[Halc]

It's not a function of acceleration, so I cannot say from just that.

Then would you say that Sabine in the video is wrong?

I am actually going to go so far as to say exactly that. I caution against taking a simple comment out of context, and I'm not much on clicking videos and actually watching them (21 minutes to wade through), and it's Sabine, so I presumed the content is accurate. Well it isn't, which is a shame.

At 0:40 she complains about trying to learn relativity from pop-science sources and failing or finding them incorrect. Many are. Here she is creating her own pop-science tutorial and she does the same thing: get it wrong.

At 1:45 she gets into the length of the path between two sets of coordinates, correctly pointing out that different paths are different lengths despite the beginning and end of the paths being the same, as it is in the twins scenario.

At 6:50 she shows how the calculation of the temporal length of an arbitrary path can be done by breaking the path into pieces and integrating over the length of the path. This is what Eternal Student has done in post 16:

Do you know any math formulas to see how acceleration and time dilation are related?

the elapsed time for the travelling twin (who goes to Andromeda) is given by:

Δτ =   

[Eqn 2]

The computation above is completely scalar. Note the complete lack of acceleration reference in the formula. I see time and speed (v) and that's it. It isn't a function of acceleration, as I said above. The formula above is from special relativity, so it only applies to the special case where gravity is not involved. Hossenfelder's video is entitled "Special Relativity: This Is Why You Misunderstand It", which means the content should stay away from gravity, or the video is mistitled.

And what's with Andromeda? Sure, with enough acceleration, Bob can get there and back before he dies, but Alice (and the whole human race for that matter) isn't going to be there upon his return. Sabine should pick a closer target.

Back to the video:
At 11:00 we get into the twins thing and she correctly says that at least one of the twins needs to accelerate to turn around. That's a biased way of putting it, but true. More correctly, at least one of them needs to accelerate in order for their paths to diverge but meet up a second time. Without acceleration, any relative velocity will just have them meet once at best and forever diverge after that. But it isn't the acceleration that causes the dilation, it is the relative temporal lengths of the paths they take, as computed by the above formula.

11:25 She says acceleration is absolute. She means proper acceleration (the kind you feel with an accelerometer) is absolute. Coordinate acceleration is relative to some coordinate system and is thus not absolute. So sitting at your computer reading this, your coordinate acceleration (relative to your house maybe) is stationary, but your proper acceleration is 1g upward because that's how hard the chair under you is accelerating you.

12:52 She correctly points out that the twins scenario has nothing to do with gravity.

13:39 She correctly points out that the twins starting and ending with the same velocity is not necessary (except to explain that they're twins and presumably had reasonably identical velocity at birth. They merely have to meet twice.

15:30 We start getting into gravity, which is out of scope for a video entitled "Special relativity". She starts with pointing out that under Einstein, gravity is not a force. It is in fact spacetime which has a geometery other than flat Minkowskian spacetime. So anything not accelerating (has no force acting on it) follows a geodesic along the local spacetime.

16:55 She first says acceleration causes time dilation. This is blatantly wrong. Contradictions follow.
17:50 Things really start falling apart. The time runs slower at sea level than on a mountain due to greater acceleration at sea level. This is completely wrong. If true, clocks would run fastest at the center of Earth where acceleration would be zero, but they in fact run slowest there than anywhere else on Earth. The acceleration on the surface of Mercury is under 40% of that on Earth, but time on Mercury runs slower, directly contradicting what Sabine is saying.

19:25 She asks if her video was any better than those incomprehensible books from way back? Well it would be if she hadn't mucked it up.

Back to Special relativity, since I want to disassemble her treatment of that as well and not just her botching the gravity bit. A couple examples contradicting her assertions:

Example 1) Alice, Bob and Chuck are triplets and age 20. Alice stays home. Bob and Check set out on a trip and accelerate identically (10g say) for a month and then coast, riding side by side for a while.  After a year on his own clock, Bob accelerates towards Earth at 10g for 2 months, going back towards home at the same speed he went out. He coasts for another year and takes a month to stop. He's aged 2 years coasting and 4 months acceleration and is age 22y4m now and finds Alice at age 23y2m, or 10 months older. They wait together for Chuck to come back.
Chuck coasts twice as long and turns back. So he ages 4 years coasting and the 4 months accelerating and comes home at age 24y4m finding Alice to be 25y5.7m and Bob to be 24y7.7m.
This contradicts what Hossenfelder says since both Bob and Chuck have experienced identical accelerations, just at different times. They should be aged identically per Hossenfelder's words, but they're not. This is one trouble with doing physics in the language of laymen instead of the language of physcs. Time dilation is not a function of acceleration and there's no mathematical formula expressing it in terms of acceleration.

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.

[alancalverd]

The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other.

Not if they were in sync before you started the second one moving. The twin "paradox" is about two clocks initially at rest and synced with respect to one another but subsequently acquiring a relative velocity, therefore one must have accelerated.

[Halc]

The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other.

Not if they were in sync before you started the second one moving.

Incorrect. If you read my post, they're both moving relative to Earth, and always at the exact same speed (~460 m/sec). The difference is in magnitude of acceleration, 1g (away from the axis) vs 1000g (towards the axis).

The twin "paradox" is about two clocks initially at rest and synced with respect to one another but subsequently acquiring a relative velocity, therefore one must have accelerated.

In the example above, both accelerate, but one far more than the other. The point (unlike the twin scenario) is to illustrate that differential aging is not a function of magnitude of acceleration, as the video mistakenly suggests. Neither clock will run faster than the other.

Since you're on the horn:

If they were "always" moving relative to one another, you had no means of synchronising them.

This is incorrect. Clocks in each other's presence can be objectively synchronised or compared to each other. They can either both be zeroed (such as at the departure event) or the either observer can note the time on the other clock as it passes by (such as at the return event). Physical events such as this are objective and not frame dependent. If Bob reads a certain value at some event, that value measured is the same regardless of frame choice.

[alancalverd]

Incorrect. If you read my post, they're both moving relative to Earth, and always at the exact same speed (~460 m/sec). The difference is in magnitude of acceleration, 1g (away from the axis) vs 1000g (towards the axis).

But the "polar" clock P started at rest relative to the earth's  surface and was therefore travelling 460m/s slower than the "equatorial" clock E. So if you synchronised them (to make twins) and then accelerated P to 460 m/s you will have altered its tick rate as seen from E. Alternatively you could wait until  their relative speed is zero and then synchronise them, in which case they will indeed remain in step.

[alancalverd]

either observer can note the time on the other clock as it passes by

That isn't the point. Time dilation concerns the tick rate of A as observed at B.

[alancalverd]

It is caused by the change in velocity of the traveling twin (he), when he is separated from the home twin (she).

And apropos another thread. when did "change in velocity" cease to  mean "acceleration"?

Also important to note that "twins" implies identity, such that when the relative velocity is zero, both clocks (physical or biological) remain in sync. Thus "instantaneous synchronisation" on a fly-by is not permitted.

[Petrochemicals]

My guess is that it would be gravity, however that works. Acceleration being the addition of relitavistic mass, space seeming to have the ability to transmit gravity waves through its medium, I have to theorise that space is sticky to mass particles and therefore giving relitavistic mass decreaces clock speed.

[hamdani yusuf]

Thought experiments are only useful to examine consistency among many assumptions taken to build a model. It can't check if the model accurately represent physical reality. That would take physical experiments.

[varsigma]

A change in direction is an acceleration.

It's also a coordinate change, which is of course, relative to the other twin.

The other key thing is the difference between comparing clocks locally (being able to synchronize clocks), and comparing them over a distance because--the speed of light is finite (!).

[Gilyermo]

In physics discussions, particularly when addressing concepts like time dilation and relativistic effects, precision in language is crucial to avoid confusion. If you believe that Don Lincoln's explanations have led to misunderstandings or misrepresented certain aspects of the topic, it's valid to provide additional context or clarification, especially if you have a strong background in the subject matter.

[hamdani yusuf]

The Twins Clock Paradox History and Perspectives
Robert L. Shuler Jr.*
NASA Johnson Space Center, Houston, TX, USA.

Abstract

The twins or clock paradox has been a subject of lively discussion and occasional disagreement among both relativists and the public for over 100 years, and continues to attract physicists who write papers giving new analyses or defending old ones, even though many physicists now consider the matter only of educational interest. This paper investigates the number of papers, which is increasing, and trends in explanations, some of which are now targeted at professional physicists and other of which are targeted at optical or radar visualization rather than problem solving. Observations of students indicate that the latest techniques help but only somewhat. An analysis is made of 21 previous treatments appearing in the education related American Journal of Physics, Einstein?s discussions and several other pedagogical papers. A new memory aid for simultaneity transformation is given that puts it on a par with ?time dilation? and ?length contraction? for quick and easy problem visualization. The point of view of a trailing twin is introduced to show how simultaneity changes account for missing time in the turnaround. Length contraction is treated on equal footing with time dilation, and Swann?s insight into clocks is extended to lengths. Treatments using the conventionality of simultaneity are seen as equivalent to choice of co-moving frames. Responses to difficult questions are suggested which avoid being dismissive, and engage students? critical thinking.
https://www.scirp.org/journal/paperinformation.aspx?paperid=47747

I guess the article here can be considered mainstream.

[yor_on]

It's about being in different frames of reference to me. Think of the muon example in physics for it. And if you want to define it to something as simple as an acceleration then?

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

you can also take a look at this one.   https://physics.stackexchange.com/questions/165179/does-light-itself-experience-time-dilation

[yor_on]

The only thing we don't define as 'accelerating' are mass less particles as light. They create a recoil though as they 'leave' which we then define to conservation laws. Everything else being of 'proper mass' or whatever one might want to call it, will have an acceleration as far as I know. We also define a carousel as 'accelerating' although it has a constant uniform speed, but we don't define infalling light, f.ex towards earth, the same way. Instead we refer to that as blue and red shifts, which will be observer defined.
=

Gravity is an example of an equivalence to mass or if you like, 'acceleration', in relativity, So is gravity time dilated? And photons, or light, is defined as a speed, a 'constant' speed. so when that 'photon' follows its geodesic, gravity 'bending the path' as defined by us?

Another example: Think of that twin traveling, as defined by you and your common 'origin'. His time, and everything being in a same reference, 'slows down' relative your own clock. Aka becoming younger than you once back. So what happens to that rockets 'velocity', as defined by you?

So no, it's not only about accelerations, although they definitely play a big role. But it also depends on your definitions. For example, if one agree on that accelerations, gravity and mass are equivalences, describing the same thing from although from different angles? Blue & red shifts being massless equivalences to different 'speeds' (including accelerations) described in a 'proper mass reference frame'?

that whole thing becomes a question
=

The funny thing, accepting the above, is that you might be able to reach a conclusion much like Newton did about 'time'. An locally 'absolute time' of no variance intrinsically, with other permutations of it described through 'frames of reference', 'masking' that invariance.

[hamdani yusuf]

It's about being in different frames of reference to me.

Let's start with the simplest frame of reference first, which is the midway observer. What will he observe when he meet both travelling twins? At that moment, what's shown by his own clock, and the clocks brought by the travelling twins?
Before these questions are answered, it's useless to switch to other frames of reference and pursue more complex questions.

[yor_on]

Observers always have a unique frame of reference. Where the twin experiment uses it by letting them leave and come back to an ''ideal' common frame of reference. We all become unique 'observers' if one f.ex use NIST gravitational time dilation experiments to define what frames of reference means.

[yor_on]

All of it comes from the same thing. Lights speed in a vacuum which is what special relativity build on. Where gravity comes into it first in General relativity, 'warping' space, giving different 'lightpaths' / geodesics. Frames of reference becomes a very complex definition to me :)
=

The only thing that twin experiment brings with it is the idea of time being malleable. But to do it right you will need to create a 'global' frame of reference for it. An unyielding time and space with the eye of a God watching it / ours. Somewhat like Newton. And Einstein himself defined it as no such frame can exist. So it's still 'observer dependent' that twin experiment

That's actually one of the trickiest parts of relativity. That no frame of reference can be a more 'privileged frame' than any other, no matter what I may think of the universe I observe. Which actually, turned around, and in a very backhanded fashion means that all frames of reference 'intrinsically' or 'locally' could be seen as equivalent

[Eternal Student]

Hi.

    I've only skim read some of the later posts but was here at the beginning,  there may be some bits in the middle I have overlooked.   So I apologise if much of this has already been said.
    The reply here https://www.thenakedscientists.com/forum/index.php?topic=86675.msg719270#msg719270 by @Halc looks good.

    There are several places where people have raised the question about whether General relativity is needed in the Twin paradox and not just Special relativity.   This is presumably because one twin has to be accelerated while the other doesn't have to be.   Some people wanted experimental results to back up the notion that SR is sufficient and GR is not required.
    It is indeed difficult to do the experiment where the travelling twin was never accelerated, we can't easily just take all the acceleration away.   However, we can add extra acceleration and that doesn't seem to affect the result,  it remains consistent with the application of just SR.
     The travelling object (maybe the travelling twin) doesn't have to take a straight line path out to some place and abruptly reverse direction.   The result still holds if the travelling object moved in a circular path and that can obviously still bring them back to the original starting location.    The obvious example of a suitable experiment is putting a clock into an aeroplane, flying it around the world and comparing with a clock that remained on the surface of the earth.    Since the travelling object is undergoing circular motion, it is experiencing a centripetal accelertion that is not present if the object had moved in straight paths out to their turn-around point and then back home.

    Experiments like this have been done.   See  https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment   

    If you do spend a moment looking at the Hafele?Keating experiment (the clock in an aeroplane),  you'll notice that they didn't consider the clock on earth as being in an inertial frame (because planet earth rotates).   Instead they assumed only that a clock at rest at the centre of the earth would be in frame that could be considered to be inertial.   Indeed, the clock on the plane actually runs faster than the clock staying on the surface of the earth when they fly westward.   Only the eastward flight resulted in the aeroplane clock running more slowly than the earth-bound clock.   If the clock staying on earth had been at rest in an inertial frame, then a clock moving either way relative to the earth bound clock should have ticked more slowly.
   Analysing the situation in the same reference frame they used, we see that the eastward and westward travelling plane actually required different centripetal accelerations.    They did not (and seemingly did not need to) consider this difference in acceleration when predicting the difference displayed on the clocks.  The only use of results from GR involved making an adjustment for the different altitudes of the planes - since there would be some gravitational time dilation.
    That's enough for this post and the question being asked here.   For a side-line people may wish to spend a moment considering whether a centripetal acceleration is indistinguishable from acceleration due to a gravitational field.   That's a separate issue that may only confuse or confound the point being made.   It is recognised that gravitational time dilation is dependant on the difference in gravitational potential of two clocks and not on the actual accelerations those two clocks may experience.   In essence then, using GR to correct for gravitational time dilation did not accidentally (or intentionally) take account of the different centripetal accelerations of the clocks.

    A more modern version of the experiment can allow for a greater variation of accelerations, speeds and total distance travelled.   Here's an outline of an experiment you could do, although I do not have the equipment and I can't find any internet reference to something like this. 
   Since centripetal acceleration  a = v² / r,  we can control the acceleration by altering the radius of a circular path while holding the speed constant.   A radioactive substance has a half-life and this can act as a clock that travels with our object.   So we can put a charged radioactive particle into a cyclotron and control its path by altering the magnetic field in the cyclotron.   The average decay time of the particle as measured in the lab frame should be longer than if the particle had been kept at rest in the lab frame.   We can try various combinations of speed, total distance travelled and centripetal acceleration experienced.   Assuming SR is sufficient, then only the speed and total distance travelled matters (acceleration doesn't).

Best Wishes.

[Jaaanosik]

There are errors in the video.

at 10:36

C's perspective and event I
(x,t)_I,C=(0,0)

This is wrong.
The event I does not start at x_C=0.
This is not the origin of the C perspective if C position is chosen as the origin of C reference frame.
Regardless, x_I,C=x_III,C has to be true.
If it is not true then the analysis is wrong.
Clearly, the video shows different x values so it is wrong.
That guy made a mistake!

[Eternal Student]

Hi.

if C position is chosen as the origin of C reference frame.

   Don (the presenter) didn't make it clear where the origin for the reference frame of C would be.   If it had been centred on C then you'd be absolutely right.    However, in this video he didn't have that frame centred on C.   All frames (A, B, or C)  were set up to have  the origin  (0,0)  identify event I   (in words, the origin of all the reference frames was planet earth at the moment when A started to travel away from it).   So only observers A and B have the origin of their reference frame centred around themselves.

    This wasn't made clear by the presenter and isn't a very conventional choice but it isn't necessarily wrong.   Since it can cause confusion it's a fault in the video of one sort.   The "confusion" isn't just something you had, it took me quite a bit of time and re-playing the video to see what had happened.

Best Wishes.

[Jaaanosik]

Hi.

if C position is chosen as the origin of C reference frame.

   Don (the presenter) didn't make it clear where the origin for the reference frame of C would be.   If it had been centred on C then you'd be absolutely right.    However, in this video he didn't have that frame centred on C.   All frames (A, B, or C)  were set up to have  the origin  (0,0)  identify event I   (in words, the origin of all the reference frames was planet earth at the moment when A started to travel away from it).   So only observers A and B have the origin of their reference frame centred around themselves.

    This wasn't made clear by the presenter and isn't a very conventional choice but it isn't necessarily wrong.   Since it can cause confusion it's a fault in the video of one sort.   The "confusion" isn't just something you had, it took me quite a bit of time and re-playing the video to see what had happened.

Best Wishes.

Then it comes back to clock synchronization and simultaneity.
The inertial frames do not agree on the simultaneity.
The time on the C spaceship is wrong.

Edit:
A question.
How do we call 'jumping' from one inertial frame to another?
Changing an inertial reference frame?
...
Answer: acceleration, momentarily comoving inertial reference frames explain it.