Seems to me I read once of an experiment in which someone took two very accurate atomic clocks, synchronized them and then took one on a airplane trip round the world and when he returned they were no longer in synchrony and the discrepancy was exactly (within the limits of accuracy) as predicted by special relativity. So the twin “paradox” has even been verfied experimentally.
In any case, the twins’ lives are not symmetric. One has undergone acceleration and the other has not.
That last paragraph does raise a question, though. Of course, the person who stays on earth does undergo a (nearly) constant 1g acceleration, right? Does this mean that the twin who goes up to near earth orbit (experiencing some additional acceleration, to be sure) orbits weightless for a year and then returns to earth actually ages faster than his twin on earth simply because the latter has been experiencing 1g acceleration the whole time?
No, you can’t. You can pick any single inertial reference frame to be “at rest”-- Any one you want. But you can’t pick two different frames to both be at rest. If you pick as your “rest frame” Tom’s frame, then you’ll find that when they meet again, Tom will be older. If you pick Bob’s outgoing frame as the “rest frame”, then you’ll still find that Tom will be older. And if you pick Bob’s returning frame as the “rest frame”, then you’ll get the same result. But you can’t pick both of Bob’s frames to be at rest.
As for your second example, where the twins never meet, or your third one, where they meet only once, they’re not answerable. In order to compare the ages of the twins, you have to look at them at the same time. But in relativity, the definition of “same time” depends on what reference frame you’re in. The only way you can say that two things are the same time, without specifying some reference frame, is if they’re also in the same place. In the classic Twin “Paradox”, we can do this: The twins start off in the same place, so our first measurement of age is at the same time for both, and the twins also end up in the same place, so our second measurement is also at the same time for both. But if one twin leaves and never returns, then we can’t do that. Our second measurement of “same time” depends on what reference frame we use.
And if we bring in orbits, then we can’t use Special Relativity, but the much more complicated General Relativity. Let’s not do that. Suffice to say that the results will be approximately as large as predicted by Special Relativity, but they might not be in the same direction, and they might be a factor of 2 or so different in magnitude.
By the way, this reassurance may come a bit late, but from your description, you were the only person in your high school class doing science. It’s absolutely essential in science to know and acknowledge the uncertainty in your measurements.
The people who is call the Twins Problem the Twins Paradox are simply propogating a myth. There is no paradox if you apply the equations correctly. The “paradox” proponents are making a glaringly obvious error in logic.
As a general principle of science, everyone should agree that when a scientist takes measurement during an experiment, that these measurements need to be made in a consistent manner. In the case of Special Relativity, Einstein clearly stated that all the measurements made during an experiment need to be made from the same inertial reference frame (IRF). Einstein never claimed that his equations would work if you ignored this requirement.
In the case of the Twins Problem, two measurements are made. One measurement (reading the brothers’ clocks) is made when one brother leaves Earth. The second measurement is made when that brother returns to Earth. The brother who stays on Earth can be used as a valid IRF observer because he never accelerates. The brother who leaves Earth travels in one IRF while he’s outbound, and different IRF (one moving the opposite direction) when he returns to Earth. In essence, the travelling brother is using one IRF to make the first measurement, and a different IRF to make the second measurement. By the rules of special relativity, this not a valid way to make measurements.
The “paradox” proponents either ignore the IRF switch or simply don’t recognize that it happened. They then go on to claim that from the travelling brother’s “point of view”, the brother on Earth is the one who gets younger. The problem is, this “point of view” isn’t an Inertial Reference Frame, and when they apply Einstein’s equations as if it were a valid IRF, they wind up with screwy results. That’s the flaw in their logic. And when you point it out to them, they respond in one of three ways:
They claim that it’s not really an IRF switch because the travelling brother is simply changing direction, not speed. Nonetheless, this violates Einstein’s definition of an IRF.
They claim that the IRF requirement is not really necessary. I assume they are saying this because it is not obvious why it’s necessary, and maybe they figure that Einstein is just trying to trick us. Or maybe they think they’re smarter than Einstein and everybody else who works in the field of physics.
They will try to distract you from the flaw in their logic by changing the story problem, maybe have the second brother move in a circle, or add a 3rd brother, etc.
To the casual observer, it may seem puzzling that the traveling brother’s IRF switch would create a problem. Nonetheless, the logic of special relativity depends upon a precise definition of IRF. And this is actually true for all of the laws of physics. The terms in an equation such as F = MA, are precisely defined so that there is no ambiguity. And if you ignore the definitions or accidently use the wrong units, then it’s just another case of garbage in = garbage out, and oops, your Mars probe crashes into the surface of Mars instead of softlanding.
btw, if you’re worried about the gravitation effect of the Earth in the Twins Problem, just use a space station instead.
The people who is call the Twins Problem the Twins Paradox are simply propogating a myth. There is no paradox if you apply the equations correctly. The “paradox” proponents are making a glaringly obvious error in logic.
As a general principle of science, everyone should agree that when a scientist takes measurement during an experiment, that these measurements need to be made in a consistent manner. In the case of Special Relativity, Einstein clearly stated that all the measurements made during an experiment need to be made from the same inertial reference frame (IRF). Einstein never claimed that his equations would work if you ignored this requirement.
In the case of the Twins Problem, two measurements are made. One measurement (reading the brothers’ clocks) is made when one brother leaves Earth. The second measurement is made when that brother returns to Earth. The brother who stays on Earth can be used as a valid IRF observer because he never accelerates. The brother who leaves Earth travels in one IRF while he’s outbound, and different IRF (one moving the opposite direction) when he returns to Earth. In essence, the travelling brother is using one IRF to make the first measurement, and a different IRF to make the second measurement. By the rules of special relativity, this not a valid way to make measurements.
The “paradox” proponents either ignore the IRF switch or simply don’t recognize that it happened. They then go on to claim that from the travelling brother’s “point of view”, the brother on Earth is the one who gets younger. The problem is, this “point of view” isn’t an Inertial Reference Frame, and when they apply Einstein’s equations as if it were a valid IRF, they wind up with screwy results. That’s the flaw in their logic. And when you point it out to them, they respond in one of three ways:
They claim that it’s not really an IRF switch because the travelling brother is simply changing direction, not speed. Nonetheless, this violates Einstein’s definition of an IRF.
They claim that the IRF requirement is not really necessary. I assume they are saying this because it is not obvious why it’s necessary, and maybe they figure that Einstein is just trying to trick us. Or maybe they think they’re smarter than Einstein and everybody else who works in the field of physics.
They will try to distract you from the flaw in their logic by changing the story problem, maybe have the second brother move in a circle, or add a 3rd brother, etc.
To the casual observer, it may seem puzzling that the traveling brother’s IRF switch would create a problem. Nonetheless, the logic of special relativity depends upon a precise definition of IRF. And this is actually true for all of the laws of physics. The terms in an equation such as F = MA, are precisely defined so that there is no ambiguity. And if you ignore the definitions or accidently use the wrong units, then it’s just another case of garbage in = garbage out, and oops, your Mars probe crashes into the surface of Mars instead of softlanding.
btw, if you’re worried about the gravitation effect of the Earth in the Twins Problem, just use a space station instead.