Anyone who has read *Exoplanets and Alien Solar Systems* will know that I disdain the use of the term “paradox” in physics and math. Invariably, it means that the result that is called a paradox has its origins in a phenomenon that is not correctly understood, either because one or more assumptions is completely wrong and/or the interpretation of something is completely wrong. Paradoxes in physics are often surronded by a lot of unjustified drama, as in, “Wow, isn’t this so weird (and cool)?” Unfortunately, when something is so commonly referred to with a familiar label, one is forced to use the terminology to some extent in order that people realize you are talking about the same thing.

What has this got to do with Exoplanets? Well, I am working on a paper which brings the so-called twin paradox of special relativity head to head with exoplanets. (The twin paradox is the one which highlights the fact that the equations of relativity are symmetric and imply that for two observers traveling at high speed relative to each other, each claims that the other person is younger..but more about this in a later post.) Hang on, I hear you say, what can relativity possibly have to do with exoplanets? The highest orbital speeds of exoplanets are tiny compared to the speed of light. You would be right, and that’s why nobody talks about relativity when talking about exoplanets. However, a true understanding of the twin paradox reveals that it is not all about high speeds approaching that of light, there are some subtle issues related to cause and effect as well as cosmic time. The results I describe in the paper are rather surprising and dare I say, will likely be controversial.

I would like to describe the results in an accessible and nontechnical form, but without some background on various issues, the results may not mean much even to scientists in a different field. So here’s what I’m going to do: in a series of blog posts (not necessarily consecutive) I will go back to “square one” and go over various issues in relativity and finally lead up to the new results. I have had an interest for many years in fine-tuning methods of explaining the resolution of the twin paradox and related phenomena with no math so this will be a good opportunity to utilize the techniques. What I find particularly fascinating about the twin paradox is that the *refereed* scientific literature on it is a total mess, wth divergent interpretations amongst different authors, and in many cases flawed reasoning. Moreover, the majority of expositions in text books are flawed or completely wrong. One of the worst cases is the text book I used as an undergraduate nearly three decades ago. If I had known then that it was completely wrong it would have saved me a lot of grief. But I didn’t realize until years later, after which I realized that the problem is widespread and I began researching presentations and interpretations of the twin paradox, with an interest in trying to understand *why* there were so many divergent and flawed interpretations. Probably a major factor is the fact that people get bogged down with the math and space-time diagrams that are so confusing that they make your head explode. I will go into more detail in a future blog post, but you will see that this is a situation in which you get more insight if you leave the equations and space-time diagrams behind and just think about the bigger picture.

Bear in mind that currently the paper is in draft form and I have given it

for criticism to some colleagues I trust in case I’ve done something stupid. So some of the results could vanish overnight. But at least you will have learned something along the way.

Now, until next time I will give you a couple of things to think about. The first is related to the twin paradox and concerns the so-called Lorentz contraction which refers to the fact that two observers traveling at a high relative speed will claim that the “other” observer is foreshortened in the direction of motion. Usually the paradox is described by a very bizzare choice of participants: a farmer, his son, a pole and a barn. I really dislike that scenario and I think it is unnecessarily complex. So I have my own version involving a train and a canyon.Suppose that a train has to pass over a narrow canyon for which the bridge is destroyed. Further suppose that the width of the canyon is a tenth of the width of the length of a single carriage. At slow speeds the train can easily pass over the canyon because the canyon is so narrow. Now if we increase the speed of the train to approach light speed, there is no limit to how small the Lorentz contraction can make the carriage (at light speed the shortening is infinite). Therefore we can increase the speed so much that the length of the carriage as it appears to someone on the ground is less than the width of the canyon. So to the onlooker the train falls down the canyon. However, the equations of relativity are completely symmetric so from the point of view of a passenger on the train, it is the *canyon* width that shrinks so the train passes over the canyon even more easily, and unharmed. So the problem is, the train cannot simultaneously fall down the canyon and not fall down the canyon, only one of those outcomes can be true. Which one is it, and what is the flawed reasoning?

Finally, consider a straw immersed in a glass of water. We are familiar with the fact that the immersed part of the straw appears to be bent. When we immerse our hand into the water we find that the bent straw does not exist, and all we feel is a straight straw. What’s more is that our fingers become bent in the process! It’s a simple optical illusion. No deep mystery. Yet the so-called paradoxes of relativity are precisely just that: optical illusions, except that they are optical illusions in the *time domain* (as opposed to the spatial domain). But physicists *never* describe the apparent paradoxes of relativity as optical illusions. Now imagine a physicist who had never seen an object immersed in a clear liquid. The physicist sees a straw in a delicious volume of lemonade as a bunch of equations. Would we not be surprised if the physicist then named this strange phenomenon as the “bent straw paradox?” Indeed.