The Twins Paradox in Relativity...

>It turns out there is a long history, with many parallel explanations:

Yep... pretty much all wrong....

..<https://en.wikipedia.org/wiki/Twin_paradox>

>Joe Gwinn

Well...... An actually correct account of the solution to the \"Twins
Paradox\" is here:

It explains the situation without accelerations, or frame switching. Yep.
Trust me, this is the real deal...:)


https://www.kevinaylward.co.uk/gr/twinsparadox/twinsparadox.htm


-- Kevin Aylward

http://www.anasoft.co.uk/ SuperSpice
http://www.kevinaylward.co.uk/ee/index.html
 
\"Martin Brown\" wrote in message news:t5tia2$6m9$1@gioia.aioe.org...

On 15/05/2022 12:05, Dimiter_Popoff wrote:
On 5/15/2022 0:35, Joe Gwinn wrote:
It turns out there is a long history, with many parallel explanations:

.<https://en.wikipedia.org/wiki/Twin_paradox

Joe Gwinn

And it explains why clocks at the equator and on the poles run
the same without involving gravity.

Actually they don\'t.

One of Einstein\'s minor errors in his 1905 paper on special relativity was
to predict how much slower a clock at the equator would tick when compared
to one at the pole (due to the extra rotational speed of a clock at the
equator). Every now and then someone points it out... eg

https://physicstoday.scitation.org/doi/10.1063/1.1897562#

They only run at the same speed when *both* the GR and SR corrections are
applied simultaneously and only then at mean sea level.

It is hard to get your head round but everybody\'s clock ticks at a
different speed. Your head ages marginally more quickly than your feet.
Click to expand...

Often quoted, but wrong. Its not how SR works.

In Special Relativity, clocks do not tick at different rates

Its a fundamental axiom of special relativity that \"the laws of physics are
indepandant of inertial motion\". This means, according to special
relativity, clocks must always tick at the same rate.

SR explains the apparent measurement of clock ticks reading slow by \"time
travel\". One travels through time at different t rates. Its a subtitle, but
important distinction.

Special Relativity holds that for example, one can cover time at a rate of
say, 100 secs/sec

Consider Dr.Who in his Tardis. He is traveling into the future , his own
ageing and clok ticks stay the same , for him, but he gets to the future
before someone else. If Dr. Who sent pulses as he is traveling, as he is
observe red to be traveling into the future, the received clock pulses would
be received as if slower .

The analogy is that there are many routes from London to Edinburgh. The
odometer will read different distances, but it always clocks up distance at
the same rate.

Clocks actually slowing down is a feature of the Lorentz Ether Theory, known
prior to the invention of SR and which Special Relativity claims to be
superior to.

The elephant in the room is that if the SR model is correct, then it leads
to the \"Block Universe\", that is, intrinsic to SR is that the future already
exists for everyone. This is in direct contradiction to Quantum Mechanics,
which holds that the future is intrinsically non deterministic.

Of note, is that QFT, is, essentially, and Ether theory in denial:

Professor (UK head of department) of Physics at Cambridge, David Tong (Adams
prize winner) has a YouTube general audience lecture on QFT:

https://www.youtube.com/watch?v=zNVQfWC_evg


0:31 - \"...What are we made of...what are the fundamental building
blocks of nature...?\"

19:30 - \"... so there is spread something throughout this room, something
we call the electron field..its like a fluid that fills ..the entire
universe..and the ripples of this electron fluid..the waves of this fluid
get tied into little bundles of energy, by the rules of quantum
mechanics..and these bundles of energy are what we call the particle the
electron....and the same is true for every kind of particle in the
universe...\"


Kevin Aylward

https://www.kevinaylward.co.uk/gr/index.html
http://www.anasoft.co.uk/ SuperSpice
http://www.kevinaylward.co.uk/ee/index.html
 
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
Click to expand...

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, 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?

--

Jeff
 

On 2022/05/16 7:18 a.m., Phil Hobbs wrote:
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, 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?


If you shine your laser pointer at two points 180 degrees apart in the
sky, the relative speed of the light pulses in your frame of reference
is 2c.  No paradox is involved.

Also, there\'s no simultaneity between separated objects moving at
different speeds.  The relativistic garage illustrates this.

Say you have a 1927 Bugatti Type 41, which is 252 inches long.  Your
garage is the standard 20 feed (240 inches) long, and has a very fast
automatically-controlled door at each end.  The doors are designed to
open and close automatically to allow the car to enter and leave.

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, waiting for you to come home from your drive, 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.

The math works out fine in both English and metric, and no paradoxes are
involved.

Cheers

Phil Hobbs
Click to expand...

How fast do the doors have to rise or close to clear the car...this
seems to be getting annoying close to the speed of light.

Pretty sure my garage door would warp if I ran it that fast! (ducking)

John ;-#)#

 
On 5/15/2022 0:35, Joe Gwinn wrote:
It turns out there is a long history, with many parallel explanations:

.<https://en.wikipedia.org/wiki/Twin_paradox

Joe Gwinn
Click to expand...

I am not a physicist but like many of us here I have been banging my
head into various technical problems so I am used to see when some
claim is somewhat questionable.
It\'s been years since I have read Einstein\'s papers but I remember
an example he gives, that with a train and a periodically flashing
light on it.
Obviously if the train is moving away from the observer because of the
fixed speed of light the period will seem somewhat longer to the
observer.
What is not addressed by this simple example is the case when the train
moves towards the observer - in which case obviously the period
will seem shorter to the observer.
A way to think of all that in terms obvious to most of us here
is that our reality is a state machine clocked (IIRC there was some
minimum time defined by Max Planck, could be the clock period) by
some clock; what we perceive as time is the resulting change of
states.
While this is a simplified and probably naive model it does
explain the train-flashing-light-period dependence on direction.
And it explains why clocks at the equator and on the poles run
the same without involving gravity.
 
Hi Kevin

What is the speed of a photon from the photon\'s POV? I think it must be
infinite, am I right?

Likewise, a sufficiently fast spaceship would have a speedometer showing
its speed as being >c? Is that right?

--
Cheers
Clive
 
John Robertson wrote:
On 2022/05/16 7:18 a.m., Phil Hobbs wrote:
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, 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?


If you shine your laser pointer at two points 180 degrees apart in the
sky, the relative speed of the light pulses in your frame of reference
is 2c.  No paradox is involved.

Also, there\'s no simultaneity between separated objects moving at
different speeds.  The relativistic garage illustrates this.

Say you have a 1927 Bugatti Type 41, which is 252 inches long.  Your
garage is the standard 20 feed (240 inches) long, and has a very fast
automatically-controlled door at each end.  The doors are designed to
open and close automatically to allow the car to enter and leave.

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, waiting for you to come home from your drive, 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.

The math works out fine in both English and metric, and no paradoxes
are involved.


How fast do the doors have to rise or close to clear the car...this
seems to be getting annoying close to the speed of light.

Pretty sure my garage door would warp if I ran it that fast! (ducking)
Click to expand...

As I mentioned upthread, the pistons would be going up and down at
impressive speeds too. ;)

The garage thing can be crispened up so as to be practically measurable.
The point of the doors is that if a collision occurs, it occurs in all
reference frames.

Cheers

Phil Hobbs


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

http://electrooptical.net
http://hobbs-eo.com
 
John Robertson wrote:
On 2022/05/16 7:18 a.m., Phil Hobbs wrote:
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, 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?


If you shine your laser pointer at two points 180 degrees apart in the
sky, the relative speed of the light pulses in your frame of reference
is 2c.  No paradox is involved.

Also, there\'s no simultaneity between separated objects moving at
different speeds.  The relativistic garage illustrates this.

Say you have a 1927 Bugatti Type 41, which is 252 inches long.  Your
garage is the standard 20 feed (240 inches) long, and has a very fast
automatically-controlled door at each end.  The doors are designed to
open and close automatically to allow the car to enter and leave.

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, waiting for you to come home from your drive, 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.

The math works out fine in both English and metric, and no paradoxes
are involved.

Cheers

Phil Hobbs


How fast do the doors have to rise or close to clear the car...this
seems to be getting annoying close to the speed of light.

Pretty sure my garage door would warp if I ran it that fast! (ducking)
Click to expand...

There are also a few other practical problems, e.g. that the kinetic
energy of a 2000 kg car going at c/2 is

m c**2 (gamma -1) =
2000 kg * (299792458 m/s)**2 * ( 1 / sqrt(1-0.25) - 1 ) =
2.87E19 J.

That\'s 6653 megatons, at the usually quoted rate of 1 MT = 1e15 cal
(4.18E15 J).

The XKCD baseball is a mere 8 MT.
<https://what-if.xkcd.com/1/>.

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
 
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,
Click to expand...

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?
Click to expand...

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
 
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