Twin Paradox Problem: Do Twins Age Differently?

[arindamsinha]

Ah... How does this take it out of the domain of special relativity? SR works just fine for accelerating frames as long as the space-time is flat.

I am referring to the 'reciprocality' of all observations in SR as a kinematic theory. Reciprocality is not conserved if we somehow ascribe a unilateral acceleration to one body but not the other in a two-body situation, unless we are defining one of them to be a preferred frame of observation (which is contrary to SR).

This is why I state it takes it out of the domain of SR. GR does seem to resolve this nicely, bringing mass and gravity (i.e. momentum conservation) into the picture, providing a tie-breaker on 'who is moving'.

This is a good discussion. Let me know your thoughts.

 

[Nugatory]

Careful there! Our stay at home twin is staying at home, presumably on the surface of the Earth. An accelerometer strapped to the side of an Earth-bound clock will say that the clock is always accelerating upward at 1g.

Since we're talking about special relativity, it would be better to remove gravitation from the picture. Place our stay at home twin in a space station that is orbiting the Sun somewhere beyond Pluto's orbit. The stay at home twin is still subject to the Sun's gravitation, but this is such a tiny, tiny effect that it can be completely ignored. Now you can say "strap an accelerometer onto the side of the clock".

By "the clock" I meant the traveling twin's clock, and I was hoping no one would catch the oversimplification with respect to the stay-at-home twin. Well, better luck next time :-)

But seriously, kidding aside, yes you are right. It's remarkable how many presentations of the twin paradox describe stay-at-home as "unaccelerated" yet leave him stuck on the surface of the Earth living his entire life subject to a constant 1g acceleration.

 

[D H]

It's remarkable how many presentations of the twin paradox describe stay-at-home as "unaccelerated" yet leave him stuck on the surface of the Earth living his entire life subject to a constant 1g acceleration.

In those presentation's favor, that 1g acceleration (better: being deep in the Sun's and the Earth's gravity well) is a tiny effect. It's about 20 seconds of time dilation compared to that inertial counterpart in deep space for a forty year round trip.

 

[Rishavutkarsh]

So can anyone tell if acceleration is not absolute what exactly causes the difference if ageing ?

 

[harrylin]

My question was - how in a kinematic framework like SR do we decide which clock moves inertially? [..]

SR is not a kinematic framework. It's similar to classical mechanics in which the derivation of the transformation of motion of an object wrt a platform that is rotating relative to another one is purely kinematics. Dynamics comes in when one identifies for example the one platform as being in uniform straight motion, in which case the laws of mechanics are valid for motion wrt that platform and not for motion wrt the other platform. The same is true for SR.

 

[harrylin]

Strap an accelerometer onto the side of the clock. In SR, as long as it always reads zero, we're moving inertially. [..]

No, that's wrong for exactly the reason that you mention next. See post #104: in the original example, the acceleration that breaks the symmetry can not be detected by a simple accelerometer.

It's more interesting in GR. There's a moderately entertaining variant of the twin paradox in which the traveling clock is turned around by doing a tight hyperbolic orbit around some massive object, thereby staying in free fall for the entire trip. There's still no ambiguity about what each clock should read at journey's end, but AFAIK the only general way of calculating those times is to do the line integral of d\tau along the paths.

Although SR does not account for gravitational time dilation, its effect is probably negligible for that example.

 

[pervect]

So can anyone tell if acceleration is not absolute what exactly causes the difference if ageing ?

The shortest distance in space between two points is a straight line. In flat space, there is only one straight line between two points. On a (large) curved surface, there can be several geodesics (the curved space equivalent of a straight line) connecting two points of unequal length connecting the same two points, so only one of the lines is the shortest distance. So a given sraight line between two points isn't necessarily the shortest, but the shortest curve is a straight line.

Similarly, the worldline with the longest proper time between two points in space time is a geodesic - the natural motion of a particle experiencing no forces other than inertial and gravitational forces.. Similar to the situation in curved space, there can be several worldlines of different proper time connecting two points in space time, only one of which is the longest.

In both cases (space and space-time) if you make the region of space-time "small enough", the multiple paths will not exist there will be only one geodesic or

It's just geometry - and the twin "paradox" is rather similar to the triangle inquality in Eulidean geometry. The velocity change is rather like the angle

It's a natural feature of nature that a clock moving under the influence of no external forces moves along a geodesic, which is a path which extermizes proper time. This is the relativistic princple of Hamilton's principle.

 

[stevendaryl]

As i read this it implies that you think that if he does take into account the jumps indicated by changed planes of simultaneity then he can meaningfully compute the age of the inertial twin.

I don't know what you mean by "meaningfully" here, but at any moment, the traveling twin is at rest in some momentary inertial reference frame. According to that frame, the stay-at-home twin has a certain age. So there is a computable function F(t) giving the age of the stay-at-home twin in the frame in which the traveling twin is at rest at time t, according to the traveling twin's clock. The function is dependent on the acceleration profile of the traveling twin, and changes discontinuously at the points where the traveling twin's velocity changes discontinuously.

I didn't make any claims about how "meaningful" this function is--what makes a mathematical function meaningful or not meaningful? But when the twins get back together, the relationship between the age A_earth of the stay-at-home twin and the age A_traveler of the traveling twin will be given by
A_earth = F(A_traveler)

 

[harrylin]

So can anyone tell if acceleration is not absolute what exactly causes the difference if ageing ?

That opinion was held by Einstein and he gave his answer in his paper on the twin paradox, see post #104.

However that solution is unpopular today, as mentioned here:
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html

As mentioned in post #127, the best known answers are "stationary ether" and "block universe"; but the first is, again, unpopular today, and the second remains debated. See for example https://www.physicsforums.com/showthread.php?t=583606. (Note the reasons for locking that thread, at the end!)

Perhaps most physicists use the "shut up and calculate" solution.

 

[stevendaryl]

So can anyone tell if acceleration is not absolute what exactly causes the difference if ageing ?

Here's an analogy that might help, or might not. In Euclidean geometry, you hop in a car in New York City and travel for 1000 miles (according to your car's distance meter). Where (at what point in space) do you end up? It depends on the direction you traveled.

In Minkowsky geometry, you hop in a spaceship and travel for 10 years (according to your spaceship's clock). Where (at what point in spacetime) do you end up? It depends on the velocity you traveled. You're traveling in both space and time. What spatial location you end up at after 10 years of travel, and ALSO what temporal coordinate you end up at after 10 years of travel depend on the path you took through spacetime.

 

[Rishavutkarsh]

The shortest distance in space between two points is a straight line. In flat space, there is only one straight line between two points. On a (large) curved surface, there can be several geodesics (the curved space equivalent of a straight line) connecting two points of unequal length connecting the same two points, so only one of the lines is the shortest distance. So a given sraight line between two points isn't necessarily the shortest, but the shortest curve is a straight line.

Similarly, the worldline with the longest proper time between two points in space time is a geodesic - the natural motion of a particle experiencing no forces other than inertial and gravitational forces.. Similar to the situation in curved space, there can be several worldlines of different proper time connecting two points in space time, only one of which is the longest.

In both cases (space and space-time) if you make the region of space-time "small enough", the multiple paths will not exist there will be only one geodesic or

It's just geometry - and the twin "paradox" is rather similar to the triangle inquality in Eulidean geometry. The velocity change is rather like the angle

It's a natural feature of nature that a clock moving under the influence of no external forces moves along a geodesic, which is a path which extermizes proper time. This is the relativistic princple of Hamilton's principle.

I do understand what you are trying to explain but how can we differentiate between the paths took by the twins (tell that which one will age faster) as speed is relative and acceleration has nothing to do with this. we can say that for the moving twin the stationary twin is moving with the same velocity so when they meet ie come at same point in spacetime
how can this be said that the traveling will be younger and he took the shorter path.

What determines whether the path took by anything will be longer or shorter?

 

[stevendaryl]

What determines whether the path took by anything will be longer or shorter?

The proper time for any path through spacetime in SR is given by

\tau = \int{\sqrt{1-(v/c)^2} dt}

where v and t are measured in any inertial coordinate system. While v and t are both relative to a coordinate system, the integral has the same value in every coordinate system. It's clear that if there is a coordinate system in which v=0 for some path, then that path will have the longest proper time.

This is very closely analogous to path lengths in Euclidean geometry. The length of a path through 2-D Euclidean space is given by

L = \int{\sqrt{1+m^2} dx}

where m (the slope of the path, relative to the x-axis) and x are relative to a coordinate system, but the integral has the same value in any coordinate system (well, any system in which m is well-defined; it diverges for vertical paths). It's clear that if there is a coordinate system in which m=0 for some path, then that path will have the shortest length.

In SR, acceleration (change of v) doesn't come into play in calculating proper time, but it is provable that the unaccelerated path has the longest proper time. In Euclidean geometry, bending (change of m) doesn't come into play in calculating path length, but it is provable that the unbent path has the shortest path length.

 

[Rishavutkarsh]

The proper time for any path through spacetime in SR is given by

\tau = \int{\sqrt{1-(v/c)^2} dt}

where v and t are measured in any inertial coordinate system. While v and t are both relative to a coordinate system, the integral has the same value in every coordinate system. It's clear that if there is a coordinate system in which v=0 for some path, then that path will have the longest proper time.

This is very closely analogous to path lengths in Euclidean geometry. The length of a path through 2-D Euclidean space is given by

L = \int{\sqrt{1+m^2} dx}

where m (the slope of the path, relative to the x-axis) and x are relative to a coordinate system, but the integral has the same value in any coordinate system (well, any system in which m is well-defined; it diverges for vertical paths). It's clear that if there is a coordinate system in which m=0 for some path, then that path will have the shortest length.

In SR, acceleration (change of v) doesn't come into play in calculating proper time, but it is provable that the unaccelerated path has the longest proper time. In Euclidean geometry, bending (change of m) doesn't come into play in calculating path length, but it is provable that the unbent path has the shortest path length.

how can you say that the path took by the moving twin is the shorter one?

 

[stevendaryl]

how can you say that the path took by the moving twin is the shorter one?

From the formula for proper time:
\tau = \int{\sqrt{1-(v/c)^2} dt}

There is no inertial coordinate system in which the velocity of the traveling twin is always v=0, but there is an inertial coordinate system in which the velocity of the stay-at-home twin is always v=0.

 

[phyti]

2 clocks:
It comes down to which clock loses the least amount of ticks.
Clocks A and B move at speed a and b respectivlely.
A and B part,and B returns to A.
If the B clock runs slower than A on the outbound segment, it must take an inbound segment at -a>v<a, avoid losing more ticks.
Since there is no speed by which a clock can gain time, the loss is permanent, and the gain on the inbound segment does not compensate for the loss on the other.
Time dilation is a function of speed (v/c). Acceleration only sets the rate of td by establishing a different speed.
The twin case with one returning is the simplest of all cases, and would require a period of acceleration. That makes one path so different from the other that it would seem to be the explanation.


jumping frames:
The time 'gap' results from eliminating the time required for deceleration and acceleration, when simplifying the problem.

 

[Dale]

Agreed there are inertial frames in SR, but the whole point in SR is that none of them are 'preferred'.

Any kinemtic acceleration will have to be completely mutual between two frames.

Look carefully at what you wrote. "None of them are preferred", where "them" refers to different inertial frames. If there is any kinematic acceleration between the frames then at least one of the frames is non inertial, so "none of them are preferred" does not even apply. There is no need for anything to be mutual or symmetric between an inertial and a non inertial frame, nor between two non inertial frames.

SR postulates the equivalence of all inertial frames, not the equivalence of all possible frames.

 

[arindamsinha]

... If there is any kinematic acceleration between the frames then at least one of the frames is non inertial, so "none of them are preferred" does not even apply. ...

Excellent point. I think we should agree that SR is not the right framework to explain why there is asymmetric measurable time dilation between two bodies (like GPS and Earth surface clocks). We need to look at GR for this explanation.

PS: In the above, I am referring to the velocity time dilation part only, not the gravitational time dilation.

 

[Rishavutkarsh]

2 clocks:
It comes down to which clock loses the least amount of ticks.
Clocks A and B move at speed a and b respectivlely.
A and B part,and B returns to A.
If the B clock runs slower than A on the outbound segment, it must take an inbound segment at -a>v<a, avoid losing more ticks.
Since there is no speed by which a clock can gain time, the loss is permanent, and the gain on the inbound segment does not compensate for the loss on the other.
Time dilation is a function of speed (v/c). Acceleration only sets the rate of td by establishing a different speed.
The twin case with one returning is the simplest of all cases, and would require a period of acceleration. That makes one path so different from the other that it would seem to be the explanation.


jumping frames:
The time 'gap' results from eliminating the time required for deceleration and acceleration, when simplifying the problem.

as said earlier what would you say when both twins go through same acceleration?
both start at the same time when they both reach 90%C one returns back while other keeps going , how will you describe this?
they both went through same acceleration and retardation but still the moving one is younger {when they meet after 10 years (say)} . this is the point i am confused about.
Any help would be greatly appreciated.

 

[pervect]

I do understand what you are trying to explain but how can we differentiate between the paths took by the twins (tell that which one will age faster) as speed is relative and acceleration has nothing to do with this. we can say that for the moving twin the stationary twin is moving with the same velocity so when they meet ie come at same point in spacetime
how can this be said that the traveling will be younger and he took the shorter path.

What determines whether the path took by anything will be longer or shorter?

Short answer: the geometry determines it.

The spatial analogy is that the shortest path between two points is a straight line. If you imagine a triangle, the sum of the lengths of the two sides of the triangle is always greater than or equal to the hypotenouse, and it's only equal when the "triangle" is degenerate.

The twin paradox is just the space-time version of the triangle inequality.

If you are in the flat space-time of special relativity , there will be one and only one path between any two points in that space-time that is straight line motion. We'll call the two points the "origin" point and the "destination" point. Straight line motion means pretty much the same thing in flat space-time as it does in Newtonian theory as you have true inertial frames.

The two points must be fixed in both space and time, and there must be enough time for light to reach and pass the destinaton point from the first for a material body to be able to do the same. The technical term for such a path is a "timelike separation" between points, to insure that a "timelike path" exists between them. For the rest of this post I'll presuppose that such a condition is satisfied.

Thus if you specify the both the origin point and the destination point, the geometry determines the unique timelike path that is also a geodesic that connects them. This path will be the path of maximum proper time. It will be represented by a body that moves in "natural motion", or "uniform motion". You can also think of this as a body that is at rest in some inertial frame, the one inertial frame that contains both the origin and destination points at the origin point of the inertial frame.

If you are in the curved space-time of general relativity, there may be more than one path if you consider a large enough time interval. But let's consider the case first where the spacing between points is close, and there's only one path.

Then the path that experiences the most proper time will be the unique path of a body in free fall - free fall paths determine geodesic motion - that starts at the origin point and ends at the destination point.

Example: If you consider a point on the surface of the earth, and another point at the same location 1 second later, the path of maximum proper time will be that of an object thrown upwards, such that it begins at the origin point and ends at the destination point.

This path will be unique up until you get a separation in time between the oriigin and destination points of one orbital period of the Earth (which is about 90 minutes, IIRC), at which points you'll have many possible paths you can take. The orbital paths will generally have short proper times and hence not be what you're looking for. It's the path that gets you furthest away from the Earth in the shortest possible time that will be the path of maximum proper time. If you look at the equations , and choose a particular coordinate system, you can talk about this path as a balancing act between gravitational time dilation which is minimzed by getting far away, and velocity time dilation, which is minimzed by not moving quickly. But it's more helpful (though more abstract) to think of the path as just being determined by the space-time geometry.

In any event, it's the geometry that determines the path of longest proper time in space-time, just as it's geometry that defines the shortest path in space.

And if you take some path that's less than optimum, in space you travel a longer distance, in space-time (assuming a purely timelike path) you travel a shorter time.

There's a little more to be said about the case where you have multiple paths in space (or in space-time), but the basics are that globally you have to try all possible geodesic paths and test them to find which is the longest / shortest. The path you're looking for will be a geodesic, but any particular geodesic may or may not be the one that you want.

 

[Jeronimus]

From the formula for proper time:
\tau = \int{\sqrt{1-(v/c)^2} dt}

There is no inertial coordinate system in which the velocity of the traveling twin is always v=0, but there is an inertial coordinate system in which the velocity of the stay-at-home twin is always v=0.

The answer is more complicated than this.

There is no inertial reference frame for the first and second phase either, in which the velocity of the traveling twin is always v=0.
There is an inertial reference frame however with an observer at rest who considers both rockets to be flying away of him at the same vrel seen from his point of view, after the instantaneous acceleration, being in phase2.

Any of the two twins could decide to turn around with the same results. Whoever turns will be the twin who aged less. (So there seems to be some symmetry BETWEEN the two twins up until phase 3, but it will not be easy to explain why)

The symmetry breaks in the turn around phase 3. Not at the initial acceleration phase 1, nor at phase 2 when they move at vrel relative to each other, nor at phase4 when the turn around twin accelerates instantaneous back into the inertial reference frame the stay at home twin is at rest with.
In fact, in phase 4 (when the twins are next to each other at vrel), either of the twins could decide to accelerate instantaneous into the inertial reference frame his twin brother is at rest with. It would not matter. The twin who accelerated at a distance (turn around) is the one who aged less.

I tried to warp my mind around this, but in the end, it gets too complicated. One of the issues is that we are talking about a symmetry between the two twins, not between two frames. The symmetry seems to be broken with any object which is not local to the acceleration. (and yet, it might not be broken, considering the next sentence)
Also, while the accelerating twin might claim that everything else is accelerating, we are not talking just accelerating along the x-axis anymore, but also accelerating along the t axis.
Let alone if we assume a real, non-instantaneous acceleration, then we can talk only about getting arbitrary close to clocks being synced after the acceleration in phase1 & 4 still. We can however choose such a high acceleration, that the effect becomes negligible small.edit: When we talk about symmetry, we usually mean along the x axis. They move at vrel relative to each other. That is along the x axis. But what if they move at vrel to each other along the t axis? This is where i get stuck for the moment.

 

[stevendaryl]

The answer is more complicated than this.

There is no inertial reference frame for the first and second phase either, in which the velocity of the traveling twin is always v=0.
There is an inertial reference frame however with an observer at rest who considers both rockets to be flying away of him at the same vrel seen from his point of view, after the instantaneous acceleration, being in phase2.

Yes, but the integral for proper time is an invariant; it has the same value in every inertial coordinate system. So if there exists one coordinate system in which one twin has v=0 throughout, then we can use that coordinate system to compute the integral.

 

[ghwellsjr]

As long as we ignore gravity or pretend that it does not exist, you can define and analyze any scenario in a single Inertial Reference Frame (IRF). This is the easiest way to solve any Special Relativity problem. All you have to do is keep track of the tick rate of each clock based on its speed in that IRF. It doesn't matter if a clock is at rest in that IRF or if it accelerates, it doesn't matter.

Stevendaryl's oft-repeated equation for calculating the Proper Time on any clock may look intimidating but it is very simple as long as we invoke instant accelerations whenever we want a clock to change its speed. Then we can chop up the activity of any clock into intervals when it is moving at a constant speed and simply keep track of how long and how fast each clock is moving in our single IRF.

So in the simple Twin Paradox where one twin remains at rest in the IRF and the other one travels the entire time between departing and reunion at a constant speed (but with instantaneous accelerations to start, change directions and stop) then we use the equation to see that the tick rate on the traveling clock is slower than the coordinate time of the IRF.

In the scenario of this thread since the traveling twin moves at 90%c, the time dilation factor is 0.435890 so the traveling twin's clock runs slower than the coordinate time (which is the same as the other twin's clock rate) by that amount. If the traveling twin was gone for 10 years according to the IRF, then his clock will accumulate 4.35890 years during the trip while the other twin's clock accumulated 10 years.

If you want to propose a more complicated scenario, for example, both twins take off at the same speed (90%c) but one of them gets back after 5 years (IRF) while the other one gets back after 10 years (but otherwise they both experience the same acceleration, just at different times), then the time on the first clock will accumulate 5 times 0.435890 or 2.17945 years during the first 5 years of IRF time plus 5 more years for the second 5 years of IRF for a total of 7.17945 accumulated time on the first clock compared to 4.35890 years for the second twin's clock.

You can do a similarly simple process for any complicated scenario with instant accelerations. If you want to have accelerations that are gradual then you will have to do actual integrations but otherwise the concepts are identical.

Now, if you want, you can transform any scenario defined in one IRF into any other IRF moving with respect to the first one to see how you get the same answer even though all the speeds and intervals may be different. And if you really want to make things complicated, you can engage in frame jumping or non-inertial reference frames but it won't change any result, they just use different speeds and intervals to do the calculations and arrive at the same final result. I don't know why anyone would want to torture them self like that but if you're one of those people, be my guest, just don't claim that any other way than the first and easiest IRF provides any more insight or information into what is actually happening.

 

[ghwellsjr]

By the way, in my previous post I emphasized that the final result comes out the same in all IRF's and other analyses because that is usually the only result that people care about when discussing the Twin Paradox but I want to make it clear that all intermediate results come out the same also. For example, in any of these scenarios, we can consider each tick of every clock to be a different event and calculate the Proper Time on each clock for each of these events and then transform to any other IRF and calculate the Proper Time again and they will all come out the same for each event. In other words, every event that determines the Proper Time on any clock is invariant (in any IRF or any other kind of analysis).

In particular, we can calculate the Proper Time on the traveling twin's clock when he turns around half way through his trip and all IRF's will give the same result. Furthermore, the Doppler analysis that I promoted in post #5 which does not depend on any IRF or other frame(s) also determines the time on the traveler's clock to be the same as any IRF analysis and we can also show that the stationary twin will see that time on the traveler's clock when he finally sees his twin turn around.

What no analysis can do is determine unambiguously what time is on the stationary twin's clock when the traveling twin turns around because that depends on the selected IRF (or other frame) but they will all agree on the time on the stationary twin's clock when he observes the traveling twin turn around.

 

[phyti]

as said earlier what would you say when both twins go through same acceleration?
both start at the same time when they both reach 90%C one returns back while other keeps going , how will you describe this?
they both went through same acceleration and retardation but still the moving one is younger {when they meet after 10 years (say)} . this is the point i am confused about.
Any help would be greatly appreciated.

In the left pic A's speed profile with an acceleration at (1) is the reverse order of B's speed profile with a deceleration at (2). The profiles are symmetric to the center of the line connecting the end points (0)& (3).
The path lengths are equal, their clocks read the same at (0) and at (3). The acceleration/deceleration did not determine the accumulated time.
The right pic has the same path for A, but a stretched path for B. Since the B path is longer, the B clock accumulates less time than the A clock. The acceleration/deceleration did not determine the accumulated time.

Examples of the 'twin' scenario without
acceleration/deceleration, exchanging info while passing, have been used to show the effect of a longer path on a clock. Einstein said in moving the B clock away from the A clock along a random path, then returning to the A clock, the B clock would show less time. He didn't state how it was moved because it's irrelevant. The point was the motion and its effect on processes (clock).

In the simple twin case with A leaving B, then returning, the change in direction is the most obvious difference, and thus is assumed to play apart in the solution.
That's the danger of making conclusions based on special cases.

 

[phyti]

Here's another approach.
View attachment clock rejoin.doc

 

[zonde]

Finally, since you want to have the traveling twin and the Earth twin jump frames at the moment of turn around, I beg you to provide us with the details of the calculations. Let's assume that the traveling twin turns around after one year on his clock and is traveling at 90%c. Can you do that? And can you also show the calculations for what each twin sees of the other twin's clock during the entire scenario, please?

And then, to address your comments to me, I'd like you to show us how you use the LT in this process, OK?

So we start with second twin waiting for one year while his home is moving away at 0.9c. After one year (from perspective of second twin) it turns around (from perspective of first twin) and meets first twin after another year (second twin's time).
And we want to know what each twin sees of the other twin's clock.

We start with this diagram:

Both twins start at "A" and first (stay at home) twin is heading away at 0.9c.
Second twin traveling along AB will see first twin as traveling along AI. So that proper time along AI divided by proper time along AB will give what second twin sees of the first twin on foward trip.
Similarly we need AB/AJ, IC/BC and BC/JC.


Now I know that t coordinate of "B" is 1y(year).
First I will find coordinates of "I".
First twin will cover distance of 0.9ly(light years) in 1y and then signal at light speed will go back to second twin for another 0.9y. So we have that in 1.9y we would receive signal from 0.9ly distance. But as our time is only 1y then x coordinate of "I" is 0.9/1.9 ly and t coordinate is 1/1.9 y.

Now I want to find proper time along AI. So I will perform LT.
I(x=0.9/1.9ly,t=1/1.9y) transforms to I(x'=0, t'=0.1/sqrt(0.19)=0.2294y)
B(x=0,t=1y) transforms to B(x'=-0.9/sqrt(0.19)=-2.065ly,t'=1/sqrt(0.19)=2.294y)

So AI in first twin's rest frame is 0.2294y and AI_p/AB_p is 0.2294 (seconds of fist twin per second of second twin)
Now because of symmetry between top and bottom of the diagram we can find AC by taking twice t coordinate of B and it is 4.588y. And for the same reason BC in second twin's rest frame is 1y.
So we get that:
AB_p/AJ_p=1/(4.588-0.2294)=0.2294 (seconds of second twin per second of first twin - what first twin sees of second twin before he turns around)
IC_p/BC_p=(4.588-0.2294)/1=4.359 (seconds of first twin per second of second twin - what second twin sees of first twin after he turns around)
BC_p/JC_p=1/0.2294=4.359 (seconds of second twin per second of first twin - what first twin sees of second twin after he turns around)

 

[Jeronimus]

Examples of the 'twin' scenario without
acceleration/deceleration, exchanging info while passing, have been used to show the effect of a longer path on a clock. Einstein said in moving the B clock away from the A clock along a random path, then returning to the A clock, the B clock would show less time. He didn't state how it was moved because it's irrelevant. The point was the motion and its effect on processes (clock)

As i can see, your text includes the keyword "return". Did Einstein specifically state that his scenario is "acceleration free"?

 

[Dale]

Excellent point. I think we should agree that SR is not the right framework to explain why there is asymmetric measurable time dilation between two bodies (like GPS and Earth surface clocks). We need to look at GR for this explanation.

PS: In the above, I am referring to the velocity time dilation part only, not the gravitational time dilation.

I don't know why you think we should agree when I have just explained why it is wrong. Ignoring gravitation there is never any need for GR, and the time dilation is entirely explained by the velocity of the clocks in any inertial frame, per SR.

Your repeated mistake appears to be an inability or unwillingness to distinguish between inertial and non inertial frames. The postulates of relativity specifically deal with the equivalence of inertial frames and the speed of light in inertial frames. There is no postulated equivalence of non inertial frames nor any postulated speed of light in non inertial frames.

To claim that SR requires the equivalence between an inertial and a non inertial frame is simply and demonstrably false.

 

[pervect]

I do understand what you are trying to explain but how can we differentiate between the paths took by the twins (tell that which one will age faster) as speed is relative and acceleration has nothing to do with this. we can say that for the moving twin the stationary twin is moving with the same velocity so when they meet ie come at same point in spacetime
how can this be said that the traveling will be younger and he took the shorter path.

What determines whether the path took by anything will be longer or shorter?

One other quick addendum to my previous long post. If your view of time dilation is that you want to explain it by "Time runs slower in Faerie,, but I can't figure out what or where "Faeirie" is, the point I'm trying to make is that this type of explanation won't work at all.

If there was such a thing as absolute time, you could compare the time of either of the twins to the absolute time, and determine which was aging more slowly. But there isn't any such thing. Instead, you have two twins, each of which has a different idea of the concept of now. So when they compare clocks, each of them compares their clock to the other clock "now" - but their idea of "now" is different!

And there isn't any objective, observer independent means of determining which notion of "now" is correct, they're all equally good - or bad.

 

[arindamsinha]

I don't know why you think we should agree when I have just explained why it is wrong. Ignoring gravitation there is never any need for GR, and the time dilation is entirely explained by the velocity of the clocks in any inertial frame, per SR.

Your repeated mistake appears to be an inability or unwillingness to distinguish between inertial and non inertial frames. The postulates of relativity specifically deal with the equivalence of inertial frames and the speed of light in inertial frames. There is no postulated equivalence of non inertial frames nor any postulated speed of light in non inertial frames.

To claim that SR requires the equivalence between an inertial and a non inertial frame is simply and demonstrably false.

I openly admit that I am a novice in relativity compared to some of you guys I have met in this forum. I am just trying to bring in a different point of view and learn in the process. Please bear with me.

Perhaps I have failed to convey the point I am trying to make. Let me try again.

When talking about GR, I am referring to the Schwarzschild metric, which I believe is an exact solution of GR equations, and encompasses both gravitational and velocity time dilation (i.e. includes SR).

I am also referring to the twin paradox, and thinking of the GPS satellite time dilation (velocity part) as an experimental proof of this. Moreover, it is always the GPS clocks that slow down w.r.t. the Earth clocks, not the other way round (ignoring the gravitational time dilation effect).

The advantage I see in using the GR Schwarzschild solution for explaining experimental observations and paradoxes is this - velocities considered here are from the CG of the two-body system under consideration, rather than absolute relative velocities between the two components. (At least, that is how I have interpreted the GPS time dilation, though I may be wrong).

This neatly explains why the traveling twin has velocity, why he should time dilate, and why GPS clocks get slower compared to Earth ones (again ignoring the gravitational TD part). This also avoids the somewhat magical 'clock jumping' that happens at the point of reversal of the traveling twin, which I have seen in some SR solutions.

In SR, we have to artificially ascribe the velocity to the traveling twin by considering that he accelerates and is not in an inertial frame. In that case, I feel that the solution goes outside the domain of SR, since we are bringing in reasons like 'feeling acceleration' which were specifically left out by Einstein when deriving SR, and included in GR.

So overall, I feel GR gives a better and more intuitive solution to these type of paradoxes than SR does. This was the point I was trying to make.

 

[Dale]

In SR, we have to artificially ascribe the velocity to the traveling twin by considering that he accelerates and is not in an inertial frame. In that case, I feel that the solution goes outside the domain of SR, since we are bringing in reasons like 'feeling acceleration' which were specifically left out by Einstein when deriving SR, and included in GR.

Why do you believe that "feeling acceleration" is outside of the domain of SR? Clearly, the concept of an inertial frame is part of the foundations of SR, so how would you define an inertial frame without reference to "feeling acceleration" or its equivalent?

 

[arindamsinha]

Why do you believe that "feeling acceleration" is outside of the domain of SR? Clearly, the concept of an inertial frame is part of the foundations of SR, so how would you define an inertial frame without reference to "feeling acceleration" or it's equivalent?

Dalespam, I was thinking of the equivalence principle and considering (perhaps incorrectly) that feeling 'acceleration' and feeling 'gravity' are one and the same thing. In SR, I thought relative velocities are the only thing considered, and we look at it kinematically, and any acceleration is mutual and translates into only the instantaenous relative velocity (which again is mutual). I am ready to stand corrected in this respect if I have misunderstood.

However, I would value your opinion on the overall thought process in my previous thread, not just this particular statement.

 

[Dale]

Dalespam, I was thinking of the equivalence principle and considering (perhaps incorrectly) that feeling 'acceleration' and feeling 'gravity' are one and the same thing. In SR, I thought relative velocities are the only thing considered, and we look at it kinematically, and any acceleration is mutual and translates into only the instantaenous relative velocity (which again is mutual). I am ready to stand corrected in this respect if I have misunderstood.

I think you have misunderstood. The concept of "kinematic" does not enter into the postulates, which are the core of SR, but the concept of an "inertial frame" does. To me it seems that you have exaggerated the ancillary concept of kinematic to the point that you have lost track of the defining concepts of SR. You cannot have SR without a definition of inertial frames, and so you can certainly use inertial frames to resolve paradoxes and distinguish between observers.

However, I would value your opinion on the overall thought process in my previous thread, not just this particular statement.

Regarding the overall thought process, I don't really get what you mean by the Schwarzschild metric without gravitation. I think that is SR in spherical coordinates.

 

[djy]

The advantage I see in using the GR Schwarzschild solution for explaining experimental observations and paradoxes is this - velocities considered here are from the CG of the two-body system under consideration, rather than absolute relative velocities between the two components. (At least, that is how I have interpreted the GPS time dilation, though I may be wrong).

This neatly explains why the traveling twin has velocity, why he should time dilate, and why GPS clocks get slower compared to Earth ones (again ignoring the gravitational TD part). This also avoids the somewhat magical 'clock jumping' that happens at the point of reversal of the traveling twin, which I have seen in some SR solutions.

The Schwarzschild metric is the solution of spacetime around a spherical, uncharged, non-rotating mass. Yes, it does closely explain the difference in passage of time on GPS satellites compared to the Earth's surface. And, as you said, there are components of time dilation due both to velocity and gravitational potential. However, you cannot use this metric to analyze the traditional twin paradox, which takes place in flat spacetime. Since the metric does not describe flat spacetime, using it is simply wrong.

In SR, we have to artificially ascribe the velocity to the traveling twin by considering that he accelerates and is not in an inertial frame. In that case, I feel that the solution goes outside the domain of SR, since we are bringing in reasons like 'feeling acceleration' which were specifically left out by Einstein when deriving SR, and included in GR.

It's a common misconception that acceleration is outside the domain of SR. On the contrary, acceleration is handled equally well by both SR and GR. In both cases, the proper time experienced by an observer is simply the length of its world line in spacetime. In GR the spacetime may be curved (but is not necessarily); in SR it is always flat.

To analyze the traditional twin paradox, simply substitute the metric of flat spacetime for the Schwarzschild metric, and integrate the lengths of the world lines of the two twins to find the difference in proper time passage.

 

[Jeronimus]

Why do you believe that "feeling acceleration" is outside of the domain of SR? Clearly, the concept of an inertial frame is part of the foundations of SR, so how would you define an inertial frame without reference to "feeling acceleration" or its equivalent?

Isn't free fall, being in a force field, also accelerating? We cannot feel that.

If we were able to create a force field into any direction which is local, then we would not feel any acceleration as all parts would accelerate evenly. That is, for an infinitesimal small volume. Unfortunately we cannot magically create a force field to freely fall towards, but instead rely on accelerating "one part" of an object, which then pushes against other parts (electromagnetic forces). By doing so, the structure of the body changes and this is why we believe to feel acceleration imo.

Do accelerometers measure acceleration or do they merely measure a chance in the structure of an object caused by different parts of the object being accelerated differently?

I also have a hard time understanding how someone can "feel acceleration". I understand how someone or something can detect a change in the structure of it's body like accelerometers do.edit: "feeling acceleration" is not required in order to arrive at the formulas of SR. The concept of changing the inertial frame of reference an object is at rest in is required. Who is responsible for changing an object's rest frame? Acceleration we say. What causes acceleration or a force field? Energy or mass (or objects "pushing against each other?). What is energy or mass? Now that's a difficult one.

 

[stevendaryl]

The Schwarzschild metric is the solution of spacetime around a spherical, uncharged, non-rotating mass. Yes, it does closely explain the difference in passage of time on GPS satellites compared to the Earth's surface. And, as you said, there are components of time dilation due both to velocity and gravitational potential. However, you cannot use this metric to analyze the traditional twin paradox, which takes place in flat spacetime. Since the metric does not describe flat spacetime, using it is simply wrong.

Well, actually, in the limit in which the gravitational field of the Earth is negligible, the Schwarzschild metric reduces to the Minkowsky metric in spherical coordinates:

ds^2 = (c dt)^2 - dr^2 - r^2 (d\theta^2 + sin^2(\theta)d\phi^2)

You can certainly use this metric to calculate the ages of the two twins in the twin paradox, and get the same answer as using the usual Minkowsky coordinates.

 

[Dale]

Isn't free fall, being in a force field, also accelerating? We cannot feel that.

Here you need to distinguish between coordinate acceleration, which is frame variant and which we cannot feel, and proper acceleration, which is frame invariant and which we can feel. Accelerometers measure proper acceleration.

"feeling acceleration" is not required in order to arrive at the formulas of SR. The concept of changing the inertial frame of reference an object is at rest in is required.

Then please define an inertial frame without "feeling acceleration" or its equivalent. I would be very interested in hearing such a definition since I cannot think of it myself.

 

[harrylin]

[..]
Then please define an inertial frame without "feeling acceleration" or its equivalent. I would be very interested in hearing such a definition since I cannot think of it myself.

Jeronimus wrote: "Isn't free fall, being in a force field, also accelerating? We cannot feel that."

This is implied in post #156. In the original space travelers example, the traveler feels no acceleration at turn-around but he is nevertheless not in uniform rectilinear motion. Originally SR was defined wrt to Newtonian (or "Galilean") reference systems; that is what is meant with "inertial frames" in the context of SR.

 

[Dale]

. Originally SR was defined wrt to Newtonian (or "Galilean") reference systems; that is what is meant with "inertial frames" in the context of SR.

And how are 'Newtonian (or "Galilean") reference systems' defined? The only way I know is through "feeling acceleration" or something equivalent.

 

[harrylin]

And how are 'Newtonian (or "Galilean") reference systems' defined? The only way I know is through "feeling acceleration" or something equivalent.

In any case, the space traveller who is in free fall is accelerating in such a frame, just as a stone in free fall is accelerating in classical physics. There is no disagreement about the working of SR between Einstein and Langevin

For a real discussion about classical reference frames it's a good question to ask in the classical physics forum; but here are my "2cts", for the case that no such thread is started.
Newton defined it as in uniform straight line motion wrt the "fixed stars", and for the traveller who falls around a star that would work rather well in practice (replacing "fixed stars" by apparently fixed distant stars).
No doubt this can be replaced (and probably was) by the definition of inertial motion at places far away from massive bodies, and/or simply correcting for the acceleration due to gravitation if a massive body is nearby; and that also works fine for the space traveller, just as elaborated.

 

[arupel]

Riskavutkarsh's statement is good. I read a book about this. Basically both twins see the same time dilation. However for the twin in which the velocity reverses, the time-space line takes a jump. Immediately before the reversal he sees his twin graduating. Immediately after, he sees his twin on his death bed.

 

[Dale]

In any case, the space traveller who is in free fall is accelerating in such a frame, just as a stone in free fall is accelerating in classical physics.

arindamshina is explicitly neglecting gravitation, so we don't have to worry about that.

Newton defined it as in uniform straight line motion wrt the "fixed stars", and for the traveller who falls around a star that would work rather well in practice (replacing "fixed stars" by apparently fixed distant stars).
No doubt this can be replaced (and probably was) by the definition of inertial motion at places far away from massive bodies, and/or simply correcting for the acceleration due to gravitation if a massive body is nearby; and that also works fine for the space traveller, just as elaborated.

That was OK for Newton, but now we know that the stars aren't fixed wrt each other, so they cannot be used to define a single reference frame.

 

[Austin0]

The problem with Relativity's explanation for the Twin paradox, is that, once back on earth, for the traveling twin's clock to have a lesser time than the stay at home twin's clock, it can be deduced that the rate of time on the traveling twin's clock must have slowed down at some point during the journey.

Once a clock has had its rate of time slowed down by acceleration, Relativity has no mechanism to return the rate of time back to 'normal' - since any further acceleration can only cause the clock's rate of time to slow down even more...

Hi
i certainly agree with your logic, that accumulated time difference requires an assumption of a difference in instantaneous rates over the course of the exercise but there is no means to determine what the relative rates are for any time interval whatsoever during transit.
As for the acceleration: Yes the term acceleration applies equally to any change of velocity irrespective of direction, but in this circumstance there is a fundamental difference between acceleration away and the deceleration required at turnaround.
The dilation factor changes with the instantaneous velocity relative to Earth on the way out.
On turnaround the initial negative acceleration reverses those changes wrt Earth up to the point where the traveler is instantly at rest wrt earth, where there is no difference (initial condition) From there the dilation factor from acceleration (instantaneous velocity) again begins to increase in magnitude to the final inertial velocity gamma of the return leg..

 

[pervect]

The problem with Relativity's explanation for the Twin paradox, is that, once back on earth, for the traveling twin's clock to have a lesser time than the stay at home twin's clock, it can be deduced that the rate of time on the traveling twin's clock must have slowed down at some point during the journey.

Once a clock has had its rate of time slowed down by acceleration, Relativity has no mechanism to return the rate of time back to 'normal' - since any further acceleration can only cause the clock's rate of time to slow down even more

I didn't see this the first time it was posted - I saw it quoted in another post. I believe that the conclusion drawn is somewhere between ill-specified and downright wrong in i'ts deduction that "the traveling twin's clock must have slowed down at some point" .

Specifically, this deduction seems to presuppose some sort of absolute time, to which the travelling's twin time can be unambiguously compared. But there isn't any such absolute time. So what is the travelling's twin's time being compared to, and how is the comparison being made?

Relativity teaches us that the process of time comparison is frame dependent, and not absolute.

 

[zonde]

Riskavutkarsh's statement is good. I read a book about this. Basically both twins see the same time dilation. However for the twin in which the velocity reverses, the time-space line takes a jump. Immediately before the reversal he sees his twin graduating. Immediately after, he sees his twin on his death bed.

Welcome to PhysicsForums, arupel!

You should be careful with your usage of word "sees". Your statement would be rather sensible if you would replace "sees" with "calculates" or "interprets".
But if you want to stick to statements about what twins see about the other twin then you can look at one example in my post #176 (hopefully clear enough).

 

[zonde]

That was OK for Newton, but now we know that the stars aren't fixed wrt each other, so they cannot be used to define a single reference frame.

You mean because of redshift?

 

[harrylin]

arindamshina is explicitly neglecting gravitation, so we don't have to worry about that.

The OP is Rishavutkarsh, and you commented on Jerominus who mentioned free fall. Free fall is used in the first full (two-observer) discussion, which is not (and never was) a problem in the context of SR (post #188 once more).

That was OK for Newton, but now we know that the stars aren't fixed wrt each other, so they cannot be used to define a single reference frame.

I next gave you three simple practical means and with modern technology there are more; please start a topic in classical physics if you don't understand how to apply any of them.

You mean because of redshift?

Please don't elaborate here; if three practical ways (not including Newton's) result in zero "clicks", then it would certainly require a long discussion to explain the reference systems of classical mechanics - and that is not the topic here.

 

[Dale]

I next gave you three simple practical means and with modern technology there are more; please start a topic in classical physics if you don't understand how to apply any of them.

It isn't a question of practical implementation, but one of definition. The distant stars are not fixed wrt each other, so they cannot be used to define a reference frame, even if from a practical standpoint the difference can be neglected.

Furthermore, suppose that you used some specific distant stars, and defined a frame where each of your set of distant stars had some well defined velocity. How would you know where or not the frame so defined is inertial? The stars cannot do it, so instead you look for the absence of fictitious forces. That is the only way I know to define an inertial frame.

http://en.wikipedia.org/wiki/Fixed_stars#The_fixed_stars_in_classical_mechanics

 

[Dale]

You mean because of redshift?

Redshift demonstrates radial motion, but there is also proper motion (transverse to us).

http://en.wikipedia.org/wiki/Fixed_stars#The_fixed_stars_are_not_fixed

 

[harrylin]

It isn't a question of practical implementation, but one of definition. [..]

In modern physics, definitions are practical implementations, but I won't go along any further with a discussion about classical mechanics in this thread. If your new practical definition of inertial frame works for Newton's falling apple as well as for Langevin's space traveler example (which I guess it does), then it is OK for classical mechanics and SR.