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I used to think that I like physics, almost as much as mathematics. But as time has gone on, this idea has changed, and I no longer see physics in such a positive light. What changed?
In the past, I saw (theoretical) physics as being a wonderfully powerful tool to explain the real world. Progress in physics seemed to give better understandings of our universe and better understandings of reality. Since then, I’ve become disillusioned with the way (theoretical) physics is done.
The physical theories that are currently in existence are incapable of modeling all physical phenomena, and some theories are even inconsistent (electromagnetism and point charges, for example). This is disappointing, but it shows that there is work that needs to be done. The ultimate goal of theoretical physics is to obtain a “theory of everything” that models the entire universe perfectly. Such a goal must remove inconsistencies and must not leave any holes. Though many people are working toward this ideal, it is not clear that it can ever be obtained. Indeed, progress in physics over the past few centuries has made improvements that supposedly come closer to approximating such a perfect theory. However, even as progress has been made, the ultimate goal still remains as distant as ever.
In fact, even if physics did reach a theory of everything, it is not possible for physicists to show that this is actually the case. As an example, consider the state of physics in the late nineteenth century. At the time, physicists thought that they were about to find a perfect model of the universe, one in which nothing is left unexplained. Then Einstein’s theory of relativity came along and shattered this view of the world. What if relativity had not been discovered? Would we now be learning that physics is no longer in need of research? Even if the ultimate goal could be achieved, there would be no way of ever showing that it has been achieved. Physics can never yield absolute certainty.
What is much worse is a consideration from pure mathematical logic. Gödel’s Incompleteness Thoerem states that any reasonable logical system must be either inconsistent or incomplete. Assuming that the goal of physicists is to find a logical system to model the behavior of our universe, we see that no such “theory of everything” can be both consistent and complete: The ultimate goal of theoretical physics is actually unobtainable. This goal is simply an ideal that we can move toward but never reach.
After these considerations, I find theoretical physics to be unsatisfying. The inconclusive nature of physical theories is deeply disturbing, and suggests that instead of being some sort of powerful tool, the study of theoretical physics is just an endless modeling problem. I’m happier with applied physics, where people are not even attempting to move toward any such ideal. In the end, though, I think I’ll stick with mathematics: a world that deals in certainties and has no relationship with reality.