Time is Passing on Earth Faster than it is on the Moon

A really interesting subject is regarding General Relativity. Where Special Relativity dealt with constant velocity, in other words, no acceleration, General Relativity is about the many situations where (constant) accelerations occur.

One specific 'thought experiment' comment of Einstein became very well known. He proposed having two identical elevators. One of the elevators is in an extremely tall building on Earth, and he cut the cable supporting the elevator carriage, where the elevator carriage would then fall downward with ever increasing velocity, but with constant acceleration (of 9.8 m/s/s). Einstein noted that an occupant of that freely falling elevator would be floating in the elevator, along with everything else there (at least until it hit the bottom!). Einstein put his second, identical elevator carriage in deep outer space, by itself, where there was no gravity at all.

Einstein then stated that the occupants of the two elevator carriages would not be able to do any experiment to find anything to distinguish these two very different situations. Einstein called this General Relativity. He had explained that 'gravity' (or actually gravitation) is indistinguishable with 'inertial acceleration'. In the one case, there was no net acceleration detected in the elevator cage because there were two effects, one of them being the Earth's gravitational field and the other being the acceleration of the entire elevator in free fall, which Einstein said always exactly matched. The combination resulted in no net acceleration effect inside the elevator cage. This gave an environment inside the elevator cage which was indistinguishable from the situation which is true in the deep outer space elevator cage.

Einstein's next General Relativity thought experiment showed a little more. This involved having two identical rockets. One is sitting on a launch pad on Earth, stationary, being subjected to the gravitational field of the Earth, which we describe as 9.8 meters/second2 or 32 feet/second2. The other space ship would again be in deep space, away from any planets, but this one was constantly accelerating due to an ever-running rocket engine at exactly 9.8 meter per second per second. Einstein noted here as well that the occupants of the two rockets could never do any experiment to tell which situation was really their case. Again, an Inertial Acceleration due to motion cannot be distinguished from the effects of a Gravitational Field.

Einstein concluded from such thought experiments that an Inertial Acceleration due to motion must be exactly interchangeable, and indistinguishable, with an Acceleration due to the gravity of a planet. We refer to that as General Relativity. An equation referred to as the Equivalency formula mathematically relates the two.

As it turns out, the set of ten Tensor Calculus solution equations for General Relativity are astoundingly complex, and NO ONE has yet fully solved them, even a hundred years later! Some assumptions were made and some simplified approaches were developed around 1960, and some new conclusions were presented after that. Because of those (questionable) assumptions, which now appear to be obviously very wrong, virtually all Physicists today agree that there must be the same Time Dilation Effect which must exist in General Relativity, as is seen in Special Relativity. The following discussion will show that they are all certainly wrong in that assumption and conclusion, and that the time passage effect of General Relativity is opposite that of Special Relativity and its Time Dilation.

I consider a new Thought Experiment like Einstein's to provide yet another new insight of great importance.

Consider the second of the Einstein thought-experiments regarding the rockets. Give each of the two occupants a precisely accurate atomic clock. We will start the accelerating rocket out far past the edge of the Solar System, where there is no gravitational effect, and we will provide the rocket with an engine that consistently and reliably provides the correct amount of thrust so that the rocket is able to accelerate at exactly 9.8 meters/second2. We then have the exact circumstances in Einstein's second thought experiment, where no experiment can ever discern between the interior of the rocket still sitting on the launch pad on Earth and the interior of the rocket that constantly accelerates at 9.8 m/sec2 in deep space.

This experiment continues for exactly two years. The occupant of the rocket sitting on the Earth is agreed as having aged exactly two (Earth) years, as proven by his Cesium clock. What about the other occupant? It might first seem that he should also age exactly two years, but there is another effect which must be considered.

During those two years, which is around 63,114,000 seconds, every one of which he could measure that he accelerated exactly 9.8 m/sec2. He should certainly have had Log Book entries, the latest of which should show him now traveling at a cumulative 618,000 km/sec.

Since the speed of light is about 299,792 km/sec, this is obviously not possible, as it would indicate that he would think that he had massively exceeded the velocity of light, which we know he could never experience! This shows that necessarily there is a relativistic effect regarding acceleration and time and distance, that is, General Relativity.

In fact, there is only one possibility which can explain this, and other similar problems. We know that his rocket engine thrust has not changed, so he believes it is still creating the same thrust every second, which could continue forever.

We know of Newton's F = m * a regarding the performance of his rocket engine. The only explanation is that there are two effects of General Relativity. The mass of his rocket is increasing at the exact same rate that the acceleration of his ship is decreasing. He would not be aware of either of these effects. But the time interval which he sees as one second is now actually taking a shorter real interval of time. What he sees as 9.8 m/sec2, and will forever see, is now actually during a shorter real time interval, and so his actual acceleration has become less. If you think about that, the effect on him is that his Cesium clock now passes more seconds of time than it used to, or that he is now living life faster than he used to!

That is the opposite effect from Time Dilation!

Am Earth observer would see a traveler in (constant velocity) Special Relativity to experience Time Dilation, that is, aging just a few weeks in a year of observing. We are familiar with that. The actual Traveler would not sense anything different. In General Relativity, the traveler would be seen (from an Earth observer) to experience exactly the opposite, such as aging a hundred years during a year of observation from Earth (during ferocious acceleration).

No other description could describe his actual personal experience, of having a rocket engine which could forever provide an acceleration of 9.8 m/sec2, and still not ever think that he would violate the speed of light.

When looked at from the Earth observer, similar but different effects are seen. Where the Traveler would never have had any sensation of change in the rate of time passage, the Earth observer would certainly see it. The Earth observer might see him appear to travel (accelerate) for a year, that Earth observer would see the occupant age by more than a year during that year of acceleration! During that one year of observed trip, the rocket would have been seen to have traveled less than one light-year in distance. Remember that the traveler would be seen to age more than a year during that acceleration, (ensuring the compliance with the speed of light) and the consequence is that the Traveler would perceive that he has traveled a greater distance than is seen by an Earth observer.

Consider a longer and faster trip.

There are four possible perspectives (only analyzing during the ferocious acceleration):

Note that both see the other one to seem to have aged faster than himself! This is only during the acceleration (and deceleration phase(s) of the trip.

We remember here that during the constant velocity portion of the trip, they both see each other appear to age slower than himself, per the long-accepted Time Dilation of Special Relativity!

The net effect of all this is that all perceptions agree that he arrives just over 100 years after he left Earth! (1) The Traveler would experience the trip to have been 50 years of acceleration, followed by a few days of constant velocity cruising, followed by 50 years of deceleration. He would have aged a total of just over 100 years during the trip. (2) The Earth observer would see the trip quite differently, maybe a year of extreme acceleration, followed by 98 years of constant velocity cruising, and then a year of severe deceleration. He would have lived a total of just over 100 years in watching the trip. (3) The Traveler, looking back at Earth, would see the Earth observer age just over fifty years during the acceleration, followed by a few hours less aging during the very brief cruising section, followed by seeing the Earth observer age just over fifty years during his deceleration. In all cases, there is total agreement that they both aged just over 100 years during the entire trip, and that they both saw the other person also age by just over 100 years during the trip and that both their calendars would have shown just over 100 years actually go by.

As is required in Relativity (when both are in the same Inertial Rest Frame), all perceptions have ultimate agreement! This requirement merely ensures that neither of them is experiencing any Acceleration at the beginning or end of the trip.


This presentation was first placed on the Internet in January 2013.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago