[varsigma]

It isn't a paradox at all. It is a measurable effect,

Maybe it isn't a paradox, but that's how it was initially introduced in a thought experiment.

It is measurable, and of course, observation isn't a paradox; the paradox arises when dummies like us try to explain it.

[Halc]

Einstein's special theory is really like the law of thermodynamics: if your theory denies the reality of SR, there is no hope for it.

If the theory is valid, then there is hope for it.  There are valid theories which deny relativity and use completely different premises.  But indeed, none of the speculations posted in any forum is one of those. It's just not how valid theories get submitted.

The twin paradox is a problem--a physics problem.

It isn't a problem since relativity (and the valid alternatives) all explain it without paradox.  It only seems paradoxical when one tries to drag in premises of non-relativistic theories like Newtonian assumptions.

Hence the distance for acceleration(s) is negligible, hence ignoring that part of the journey has a negligible effect. Logic.

The distance of acceleration is whatever the scenario specifies.  Most realistic descriptions of space travel involve acceleration during the majority of the journey, so that portion of the journey cannot be negligible.

Some  people said that acceleration is relative, thus it's undefined without a frame of reference. Some others said that it's absolute, thus acceleration of an object can be determined without a frame of reference.

Proper acceleration (that which an accelerometer measures) is absolute.  Coordinate acceleration is frame dependent.  'acceleration' without adjective is ambiguous.

Proper acceleration can continue indefinitely, so a proper acceleration of 1G for 2 proper years will get you going a proper speed of about 2c, meaning you're traveling 2 light years (as measured in the inertial frame where you were originally at rest) for every year you age.  Constant coordinate acceleration cannot continue indefinitely (unbounded coordinate time) since it would result in a speed greater than light speed.

A and B set their clocks to zero as they whizz past each other

It is good to see you supporting the possibility of doing this. In prior times, you had asserted that the two must become relatively stationary in each other's presence in order to set their clocks to the same value. Indeed, it can be done in passing, as is done in several scenarios found on the web.

For simplicity, let A remain at rest or travelling in a straight line at constant velocity. He knows this because his accelerometer reads zero throughout the experiment.

How, then, can B fly past him again? Not if he is travelling at a constant velocity because their position vectors would continue to diverge. So he must....accelerate.

True in flat (Minkowskian) spacetime.  In curved spacetime, as in non-Euclidean spacetime, two straight lines (no proper acceleration) can meet in more than one place, and with differing lengths between the meetings.
This is seen in simple eccentric orbits.  The perigee of one orbit (of just a clock say) might be the same event as the apogee of another.  The latter might have an orbital period of twice the former, so the two objects meet regularly, and show different elapsed times between these meetings, all without registering any proper acceleration at all.

[varsigma]

The distance of acceleration is whatever the scenario specifies.  Most realistic descriptions of space travel involve acceleration during the majority of the journey, so that portion of the journey cannot be negligible.

Ok. But the twin (non)paradox doesn't have that description. Instead, it describes a journey then a return at constant velocity, usually the same velocity. It restricts the problem (it is a problem, even if it has a solution) to constant velocities and accelerations can be ignored. It isn't mysterious or a way to somehow cheat. It makes perfect sense to simply apply a single change of coordinates--the turnaround, rather than the continuous change that accelerations require.

I see this problem as a good way to investigate the significance of the Lorentz factor.

[alancalverd]

Instead, it describes a journey then a return at constant velocity, usually the same velocity. It restricts the problem (it is a problem, even if it has a solution) to constant velocities and accelerations can be ignored.

You can't ignore acceleration - regardless of the speed profile, the journey won't begin without an acceleration.

[alancalverd]

It is good to see you supporting the possibility of doing this. In prior times, you had asserted that the two must become relatively stationary in each other's presence in order to set their clocks to the same value.

There is no problem setting clocks to the same instantaneous value, but that isn't synchronisation - they could be running at widely different speeds before and after the "reset". Huge difference between reset (instantaneous push on the zero button) and synchronise (check they still read the same value a minute later).

I actually encountered this as a problem when dealing with a famous precision watchmaker back in the days of mechanical watches. He insisted that his master clock was correct because it reset to zero on the midnight GMT transmission. Problem was that by 4 pm it was a minute slow, and so his very expensive chronographs couldn't be used for navigation.!

[paul cotter]

The only way acceleration has a role is that it results in speed. The acceleration has no other significance.

[alancalverd]

If you start with two identical clocks at rest with respect to one another, they will stay in sync indefinitely unless you do something to one of them. Like accelerate it. There's the significance. No acceleration = no relative velocity = no dilation effect.

[varsigma]

You can't ignore acceleration - regardless of the speed profile, the journey won't begin without an acceleration.

Sure. Ok.

What you can do instead is say that, as long as accelerations are limited to distances much shorter than the total distance in the journey, there and back, they can be left out of the equations of motion. The result will be approximate, but you can still estimate this.

Why do artillery shells have a muzzle velocity? Why isn't the acceleration of an artillery shell in the barrel of a field gun part of the firing solution, when the approximate shell speed after it leaves the barrel is known?

[alancalverd]

The relativistic correction to the age of an artillery shell is irrelevant since it is not normally returned to its twin. The correction to the atomic clock on a GPS  satellite is very relevant (particularly if we want the shell to land in the right place). The satellite wasn't born in orbit but was accelerated from a position considered stationary with respect to the battlefield.
.

[hamdani yusuf]

Some  people said that acceleration is relative

An accelerometer consists of a mass attached to one end of some kind of spring, the other end of which is attached to the object being accelerated. An observer within any accelerating object will see a deflection on his accelerometer. Acceleration is therefore absolute.

ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.

[hamdani yusuf]

Proper acceleration can continue indefinitely, so a proper acceleration of 1G for 2 proper years will get you going a proper speed of about 2c, meaning you're traveling 2 light years (as measured in the inertial frame where you were originally at rest) for every year you age.

Does it mean I will see the earth recedes with speed 2c? What happens to the cosmic speed limit?

[hamdani yusuf]

I actually encountered this as a problem when dealing with a famous precision watchmaker back in the days of mechanical watches. He insisted that his master clock was correct because it reset to zero on the midnight GMT transmission. Problem was that by 4 pm it was a minute slow, and so his very expensive chronographs couldn't be used for navigation.!

https://control.com/textbook/instrument-calibration/zero-and-span-adjustments-analog-instruments/
Some instruments that we use have 1 point calibration. Some have 2 points of calibration. Some have a few more points of calibration.

[alancalverd]

You have put your finger on  the misunderstanding that pervades much of this discussion!

Accelerating a clock alters its tick rate, so when the traveller returns, the discrepancy between the elapsed times of the erstwhile twins depends on how long he has been away and what accelerations he has experienced in the trip.

[alancalverd]

ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.

Only if it read +1g before launch. The difference is the centripetal acceleration.

[paul cotter]

With respect to #70: yes the earth will appear to recede at 2c because your rapidity will be 2c. From the earth you will be seen to be travelling at <c.

[Janus]

You have put your finger on  the misunderstanding that pervades much of this discussion!

Accelerating a clock alters its tick rate, so when the traveller returns, the discrepancy between the elapsed times of the erstwhile twins depends on how long he has been away and what accelerations he has experienced in the trip.

No, it does not effect it's tick rate, it alters how it would consider other clock's tick rates compared to it own.  Clocks in the direction of the acceleration would be ticking faster compared to his own, and those in the opposite direction slower ( this is in addition to any Doppler shift due to relative velocity).   The difference in tick rate increases with distance in these directions.

[varsigma]

The relativistic correction to the age of an artillery shell is irrelevant since it is not normally returned to its twin.

Relativity is irrelevant if the topic is just acceleration. That is, how relevant is it, and to what.

[Halc]

ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.

Read my post.  Any accelerometer shows proper acceleration and an orbiting satellite will undergo no proper acceleration. The acceleration you speak of is coordinate acceleration, and even that might be zero. I mean, in the coordinate frame of my house, my orbiting sat-TV satellite is stationary (no coordinate acceleration) which is why I can point my dish at it and not have to move the dish.

Does it mean I will see the earth recedes with speed 2c? What happens to the cosmic speed limit?

With respect to #70: yes the earth will appear to recede at 2c because your rapidity will be 2c. From the earth you will be seen to be travelling at <c.

There's no direct appearance to a recession speed.  It is very frame dependent.
Relative to the inertial frame in which the ship is momentarily stationary, the Earth will be receding at around 0.964c.  Nothing can exceed c relative to an inertial frame. But if there was a tape measure glued to Earth that goes all the way along your journey, with a tick mark every light second, you'd see two of those tick marks go by your ship every second. That's what it means to be moving at a proper velocity of 2c relative to Earth.

Relative to the ship's accelerating frame, Earth will be seen receding almost not at all, and will never reach a light year away even after indefinite ship time, all very much like dropping a clock into a black hole.

Celerity (and not rapidity) is another word for proper velocity, at least they're the same in Minkowskian spaceitme.  One must be careful to use the correct term in other contexts.  And yes, the >c recession of galaxies relative to the expanding cosmic frame (not an inertial frame) is like a celerity of sorts. The proper distance between us and the distant thing (measured along a line of constant cosmologtical time) grows at a rate of >c.  Inertial frames are not even relevant at such distances, but if you remove all energy, the distant galaxy would not be moving faster than c relative to any inertial frame since the distance would not be along a line of constant cosmological time. It would be far closer, and its velocity in that frame would be sub-luminal.  It would still be moving at well over c in the non-inertial expanding frame, but that's a coordinate difference, not a physical one.

Accelerating a clock alters its tick rate

Not true.  I gave examples early in this topic that demonstrates otherwise, bottom of post 20.

[paul cotter]

Yes, of course Halc I got that one wrong. Travelling in an ever accelerating vehicle distances will be shortened and this effect will become more and more extreme as one asymptotically approaches c. SR, as opposed to GR, can appear to be deceptively simple but it can catch one out if not thinking clearly. In your tape measure example although the appearance of two light seconds per second will be observed at the point in question the tape will be shrinking as one progresses.

[hamdani yusuf]

I gave examples early in this topic that demonstrates otherwise, bottom of post 20.

Example 2)
I have a pair of wheels or gears. One wheel is 1000 times the radius of the other, and they meet at one point and move at the same velocity there. I put a clock on each wheel at the point at which they meet. The wheels get turned with the small  one going around at 1000 times the RPM and hence 1000 times the centripetal acceleration. Both clocks are moving at the same speed relative to the inertial frame of the setup. The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other. This also contradicts what Hossenfelder says in the video, but is entirely consistent with the formula that ES provided.

Is the bold statement backed up by experimental evidence?