B Why the stay-at-home twin is not considered to be accelerating?

[dayalanand roy]

And also with accelerating non-inertial motion.
Not quite. When we talk about aging of the twins we are talking about them comparing their clocks when they share the same location. Thus the traveling twin must return to the location of the staying twin to compare ages. If all the traveling twin does is move away from the staying twin there is no objective way to compare their ages. Each will observe that the other's clocks are running slow, and the comparison is complicated by the fact that the twins don't share the same location. In addition to the clock that each twin keeps with them, they will each need a second clock synchronized with their near-by clock, and placed at the location of the other twin. Each twin will claim that the other twin has performed the synchronization incorrectly (this is called the relativity of simultaneity) and so they will disagree as to which twin has aged more. They need to share the same location to get around this difficulty.
See the above explanation involving the relativity of simultaneity.
It is A who changes direction. B does not. That's why the situation is not symmetrical.

Before you try to understand the twin paradox you must first understand the symmetry of time dilation. When two people are in motion relative to each other, each will claim that the other's clock is running slow. You can't gloss over this apparent contradiction. You must understand how the relativity of simultaneity makes it possible. And it does involve some math, but the math is not complicated, it just involves multiplication and addition.

Thank you so much sir for your enlightening reply. Your answer removed many doubts from my mind. But the major doubt is still remaining.
I want to know that when A is accelerating away from B, or changing direction in relation to B, why not B too is considered to accelerate or change direction? For example, suppose both A and B are standing side by side. Their relative speed is zero. A starts moving and his speed increases from zero to 100 m/s in 1 second. His acceleration is 100 m /s 2. Relativity says that both are moving in relation to each other. So B's speed also increases from zero to 100 m /s. Thus, B should also be accelerating at 100 m /s2. So, why can't B too said to be accelerating.
Similarly, let us suppose both are standing side by side, and A starts moving towards his left. Then, if B is also considered to be moving in relation to A, definitely he is moving towards A's right. Or, suppose both are walking together at equal speed towards east. A suddenly turns left and starts walking towards north. Now, though B has not changed direction, yet, in relation to A, his direction is changed now. So, if A is said to accelerate according to relativity, why not B is also accelerating. If movement is relative, speed is relative, why not acceleration or direction is relative too? This is my doubt.
Thanks and regards

 

[dayalanand roy]

See the space-time diagram below.

The Twin Paradox

One twin stays on earth.
One twin leaves Earth at high speed (0.4142c), travels for 5 Earth years, and then returns.
The stay-at-home twin says that 10 years have elapsed since the traveller left.
The traveller says only 9 years have elapsed since she left.

Two things need to be explained:

Paradox 1. Why is the traveller only 9 years older whereas the stay-at-home twin is 10 years older?

Paradox 2. All the time that the traveller is travelling, the traveller observes stay-at-home's clock to be running slower than traveller's clock. And, all the time that traveller is travelling, stay-at-home observes traveller's clock to run slower than stay-at-home's clock. So each observes the other's clock to be running slower than his own clock so each must be younger than the other!

The resolution is given in the space-time diagram below based on Earth = 10 (years) and traveller (purple line), traveling at 0.4142c relative to earth, taking 9 years, 4.5 years on his blue axes to get to the turn round, and 4.5 years on the blue axis to get back. Note that I should really have drawn a yellow grid angled the other way for the traveller's return journey but the angles are the same so the values read off are the same.

An Event is a point on the diagram. The Earth observer uses the black grid lines to measure the time and space coordinates of the Event in their frame. The traveling observer uses the sloping blue grid lines to measure the time and space coordinates of that same Event in their frame.

Notice that, as he is traveling away, just before he turns round, traveller measures Event A on Earth (earth time t = 4.2) to take place at traveller's time t = 4.5 (dotted purple line of traveller's simultaneity). So traveller measures Earth's clock (4.2) to be running slower than traveller's clock (4.5).

Note that Earth observes the traveller to turn round at Earth time t = 5, but traveller's clock reads only 4.5. So Earth observes traveller's clock to run slower than Earth's clock.

That is, each observes the other's clock to run slower than their own clock.

When traveller is stationary at the turn round, he says time on Earth is now 5 (the dotted purple line would now be horizontal).

When traveller is up to speed going back (but before he has moved any distance) he measures Event B (earth time t = 5.8) to be at traveller's time of 4.5. So traveller jumps (instantaneously) from Earth time = 4.2 to Earth time = 5.8, and "jumps across" 1.6 years at the turn round point.

Similarly, on the way back, it takes traveller 4.5 years.

So, traveller's journey time = 4.5 + 4.5 = 9 years on traveller's clock. But the 10 years of Earth's time is made up of comprises 4.2 Earth years out, plus a gap of 1.6 Earth years, plus 4.2 Earth years back, for a total of 10 Earth years.

Note also that the faster the traveling twin moves the bigger the gap between Event A and Event B becomes. A photon traveling at c (the green line on the diagram) sees no time elapse between departing Earth and arriving back on Earth - the gap between Event A and Event B is now the full ten years.
View attachment 266257

Thanks sir for your reply.

 

[Herman Trivilino]

A starts moving and his speed increases from zero to 100 m/s in 1 second. His acceleration is 100 m /s 2. Relativity says that both are moving in relation to each other. So B's speed also increases from zero to 100 m /s. Thus, B should also be accelerating at 100 m /s2. So, why can't B too said to be accelerating.

They are in motion relative to each other. You can choose a frame of reference where A is at rest and B is moving, or B is at rest and A is moving, but those are just choices of reference frames. They have nothing to do with the physical fact that A and B are in motion relative to each other.

Acceleration, on the other hand, is absolute. You can, for example, attach a weight to a spring. When the spring stretches or compresses you know you're accelerating.

 

[Sagittarius A-Star]

If movement is relative, speed is relative, why not acceleration or direction is relative too?

A is accelerating relative to an inertial frame (=proper acceleration), B not (only coordinate acceleration). That is an asymmetry of the scenario whith relevance to time-dilation.

 

[dayalanand roy]

Coordinate acceleration is relative:
https://en.wikipedia.org/wiki/Acceleration

Proper acceleration is not relative:
https://en.wikipedia.org/wiki/Proper_acceleration

Thanks for this help. Got to learn the difference between coordinate acceleration and proper acceleration, and the doubt is now clear to some extent. Thanks again.

 

[dayalanand roy]

You missed out two important words:

According to special relativity, inertial motion is relative.

Yes. Thanks for the correction.

 

[dayalanand roy]

Suppose both twins are carrying accelerometers. The stay-at-at-home accelerometer reads zero throughout, while the traveler’s accelerometer shows non-zero acceleration at the time of the turnaround. That’s how we know that the traveler is accelerating.

You will also want to follow up on what @A.T. says in post #2 above: the distinction between coordinate acceleration and proper acceleration. We have many good threads on this.

Thanks. Yes, I learned the difference between coordinate acceleration and proper acceleration from the links given in above post. Thanks and regards

 

[dayalanand roy]

In addition to the comments by other posters, this is wrong. Special relativity deals with any motion, inertial or otherwise, in flat spacetime.

Ok. Thanks. I think at some places I have read that SR deals with non-accelerating motion and GR with accelerating one. I shall check. Thanks again.

 

[dayalanand roy]

We can build self-contained accelerometers but not self-contained velocitimeters. The velocity meters that we do have are all based on measuring the velocity with respect to some external reference.

As to “why” there is no particular reason that the universe should be any specific way. It just is this way and so we must build our physical laws to reflect the observed facts of the universe.

Yes. Thanks. Now I am slowly getting the point. Thanks.

 

[dayalanand roy]

That is wrong.

Special Relativity deals with things where the observer is not accelerating. ie the observer is in an inertial frame.

Objects the observer measures can be accelerating.

Remember, paradox means apparently wrong until the explanation is given showing it is actually correct.

The apparently wrong "the moving twin ages less" is actually correct. It arises because the moving twin does not remain in an inertial frame for her entire journey so she is not an inertial observer.

Just before she reaches her turn point and while still traveling away from earth, she observes that the time on Earth is one value. Note she is an inertial observer at this point.

She then decelerates and accelerates back to speed traveling towards earth. She is now an inertial observer again but she is a different inertial observer than when she was traveling away from earth.

Different inertial observers do not agree on things distant to them being simultaneous.

She now observes the time on Earth and finds it is very different - years different - from the time she observed just before she turned. The time has jumped forward dramatically and this jump, together with the time dilation factor due to her speed, accounts for the age difference on her return.

Incidentally, this jump in the "observed time on earth" also explains for something you rarely see mentioned.

A stationary observer sees a moving clock run slow.

So, during all her journey she sees her twin on Earth ageing more slowly than her.

Similarly, her twin on Earth sees her age more slowly than him.

The only way you can resolve these two facts is by there being a jump in someone's measurement of time.

You are not alone in your confusion. In Professor Jim Al Khahili's 2012 book Paradox, Chapter Six - The Paradox of the Twins deals with the paradox and he gives a completely wrong explanation!

Thanks a lot for your illuminating reply. Gradually I am getting closer to the point. Thanks and regards.

 

[dayalanand roy]

SR can deal with non-inertial frames just fine.

The kernel of truth that the mistake is based on is that the famous two postulates both refer explicitly to inertial frames.

Yes. Thanks.

 

[dayalanand roy]

I don't know the exact date. But Einstein said in a speech, hold in Kyoto on 14 December 1922:

Source:
https://web.archive.org/web/2015122...winter2012/physics2d/einsteinonrelativity.pdf

nice article. Thanks

 

[dayalanand roy]

A is accelerating relative to an inertial frame (=proper acceleration), B not (only coordinate acceleration). That is an asymmetry of the scenario whith relevance to time-dilation.

Yes. Getting the point. Thanks

 

[dayalanand roy]

They are in motion relative to each other. You can choose a frame of reference where A is at rest and B is moving, or B is at rest and A is moving, but those are just choices of reference frames. They have nothing to do with the physical fact that A and B are in motion relative to each other.

Acceleration, on the other hand, is absolute. You can, for example, attach a weight to a spring. When the spring stretches or compresses you know you're accelerating.

Thanks. Getting the point.

 

[Ibix]

I like that convention. This issue is always a source of confusion.

I don't agree, because "see" is a part of the meaning of "observe" - in fact, it's the first meaning that occurs to me. As I noted above "If I observe a light 186,000 miles away flash at exactly noon, I observe that it flashed a second before noon" is a bad idea but a perfectly legal sentence.

It's also that things like time dilation are not direct observables - you cannot build an assumption-free time dilation detector. So I think specifically using observe about something that isn't observable is a bad idea.

I agree that a clear distinction between the verbs used for direct observables and derived quantities is a good idea. I just don't think this is the right one.

 

[Ibix]

I want to know that when A is accelerating away from B, or changing direction in relation to B, why not B too is considered to accelerate or change direction?

Because B's accelerometers read zero at all times.

Imagine being in a train traveling next to another train at the same speed. You can see the other train's passengers through your window. One train puts on its brakes. According to the passengers on both trains, the previously stationary passengers in the other train start to move. This is coordinate acceleration, where the velocity of something relative to you changes. However, only one set of passengers will feel a jolt and be pushed back in their chairs - that's proper acceleration.

In the twin paradox only one of the twins feels proper acceleration. It's the proper acceleration that's important because coordinate acceleration is an effect of your choice of what "at rest" means whereas proper acceleration is actually felt.

 

[Ibix]

Ok. Thanks. I think at some places I have read that SR deals with non-accelerating motion and GR with accelerating one. I shall check. Thanks again.

You do see it in old textbooks and some popsci. As I noted in another post, it's a human decision what to call SR and what to call GR. The eventual consensus seems to be that it made sense to draw the line where there was a physical difference - flat vs non-flat spacetime.

 

[A.T.]

I don't agree, because "see" is a part of the meaning of "observe" ...

Unfortunately "observer" is often used as a synonym for "reference frame". This creates lots of confusion.

Ideally one would just stick to "frame", and describe the situation "according to that frame", without mentioning the active act of "observation" by some "observer", unless one actually means direct observation.

 

[Ibix]

Unfortunately "observer" is often used as a synonym for "reference frame". This creates lots of confusion.

Ideally one would just stick to "frame", and describe the situation "according to that frame", without mentioning the active act of "observation" by some "observer", unless one actually means direct observation.

One more reason to stay away from "observe" as a verb in this context, I think.

 

[Dale]

I want to know that when A is accelerating away from B, or changing direction in relation to B, why not B too is considered to accelerate or change direction?

An accelerometer attached to B reads 0. Only A is accelerating according to attached accelerometers.

If movement is relative, speed is relative, why not acceleration or direction is relative too?

Because accelerometers show that it is not relative.

 

[Frodo]

The key point to take away from the twin paradox is that the time difference is due to the moving twin's change of frame.

The acceleration is essentially irrelevant except for the fact that the moving twin must decelerate and accelerate so that they can change their frame.

You can easily set up a twin paradox without any accelerations. I use the values from above.

Set up a stationary observer on earth, another at the turning poiint and another at twice the distance of turning point. All three synchronise their clocks to read 0.

The moving twin_1 accelerates before the experiment starts in such a way that she is traveling at V when she passes earth, and she passes when the Earth clock reads 0. She looks at the Earth clock and sets her clock to 0.

A similarly moving twin_2 passes the point twice the turning point distance away, traveling at V towards earth.

The two moving travellers meet at the turning point. The stationary person's clock reads 5 but twin_1's clock reads only 4.5.

twin_2 sets her clock to be the same at twin_1, or 4.5. twin_2 continues to Earth and arrives at Earth when Earth says it is 10. However, twin_2's clock reads 9, made up of the 4.5 which she set, plus the 4.5 for her journey time, totalling 9.

So, whereas the Earth bound twin says 10 years have elapsed since twin_1 left, the total travel time measured by the two moving twins is only 9 years.

So, we have the same time difference but there have been no accelerations.

Acceleration has nothing to do with the twin paradox other than it is necessary for the moving twin to accelerate and decelerate to change her frame. The twin paradox is about changing frames.

 

[Frodo]

If I see a light 186,000 miles away flash at exactly noon, I observe that it flashed a second before noon.

I like that convention. This issue is always a source of confusion.

It is one which I thought was in general use so I am very surprised by those who appear never to have heard of it or recommend it not be used. All here seems to cite wiki as their authority so I shall too. See Special relativity and go to Measurement versus visual appearance to find (my underlines):

Scientists make a fundamental distinction between measurement or observation on the one hand, versus visual appearance, or what one sees.

Energy has one meaning in normal life and a different, formal meaning in science. So does observe.

 

[A.T.]

Acceleration has nothing to do with the twin paradox other than it is necessary for the moving twin to accelerate and decelerate to change her frame. The twin paradox is about changing frames.

Acceleration doesn't affect the clock rate directly, but it makes no sense to present it as irrelevant but also necessary. This just confuses people.

The analogy I would use is a car at constant speed:

proper acceleration <-> changing the cars direction
proper time <-> traveled distance

Changing direction doesn't directly affect the rate at which distance is traveled, but it can affect the total traveled distance between two points.

 

[Dale]

The acceleration is essentially irrelevant except for the fact that the moving twin must decelerate and accelerate so that they can change their frame.

I wouldn’t go that far. It is irrelevant in the calculation of the final difference in age, but it is relevant in breaking the symmetry. Any scenario which avoids acceleration must break the symmetry in some other way.

 

[Frodo]

The Wikipedia page is a good start. Two or three of the editors in the history have usernames that are suspiciously familiar from here.

Thank you.

I have discovered The Equation of Motion in Rindler Space

Consider a frame traveling at velocity v relative to a fixed frame, and at (local) acceleration a as depicted by the top pair of frames below.

We can instead consider this moving frame to be at rest relative to the stationary frame, where v and a are zero; as long as we consider that the frame experiences a gravitational field determined by the rate of acceleration. We now use Rindler coordinates and the Lorentz transformation equations does not have a term v in them. This is depicted by the lower pair of frames below.

In the diagram , the top pair of frames are in conventional mode. The lower two frames are in Rindler coordinates.

 

[Frodo]

Acceleration doesn't affect the clock rate directly, but it makes no sense to present it as irrelevant but also necessary. This just confuses people.

If, as in the twin paradox, the acceleration causes a change in speed then this does does affect the clock rate.

I think therefore your statement is both incorrect and very misleading.

99% of the explanations of the twin paradox say "It is caused by the fact that the traveling twin accelerates" but they never give a calculation showing how it comes about, nor provide an equation relating the age difference to the rate and duration of the acceleration experienced. I suggest the statement is therefore as meaningless as saying "It is caused by the fact that the traveling twin is wearing a bikini".

The twin paradox is explained by the fact that the moving twin changes their frame of reference. That is the essential kernel of the solution - everything else is second order. It is a simple application of the Lorentz transformation equations to get the resultant time difference.

Secondly, no-one citing acceleration as the cause ever shows how acceleration can account for the fact that both twins see each each other age more slowly than themselves during the entire time. This can only be resolved by invoking a frame change. It has nothing to do with acceleration.

Perhaps we could ask the original poster dayalanand roy , who has obviously worked on the subject, whether he found the change of frame explained things to him.

 

[A.T.]

Acceleration doesn't affect the clock rate directly, ...

If, as in the twin paradox, the acceleration causes a change in speed then this does does affect the clock rate.

I think therefore your statement is both incorrect and very misleading.

What I'm referring to is the clock hypothesis:

https://en.wikipedia.org/wiki/Time_dilation#Clock_hypothesis
The clock hypothesis is the assumption that the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity.

Note that I explicitly wrote "directly".

 

[Frodo]

In the thread Twin paradox not including accelerations, it is wrong where? Andrew Kirk, a Science Advisor, Homework Helper, Insights Author and Gold Member states something identical to my assertion, namely (my underlines):

In the Twin Thought Experiment, acceleration is not the key explanation of why the traveling twin ages less than the non-travelling twin. Rather, it is the fact that the inertial frame of the traveling twin has changed. The inertial frame while going out is very different from the one while coming back. That reason applies whether we are considering the original thought experiment (in which there is acceleration) or the one you describe (in which there is no acceleration).

In both cases the time measurement that is delivered back to the home twin (in your case the measurement is by the amount of fading of the photo) is based on two very different inertial frames, and hence is less than the measurement based on the home twin, which relates to only one inertial frame.

In summary, it is the number of different inertial frames that contribute to each time measurement, rather than the acceleration, that allows to see why the traveled and the non-travelled time measurements differ.

 

[PeterDonis]

In the thread Twin paradox not including accelerations, it is wrong where? Andrew Kirk, a Science Advisor, Homework Helper, Insights Author and Gold Member states something identical to my assertion

And if you go read my post #60 in that same thread, you will find this, in response to a similar statement by another poster:

it's important to understand that this is a convention, not required by the laws of physics. And it's not what causes the two clocks to have different readings at the end--the cause of that is the different lengths of the two paths through spacetime.

Here the "this" that is a convention is what Andrew Kirk described as "the inertial frame changing". And, as my quote just above says, that is not what causes the twins' clocks to have different readings at the end; the cause of that is the different lengths of the paths they take through spacetime.

 

[Janus]

99% of the explanations of the twin paradox say "It is caused by the fact that the traveling twin accelerates" but they never give a calculation showing how it comes about, nor provide an equation relating the age difference to the rate and duration of the acceleration experienced. I suggest the statement is therefore as meaningless as saying "It is caused by the fact that the traveling twin is wearing a bikini".

If you were only concerned with how much much the "traveling twin" ages during the trip according to the "stay at home twin" or according to the traveling twin, then you don't have to consider the acceleration of the traveling twin. The stay at home twin gets his answer by measuring time dilation for the traveling twin, and th traveling twin gets his answer by measuring length contraction between his twin and turn around point.

Acceleration of the traveling twin does become important when you are concerned with how the traveling twin arrives at the conclusion that his stay at home twin ends up being older than he is upon his return.
During the outbound leg, the traveler would say that his twin aged more slowly than he did, and would say the same during the return leg. It during his acceleration at turn around that he will say that his stay at home twin aged more rapidly.
There is an equation for how an accelerating observer measures non-local clocks:
$$ T = \frac{t}{\sqrt{1-\frac{2ah}{c^2}}}$$

t is the time rate as measured by the observer's own clock
T is the time rate on a clock a distance of 'h' from the observer in the direction of the acceleration.
a is the magnitude of the acceleration.

In essence, clocks in the direction of the acceleration run fast according to the accelerating observer at a rate that depends on how far away they are and the magnitude of the acceleration.

It does not matter if the distant clock doesn't share the observer's acceleration (though this will mean that the distance between the two doesn't remain constant over the period of acceleration, and this, in turn, has to be factored in when calculating the total time difference over the acceleration period).