Concerning the Twin Paradox, isn't the cartoon actually giving us the resolution to the paradox and not the paradox itself?
It mentions that the space-travelling twin will be older than the earth-bound twin. But, as I understand it, that isn't the paradox. The paradox is that, according to the space-travelling twin, it is the earth-bound twin that has slower time (and vice versa). So who has the slower clock and which twin will be older?
But the cartoon has the space-travelling twin land on a planet and, thus, break his inertial frame of reference. This, the acceleration of his return flight, and the fact that the earth-bound twin has maintained his inertial frame of reference resolves the paradox, making the space-travelling twin the one who is older.
I never really understood why the paradox couldn't be maintained if the space-travelling twin simply turned the ship in a large arch to return home, maintaining his speed.
I should say since I'm in a different scientific field than physics, perhaps my response will prove no more than a rudimentary one. Plus it's been a while since I last took physics. Anyway no doubt a physicist could give you a much better answer. Maybe some will weigh in.
That said I think I'd agree with you save for one or two tweaks:
1. Given the special theory of relativity, the speed of light is constant, but space and time are relative - i.e. length contraction and time dilation.
If the space-traveling twin is on a spaceship traveling at 99.9% of the speed of light, then the space-traveling twin could think he's moved away from the earth at 99.9% of the speed of light. He could be observed by an outsider to age more slowly than his earth-bound twin.
However, the earth-bound twin could just as well think the earth has moved away from the spaceship at 99.9% of the speed of light. He too could be observed by an outsider to age more slowly than his space-traveling twin.
After all, we know per the special theory of relativity time moves at a different rate for different observers depending on their motion relative to one another. (BTW, time dilation is calculated by this equation where t = time (earth reference frame), t0 = time (proper), v = velocity, and c = speed of light.)
Hence the twin paradox. An outsider observing both twins could conclude both twins are correct. But how could each twin be observed to age more slowly than the other twin?
As you point out, the resolution is due to the acceleration/deceleration of the spaceship which causes one twin to jump from one inertial reference frame to another. The special theory of relativity only applies to relations between inertial frames of reference. If one accelerated or decelerated, one would break their intertial frame. As such there is asymmetry between the twins. It's not completely asymmetrical, there is partial symmetry, but the point is the space-traveling twin and the earth-bound twin aren't perfectly equivalent to one another.
2. BTW, as you may know, time dilation could also be caused by gravity. Such as by a black hole.
3. My guess is the BBC (or whoever is sponsoring and presenting this video) is presenting this video more as a general way to whet the public's appetite for math, science, and philosophy than anything more specific. However, I think it wouldn't be so exciting to present the paradox without its resolution. Maybe that's why the BBC is presenting it this way.
4. Actually, FWIW, if anything, I don't recall ever reading or seeing anyone present the twin paradox without also presenting its resolution.
5. In the case of Einstein's twin paradox, I don't think presenting the resolution takes away too much from the paradox as far as the intrigue a layperson would have about relativity. Sometimes knowing spoilers would ruin a movie. But other times knowing spoilers has the opposite effect. It makes one want to watch the movie even more. At least that's my thinking.
6. We could take similar issue with some of the other thought experiments or paradoxes in this short video as well.
BTW, too bad they didn't do the ladder paradox. I guess that one isn't as cool to most people since it doesn't involve spaceships, twins, and time, but more mundane objects like ladders and garages.
Schrödinger's other cat: the theory is that there's only one cat. The question is how does everyone generate enough ionization by stroking it to build up static charges.
On another note, I believe it's questioned if the speed of light is truly constant between different frames of reference or if we consider it because we need to hold something constant in order to make any dilational computation. Since time isn't necessarily uniform, we need to measure the speed of light from a relatively uniform temporal system. The question is: how do we measure if our frame of reference for measurement is "relatively uniform" temporally at any given moment, or do we just assume it is and go on about our measurements anyway?
As a thought experiment for this, I offer a machine based on the classic Scrambler carnival ride where each axis contains a system that duplicates the mechanism in relatively smaller scale down to a point where final carriages between the largest bifurcations pass one another at relative velocities approaching the speed of light. Each axis and the axes that are directly connected to it are part of the same frame of reference because their distances don't change. However, the axis above and the axes below any given axis are not part of the same frame of reference because their distances do change. Finally, as I mentioned, the smallest carriages pass one another at velocities approaching the speed of light indicating a significant inertial, and subsequent temporal, differential.
How could this be, or would an impossible energy be required to power it? I think this gets at the heart of the time/space dilational paradox.
Concerning the Twin Paradox, isn't the cartoon actually giving us the resolution to the paradox and not the paradox itself?
ReplyDeleteIt mentions that the space-travelling twin will be older than the earth-bound twin. But, as I understand it, that isn't the paradox. The paradox is that, according to the space-travelling twin, it is the earth-bound twin that has slower time (and vice versa). So who has the slower clock and which twin will be older?
But the cartoon has the space-travelling twin land on a planet and, thus, break his inertial frame of reference. This, the acceleration of his return flight, and the fact that the earth-bound twin has maintained his inertial frame of reference resolves the paradox, making the space-travelling twin the one who is older.
I never really understood why the paradox couldn't be maintained if the space-travelling twin simply turned the ship in a large arch to return home, maintaining his speed.
Hi Jonathan,
ReplyDeleteI should say since I'm in a different scientific field than physics, perhaps my response will prove no more than a rudimentary one. Plus it's been a while since I last took physics. Anyway no doubt a physicist could give you a much better answer. Maybe some will weigh in.
That said I think I'd agree with you save for one or two tweaks:
1. Given the special theory of relativity, the speed of light is constant, but space and time are relative - i.e. length contraction and time dilation.
If the space-traveling twin is on a spaceship traveling at 99.9% of the speed of light, then the space-traveling twin could think he's moved away from the earth at 99.9% of the speed of light. He could be observed by an outsider to age more slowly than his earth-bound twin.
However, the earth-bound twin could just as well think the earth has moved away from the spaceship at 99.9% of the speed of light. He too could be observed by an outsider to age more slowly than his space-traveling twin.
After all, we know per the special theory of relativity time moves at a different rate for different observers depending on their motion relative to one another. (BTW, time dilation is calculated by this equation where t = time (earth reference frame), t0 = time (proper), v = velocity, and c = speed of light.)
Hence the twin paradox. An outsider observing both twins could conclude both twins are correct. But how could each twin be observed to age more slowly than the other twin?
As you point out, the resolution is due to the acceleration/deceleration of the spaceship which causes one twin to jump from one inertial reference frame to another. The special theory of relativity only applies to relations between inertial frames of reference. If one accelerated or decelerated, one would break their intertial frame. As such there is asymmetry between the twins. It's not completely asymmetrical, there is partial symmetry, but the point is the space-traveling twin and the earth-bound twin aren't perfectly equivalent to one another.
2. BTW, as you may know, time dilation could also be caused by gravity. Such as by a black hole.
3. My guess is the BBC (or whoever is sponsoring and presenting this video) is presenting this video more as a general way to whet the public's appetite for math, science, and philosophy than anything more specific. However, I think it wouldn't be so exciting to present the paradox without its resolution. Maybe that's why the BBC is presenting it this way.
4. Actually, FWIW, if anything, I don't recall ever reading or seeing anyone present the twin paradox without also presenting its resolution.
5. In the case of Einstein's twin paradox, I don't think presenting the resolution takes away too much from the paradox as far as the intrigue a layperson would have about relativity. Sometimes knowing spoilers would ruin a movie. But other times knowing spoilers has the opposite effect. It makes one want to watch the movie even more. At least that's my thinking.
6. We could take similar issue with some of the other thought experiments or paradoxes in this short video as well.
BTW, too bad they didn't do the ladder paradox. I guess that one isn't as cool to most people since it doesn't involve spaceships, twins, and time, but more mundane objects like ladders and garages.
ReplyDeleteJust an FYI: Einstein's relativity song is a fun little ditty from a pair of MIT physicists.
ReplyDeleteSchrödinger's other cat: the theory is that there's only one cat. The question is how does everyone generate enough ionization by stroking it to build up static charges.
ReplyDeleteOn another note, I believe it's questioned if the speed of light is truly constant between different frames of reference or if we consider it because we need to hold something constant in order to make any dilational computation. Since time isn't necessarily uniform, we need to measure the speed of light from a relatively uniform temporal system. The question is: how do we measure if our frame of reference for measurement is "relatively uniform" temporally at any given moment, or do we just assume it is and go on about our measurements anyway?
As a thought experiment for this, I offer a machine based on the classic Scrambler carnival ride where each axis contains a system that duplicates the mechanism in relatively smaller scale down to a point where final carriages between the largest bifurcations pass one another at relative velocities approaching the speed of light. Each axis and the axes that are directly connected to it are part of the same frame of reference because their distances don't change. However, the axis above and the axes below any given axis are not part of the same frame of reference because their distances do change. Finally, as I mentioned, the smallest carriages pass one another at velocities approaching the speed of light indicating a significant inertial, and subsequent temporal, differential.
How could this be, or would an impossible energy be required to power it? I think this gets at the heart of the time/space dilational paradox.