Here are a few questions and comments that were emailed to me.
The questions and comments are in red.
My responses are in blue
I stumbled across your science page and read your relativity article recently. You look at many different explanations to the twin paradox as if they are mutually exclusive, but if you think about it, each result could be correct from different frames of reference. There are many versions of the twin paradox, and perhaps each has a different solution. CK: In the article, I provide specific examples of various resolutions to the paradox. The direct quotes of various authors demonstrate clearly that they not only view their respective version as correct, but that the alternate explanation is not correct. For example, on page 356 of Einstein's Theory of Relativity (revised edition 1965), Max Born completes his mathematical analysis of the necessity of acceleration (in which he agrees with Einstein's resolution published in 1918) with the following statement: Thus the clock paradox is due to a false application of the special theory of relativity, namely, to a case in which the methods of general relativity should be applied.
Meanwhile, Ronald Lasky, in his 2003 Scientific American article said: Some people may falsely assume that the acceleration causes the age difference and that the general theory of relativity, which deals with noninertial or accelerating reference frames, is required to explain the
paradox. But the acceleration incurred by the traveler is incidental, and the paradox can be unraveled by special relativity alone.
These two remarks couldn't be any more opposing. If you look at what a majority of the mainstream physics community has endorsed throughout the years, it is the version closer to that described by Lasky than that of Einstein and Born. A typical example would be what Carroll O. Alley stated in his Proper Time Experiments article that among other things, provided analysis of the Hafele/Keating atomic clock experiments. Alley said: It is important to note the absence of any explicit dependence of elapsed proper time on the acceleration of the clock, or
on any of the higher derivatives of the motion. Only the instantaneous velocity enters the equation.
Clearly, the endorsement of either resolution excludes the possibility of the alternative being possible as well. For instance, the classic twin paradox involves a clock traveling away from a planet, turning around, and coming back. To understand this version of the twin paradox quantitatively we need to understand acceleration, which can be done with special relativity as long as we calculate from inertial frames. However, to see things from the perspective of the non-Earth bound clock requires calculating IN an accelerating frame, this requires using a non-inertial frame (usually considered to be GR). Alternatively, we can let the acceleration happen entirely in one instant, so that the clocks are always in inertial frames (thought the non-Earth bound clock is in TWO different inertial frames), and avoid dealing with accelerations entirely (this situation is nicely explainable with a spacetime diagram). CK: So, the question is: Can we consider the acceleration portion of the journey to be essentially the same as the inertial phase as long as we use a calculus treatment of the equations used in special relativity to represent the instantaneous rate of velocity change? If we endorse Einstein’s version of relativity, the answer to that is no. Einstein's description of how each clock runs during the inertial phase, from the perspective of the other observer is symmetrical. Meaning, that the traveler sees the stationary clock run slower, while at the same time, the stationary person sees the traveler's clock run slower. It is during the traveler's turnaround that Einstein equates his acceleration phase to being in a gravitational field. Einstein attributes the difference in clock rates to the clocks being in different positions relative to the simulated gravitational field. This is demonstrated by Einstein, Born and others to be an asymmetrical effect. This is how the Earth clock is allowed to catch up to and surpass the time on the traveler's clock, by the time they reunite. If acceleration were simply viewed as velocity with a rate of change that remained within the confines of special relativity, then by Einstein's definition, this phase would be symmetrical as well, and the clocks would not be able to resolve their times by the time the traveler returned. So, if you endorse Einstein's resolution - you are endorsing the relative nature of time
resulting from two completely separate mechanisms during different parts of the journey. If you endorse the alternative view that is seemingly embraced by a majority of the scientific community, then you are saying the difference in clock times after the traveler returns is due to special relativity and there is asymmetry during the inertial phase of travel.
Another version of the twin paradox may involve no acceleration at all, and have many moving clocks that never change velocity. These could have further explanations.
CK: They sure could! But they would not agree with Albert Einstein's resolution. Given that special and general relativity have been proven to be consistent, doesn't that imply that any inconsistency must involve a mistake? CK: Are you sure the entire theory is consistent? What if the tables were turned? What if we already knew about velocity and gravity's effect on clock times for decades but had no working explanation as to why these behaviors were so? What if there were no Albert Einstein and in the year 2003, some nonscientist came out of nowhere with a theory identical to what Einstein published years ago. How would the scientific community scrutinize those same postulates and statements? Examine everything that Einstein said about time dilation and his explanations for why a traveling clock will be running behind his earthbound counterpart upon return. Is it all consistent and does the current evidence support it? There is evidence found in GPS system operations and recorded muon decay rates that support some of Einstein’s statements. There is no evidence (that I’m aware of) that supports Einstein’s entire theory. |