On 15/05/2022 09:46, Jeff Layman wrote:
> On 14/05/2022 22:35, Joe Gwinn wrote:
>> It turns out there is a long history, with many parallel explanations:
>>
>> .<https://en.wikipedia.org/wiki/Twin_paradox>
>
> It can be expanded to the Triplets Paradox, for example
> <http://www.mysearch.org.uk/website1/html/251.Triplets.html>
>
> SRT is well above me, I'm afraid. Some of the explanation of the Twins
> Paradox refers to the twins' clocks transmitting their time to the other
> twin (the clock signal is transmitted at the speed of light). Even
> allowing for the travelling twin's speed when approaching the speed of
> light, and the relativistic effect it has on each clock's perceived
> time, as the travelling twin's speed doesn't exceed that speed, each
> twin will, eventually, receive the clock time of the other.
>
> But what happens with the Triplet Paradox where the moving triplets are
> accelerating away from each other? Once they've "exceeded" C in relation
> to each other,

That never happens. Their relative velocity is *always* less than c as
viewed from one of their fast moving rest frames (doesn't matter which one).

You are applying a Galilean/Newtonian addition of velocities as measured
in the rest frame of the Earth in a situation where the full
relativistic treatment for addition of velocities is required. see

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

u = (v + u')/(1+vu'/c^2)

Mr stay at home with v=0 sees his two twins going away from him at +/-w

u[stay at home] = w

On either of the fast moving rockets they also see Mr Stay at home
receding from them at velocity w and their other twin receding at

u[other traveller] = (w+w)/(1+w^2/c^2) = 2w/(1+(w/c)^2)

To see why set w = c*(1-e)

= 2c*(1-e)/(1+(1-e)^2) = c*(2-2e)/(2-2e+e^2)

Common sense doesn't work with relativity at all. You can really only
trust the mathematics and the laws of physics always remaining self
consistent. Everything else derives from that basic axiom.

> although they can receive the stationary triplet's clock
> reading (and he can receive theirs), can one moving triplet still
> receive the other moving triplet's clock signal? If there is such a
> moment when they can no longer receive each other's signal, when they
> finally stop moving away and start moving towards each other again, will
> there be a moment when they suddenly start receiving that "missing"
> clock signal as they catch up with it (or perhaps it catches up with
> them)? Will there be a specific moment when they not only receive a
> missing clock time, but coincidentally receive the "accurate" time as
> transmitted by the other moving triplet, so appear to be receiving two
> different clock readings at the same time?

Spacetime itself can expand faster than the speed of light but that is a
consequence of GR. There are parts of the (presumed infinite) universe
that will remain forever inaccessible to us at any sub light speed.

--
Regards,
Martin Brown

On May 16, corvid wrote:
> >>> Also, there's no simultaneity between separated objects moving at
> >>> different speeds. The relativistic garage illustrates this.
> >>> Because the Bugatti is so fast, you drive towards the open end
> >>> of the garage at 0.5c. You measure the length of the garage as
> >>> 240 inches * sqrt(1-0.5**2) = 207.8 inches.
> >>> The hood of the car passes through the open door, then the closed
> >>> door opens before the back bumper has passed through the
> >>> doorway. No collision occurs, because the second door opens
> >>> before the first one closes.
> >>> Your spouse measures the length of the car as
> >>> 252 inches * sqrt(1-0.5**2) = 218.2 inches.
> >>> The car fits into the garage, so as it enters, the first door
> >>> closes before the second door opens. Once again no collision
> >>> occurs, because the car is shorter than the garage.
>
> Now I want to tweak the car and garage lengths, and the speed, so that
> the car goes thru unscathed in one frame but gets smashed in the other.
> Is it possible?

heh
Einstein skeptics have been trying to do that for a hundred years.

Playing around with the the numbers does make a nice exercise for the student.

You can also gin up variations on this paradox. For instance, the garage
becomes a two lane highway, with north and southbound lanes. Two cars
approach, simultaneously, as seen from the garage. In the garage frame, it's
much the same as before, both cars fit inside.

Then work out the various door sequences, as seen from each vehicle, for some
real brain twisting -

--
Rich

RichD wrote:
> On May 16, corvid wrote:
>>>>> Also, there's no simultaneity between separated objects moving at
>>>>> different speeds. The relativistic garage illustrates this.
>>>>> Because the Bugatti is so fast, you drive towards the open end
>>>>> of the garage at 0.5c. You measure the length of the garage as
>>>>> 240 inches * sqrt(1-0.5**2) = 207.8 inches.
>>>>> The hood of the car passes through the open door, then the closed
>>>>> door opens before the back bumper has passed through the
>>>>> doorway. No collision occurs, because the second door opens
>>>>> before the first one closes.
>>>>> Your spouse measures the length of the car as
>>>>> 252 inches * sqrt(1-0.5**2) = 218.2 inches.
>>>>> The car fits into the garage, so as it enters, the first door
>>>>> closes before the second door opens. Once again no collision
>>>>> occurs, because the car is shorter than the garage.
>>
>> Now I want to tweak the car and garage lengths, and the speed, so that
>> the car goes thru unscathed in one frame but gets smashed in the other.
>> Is it possible?
>
> heh
> Einstein skeptics have been trying to do that for a hundred years.

There's a class of things, called _Lorentz_scalars_, that are the same
in all reference frames, i.e. hitting them with a Lorentz transform
doesn't change the answer. On example is phase. (It's based on
counting, not length measurements.) Whether a collision occurs is one
of those.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com