Time Dilation and Special Relativity - A Clear Flaw

A Total Neglect of Einstein's General Relativity

This presentation was first placed on the Internet in February 2009. The Twins Paradox is Wrong presentation was first placed on the Internet in August 2004.

There are clearly two major flaws in the description of Time Dilation as related to Special Relativity, or at least, as commonly interpreted. The flaws seems to be completely overlooked in both the Physics community and the general public, but it is quite simple and obvious to see.

There IS a logical explanation for this, but it is quite different from anything that seems to have ever been presented before.

First, we need to remember that Einstein's Special Relativity is where there is no acceleration occurring, where only constant velocity motion is present. Every Physics student learns to derive the simple formula for the effect of Time Dilation, where there is an appearance of time having slowed down for the person or environment which is observed moving either toward the observer or away from the observer at relativistic speed.

The first flaw exists because only one of the two (necessarily symmetric) views has ever been considered before, generally the perspective from the Earth.

The Special Relativistic Doppler effect is given by:

where z is given as usual in octaves of wavelength shift, v is the observed velocity of the object and c is the speed of light.

The Special Relativity Time Dilation effect (time slowing factor) is given by:

equation - Time Dilation time-rate factor

For an object actually receding from us at v = 0.6c, this gives a Time Dilation factor of 0.8, a ratio of the apparent passage of time based on the observer's own time clocks. This means that the observer would see time seem to pass on the other object and clock at 4/5 as fast, so the observed person would seem to be moving in slow motion.

For an object actually receding from us at v = 0.8c, this gives a Time Dilation factor of 0.6. For an object moving relative to us at v=0.9c, this formula gives a Time Dilation factor of about 0.44. So if the relative velocity is at 90% of the speed of light, the observed rate of time passage seen is slower than half what might be expected.

Now, consider two stars and planets which happen to be moving such that the distance between them is decreasing extremely rapidly. Observers on each of the two planets will consider themselves to be stationary, and therefore that the other planet is moving at high constant velocity, complying with Special Relativity. For this example, we will assign a very high approach velocity which will be precisely measured on each planet as being 0.999999 c. This velocity would be within 300 meters per second of the speed of light.

Consider the observer on Planet A first. He sees that approach velocity and uses the calculation above to determine that time on Planet B necessarily appears to be passing at 1/700 as fast as he experiences. He would therefore see the atomic clocks running on Planet B to be appearing to run 1/700 as fast as the one in his own lab. He would hardly see the persons in that lab to ever even move at all, since they would only appear to move at 1/700 of our movements! (This is essentially the same as the conventional description of Time Dilation.) The very long-lived observer on Planet A, in 7,000 years of his life, then would necessarily watch a person on Planet B live through ten years of history.

Here is the part that everyone has overlooked before. Now consider the situation of the very long-lived observer on planet B. His interpretation is that he is stationary and that Planet A is rapidly approaching. Therefore, he uses the same formula to determine that time he finds that time on Planet A necessarily appears to pass at 1/700 as fast as he experiences in his laboratory on Planet B, alongside his atomic clock.

In principle, this is logically possible! Each of the two observers would have to live for 7,000 years, just to watch ten birthdays of the other!

The traditional description of Time Dilation only considers one view of this situation, the view from the Earth. But that necessarily assumes that the Earth is stationary, and the other planet is approaching at extreme (constant) velocity. The reality is that the other observer would have exactly the same logic and the same experimental measurements.

The traditional description of Time Dilation (and the Twins Paradox) applies an assumption that is not correct. The entire concept of relativity is that neither of the two observers can possibly have any "preferred" Inertial reference frame.

There is clearly a major flaw in that description of Time Dilation. The solution involves an inter-relationship between effects of General Relativity and Special Relativity, where SR does have the Time Dilation (slowing) effects but that GR has an opposite time-rate effect of causing a person or an event being viewed to appear to occur faster than otherwise expected.

For either of our two planetary observers above, as long as they remain traveling at that extreme velocity to each other, they actually could see each other as living life at a rate 1/700th as fast as they do themselves. But their mutual encounter would be extremely brief, two ships passing in the night, in a microsecond or shorter time! Now, should either or both decide to slow down, things get very interesting! During the rapid deceleration from that extreme relative speed, down to a speed where they would eventually be moving at the same velocity and that they might therefore actually meet, an unexpected situation occurs! Where they observed each other to appear to be living very slowly during the constant-velocity Special Reelativity portion, the opposite is true during the deceleration (or acceleration) General Relativity portion of their journey. During that time, the non-decelerating one would see the decelerating one appear to age immensely fast!

It is easy to see why this must necessarily be true. We just need to consider an entire trip rather than only looking at the Special Relativity portion of it. We have an entire presentation which does this in great detail, which shows that the popular Twins Paradox is not a paradox at all, as it is not anything like what is usually described! Specifically, yes, during the middle of such a trip, the Earth observer does see the space traveler appear to be moving in slow motion. However, at the same time, the space traveler sees the Earth and the Earth twin moving in apparent slow motion to himself! both actually do see the other appear to be moving and living more slowly than himself!

But that is only a brief condition. During the acceleration phase of the trip, where the rocket sped up from sitting still on Earth to having an extreme relative velocity, each would then see the other as moving and living faster than himself! But at different rates from each other's perceptions.

In any case, if the Earth twin watched the traveling twin make a trip to a planet near Alpha Centauri (4.3 light years away), and he had an extremely powerful telescope to be able to watch his brother's every action and clock, he would see the brother appear to accelerate for maybe a month (Earth time) while he saw the traveling twin age more than two years (spacecraft time). He would then see the traveling twin appear to age very slowly during the coasting, Special Relativity portion of the trip (as is universally known by everyone!) The Earth observer would see that coasting portion of the trip to seem to take more than four years (Earth time) while he saw the traveling twin age only a few weeks (spaceship time). And then he would see the spacecraft intensely decelerate toward the A.C. planet, which he would see as taking maybe a month (Earth time) while watching the traveling brother appear to age by more than two years.

The Earth observer would see a total effect where around 4.4 years of Earth time was required for the trip (0.1 year accel + 4.2 years coasting + 0.1 year decel). He would have seen the traveling brother age rather differently, but the same total (2.1 years fast aging during accel + 0.2 years of very slow aging during cruising + 2.1 years of fast aging during deceleration) of 4.4 years.

What would the traveling brother experience? He would experience more than 2 years of pretty logical acceleration, followed by a few weeks of constant velocity cruising, followed by more than two years of deceleration, where he would record in his Log Book a total of 4.4 years of total time passage. (Note that his actual experience matches what the Earth brother had observed!)

And if he had spent the trip looking back toward Earth with a powerful telescope of his own? He would see the Earth brother appear to age slightly more than the two-plus years he was experiencing (in other words, aging faster than he was, but only slightly) during the two years of his acceleration. Then, once he shut off the engines and started to coast, he would see the Earth brother appear to age slightly more slowly than himself. Where he would experience several weeks of constant velocity cruising (as described above), he would see the Earth brother appear to age a few days less than that.

Note that they both actually see the other as aging more slowly than themselves during the cruising! They also both actually see the other as aging more rapidly during the acceleration and deceleration!

So his perception of the Earth brother would be in aging 2.11 years during his 2.1 years of acceleration, 0.18 years of slightly slowed aging during his 0.20 years of cruising, and another 2.11 years of faster aging during the deceleration, so he would see the Earth brother as having aged a total of 4.4 years.

Note that this all describes where each actually experiences exactly 4.4 years of actual life and each also observes the other as having experienced a total of exactly 4.4 years of life. There is no paradox at all! And there is no speculative advantage regarding time travel or being able to travel tremendous distances in short periods of time. That is possible if the relative velocities are never accelerated or decelerated, but it is not possible if they are ever to return to a mutual velocity where they could meet!

The Twins Paradox presentation includes the entire reasoning and math for this subject.

Twins Paradox of Relativity Is Absolutely Wrong

This presentation was first placed on the Internet in February 2009.

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