- #36
Ian Davis
- 19
- 0
The article cited is not much use in explaining the twin paradox because it introduces acceleration to explain the paradox which a red herring. The paradox exists without introducing acceleration, so introducing acceleration to explain it is a real cheat.
Consider two observers who each have clocks consisting of a light pulse bouncing between 2 vertical mirrors set 4 ft apart. Let one observer pass the other at a speed
of 3/4c. Then they and their clock travel 3 ft every time the light travels 4ft. The observer moving with their clock sees light move 4 ft, the stationary observer 5ft (3-4-5 right angle triangle)/ For the two observers to agree on its velocity as c, since velocity = distance/time we have 4/t1 = 5/t2 or t1/t2 = 4/5 where t1 and t2 are the observed passage of time for the light to travel from one mirror to the other. So the moving observers clock ticks 4 ticks for every 5 the stationary observers light clock ticks.
The stationary observer can compute this, and thus conclude that the moving observer
is aging more slowly, because their light clock is running slower. But the entire arrangement is entirely symmetric, and the moving observer can conclude that because they are stationary, the actual equation is t2/t1 = 4/5. The paradox is to explain how 4/5 = 5/4. Worse by symmetry have each travel 3/8c away from the other, at the same speed but in opposite directions, instead of arbitrarily claim one stationary and the other moving. Then they will conclude that while each has a clock somewhat slowed by their mutual but opposite velocities, their clocks are each slowed by the same amount relative to a stationary clock and thus are in sync, contradicting the earlier observations.
So it appears that the two observers can choose how much time they wish to trade for how much distance, merely by changing the rules about what constitutes the means of measuring distance. The geometry of how they measure distance is easily grasped. It is simply a consequence of the universal metric (x^2+y^2+z^2-t^2) being the same in all inertial frames, but none of the individual variables necessarily agreeing between two observers.
The hard part is understanding what actually happens to an individuals watch, merely as consequence of declaring light travels 4ft or 5ft. It may be that merely announcing that I am traveling at 3/4c, slows my watch by 4/5, which being slowed myself I fail to observe any change in, but this makes something of a mockery of the notion of time being fixed, even for one in an inertial frame. And what exactly is meant by two observers each having clocks that run slower than the others.
Consider two observers who each have clocks consisting of a light pulse bouncing between 2 vertical mirrors set 4 ft apart. Let one observer pass the other at a speed
of 3/4c. Then they and their clock travel 3 ft every time the light travels 4ft. The observer moving with their clock sees light move 4 ft, the stationary observer 5ft (3-4-5 right angle triangle)/ For the two observers to agree on its velocity as c, since velocity = distance/time we have 4/t1 = 5/t2 or t1/t2 = 4/5 where t1 and t2 are the observed passage of time for the light to travel from one mirror to the other. So the moving observers clock ticks 4 ticks for every 5 the stationary observers light clock ticks.
The stationary observer can compute this, and thus conclude that the moving observer
is aging more slowly, because their light clock is running slower. But the entire arrangement is entirely symmetric, and the moving observer can conclude that because they are stationary, the actual equation is t2/t1 = 4/5. The paradox is to explain how 4/5 = 5/4. Worse by symmetry have each travel 3/8c away from the other, at the same speed but in opposite directions, instead of arbitrarily claim one stationary and the other moving. Then they will conclude that while each has a clock somewhat slowed by their mutual but opposite velocities, their clocks are each slowed by the same amount relative to a stationary clock and thus are in sync, contradicting the earlier observations.
So it appears that the two observers can choose how much time they wish to trade for how much distance, merely by changing the rules about what constitutes the means of measuring distance. The geometry of how they measure distance is easily grasped. It is simply a consequence of the universal metric (x^2+y^2+z^2-t^2) being the same in all inertial frames, but none of the individual variables necessarily agreeing between two observers.
The hard part is understanding what actually happens to an individuals watch, merely as consequence of declaring light travels 4ft or 5ft. It may be that merely announcing that I am traveling at 3/4c, slows my watch by 4/5, which being slowed myself I fail to observe any change in, but this makes something of a mockery of the notion of time being fixed, even for one in an inertial frame. And what exactly is meant by two observers each having clocks that run slower than the others.
