, assume B is in motion with respect to A with some velocity v. Now, let's look at what B's axes look like with respect to A when A and B's origins coincide.

Since B is in motion with respect to A, B's clock is running slower than A's so B's time axis is inclined at some angle with respect to A's time axis (the tangent of the angle will give you B's velocity).

Now, to find where B's x (space) axis lies with respect to A's x axis, we switich for a second to B's frame. Consider a beam of light emitted from an event at x = 0, t = -a in B's frame. This beam will reach B's x axis at x = +a since in our coordinate system, c = 1, which means light travels at a 45 degree angle with respect to where it is emitted or reflected. If it is reflected back to the t axis, it will arrive at t = +a. So, we can consider B's x axis as the locus of all events that reflect light rays in such a manner that they return to B's t axis at +a if they left it at -a.

Drawing B's x axis to satisfy this property, remembering the fact that the velocity of light is constant for all observers regardless of the state of motion of the source, (in other words we need to maintain the 45 degree thing) we find B's x axis makes some angle with A's x axis. In other words, the two x axes don't coincide. What this means is that events that are simultaneous in A's frame are not simultaneous in B's frame.

Twistedseer:
OK if your observer is at rest, in relation to the light sources one in front of him/her and one behind, but travelling a say 90% of the speed of light. how do you get the idea that the light from both arrives at the observer at the same time???
This is the Einstein experiment. His first condition was in a rest frame, no velocity. This is the proper time frame. This was Einstein’s starting point. He showed that two light, or all light, sources at equal distance reached the observer at the same time.

The second condition of his experiment is your description of a moving frame. He showed that the time of the arrival of the two flashes is dependent on the velocity of the moving frame. That is relativity of observation and action. Since no action or light can reach another point faster than the speed of light.

Change of position or velocity has no effect on the two sources of light, if they were simultaneous they remain simultaneous no matter the action of the observer.

4newton said:
Change of position or velocity has no effect on the two sources of light, if they were simultaneous they remain simultaneous no matter the action of the observer.

Not so. Any events that appear simultaneous to frame A, will not appear simultaneous in any frame in motion with respect to A.

geometer:
Not so. Any events that appear simultaneous to frame A, will not appear simultaneous in any frame in motion with respect to A.
The key word in your reply is “appear” relativity only applies to observation or actions at a distance, the condition of the limitation of the speed of light.

If you have two lights flashing at the same time in the same place you of course consider their action to be simultaneous. Their action of simultaneous flashing does not change with your change of position. If you now move the two lights just a few feet apart their flashing will stay simultaneous again your change of position has no effect on the flashing lights only your observation changes. This is the difference between real and observed.

In Minkowski space-time all frames of zero velocity, proper time, have clocks that tick at the same rate independent of position. SR only considers moving frames. You can not take a proof that started from a zero reference frame, proper time, then take your results and change the source of your proof.

The twin paradox continues to be a paradox - it is not resolved by acceleration, either at the beginning of the outward bound journey, nor at the turn around point. The triplet version of the event eliminates any acceleration (outbound traveler simply transfers his clock reading to an inbound traveler without slowing down) - moreover, even if acceleration forces were experienced, they have no effect upon local time except to the extent they modify the velocity), and any shift that is experienced by the distant twin as he observes the earth clock cannot actually add time to the earth bound twin's clock... this time shift if it is actually observed can only be apparent, and for the two twins to have different ages, the time difference(s) must be actual - which presumes some physical cause.

Follow up - I think it was Michio Kaku in one of his recent popular treatise on SR that he posed the question of what happens if the traveling twin never turns around - could we live in a universe where each twin continues to be younger than the other?

Fredrik
Staff Emeritus
Gold Member
The twin paradox is not a paradox. SR is very clear about what actually happens. Both twins will see the other aging more slowly, but when the spaceship has turned around the astronaut twin will be in another inertial frame than he was before, and in that frame his twin on earth is (still) aging more slowly than him, but is much older than him to begin with.

This may be difficult to understand, but it's not a contradiction, and not a paradox.

I'm surprised that no one in this thread has mentioned that there are lots of other threads about the twin "paradox" in this forum. It seems like a new one is opened up once a week. My suggestion to those of you who are interested is that you read those. This is one of them. You can find the others by using the search feature.

geometer: I agree with your recommendation of Schutz's book, and most of what you said. But please don't say things like "he is the one really moving". It hurts my eyes.

Geometer and yogi:
If again you look at Minkowski space-time you find that clocks do not measure time. In Minkowski space-time proper time is the same everywhere. In Minkowski space-time diagram all vertical lines are proper time transition lines and all horizontal lines are spatial transition lines. Light is on a line that is 45 degrees to both lines. This is because light must travel at the speed of light in the spatial dimension and all things are also transitioning in the time dimension at the same rate as the speed of light.

In Minkowski space-time light starts from source S on proper time line A and transitions to proper time line B. light then returns back to proper time line A and arrives at proper time line A at the same point where source S has transition to on time line A.

You now have a condition that source S has moved only in time from S0 to S1. Light has transition from S0 to B1 and back to S1. Both the transitions of S0 to S1 and the transition of light occur in the same amount of time. The transition of light must then be faster that the speed of light in space-time. The products of space and time do not vector add to a limited transition to the speed of light.

If you now take the two twins and one twin again takes off from earth at S0. Twin 1 then travels at a rate a little less than the speed of light to some point B1. Twin 1 then turns around and heads back toward earth at the same speed and reaches earth when earth is at point S1.

Twin 1 must exceed the speed of light in space-time to arrive back on earth. If he did not exceed the speed of light in space-time he would never be able to return to earth at the location that he left. He would drop behind the proper time of earth and disappear from our universe forever.

All frames therefore must stay in proper time and as we have proved before in posts 6,9,11 all actions in proper time are simultaneous.

At the same time that twin 1 is on his trip his clock slowed down. On returning to earth he finds his clock is way behind proper time. Clocks therefore do not control real time. Clocks do have a relation with real time but that is another thread,

There is no twin paradox of SR. Minkowski space-time is based on SR. As you can see Minkowski space-time is the correct interpretation of SR. It does clear up many misconceptions about SR. there are rest frames in SR Anything on the proper time lines is in a rest frame. The speed of light does not limit transitions in space-time, and clocks do not indicate real time. Real or proper time is absolute. Real actions, simultaneity, is the same everywhere in the universe under all conditions.

4NEWTON - that is an interesting analysis - but if clocks don't measure real time - what do they measure? Reminds me of the comment by William Randoff Hursh: if "burd" doesn't spell "bird" what the hell does it spell ?

The explanation of the TP is almost always resolved by postulate - not by any physical evidence - we have no reason to suspect that simply changing from one reference system to another causes any physical event to occur that is going to result in an age difference when the twins are reunited. You as well as all those who rely upon this assumption do not have an evidenciary basis - what we do know is that decaying particles live longer when they are traveling at a high velocity with respect to the earth frame (the one way twin paradox with no turn around) - we have never done the twin experiment although we have flown clocks around the earth and measured that they log different times with respect to each other and the earth centered reference frame in which they were synchronized - this looks to be a real time dilation consequence.

For those who wish to read the many hundreds of articles dealing with the twin paradox with an open mind, they will be surprised find some very intelligent, educated and thinking persons in universities all over the world, who believe the issue is unresolved. The successes of SR are legion, but the explanations that attempt to resolve this particular aspect of the theory are not at all consistent with one another.

Fredrik
Staff Emeritus
Gold Member
yogi said:
we have no reason to suspect that simply changing from one reference system to another causes any physical event to occur that is going to result in an age difference when the twins are reunited.
This comment makes it clear that you have misunderstood SR, and in particular the concept of simultaneity and the resolution of the twin "paradox". No one has said that the change from one frame to another will cause any kind of event to occur.

In one frame, a certain set of "slices" of space time (technically 3-dimensional spacelike hyperplanes) can be thought of as "space, at different times". (Each "slice" consists of events that are simultaneous in that frame). In another frame, a completely different set of "slices" are "space, at different times". That is what you need to understand to understand the twin "paradox".

yogi said:
...but the explanations that attempt to resolve this particular aspect of the theory are not at all consistent with one another.
So? That's probably true, but if it is, it only means that some of them did something wrong. There are plenty of ways to misunderstand SR.

I suggest you explain your analysis to Selleri, Resnic and some of the others who have written college text(s) on relativity .. and who have come to entirely different conclusions re the twin(s). Your comment is typical of relativists - "if you don't see it my way, you just dont understand relativity"
Only problem is, there are several different relativity churches each preaching a different gospel, and they all claim to be absolutely right

The simple fact of the matter is, if two clocks log different ages between the time they are separated and the time they are returned to the same reference frame, there must be a physical reason - you can take all the time slices you want, but what you get is observational information - from which you make a transition to real time discrepency. All explanations purporting to resolve the paradox of the twin(s), somewhere in the analysis, make this shift (sometimes the transition is subtile, but it is always there).

Einstein intuited that a returning two-way traveler would log a lesser time than a clock which remained in the same frame (1n 1905 - long before there was any evidence of actual time dilation). He guessed that the answer was somehow connected with the turn around acceleration. But we now know that acceleration (in and of itself) has no influence upon local clock rate. Any effect can only be observational vis a vis what the returning twin judges to be a change in the earth time (if he does in fact so observe). Moreover- in the triplet version - there are no accelerations.

pervect
Staff Emeritus
yogi said:
I suggest you explain your analysis to Selleri, Resnic and some of the others who have written college text(s) on relativity .. and who have come to entirely different conclusions re the twin(s). Your comment is typical of relativists - "if you don't see it my way, you just dont understand relativity"
Only problem is, there are several different relativity churches each preaching a different gospel, and they all claim to be absolutely right

There are in fact many different explanations for the twin paradox. The specific objection that there are "too many" explanations is even covered in the sci.physics.faq.

faq said:
Too Many Explanations: a Meta-Objection

An old lawyer joke:

"Your Honor, I will show first, that my client never borrowed the Ming vase from the plaintiff; second, that he returned the vase in perfect condition; and third, that the crack was already present when he borrowed it."

Or to quote Shakespeare: "Methinks the lady doth protest too much."

Why so many different explanations? Are the relativists just trying to bamboozle their opponents? To prevail, a defense attorney just has to stir up doubt about the plaintiff's case; she's not required to give her own theory of what happened. But a physical theory should tell a single coherent story.

Relativity here pays the price of permissiveness. It says to us, "Pick whichever frame you like to describe your results, or use spacetime diagrams and don't choose a reference frame at all. They're all equivalent, I don't mind." No wonder that one explanation ends up looking like three or four.

Most physicists feel that the Spacetime Diagram Explanation is the most fundamental. It does amount to a sort of "Universal Interlingua", enabling one to see how superficially different explanations are really at heart the same.

Note specifically that the math is not ambiguous. One can generate a large number of different English explanations. The math, however, is very clear about which clock reads a longer time - there are no "different" versions of relativity as Yogi attempts to claim. Relativity unambiguously tells one what clocks read when they are reunited after a journey through space-time, and which one readds the longest.

The reference for the original quote:

Too Many Explanations

A reference to the entire sci.physics Twin Paradox FAQ

yogi said:
The simple fact of the matter is, if two clocks log different ages between the time they are separated and the time they are returned to the same reference frame, there must be a physical reason - you can take all the time slices you want, but what you get is observational information

so far so good

yogi said:
- from which you make a transition to real time discrepency. All explanations purporting to resolve the paradox of the twin(s), somewhere in the analysis, make this shift (sometimes the transition is subtile, but it is always there).

There isn't anything else to explain other than what clocks measure. The rest of the interpretation after my "so far so good" comment, including any notion of "real time", or any notion of "shifting", or "transition" is occuring in one's (Yogi's, in this case) own head, due to philosophical concerns.

Having seen this type of response before, it seems very likely that Yogi has a pre-conceived philosophy of how time "should" act that is at variance with how clocks actually do act. Prefering to believe his philosophy rather than the measured results, he simply discounts observational evidence, claiming that the clocks aren't actually measuring "real" time.

There isn't anything else to explain other than what clocks measure. The rest of the interpretation after my "so far so good" comment, including any notion of "real time", or any notion of "shifting", or "transition" is occurring in one's (Yogi's, in this case) own head, due to philosophical concerns.

Having seen this type of response before, it seems very likely that Yogi has a pre-conceived philosophy of how time "should" act that is at variance with how clocks actually do act. Preferring to believe his philosophy rather than the measured results, he simply discounts observational evidence, claiming that the clocks aren't actually measuring "real" time.

I think you should read my posting before you criticize Yogi. His question is legitimate in light of my posting. You seem to have a pre-conceived philosophy that clocks are time.

If you take clocks on two different paths and when you bring them back together they read different elapse time then you can not by any reason, logic, of law of physics say that both kept real time. If you purpose is to keep the nature of time a mystic art that only a select few can understand then you approach works fine.

All clocks keep an indication of time through a mass energy relationship. Mass is subject to change with spatial transition, velocity. All the clocks up to this point measure mass or changes in mass.

Real time and clock time agree on any proper time line ( t,0,0,0) where time is on the Y-axis and spatial position is on the X-axis. Any frame that is not changing with respect to distance is a rest frame at any point in space.

When you transition in the spatial dimension you still stay in sync with real time but your clock slows down because the mass of all parts of the clock increase. The reason for the increase is another thread.

I hope this post makes things clearer.

pervect
Staff Emeritus
4newton said:
I think you should read my posting before you criticize Yogi. His question is legitimate in light of my posting. You seem to have a pre-conceived philosophy that clocks are time.

If you take clocks on two different paths and when you bring them back together they read different elapse time then you can not by any reason, logic, of law of physics say that both kept real time.

Why not? In fact, both clocks do measure time. You are apparently imputing some properties to "real" time that has no basis in observation or measurement. The only basis I can see for your statement is that you have some preconceived notions as to how clocks "should" work. Then, when you notice a variance of how clocks actually do work compared to how you think they should work, you decide that the clocks must be wrong.

russ_watters
Mentor
Careful, 4newton - we've been down this road before and you know where it goes.

Clocks, by definition, measure time. "Real" time. In fact, it takes a leap of logic (or, rather, illogic) to assume that something that by definition keeps "real time" doesn't keep "real time."

Fredrik
Staff Emeritus