conscienta
Registered Member
The standard twin paradox has generated considerable controversy. The thought experiment involves the experience of twins – one twin remains on earth while the other twin makes a journey in space at a high rate of speed and upon returning to earth finds that she has aged less than her earthbound twin. If we search the internet for an explanation of this effect, one finds web page after web page after web page of posts purporting to explain how this thought experiment is consistent with the special theory of relativity. An earlier thread in SciForums is a case in point. The question was: Can the Twin Paradox Be Simplified? After 37 pages of sometimes heated exchanges I would say it is still an open question.
First of all, I would stipulate that the Twin's Paradox is not a paradox and that it should simply be called the Twin’s Effect. To add content to that general statement, let us say for arguments sake that two twins, Twin A and Twin B are twenty years old and it is the year 2000. Twin A remains on Earth while Twin B rockets to a star 8 light years away traveling at 80 percent the speed of light and then returns to Earth at the same speed. In Twin A's reference frame the journey should take 20 years. In Twin B's frame of reference the trip only takes 12 years and upon return to Earth Twin B will agree with Twin A that on earth 20 years have passed and that the year is 2020. According to Twin B’s clock however, only 12 years transpired during Twin B's journey and accordingly she will be only 32 while Twin A will be 40.
To keep it simple, I will suggest the acceleration/deceleration phases of the journey are instantaneous with the stipulation that a uniform acceleration can be handled within the framework of special relativity at the price, however, of making the mathematics more complicated. I would just say about acceleration that in order to change a clock’s timing rate requires a change of inertial frames which would require a change of velocity which would – by definition - require an acceleration. The acceleration, however, has no affect on the timing rate itself.
As far as the resolutions to the twin paradox I would suggest they follow a certain progression. In most cases the author will state that although the controversy over the Twin Paradox was resolved 50 years ago, the explanation they are about to provide is definitive and should once and for all resolve the paradox. The author will begin by suggesting that the experiences of the twins are not symmetrical. The stay-at-home twin will not change inertial frames while the traveling twin will accelerate to a high rate of speed then cruise (inertially) for a lengthy period of time, decelerate at her destination, then accelerate again and travel at a high rate of speed (inertially) on her journey homeward and finally decelerate upon arrival back at earth. They will then say that the special theory of relativity applies only to uniform motion and not accelerated motion. Then they will say, however, that it is not the accelerations/decelerations per se that causes the age differential; i.e. that clock rates only depend on the traveling twin’s velocity and not on any derivatives of velocity such as acceleration. And then finally they will apply the equations of special relativity to calculate the time differential between the two twin’s experiences. A convoluted sort of logic but not necessarily inaccurate. If the aforementioned author’s of the numerous explanations of the Twin Paradox on the internet (at least those with PhD’s in physics) were pressed they would probably say that the time dilation is a consequence of changes in the geometry of space and time – whatever that may mean.
What I would like to propose for consideration in this post is what I call the Twin Earth Paradox. In this variation there is an earth like planet at the star visited by Twin B. The star is exactly the same mass/gravity as our sun, the planet has exactly the same mass/gravity as Earth and has a 24 hour day and is the same distance from the star so it has a 365 day year. We have a relationship with our twin planet and over the years atomic clocks on both planets have been synchronized such that the year 2000 on Earth is the same as the year 2000 on Twin Earth. I would suggest that upon Twin B’s arrival at Twin Earth the year in Twin Earth’s frame of reference will be 2010. However, according to Twin B’s clock only 6 years will have passed and Twin B will be 26 upon his arrival at Twin Earth.
The proposal seems to short circuit many arguments for the asymmetry between the two perspectives but instead focuses on what “really” happens to Twin B’s clock and more generally what we “really” mean by time. From an outside observer, time in Twin B’s frame of reference is measured to be dilated by 60 percent. However, during the inertial part of Twin B’s journey, Twin B faithfully conducted experiments that indicated the clock in her frame of reference was operating normally; i.e. no evidence of time dilation. Twin B concludes therefore that it was the distance from Earth to Twin Earth that was foreshortened by 60 percent; i.e. the distance was only 4.8 light years.
Did the distance really contract or was time really dilated? Or is it simply a function of measurement; i.e. the distance/time was measured to be contracted/dilated – motion affects those measurements and hence reality? Or is it as the theory of special relativity seems to imply that we are all moving through time at the speed of light (at rest) and as our motion through space increases our motion through time decreases? At all times, however the total of our motion through time and our motion through space must equal the speed of light. From this perspective Twin B was traveling through time at 60,000 km/sec while she was moving through space at 240,000 km/sec and hence time was dilated by the Lorenz factor. Is this what they mean by changes in the geometry of space and time and if so what does it mean to move through time?
First of all, I would stipulate that the Twin's Paradox is not a paradox and that it should simply be called the Twin’s Effect. To add content to that general statement, let us say for arguments sake that two twins, Twin A and Twin B are twenty years old and it is the year 2000. Twin A remains on Earth while Twin B rockets to a star 8 light years away traveling at 80 percent the speed of light and then returns to Earth at the same speed. In Twin A's reference frame the journey should take 20 years. In Twin B's frame of reference the trip only takes 12 years and upon return to Earth Twin B will agree with Twin A that on earth 20 years have passed and that the year is 2020. According to Twin B’s clock however, only 12 years transpired during Twin B's journey and accordingly she will be only 32 while Twin A will be 40.
To keep it simple, I will suggest the acceleration/deceleration phases of the journey are instantaneous with the stipulation that a uniform acceleration can be handled within the framework of special relativity at the price, however, of making the mathematics more complicated. I would just say about acceleration that in order to change a clock’s timing rate requires a change of inertial frames which would require a change of velocity which would – by definition - require an acceleration. The acceleration, however, has no affect on the timing rate itself.
As far as the resolutions to the twin paradox I would suggest they follow a certain progression. In most cases the author will state that although the controversy over the Twin Paradox was resolved 50 years ago, the explanation they are about to provide is definitive and should once and for all resolve the paradox. The author will begin by suggesting that the experiences of the twins are not symmetrical. The stay-at-home twin will not change inertial frames while the traveling twin will accelerate to a high rate of speed then cruise (inertially) for a lengthy period of time, decelerate at her destination, then accelerate again and travel at a high rate of speed (inertially) on her journey homeward and finally decelerate upon arrival back at earth. They will then say that the special theory of relativity applies only to uniform motion and not accelerated motion. Then they will say, however, that it is not the accelerations/decelerations per se that causes the age differential; i.e. that clock rates only depend on the traveling twin’s velocity and not on any derivatives of velocity such as acceleration. And then finally they will apply the equations of special relativity to calculate the time differential between the two twin’s experiences. A convoluted sort of logic but not necessarily inaccurate. If the aforementioned author’s of the numerous explanations of the Twin Paradox on the internet (at least those with PhD’s in physics) were pressed they would probably say that the time dilation is a consequence of changes in the geometry of space and time – whatever that may mean.
What I would like to propose for consideration in this post is what I call the Twin Earth Paradox. In this variation there is an earth like planet at the star visited by Twin B. The star is exactly the same mass/gravity as our sun, the planet has exactly the same mass/gravity as Earth and has a 24 hour day and is the same distance from the star so it has a 365 day year. We have a relationship with our twin planet and over the years atomic clocks on both planets have been synchronized such that the year 2000 on Earth is the same as the year 2000 on Twin Earth. I would suggest that upon Twin B’s arrival at Twin Earth the year in Twin Earth’s frame of reference will be 2010. However, according to Twin B’s clock only 6 years will have passed and Twin B will be 26 upon his arrival at Twin Earth.
The proposal seems to short circuit many arguments for the asymmetry between the two perspectives but instead focuses on what “really” happens to Twin B’s clock and more generally what we “really” mean by time. From an outside observer, time in Twin B’s frame of reference is measured to be dilated by 60 percent. However, during the inertial part of Twin B’s journey, Twin B faithfully conducted experiments that indicated the clock in her frame of reference was operating normally; i.e. no evidence of time dilation. Twin B concludes therefore that it was the distance from Earth to Twin Earth that was foreshortened by 60 percent; i.e. the distance was only 4.8 light years.
Did the distance really contract or was time really dilated? Or is it simply a function of measurement; i.e. the distance/time was measured to be contracted/dilated – motion affects those measurements and hence reality? Or is it as the theory of special relativity seems to imply that we are all moving through time at the speed of light (at rest) and as our motion through space increases our motion through time decreases? At all times, however the total of our motion through time and our motion through space must equal the speed of light. From this perspective Twin B was traveling through time at 60,000 km/sec while she was moving through space at 240,000 km/sec and hence time was dilated by the Lorenz factor. Is this what they mean by changes in the geometry of space and time and if so what does it mean to move through time?
