The Twin Paradox: Exploring Its Complexity

[nakurusil]

Last little word before I allow you all to come down on me like a ton of bricks. The standard answer is that the traveling twin ages less, because he changes his reference frame. The contra to this is that he is changing only because you use the Earth/Alpha as "fixed". Why can I not use Alpha as changing reference frame and the spaceship as fixed? This is one of the basic postulates of SR.

Because an inertial frame is not equivalent to an accelerated frame.Turning around requires acceleration. So, the frames for the twins are NOT equivalent. Now try doing the calculations.

 

[Monnik]

How do you determine who turned around/accelerated? Take the example of two (make it four if you want) spaceships. Unless you assume a preferential inertial frame (postulated not to exist to deduce SR), you can pick which frame accelerates.

 

[ZapperZ]

How do you determine who turned around/accelerated? Take the example of two (make it four if you want) spaceships. Unless you assume a preferential inertial frame (postulated not to exist to deduce SR), you can pick which frame accelerates.

A non-inertial reference frame is detectable! Even in Newtonian mechanics this is true.

Zz.

 

[George Jones]

How do you determine who turned around/accelerated? Take the example of two (make it four if you want) spaceships. Unless you assume a preferential inertial frame (postulated not to exist to deduce SR), you can pick which frame accelerates.

As ZapperZ has said, accleration is detecable. Here is one way.

Consider an accelerometer in a spaceship located deep in in interstellar space.

The accelerometer consists of two main parts - a hollow sphere like a basketball inside of which is a slightly smaller sphere. Initially, the centres of the spheres coincide, so that there is a small, uniform gap between the spheres.

If the ship is accelerating, the gap will be closed, and contact between the spheres will be made. An alarm that indicates accelerated motion will sound. If the ship is not accelerating, no alarm will sound, and constant speed, straight line motion is indicated.

 

[jtbell]

How do you determine who turned around/accelerated?

The same way that you can tell whether a car that you are riding in is accelerating or braking, even with your eyes closed.

 

[robphy]

The same way that you can tell whether a car that you are riding in is accelerating or braking, even with your eyes closed.

...which is one important reason to always wear seat belts.

 

[nakurusil]

How do you determine who turned around/accelerated?

Acceleration is detectable from within a closed system.You can use your senses or you can use an accelerometer (google the term)

Take the example of two (make it four if you want) spaceships. Unless you assume a preferential inertial frame (postulated not to exist to deduce SR), you can pick which frame accelerates.

Are you making up all this stuff? Because it is wrong.

 

[pervect]

You don't want to use the Lorentz tranforms in conjunction with accelerated motion. Because they don't aplly. This is one of the reasons I liked "robphy" 's paper, it is done cleanly.

I'm not sure of the context of this remark, but it is possible to apply the Lorentz transforms in conjunction with accelerated motion if it is done properly. The point is that it has to be done correctly.

See for instance http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

It's often said that special relativity is based on two postulates: that all inertial frames are of equal validity, and that light travels at the same speed in all inertial frames. But in real world scenarios, objects almost never travel at constant velocity, and so we might never find an inertial frame in which such an object is at rest. To allow us to make predictions about how accelerating objects behave, we need to introduce a third postulate.

This is often called the "clock postulate", but it applies to much more than just clocks, and in fact it underpins much of advanced relativity, both special and general, as well as the notion of covariance (that is, writing the equations of physics in a frame-independent way).

The clock postulate can be stated in the following way. First, we take the rate that our frame's clocks count out their time, and compare that to the rate that a moving clock counts out its time. Before the clock postulate was ever thought of, all that was known was that when the moving clock has a constant velocity v (measured relative to the speed of light c), this ratio of rates is the Lorentz factor

gamma = 1/sqrt(1-v2)

The clock postulate generalises this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, it only depends on v, and does not depend on any derivatives of v, such as acceleration. So this says that an accelerating clock will count out its time in such a way that at anyone moment, its timing has slowed by a factor (gamma) that only depends on its current speed; its acceleration has no effect at all.

 

[nakurusil]

I'm not sure of the context of this remark, but it is possible to apply the Lorentz transforms in conjunction with accelerated motion if it is done properly. The point is that it has to be done correctly.

See for instance http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

Thank you

The quote from Baez deals with time dilation.

The context in discussion in my post was an inappropriate calculation of the separation distance between the two rockets in the Bell paradox. Using Lorentz transforms, the OP calculated that the string will stretch. In order to calculate whether the string will break (the Bell problem) one needs to calculate by how much the string will stretch. One cannot calculate this applying the Lorentz transform as the OP did, one needs to use the equations of hyperbolic motion in order to determine the rocket separation as a function of time. Hence, my criticism.

 

[Monnik]

You are actually missing my point. I agree the turn around plays a role in the problem, but it is not acceleration that causes the problem. It is the change of reference frame and the accompanying clock resynchronisation in the "travelling" frame. It is a mathematical artifact. The problem occurs before the turnaround. How do you determine which twin ages less before the turnaround?

Let us not have the twin turn around, but go in one direction (the first leg of the trip). Do this with two spaceships approaching each other (call them Hawking and Enterprise). Each have a pilot ship 4 ly ahead of them "stationary" in their respective reference frames. According to the Enterprise, Hawking is approaching at 0.8c. Take T0=T0'=0 to be when the pilot ships pass each other.

This is a symmetrical problem. One of the postulates necessary to deduce SR is that there is no "absolute rest" and that selecting a "rest frame" is therefore arbitrary. If you can not select the one frame as rest frame, calculate the answer in the other, then select the other frame as "stationary" and calculate back the same answer, you are either breaking the postulate, or you are using the equations wrong.

 

[Monnik]

Acceleration is detectable from within a closed system.You can use your senses or you can use an accelerometer (google the term)



Are you making up all this stuff? Because it is wrong.

Actually no. I expressed myself wrong though. My problem is not in the acceleration part, but in the decision of which twin ages most on a single leg. All inertial reference frames are "equal" - The Principle of Relativity. Take away the turn around and you are left with two inertial reference frames and a symetrical problem if you leave the Earth out of the problem and only work from Alpha.

Quote Einstein 1905:
"Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the ``Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a ``luminiferous ether'' will prove to be superfluous inasmuch as the view here to be developed will not require an ``absolutely stationary space'' provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."

 

[nakurusil]

You are actually missing my point. I agree the turn around plays a role in the problem, but it is not acceleration that causes the problem. It is the change of reference frame and the accompanying clock resynchronisation in the "travelling" frame. It is a mathematical artifact. The problem occurs before the turnaround. How do you determine which twin ages less before the turnaround?

The twin that stays put ages more.
The twin who accelerates from the starting point, decelerates, turns around, accelerates again and comes back ages less. It is all explained mathematically here.

Let us not have the twin turn around, but go in one direction (the first leg of the trip). Do this with two spaceships approaching each other (call them Hawking and Enterprise). Each have a pilot ship 4 ly ahead of them "stationary" in their respective reference frames. According to the Enterprise, Hawking is approaching at 0.8c. Take T0=T0'=0 to be when the pilot ships pass each other.

Very simple : in this case both twins age the same. There is no acceleration and no turning around. This is an uninteresting case.

 

[Monnik]

Very simple : in this case both twins age the same. There is no acceleration and no turning around. This is an uninteresting case.

Finally we agree on something. The twins age the same. All we have to agree on now is by how much they age? 6 years or 10 years?

How is this mathematically or physically different from the return leg of the twin paradox? Or if I had a triplet on Alpha from the outgoing leg?

 

[Monnik]

We agree !

Very simple : in this case both twins age the same. There is no acceleration and no turning around. This is an uninteresting case.

Finally we agree on something. The twins age the same. All we have to agree on now is by how much they age? 6 years or 10 years?

How is this mathematically or physically different from the return leg of the twin paradox? Or if I had a triplet on Alpha from the outgoing leg?

 

[nakurusil]

Finally we agree on something. The twins age the same. All we have to agree on now is by how much they age? 6 years or 10 years?

This is a totally uninteresting case, both twins are in inertial frames. Why don't you try reading and understanding the case where the twins are in a non-symmetric situation? I gave you all the info.

How is this mathematically or physically different from the return leg of the twin paradox? Or if I had a triplet on Alpha from the outgoing leg?

The "returning" twin needs to slow down, stop, turn around, speed up , cruise, slow down and land on Earth. So, the situations are totally different . Why don't you try reading the wiki link?

 

[JesseM]

Finally we agree on something. The twins age the same. All we have to agree on now is by how much they age? 6 years or 10 years?

If each ship starts their timer when the other ship is 4 ly away in their own rest frame, and each ship sees the other approaching at 0.8c, then each ship ages 5 years between starting their own timer and meeting the other ship. However, since they define simultaneity differently, each ship would say that the other one started their timer earlier then they did, so that by the time they themselves started their own timer, the other ship's timer had already been running for 2 years. Thus each ship says that in the interval between starting their own timer and meeting the other ship, the other ship has only aged 3 more years, ensuring that both ships agree their timer has run a total of 5 years between the time it started and the time the two ships met.

 

[Blazah]

The twin paradox is very confusing, and even after reading the explanation, I still get questions.

http://www.sysmatrix.net/~kavs/kjs/addend4.html" offers stunning clarity IMHO.