#### dseppala

Using Einstein's concepts I cannot make any sense of the following simple scenario.
There are two identical twins at rest in an inertial reference frame F0. They are separated by a distance L along the x-axis. When they turn 20 years old, they simultaneously step on to an inertial reference frame, F1, that has a relative velocity V along the x-axis with respect to frame F0. Per Einstein, the twins are no longer the same age. How can that be?
Any insights would be appreciated.
Thanks,
David Seppala
Bastrop TX

#### Woody

One point is that many of these thought experiments that require instantaneous changes of velocity can give odd results.
But you are specifying unrealistic conditions (instantaneous acceleration) so you can expect unrealistic results.

Another point might be, are you sure you have interpreted the scenario correctly?

Also how did the twins get separated by the distance L, in reference frame F0,
without relative acceleration, and thus a relative change of age?

#### dseppala

Woodie, I clarified things for you calling the twins clones.

Given info: Clone 1 and Clone 2 were born at the same time as measured in frame F0. They each have a clock that was set to zero when they were born. One was born at point x=X and the other was born at point x=X+L as measured in frame F0. For twenty years they were each at rest in frame F0.
When each clone turned twenty years old (and each of their associated clocks read 20 years as measured in frame F0), they simultaneously accelerated and came to rest in frame F1. Frame F1 has a velocity V along the x axis of frame F0. It took each clone a time T (as measured by each of their clocks) to accelerate into frame F1. When each clone came to rest in frame F1, each of their clocks read 20+T.

Now they are at rest in F1. They are now separated by a distance L'. When they compare their ages, per Einstein's theory, they are no longer the identical age. Per Einstein, one clone arrived in frame F1 before the other clone arrived in F1 (as measured in frame F1). Why do the two clones say one clone aged differently than the other clone when everything they did was identical?

David Seppala
Bastrop TX

#### GatheringKnowledge

One point is that many of these thought experiments that require instantaneous changes of velocity can give odd results.
But you are specifying unrealistic conditions (instantaneous acceleration) so you can expect unrealistic results.
But isn't it exactly, why thought experiments are being used in theoretical physics after all - to test a theoretical mechanism in a completely hypothetical scenario? If a theory can't handle a simple thought experiment, then how can it be correct?

So called "twin paradox" is designed as a "crash-test" for a VERY important part of SRT - that is time dilation due to relative velocity. And to see, if SRT will be able to handle simple logic, we need to make the test-scenario as simple, as it can be - so in the "twin paradox" scenario we shouldn't include ANYTHING accept 2 frames in a constant and linear relative motion. The question, we should ask here should be: "will there be a difference in the rate of aging process for 2 twin brothers, if one of them will be moving at velocity v in relation to the second one?".

If we will start adding to the scenario other factors, like the resistance of a rest mass to acceleration/deceleration or gravity of Earth, then we won't test SRT, but GRT. I will go now even further and make the scenario as simple, as it possibly can get, by using the physics of "Star Trek" franchise

We have 2 spaceships: Enterprise, which remains stationary and Voyager, which is closing to the 1'st ship at 0,5c
Let's say, that Federation doesn't care any longer about ethics and there are 2 human clones at the same age onboard the USS Enterprise. In the moment, when the distance between both ships is equal to 2 space units, Scotty beams-up one of the 2 clones to Voyager. Because of the nature of teleportation, clone, which is being beamed-up doesn't experience acceleration nor any other change of his motion, as Voyager becomes his new inertial frame and now from his perspective it's the Voyager, which is stationary and it's Enterprise, that is closing in at 0,5c

One of the main postulates of relativity tells, that any velocity other than c is RELATIVE, instead of being an intrinsic property of a frame, while according to the law of inertia equivalence, perspectives of both clones have to be just as valid. If at the time, when Voyager will pass right next to Enterprise, clones will be at different age, both those rules will be brutally violated...

And now let's look at the spacetime diagrams for both clones - of course, we use the laws of SRT, to transform the coordinates. Ready...?
I've used the tool from this site:
frame of Enterprise:

frame of Voyager:

Uh oh! Clone onboard the Voyager is apparently 0,5 time unit younger, than clone onboard the Enterprise... Conclusion - now both clones can say that Enterprise is stationary and Voyager moves at 0,5c... Critical error 404: main postulate of relativity is broken: relative motion becomes a definitive property of a frame...

And this is the most simple scenario, you can make out, to see if the idea of time dilation due to velocity makes any sense - obviously it doesn't... I didn't even mention that in the frame of Enterprise both crafts emit simultaneus pulses of light at t=0, as I don't enjoy to beat a horse, which is clearly dead already...

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#### studiot

One was born at point x=X and the other was born at point x=X+L as measured in frame F0.
How do you perform this measurement to be able to make this statement?

topsquark

#### Pmb

PHF Hall of Fame
One point is that many of these thought experiments that require instantaneous changes of velocity can give odd results.
But you are specifying unrealistic conditions (instantaneous acceleration) so you can expect unrealistic results.

Another point might be, are you sure you have interpreted the scenario correctly?

Also how did the twins get separated by the distance L, in reference frame F0,
without relative acceleration, and thus a relative change of age?
In this experiment their age remains the same. But this is not the twins experiment. In that case one twin remains at rest while the other accelerates to and from a distant planet and back.

topsquark

#### GatheringKnowledge

In this experiment their age remains the same. But this is not the twins experiment. In that case one twin remains at rest while the other accelerates to and from a distant planet and back.
And what about the case, where the rate of aging process is different due to constant and linear motion (look at the diagrams above)? If one of the twins is moving at 0,5c in relation to his brother, then from the perspective of moving twin, it's his brother, that is moving at 0,5c. How in such case, their aging process can be different? According to SRT moving twin will be aging slower, than stationary one - how can it be, if in relative motion, being stationary is just a point of view and not an actual property of frame?

#### Woody

It is an odd thing but;
Twin A will see twin B moving at 0.5c relative to himself, and therefore aging slower,
Twin B will see Twin A moving at 0.5c relative to himself, and therefore aging slower,
in other words they both see the other one as aging slower!

The bizarre swapping of relative velocity in time due to relative velocity in space is a consequence of the fundamentally 4 dimensional nature of spacetime
it makes (mathematical) sense in 4 dimensional spacetime, but gives rise to counter intuitive results when you only consider the 3 space dimensions.

The paradox of them being at different ages when they subsequently meet can only happen if (at some stage) they accelerate (or decelerate) relative to each other to match speeds.
It will turn out that the one that has traveled further in space will have moved less far in time and visa versa.

#### GatheringKnowledge

The paradox of them being at different ages when they subsequently meet can only happen if (at some stage) they accelerate (or decelerate) relative to each other to match speeds.
Does it actually matter, which frame did accelerate/decelerate at some point in time? It could theoretically happen way before both frames meet in space, while both twins/clones were kept frozen in state of hibernation, up until some specific moment of time - so that during the time of acceleration/deceleration the aging process was paused for both of them. In such case, they won't know, which frame accelerated/decelerated in the past, until they won't meet in space and compare their ages - and after that, both will be able to learn about their motion in relation to the other twin/clone, as relative velocity of the younger one, will become a definitive property of his frame.

It will turn out that the one that has traveled further in space will have moved less far in time and visa versa.
But isn't the space RELATIVE as well? If for both twins/clones, it's the other one, that moves at 0,5c, then how could they pass different distances in space? If this would be true, then (again!) motion of one frame would become a definitive property. Here are 2 movies, which show the relativity of distances in space - how can we can possibly know, which object is passing there through a longer/shorter distance?

And there's more - what about the symmetry of Doppler's effect? Let's say, that both objects are emitting a pulse of light for every passing unit of time in their respective inertial frames. According to the diagram below, there won't be no symmetry in the observed Doppler's effect at all and both objects will observe completely different frequencies of light pulses, emitted by the incoming source - and while such situation might be true for waves, which propagate in a medium, this shouldn't happen for light propagating in a vacuum...

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