I How Does Time Dilation Affect the Twin Paradox in Special Relativity?

[sennetor]

TL;DR Summary

Lorentz Transforms and Paradoxes driving me insane

I'm struggling to wrap my head around the twin paradox in special relativity especially when dealing with multiple vectors.
In my thought experiment say I have a set of twins. Both set out in opposite directions and intend to sling shot around two different black holes(luckily equidistant from the milky way) and rendezvous back where they started.

As they accelerate away towards 99.999%C(in perfectly opposite directions) observers in the Milkyway will notice that the occupants on the ship will almost freeze in time and will come back having aged slower than the Milkwayers.

My question is this...how will the two ship's clocks compare for

1. The outbound journey?
2. The Inbound Journey?
3. at the rendezvous location?

I'm also assuming their journey's are a perfect symmetry of each other(?)
If they end up having a synchronized clock at the end does this also reflect the experience of massless particles as they bound around the entire universe(like photons?) e.g. an emitted photon could in theory bounce off an event horizon and instantly find itself energizing the same electron orbit that emitted it? Surely this would also make us holograms!

 

[Ibix]

My question is this...how will the two ship's clocks compare

You need to look up the relativity of simultaneity, which is a really important part of the theory[1] and gets little air time. In short, what "during" each leg of the trip means is different for the different legs of the journey, and a naive time dilation analysis doesn't account for the bits of the other twins' experiences that aren't "during" any part of the trip (at least, not according to that naive analysis).

If they end up having a synchronized clock at the end does this also reflect the experience of massless particles

Massless particles travel along null worldlines and time isn't defined for them, so you can't describe their experience.[1] In deference to Orodruin, I will say "a really important part of the theory if you start with length contraction and time dilation instead of Minkowski geometry".

 

[PeterDonis]

I'm also assuming their journey's are a perfect symmetry of each other(?)

If that is the case (not sure why you have question marks after it, you are specifying the scenario and if you say the two journeys are symmetric, then they are), then this...

If they end up having a synchronized clock at the end

...will also be true.

an emitted photon could in theory bounce off an event horizon and instantly find itself energizing the same electron orbit that emitted it?

I have no idea where you're getting this from, but it's (a) unfounded and erroneous speculation, and (b) irrelevant to the scenario you describe in the OP of this thread. I would advise dropping this line of thought entirely.

 

[PeterDonis]

sling shot around two different black holes

Note that this is not "bouncing off" the event horizons of the holes.

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[Orodruin]

1] In deference to Orodruin, I will say "a really important part of the theory if you start with length contraction and time dilation instead of Minkowski geometry".

I would just refer to my signature... :)

Edit: Additionally, what I would consider questionable is the introduction of the simultaneity concept. However, once you do introduce it, that it is relative is extremely important.

 

[sennetor]

If that is the case (not sure why you have question marks after it, you are specifying the scenario and if you say the two journeys are symmetric, then they are), then this......will also be true.I have no idea where you're getting this from, but it's (a) unfounded and erroneous speculation, and (b) irrelevant to the scenario you describe in the OP of this thread. I would advise dropping this line of thought entirely.

Thanks Peter, You are right that last statement was erroneous and I was loosely trying to reconcile special relativity with quantum physics. If the two travellers have perfectly symmetrical journeys then in theory they could travel billions of light years apart but on the rendezvous still be in perfect sync with each other?

 

[Ibix]

If the two travellers have perfectly symmetrical journeys then in theory they could travel billions of light years apart but on the rendezvous still be in perfect sync with each other?

When they return, yes, they will be in sync. But during the journey most notions of simultaneity (pretty much all except the stay-at-home's notion, in fact) will say they are out of sync.

 

[PeroK]

If the two travellers have perfectly symmetrical journeys then in theory they could travel billions of light years apart but on the rendezvous still be in perfect sync with each other?

If their journeys are symmetric, which one would you expect to younger at the end?

 

[vanhees71]

I would just refer to my signature... :)

Edit: Additionally, what I would consider questionable is the introduction of the simultaneity concept. However, once you do introduce it, that it is relative is extremely important.

I think you cannot avoid to introduce the simultaneity effect. The important point in all theorizing is to make sure that you describe what's measured in a given measurement procedure. That's true for classical physics as it is (even more so) in quantum physics. E.g., the definition of the "length of an extended object" is necessarily relying on the definition that an observer, having established a frame of reference, reads off the spatial coordinates of the endpoints of the object simultaneously, where the definition of simultaneity is due to a clock-synchronization procedure, which is part of the definition of a reference frame.

In special relativity there are global inertial frames, and the standard syncrhonization convention is Einstein's of 1905 using the two-way speed of light and the assumption of isotropy. Only with this synchronization convention establishing the standard inertial reference frames the "kinematic paradoxes" like time dilation, length contraction, twin paradox, etc. follow and at the same time are resolved. Indeed they only appear as paradox, because we are used to the "Newtonian everyday experience" that simultaneity/time is absolute, but that's not the case in relativity (and obviously in nature, because relativistic spacetime models are the far better description than the Newtonian spacetime model).

In general relativity the concept of inertial frames is, by construction, local and thus all that is left to be clearly definable are strictly local observations and synchronization over larger distances is completely arbitrary, i.e., there is no in any way preferred "standard procedure" anymore.