The Slowing of Clocks and the Twin Paradox
An example of clocks changing their rates with changes in motion is the so called Twin Paradox where one twin travels at very high speed to a star and back and returns younger than the twin that stayed home.
The term “twin paradox” is often used within Special Relativity theory to explain how a paradox occurs when the attempt is make to describe the rate changes in clocks based only on differences in relative motion between the clocks. The paradox arises because it is absolute inertial motion and absolute gravitational motion that changes the rate of clocks and not relative motion. Relative motion between clocks may or may not cause them to have different rates.
The clock “paradox” thought experiments discussed here are based on the mechanics of clock slowing experiments. Neither Special Relativity nor any other theory is used to interpret the results of these measurements. Measurements show that atomic clocks change their rates from both gravity and motion according to the equations of the Lorentz transformation. The Lorentz transformation is not a theory. It is simply a relationship that we measure between mass, space and time. Measurements show that all atomic clocks run at a maximum and identical rate at a position of rest. Any velocity relative to this position of rest increases the mass of the atoms within the clocks. This increased mass within the atoms causes their internal motions to slow in order to conserve angular momentum. It is this internal slowing of the clock’s atoms that slows the clock’s rate.
An atomic clock does not measure “time”. A clock is a cyclical device that monitors the conservation of angular momentum. Time does not have a physical existence other than as our idea of the motion within angular momentum. Time is merely the idea that we use to quantify the motion of mass. In the same way, space does not have a physical existence. Space is the other idea that we use to quantify its motion.
There is no paradox in the interpretation of these experiments that requires the logic of a theory to explain. There are real triplet “paradox” experiments that have been performed with atomic clocks. A triplet who spends a long time at the space station will find that his watch has lost time relative his brother’s on the earth. Conversely, the third triplet who spends his time in a communication satellite orbit can tell by his watch that he is older than both his brothers. There is no way that the different ages of these triplets can be considered as a paradox.
The Triplet Paradox
To better understand the twin paradox within the principle of absolute motion, we will consider a special case using triplets where it is possible for the two traveling triplets to actually come home older than a third stay at home triplet.
Equal red and blue Doppler shifts occur in the 2.7° CBR on opposite sides of the universe on a line that passes through a point near the constellation of Aquarius on one side and a point near the constellation Leo on the other side. Measurements of these shifts show that the solar system is moving in the direction of Leo at about 375 km/s relative to the speed of light motion of the CBR photons.
In this thought experiment, there are triplets Adam, Bob & Chad. Adam stays on earth for two years. Bob accelerates to 375 km/sec in the direction toward Leo for one year and then turns around and travels back to earth at 375 km/sec. Chad accelerates to 375 km/sec in the direction of Aquarius and then after one year he turns around and returns to earth at the same velocity.
On Bob’s trip toward Leo, he is actually traveling at 750 km/sec relative to the photon rest point of the CBR. This causes his atomic clock to run slower by twice the amount that Adam’s clock is slowed by the motion of the earth. When Bob turns around, he has to accelerate to 750 km/sec to put him at 375 km/sec back toward the earth. In actuality, this is deceleration that brings Bob to a position of absolute rest. On Bob’s “trip” back to earth, he is actually sitting still while it is the earth that travels to meet him. With no gamma factor to slow it, Bob’s clock is running faster than Adam’s clock. Also, Bob’s body clock is aging faster than Adam’s.
When Chad accelerates to 375 km/sec towards Aquarius, he is actually decelerating to a stop. This will cause his clock to run at the maximum Rest rate. He sits at rest while the earth moves away from him at 375 km/s. When he accelerates to 750 km/sec for his return to earth, his clock will be running twice as slow as Adam’s clock.
We might assume that when Bob and Chad return to earth, everyone’s clock would have recorded the same amount of time since all three triplets had each spent two years traveling at the same average velocity of 375 km/sec. However, this is not quite true because we would be neglecting the clock slowing caused by the earth’s gravitational motion. This gravity can be translated to the earth’s surface escape velocity of 11.2 km/sec. Since Bob and Chad were virtually free from gravitational force on their journeys, their clocks will both record more time than Adam’s clock that was slowed by both gravity and the earth’s velocity of 375 km/s.
In this special case, both traveling triplets will return home slightly older than their stay at home brother. This same effect will occur for any velocities less than 375 km/sec. Actually it is only for velocities greater than 375 + 11.2 km/sec that the travelers will return to earth younger than their stay at home sibling.
In reality, these low velocity time dilations would only be noticeable with very accurate clocks. For meaningful differences to occur in the triplet’s actual aging, they would have to travel at velocities closer to the speed of light. 375 km/s might seem very fast but at this velocity it would take about 6,400 years just to get to the nearest star and back.
Many experiments with orbiting clocks have shown that a clock’s rate of ticking will slow down when its absolute velocity is increased and will then speed up when it is decelerated to a lower velocity. These experiments show that there is no paradox between the triplet’s differences in aging rates.