Diminishing Marginal Returns to Assumed Limit

The speed of light is an assumed limit chosen by Einstein to demonstrate the principles of relativity as a curve of diminishing marginal returns rather than a de facto barrier to powered object velocity.

Interstellar travel is by nature reserved best for the speculation of an economist not a physicist, since the definition of economics is the science of the allocation of limited resources. This is not the basic assumption of physics. Indeed Einstein's theory of relativity from an economist’s point of view is the equivalent to the law of diminishing returns. Commonly understood as the speed of light is approached, the marginal return of applying more energy produces a smaller gain in speed. Economists apply the law of diminishing returns to many situations and one is to suspect that most sciences have developed a form of this theory. In economics a curve is produced that shows at the top end of the graph, the marginal return becoming infinitesimally small but never reaching zero. Likewise Einstein's application allows the approach to light speed to be infinitesimally close, but of course at this stage such huge application of energy is being applied that it would not be practical to approach such a speed.

Yet Einstein was certainly not concerned with the question of interstellar travel. He is not to be assumed to be concerned with the economist's central issue of limited resources and how to expand the limited (e.g. exploitation of another planet outside the solar system). Even more importantly he developed the theory when payload performance maturity was very young and the threat of mutually assured destruction was small. Hence there was no clear carrot (the ease and efficiency of rocket launches into orbit did not suggest humans to be nearing an interstellar capability) and there was little stick (there was less danger of nuclear conflict destroying earth). With this in mind, as a theoretical physicist he must have had no choice but to set the speed of light as the top limit. A graph has to be drawn to show a curve as with the economist's law of diminishing returns, so where else could he possibly put the point to which marginal return becomes practically zero.

There is no known speed after light so unless he was an economist subject to the scientific objective of expanding the definition of limited resources he would not plot the graph to reach zero at 100 times the speed of light. An economist would have of course a clear objective in stretching the curve of diminishing returns along an axis that established a desired speed limit for trade functions and economic growth. How could Einstein possibly base an assumption of such a projection beyond the speed of light? It would be unlikely that such a great physicist would want to establish something that wasn't true, but the purpose of Einstein's theory of relativity is to create the economist's equivalent of a curve of diminishing returns.

Diminishing Marginal Returns to Assumed Limit continue

Hence it is possible to conclude that the point chosen is quite arbitrary, chosen because with no other evidence to the contrary it would be wrong to speculate at another limit. There was no choice, no economist's prerogative to set a speed limit that would encourage human expectation of journeys outside the solar system. Any speculation beyond light speed would have been arbitrarily made and been against the good judgement that light speed itself is a significant milestone. However any assumption that the theory of relativity was built to establish light speed as a top speed de facto (without challenge) is to misunderstand the theory. In economics the theory of the law of diminishing returns is very important to nearly all development models. Likewise in Quantum physics the principle underlying the quantum theory depends on this diminishing returns principle. This is more fundamental than the speed of light being a limit. The point to where the curve has to diminish has to be set somewhere, without additional examples from natural science the speed of light was the only option. However if Einstein could have been allowed to choose an arbitrary top speed (say 100 times the speed of light) the curve so vital to quantum physics would have merely diminished to this point. The essential elements of quantum physics and relativity that the marginal return decreases in a curve to a point infinitesimally close to zero would have still applied. All the theory dependent on understanding the nature and effects on the principle of diminishing returns would have still applied. Of course Einstein could not do this, as without any natural indication of such a speed and without for example an economist's prerogative to suggest convenient travel times between resource and market, there is no reason to make such speculation.

The speed of light had to be chosen, not because Einstein saw the limit as important but so as to make the curve that illustrates the principle of diminishing returns clear to his fellow physicists. Thus law of diminishing returns applies in shape of the theory of relativity to physics, regardless of which top speed draws marginal return infinitesimally close to zero. Yet some commonly agreed top speed must be chosen for the curve to be drawn! What a mistake to think it this almost arbitrary selection (the choice of light speed being the best in face of no other evidence or intentions) to be unquestionable! The effect upon Newton's F=MA can allow M (Mass) to increase so as to decrease A (Acceleration) with equal validity across any chosen curve to and beyond light speed. It is not easy therefore to propose any adjustment to the theory without any good reason. However it must be understood that the top speed was a natural choice to demonstrate an important theory, not an unusual theory to demonstrate a vital limit.