I Twin paradox not including accelerations, it is wrong where?

[Luis Babboni]

Hi people!
(Sorry for my poor english).

I found everywhere that twin paradox need aceleration to explain it.

Let me change the twin paradox a little:

Suppouse that in Earth and before the traveller twin start his trip, you take two photos with old Polaroid camera, one to each twin. As we remember, those kinds of photos become older, degrading its colours, a little fast.

Some day the traveller twin left his own photo pasted in one window of his house looking outward and takes the Polaroid camera and start a trip in his capable of reach near light speed spaceship. And he goes to the left respect to Earth. Goes to left far enough to be able to stop and start to travel to right in the direction to Earth in a way he could pass Earth going right at near speed of light without any aceleration.
When pass Earth he points his Polaroid to his house and take a Polaroid photo of his Polaroid photo still on Earth and pasting it looking outwards in one of his capable of reach near speed of light spaceship window.

Time later he pass another spaceship coming at the same absolute speed (in a frame at rest respect the non traveller twin) but with opposite direction, to left, and with no aceleration, and the captain of this spaceship take a Polaroid photo of his Polaroid photo and paste it looking outwards in one of his spaceship window.

Time later this second spaceship pass Earth without change its speed, so no aceleration here neither, and the non traveller twin take a Polaroid photo of the Polaroid photo of the Polaroid photo of the Polaroid photo taked time ago in Earth.

Then he compared his old Polaroid photo of him whith this new Polaroid Photo of his twin.

Having both Polaroids photos images of them in younger ages, is this new Polaroid photo less degraded colours than the old Polaroid photo no matter none Polaroids photos suffered any aceleration never?

If all motions are relative, why not the opposite?

I hope I could explain my idea even with my poor english.

Where I´m wrong if I say that yes, the new Polaroid have less degraded colours than the old one?

Thanks!

Luis.

 

[andrewkirk]

Yes, the photo taken from the passing spaceship is less degraded than the one that stayed on Earth, even though it has undergone no acceleration.

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.

 

[Luis Babboni]

Thanks for your fast answer Andre!

So... why most answers (in fact yours is the first I saw that not) use aceleration to explain it? :-O

Regards,

Luis.

 

[Orodruin]

So... why most answers (in fact yours is the first I saw that not) use aceleration to explain it? :-O

They do not. At least not any serious ones.

Acceleration explains why there is an asymmetry between the twins and why you cannot blindly apply the time dilation formula to the accelerating twin. A more accurate explanation would involve relativity of simultaneity rather than acceleration.

 

[Luis Babboni]

Thanks! :-)

 

[Herman Trivilino]

The twin that takes the shorter path through spacetime experiences the smaller amount of aging.

To accomplish that a switch in inertial frames, which requires either acceleration or the clever way you've done it with photographs, is required.

The usual way is with acceleration, though, so that's why you may have seen it mentioned that the twin who accelerates is the one who ages less. It's a very common misunderstanding. Another is that general relativity is required to explain things. Both mistakes can be found in many textbook presentations.

 

[sweet springs]

I found everywhere that twin paradox need aceleration to explain it.

How about this.
When rocket A of speed v to the Earth passes by the Earth, rocket A pilot adjusts his clock to the observed Earth clock E.
Then when rocket A and rocket B of speed -v to the Earth pass by, the rocket B pilot adjusts his clock to the observed A clock.
Then when rocket B passes by the Earth, the Earth and pilot B observe commonly that clock B time < clock E time.
No acceleration appear in it.

 

[Luis Babboni]

How about this.
When rocket A of speed v to the Earth passes by the Earth, rocket A pilot adjusts his clock to the observed Earth clock E.
Then when rocket A and rocket B of speed -v to the Earth pass by, the rocket B pilot adjusts his clock to the observed A clock.
Then when rocket B passes by the Earth, the Earth and pilot B observe commonly that clock B time < clock E time.
No acceleration appear in it.

Is exactly the same than mine and far more simply... but without twins! :-D

 

[A.T.]

I found everywhere that twin paradox need aceleration to explain it.

In this context "acceleration" means that the world line along which you accumulate proper time is not inertial.

 

[Luis Babboni]

In this context "acceleration" means that the world line along which you accumulate proper time is not inertial.

Sorry, not sure if I understand you... but seems to me there is none no inertial frames in mine or, most simplier, sweet spring´s example.

 

[sweet springs]

Twin E stays in one inertia system but rocket twin transfer the inertia frames A to B. This makes difference.

 

[A.T.]

Sorry, not sure if I understand you... but seems to me there is none no inertial frames in mine or, most simplier, sweet spring´s example.

There are no non-inertial physical objects, but the proper time is accumulated along an non-inertial world line.

 

[Luis Babboni]

There are no non-inertial physical objects, but the proper time is accumulated along an non-inertial world line.

Sorry, I do not know what is a non inertial world line...
Are not non straight world lines?
Here I think all world lines are straights.

 

[vanhees71]

Of course, not all world lines are straight lines. E.g., an electron moves on a curved world line in a magnetic field.

 

[Luis Babboni]

Of course, not all world lines are straight lines. E.g., an electron moves on a curved world line in a magnetic field.

OK, but in our example* I think all world lines are straights. I´m wrong?

*:To be more precise, we could change the Earth by a Saint Exupery little prince´s asteroid.

 

[Orodruin]

OK, but in our example I think all world lines are straights. I´m wrong?

This is like saying that the sides of a triangle are straight when arguing for the triangle inequality. While it is true that each individual side is straight, one of the lengths involved is the length along a curve that has a kink (the length that involve two sides of the triangle).

 

[Demystifier]

For more details about the role of acceleration in twin paradox see https://arxiv.org/abs/physics/0004024

 

[Luis Babboni]

This is like saying that the sides of a triangle are straight when arguing for the triangle inequality. While it is true that each individual side is straight, one of the lengths involved is the length along a curve that has a kink (the length that involve two sides of the triangle).

Han Solo´s line of world is not Mr. Spock´s line of world bended in a kick, is Han Solo´s straight line of world:

 

[Orodruin]

Han Solo´s line of world is not Mr. Spock´s line of world bended in a kick, is Han Solo´s straight line of world:

I am sorry, but this makes no sense. Please use the appropriate nomenclature. Neither the world line of Han Solo or that of Mr Spock is the world line along which your total proper time is accumulated.

 

[Ibix]

In the standard twin paradox Minkowski diagram there is a triangle formed of a vertical straight line (the stay-at-home worldline) and a > shape (the traveller worldline). In your variant you have a vertical line (the stay-at-home) a line slanted to the right (the outbound traveller) and a line slanted to the left (the inbound traveller). These three lines form the exact same triangle on the Minkowski diagram as is formed in the standard setup. So the outcome must be the same.

 

[Luis Babboni]

What I think becomes more complicated to see in the Little Prince-Han Solo-Mr.Spock paradox is the paradox :-/
That is, which is the equivalent situation where is the Little Prince who is moving? :-/

But... in the classical twin paradox... which is the equivalent situation where the on Earth twin moves?
I tried to clarify it detailed and is not easy... :-/

Anyone could do it?
Thanks.

 

[Luis Babboni]

What I think becomes more complicated to see in the Little Prince-Han Solo-Mr.Spock paradox is the paradox :-/
That is, which is the equivalent situation where is the Little Prince who is moving? :-/

But... in the classical twin paradox... which is the equivalent situation where the on Earth twin moves?
I tried to clarify it detailed and is not easy... :-/

Anyone could do it?
Thanks.

This is the more near I could imagine:

 

[Luis Babboni]

Here with more detail.
As previously, A (twin paradox situation from on Earth twin view) is not symmetric to twin paradox situation (B)
The true symmetric situation to twin paradox (B) is C.
I dot not calculate yet the distance <2| <1| at the end of A and C cause simultaneus turnarounds of spaceships in system |2>|1> are not simultaneus turnarounds in system +x.

 

[Luis Babboni]

Here a correction to the first part of my previous draw:
(As I said, and forgot in the first part of the previous draw, the turnarounds are not simultaneous in Earth system)

 

[Luis Babboni]

Please, I need someone tell me if I´m doing a nonsense or not.

Thanks!

 

[Herman Trivilino]

Han Solo´s line of world is not Mr. Spock´s line of world bended in a kick, is Han Solo´s straight line of world:

If you draw a spacetime diagram of the scenario you proposed in your original post, and then traced your finger along the paths used to determine the age of each photograph, you would find that the paths you traced are not both straight. For a path to match the path of an inertial motion, it must be a straight line.

Thus the reason that the photographs have different ages is because they traced out different paths through spacetime and that the lengths of those paths are unequal, or equivalently that the proper time associated with each path is different.

 

[Luis Babboni]

If you draw a spacetime diagram of the scenario you proposed in your original post, and then traced your finger along the paths used to determine the age of each photograph, you would find that the paths you traced are not both straight. For a path to match the path of an inertial motion, it must be a straight line.

Thus the reason that the photographs have different ages is because they traced out different paths through spacetime and that the lengths of those paths are unequal, or equivalently that the proper time associated with each path is different.

Sorry, not understand.
This is, I think, an spacetime diagram of the scenario I proposed in my original post.
3-4 and 4-5 are straight in my point of view, I´m wrong?

 

[jbriggs444]

3-4 and 4-5 are straight in my point of view, I´m wrong?

3-4 is straight. 4-5 is straight. 3-4-5 is not straight. That's the point.

3-4-5 is a valid world-line but it's not a straight world-line.

 

[Luis Babboni]

3-4 is straight. 4-5 is straight. 3-4-5 is not straight. That's the point.

3-4-5 is a valid world-line but it's not a straight world-line.

There is no thing that moves along 3-4-5

 

[Ibix]

There is no thing that moves along 3-4-5

The information you are passing around does.

 

[Luis Babboni]

The information you are passing around does.

Yeap... but at this point I miss what I discuss!

 

[Luis Babboni]

At this moment what most concerned me is how to describe properly the "symmetrical" situation in respect to twin paradox.

May be it deservs another thread.

 

[PeterDonis]

At this moment what most concerned me is how to describe properly the "symmetrical" situation in respect to twin paradox.

The situation is not symmetrical. Not in the original twin paradox, and not in your version. In your version, the twin who stays on Earth just has one Polaroid and keeps it for the entire time. But the traveling "twins" (there is more than one person playing this role in your version) have to keep taking new Polaroids and switching them around. That is an observable difference--a lack of symmetry--between the traveling and the stay-at-home "twins".

 

[Ibix]

At this moment what most concerned me is how to describe properly the "symmetrical" situation in respect to twin paradox.

May be it deservs another thread.

It isn't symmetrical. That's kind of the point.

All that really matters is the proper time, $\sqrt {c^2\Delta t^2-\Delta x^2}$, along the line 3-5 and along the lines 3-4 and 4-5. Whether those lines are interesting to you because one person followed the path 3-4-5 or because one person followed 3-4 and handed a measure of elapsed time to someone else who followed 4-5 doesn't make any difference. The proper time for 3-4 plus the proper time for 4-5 is the same either way.

 

[Luis Babboni]

The situation is not symmetrical... .

It isn't symmetrical... .

I agree... so there is no paradox without need to use aceleration to explain it! Right?

 

[Herman Trivilino]

The length of the 3-4-5 path differs from the length of the 3-5 path.

Nothing travels along the 3-4-5 path but if something did it's age would equal the age of your less-aged photograph. Its motion would be noninertial.

 

[PeterDonis]

so there is no paradox without need to use aceleration to explain it! Right?

There is no actual paradox, period. What explains the different elapsed times, as has already been said in this thread, is the geometry of spacetime: different paths through spacetime can have different lengths. Sometimes the different paths are due to acceleration; sometimes they are due to something else, like people taking new Polaroids and exchanging them. But it's the different paths that matter.

 

[PeterDonis]

Nothing travels along the 3-4-5 path

That's not correct. Earlier it was said that "information" travels along the 3-4-5 path; but that "information" has a physical embodiment. There are physical interactions that have to take place for the chain of Polaroids along the 3-4-5 path to carry the information that gets compared with the stay-at-home Polaroid at the end. In other words, "information" really means a causal chain of physical processes along the 3-4-5 path, whose end result gets compared with the end result of a (much simpler) causal chain of physical processes along the 3-5 path. That causal chain of physical processes is not "nothing".

 

[vanhees71]

It's all too complicated ;-)). Just keep in mind that a clock moving along a (necessarily timelike) worldline $x^{\mu}(\lambda)$ (where $\lambda$ is an arbitrary parameter) shows the time
$$\tau=\int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{\dot{x}^{\mu}(\lambda) \dot{x}^{\nu}(\lambda) \eta_{\mu \nu}}.$$
That's all there is. So the proper time, shown by a clock (and measuring the aging of each of the twins) is simply a functional of the worldline each of the twin moves. It's like in ordinary geometry: The travel length between two points is a functional of the path taken to connect the points. There's nothing paradoxical or mysterious about this.

 

[Luis Babboni]

OK, but what about this, is not the on Earth twin the younger at the reencounter?

 

[sweet springs]

Yes, younger twin on Earth. But you need giant engine set on the Earth to accelerate the Earth in a moment.　　　ref. Japanese Si-Fic movie to build huge atomic rocket engines on the south pole continent to evacuate from an approaching gravity monster. 　(^.^)

 

[Luis Babboni]

Yes, younger twin on Earth. But you need giant engine set on the Earth to accelerate the Earth in a moment.　　　ref. 　(^.^)

I do not think that is necesary, just need an engine able to change the direction of the spaceship and a frame* attached to it.

*: that frame could be many other numbered spacheships remaining at the same distance to the "traveler" twin´s spaceship and with coordinated clocks and instructions in a way all them change direction at the same time in proper spaceships time.

 

[jbriggs444]

I do not think that is necesary, just need an engine able to change the direction of the spaceship and a frame* attached to it.

You misunderstand what a frame is. It is not just a bunch of hypothetical rulers all laid out in a hypothetical right-angled grid. It also contains a bunch of hypothetical and synchronized clocks. Accelerate the "frame" and the synchronization does not work the way you imagine -- it is systematically skewed as a result of the acceleration.

 

[Luis Babboni]

You misunderstand what a frame is. It is not just a bunch of hypothetical rulers all laid out in a hypothetical right-angled grid. It also contains a bunch of hypothetical and synchronized clocks. Accelerate the "frame" and the synchronization does not work the way you imagine -- it is systematically skewed as a result of the acceleration.

I bet you are right, but please let me know where is my mistake!
My proposed frame have content hypothetical and synchronized clocks.
If all spaceships, with synchronized clocks, planed before to accelerate at the same amount at the same time, the frame do not suffer any distorsion in proper time and proper distances. I´m wrong?

 

[Ibix]

the same time

Almost every time when you write these words in relativity, that is where you are going wrong. "At the same time" assumes an absolute definition of simultaneity, which is wrong in relativity.

Your ships can't accelerate "at the same time" because before and after the acceleration they won't agree what "at the same time" means.

 

[Luis Babboni]

Almost every time when you write these words in relativity, that is where you are going wrong. "At the same time" assumes an absolute definition of simultaneity, which is wrong in relativity.

Your ships can't accelerate "at the same time" because before and after the acceleration they won't agree what "at the same time" means.

Mmmm... if all are at rest respect each other, I think they can cause all clocks run at the same speed.
For the on Earth twin instead, differents spaceships change theire direction at different time. I´m right?
But in this last case, for the traveller twin that goes to a near star and then return, the star change direction at the same time than Earth or not?

 

[Luis Babboni]

To start from the beginning and in agree.

Is this way to see it correct?:

 

[vanhees71]

OK, but what about this, is not the on Earth twin the younger at the reencounter?

View attachment 211994

Well, why don't you calculate it? Let's take the Earth's twins coordinate time as the parameter of the world line. Then we need to evaluate only one integral, namely the propertime of the traveling twin. I use natural units with $c=1$. The world line of the traveling twin is
$$x(t)= \begin{cases} v t & \text{for} \quad 0 \leq t<t_0, \\
v (2 t_0-t) & \text{for} \quad t_0 \leq t \leq 2 t_0.
\end{cases}$$
Then the eigen time of the traveling twin is
$$\tau=\int_0^{2 t_0} \mathrm{d} t \sqrt{1-v^2}=2 t_0 \sqrt{1-v^2}.$$
The twin's proper time staying on Earth is obviously his coordinate time, i.e., $2 t_0$. So the traveling twin is aged less by a factor of $1/\gamma=\sqrt{1-v^2}$.

 

[jbriggs444]

Mmmm... if all are at rest respect each other, I think they can cause all clocks run at the same speed.
For the on Earth twin instead, differents spaceships change theire direction at different time. I´m right?
But in this last case, for the traveller twin that goes to a near star and then return, the star change direction at the same time than Earth or not?

You used the words "at the same time" without specifying a reference frame. That's a non-starter.

 

[Luis Babboni]

You used the words "at the same time" without specifying a reference frame. That's a non-starter.

I said "for the traveller twin... the star change direction at the same time than Earth or not?"
With it I tried to said for his reference frame.