(Lectures have started again at universities across europe and thus our time left for writing articles for Ex Falso … has been shortened significantly. I did however find the time to look at one of Mathis’ most recent papers about time travel.)

In one of his papers (Is time travel possible?) Miles Mathis, inspired by a Star Trek episode, ponders the possibility of time travel, mainly in connection with the so-called Twin Paradox in special relativity.

Special relativity is a delicate subject and this post can neither give you a full explanation of how it works nor clear up all the misconceptions about it. However, we’d at least like to point out some of the more obvious mistakes and places where Mathis is being too vague.

Right at the beginning of his paper, Mathis writes that the Lorentz transformations used in calculating the twin paradox “relies on treating velocity as a directionless vector”. That is certainly not true. So called Lorentz boosts (a special kind of transformations into a coordinate system of an observer moving with a certain velocity) depend both on the modulus and the direction of the velocity (see here). However, when doing calculations, one often simplifies things as much as possible. Since for the twin paradox one is only interested in the proper time of the observers, the calculations can be simplified greatly be only considering how changes. Since furthermore it turns out that time dilation does not depend on whether you are moving away or towards another observer, in this case it suffices to simply know the modulus of the velocity.

Mathis writes “The current interpretation implies that time passes more slowly for some events”. Although not a mathematical error, Miles’ usage of the term “event” is problematic. He has certainly picked it up from the literature on special and general relativity, but there it has a precise meaning, namely it is a point on the space-time manifold. It has different coordinates in different coordinate systems or reference frames, but the physical point in space-time it describes is unique. Time does not “pass” for events, just like time does not pass for the event “Paris, November 11th 2010 22:02”. If Mathis were a little more careful when using terms that have precise meanings (or defining his own terms), he would quite certainly become less prone to the many mistakes in his papers.

Although Miles repeatedly claims to agree with many of the results of special relativity, he suffers from a grave misconception about one of the most astonishing of its properties. He suggests that there is no actual time travel happening in the Star Trek example because Kirk and Spock can always “*synch up their ‘nows’*“. If we ignore special relativity for a moment and think about this with our intuition gained from day-to-day experience, it is clear what Mathis is talking about: Kirk does not travel into the future because at every instant, he is in the same instant together with Spock – His brain and body are just working a lot faster!

In Special Relativity however, the simultaneity of events (that is, whether an observer assigns the same time coordinate to two distinct events) is *relative* to the observer’s frame of reference. Two observers do not agree on what is “happening now” (see this video on youtube for a really short illustration). Even though this seems very counter-intuitive, it is one of the fundamental results of Special Relativity and Miles’ argument about synching up “now” shows that he does not fully understand its implications. (Miles is of course free to believe that the Theory of Relativity is fundamentally wrong . We think, however, that had he really understood its results, he would have at least mentioned that his arguments contradict them.)

At the end of his paper, Miles discusses the situation of an observer circling another observer at a certain radius. He argues that because of the very short distance between the observers, it will take light only a very short time to travel between them. This in turn will not be enough time for the “*data*” carried by the photons to be “*skewed*“. As in one of his earlier papers, neither does he give an explanation of what “data” or “skewing” is supposed to mean in this context and the meaning thus remains elusive. Reading Miles paper it rather seems that for a very distant observer (circling the other observer in a very large circle), there should be effects similar to those in special relativity (like time dilation), independent from the circling observer’s speed. This again, is in contradiction not only with the theory of special relativity but also with experiments.

(A calculation of this situation in the framework of special relativity can be found in N.M.J. Woodhouse’s very good book on special relativity)

Although the Star Trek example is amusing and might illustrate the point that even in special relativity the words “time travel” must be interpreted with caution, Miles article does in no way shed light either on the nature of time and space (as does relativity) nor on Miles own theory of “data”.

The train video (and SR) states that two observers will never agree on observations because their reference frame is never the same, which is obviously true. The perceptions of the two observers are always only relative to each others reference frame. But I have to agree with Mathis when he compares this to the doppler effect. If their clocks are synchronized, either observer can calculate the same time for each lighting strike if they account for the speed of light, since c is the same for both. We could just as easily transfer the problem from seeing the strikes to hearing the thunders. They’d only have to account for the speed of sound instead of c. If we access reality only through the different forms it reaches us (the senses), i believe his reasoning is right when he states there’s one underlying reality and different perceptions of that reality within each observers reference frame. If you take the speed of sound and your distance from the place where the lightning stroke, you can calculate when it stroke, relative to your clock. If I, some distance apart from you, do the same thing (given our clocks are synchronized), then we can calculate the same time of strike, even though we may have heard it at different times. We can calculate an underlying single reality, even though comparing our perceptions we would disagree. It seems to me that it is not the reality that is relative, but perception.

Dear Erto,

In Galilean relativity, the order in time of two events always stays the same. If the two bolts of lightning strike at the same time in one frame of reference, it does so in all others (even though one might not hear their thunder simultaneously everywhere). That however, is not true in special relativity. Different observers will not just hear the thunder at different times, they will actually calculate the time of the lightning to be different for the two separate strokes, depending on their own relative movement to the events.

Cee

It is perfect time to make some plans for the future and it is time to be happy.

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