The most trivial unsolved formula in physics

Our first excursion, without a general solution, will be into the most trivial formula in physics. It is the formula of speed equal to distance divided by time. As long as we remain very provincial in a certain sense, so to speak, we may be able to calculate speeds for a specific earthly location, with earth time and earthly calibrated distances, and then we are home and dry. But that is not the end of the story.

Our real quest will be to solve the formula for any location in the universe using universal time and universal distances. For that we will need to move totally away from the Aristotelian idea that the earth is the centre of the universe. In fact, our home base will be anything from one to a trillion light years away, still a small fraction of the age of the finite universe, because in our case locality does not matter at all as we want a general solution of the formula applicable anywhere in the universe, if such a solution can be found at all. Even the word locality we will have to redefine in terms of many more dimensions of energy, distance and time.

It may sound antiquated, but we are still cloistered to the Aristotelian idea of thinking of the centre of earth as the centre of the universe in the sense that we have named earth time officially as UTC, being Coordinated Universal Time. There is absolutely nothing universal about that, firstly because it is only applicable to planet earth on or near the surface, and secondly because it is based on earth’s position relative to other moving celestial bodies which we regard as stationary. That is about as fuzzy as time can get.

We also have this notion that time is a continuous function in terms of the above definition and it works out quite well for our earthly purposes, but if we wish to venture into the universe, that defintion is not applicable at all anymore. The chances are better that time is a discrete quantum function like quantum fields and probably connected to it, than being a continuous function. In this regard I do not refer to time dilation in terms of the Relativity Theory, although it may also enter into that fray.

 

On earth we already run into difficulties with our definiton of time, as there is a difference between solar time and sidereal time. If we look at solar time, we see that it differs from the continous sidereal time function defined for UTC. The reason for this is that the earth moves about one degree per day in its orbit around the sun, and this reflects in the measurement of solar time. So we call it a mean time, like Greenwich Mean Time, in the meantime.

And as for distance, it is even more fuzzy, because we mostly observe relative motions and speeds, not only in terms of the Relativity Theory, but in terms of relative motion in the same inertial frame.

Well, that is enough already to make us reach for our daily tonic in a vastly unfathomable, yet simple, universe.

Next time we will start by considering speed and time in a very local domain within easy sight distance in one inertail frame.