Twins flying at the speed of light in opposite directions

[Feeble Wonk]

Having reviewed a portion of the thread I had previously overlooked, I find myself confused by the role of acceleration as it pertains to GR. I'm hoping someone can enlighten me.
If we consider a single spaceship launching from earth, obtaining near-light speed, and then returning to earth, the spaceship and occupants will have aged more slowly than Earth and it inhabitants. If it is not the boost/acceleration forces that alter the space ships inertial frame state, what determines the "object" in motion? If it's only the distance and velocity that matter, why can't we say that the Earth launched away from the spaceship and then returned. I've always had the layman's understanding that the acceleration and change in inertial state experienced by the spaceship is what determines relative time dilation. Can anyone explain my misconception without resorting to complicated mathematical formulation that will definitely be over my head.

 

[Herman Trivilino]

If it is not the boost/acceleration forces that alter the space ships inertial frame state, what determines the "object" in motion?

Nothing! That's the entire point of the Principle of Relativity. There is no way to determine which twin is in a state of motion and which isn't, as long as the motion is uniform.

It is the acceleration of the traveling twin, though, that distinguishes his experience from that of the stay-at-home twin.

If it's only the distance and velocity that matter, why can't we say that the Earth launched away from the spaceship and then returned. I've always had the layman's understanding that the acceleration and change in inertial state experienced by the spaceship is what determines relative time dilation. Can anyone explain my misconception without resorting to complicated mathematical formulation that will definitely be over my head.

Because it's not only the distance and velocity that matter in the full analysis. There's more to the analysis than just that. The difference in aging of the twins is due not only to time dilation but to a combination of time dilation and the traveling twin's acceleration.

Now, if you want to understand this on a conceptual level, delving into the math only when necessary, you have two options.

The first is to understand things only from the perspective of the stay-at-home twin. His situation is different than his brothers because of the reason mentioned above. And because of that reason, his situation is easier to understand. You can use time dilation alone to understand things from his point of view. With a bit of easy arithmetic you can calculate the time dilation factor knowing only the speed. For example at a speed of 0.87 c the factor is about 2. So if the traveling twin ages 10 years, the stay at home twin ages 20.

To complete this first way of understanding you need a reason to not be able to use this same approach to analyze things from the traveling twin's perspective. And that reason is because the traveling twin's motion is not inertial, for the reason previously discussed.

The second way of understanding involves all of the above, plus an analysis of the situation from the traveling twin's perspective. That analysis includes not only the time dilation as discussed for the stay-at-home twin, but also the effect due to the relativity of simultaneity that occurs when the traveling twin changes direction. If you want to explore this let us know. The math involves only arithmetic, but the level of detail of the analysis is deeper and requires greater mental effort.

 

[Feeble Wonk]

So... The acceleration, and related shift in inertial state, of the traveling twin IS the factor that causes the time dilation experienced by the stay at home twin relative to the traveling twin? Orodruin's post here confused me.

While this is true, it gives the impression that acceleration plays a central role, which it does not. Any effects from the accelerating parts of the journey can be made completely negligible simply by extending the constant velocity parts. The twin "paradox" comes about simply from missing out on the relativity of simultaneity and blindly applying the time dilation formula.

Regarding the acceleration, it is relatively simple to show that the straight, unaccelerated path in Minkowski space between two events will maximise the proper time between them. This is no stranger than a straight line minimising the length of a curve between two points in Euclidean geometry.

 

[Herman Trivilino]

So... The acceleration, and related shift in inertial state, of the traveling twin IS the factor that causes the time dilation?

No, it's not. For the reasons I stated.

Orodruin's post here confused me.

Everything he said is not only correct, it's vital to an understanding.

 

[Feeble Wonk]

To complete this first way of understanding you need a reason to not be able to use this same approach to analyze things from the traveling twin's perspective. And that reason is because the traveling twin's motion is not inertial, for the reason previously discussed.

The second way of understanding involves all of the above, plus an analysis of the situation from the traveling twin's perspective. That analysis includes not only the time dilation as discussed for the stay-at-home twin, but also the effect due to the relativity of simultaneity that occurs when the traveling twin changes direction. If you want to explore this let us know. The math involves only arithmetic, but the level of detail of the analysis is deeper and requires greater mental effort.

Thanks. Let me think about this some before I waste your time. I had a general understanding that it was the change of directions and shift in inertial states that caused the relative time dilation, but now I don't think I properly understood the reason WHY that occurs. I'll have to ponder that.

 

[Herman Trivilino]

Note that the analysis of the situation from the stay-at-home twin's viewpoint involves only time dilation. His brother's acceleration has nothing whatever to do with his analysis.

It's when you try to understand or explain why the same analysis doesn't apply to the traveling twin that the acceleration comes into it. Or if you go deeper and try to explain things from the traveling twin's perspective.

 

[Feeble Wonk]

It's when you try to understand or explain why the same analysis doesn't apply to the traveling twin that the acceleration comes into it.

Yes. That's what I meant. My previous GENERAL understanding was that the "relative" time dilation (resulting in the traveling twin aging less than the stay-at-home twin) was due to the change in direction and shift in inertial states... and that was why the same analysis doesn't apply to the traveling twin. But there is obviously more to it than that. As I suggested in regard to the OP, the relativity of simultaneity is also difficult for me to wrap my head around. I think that's the issue I've got to understand better.

 

[Orodruin]

the relativity of simultaneity is also difficult for me to wrap my head around

Try reading this: https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/
It really is nothing but an effect of using different coordinate systems.

 

[Ibix]

The elapsed time for any observer is the length of their path through 4d spacetime. The rate at which someone else's clock is ticking depends on the angle between their path and yours.

The two twins took different length paths through spacetime, which is why they end up different ages. But (for any agreed definition of an instant) the angle between the two paths is the same measured from either path at the same instant, which is why both twins see the other's clock ticking slow.

As Mr T says, relativity of simultaneity is a big part of making all of this add up, but the above is basically "why".