Teaching relativity to a skeptic

[harrylin]

[..] If there is one human activity that really doesn't care much about qualitative aspects of scientific theory surely it must be engineering (technology). For example I am planning to build an electrical device which uses electrons traveling at relativistic speeds. I will certainly require Einstein's special theory in order to predict the mechanics and behavior of those electrons. I don't need to be able to answer why the equations give accurate predictions. I just have to know that they do and then use them as they were intended. Plug and chug.

And that is exactly how that theory was intended.
Its postulates were inferred from observation and are about phenomena; they do not require a physical model of hidden reality (which he called "superfluous"). Thus the theory lacks that kind of "why" on purpose. See: http://www.fourmilab.ch/etexts/einstein/specrel/www/

These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

 

[The_Duck]

The leap from the math to a model of the world where massive objects create 'depressions' in a 4th (temporal) dimension needs its own proof.

Ultimately a physical theory is an assertion that if you go out into the real world and measure certain numbers, then some specific mathematical relationships between those numbers will hold. Imagery like "curved spacetime" is just words to help us intuit the behavior of the equations and can't be proved. In fact Steven Weinberg in his GR textbook deemphasizes the idea that general relativity is about "curved spacetime," writing

...the geometric interpretation of the theory of gravitation [i.e., that gravity is really the curvature of spacetime] has dwindled to a mere analogy, which lingers in our language in terms like "metric," "affine connection," and "curvature," but is not otherwise very useful. The important thing is to be able to make predictions about images on the astronomers' photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effect of gravitational fields on the motion of planets and photons or to a curvature of space and time. [Weinberg adds the caveat:] (The reader should be warned that these views are heterodox and would meet with objections from many general relativists).

In this particular case that experimental proof may very well exist. In fact I'm assuming that it does and I'm trying to find it. Even if there is no direct proof, it may be possible to prove starting from the equations. The first thing I would do is examine the equations and try to prove that they are unique. That the same relationships between variables cannot be represented in any other form except through Minkowski's math. Once you've proven that then you just have to show spacetime is the only option. That without it the equations, with their great predictive value, just wouldn't work.

This seems off base. Mathematical relationships can often be expressed in many different forms, some amazingly different in appearance. The important thing, again, is the predictions that come out of the math, which must be the same if the different forms of the math are really equivalent.

To give an example that has gotten a lot of interest recently, the "AdS/CFT correspondence" is the statement that two very different specific mathematical theories actually (and very surprisingly) describe the same physics. But these two theories seem very different--for example, they posit different numbers of spacetime dimensions! So one theory might say that spacetime has 4 dimensions while the other says that spacetime has 5 dimensions. Since both predict the exact same results, it becomes clear that the mathematics of a physical theory doesn't tell you how you should picture the universe described by the theory. You can think of it as a 4-dimensional spacetime with one set of physical laws. You can think of it as a 5-dimensional spacetime with a different set of physical laws, and this turns out to be completely equivalent to the other description. You can think of it as a simulation proceeding in a cellular automaton computed by a sentient frog (though this is probably a less useful picture), so long as you posit that the simulation is programmed in a way that corresponds to the predictions of the theory.

 

[Dale]

This is very popular position but I am not sure I fully agree with that. Traditionally the core of the theory is explanation and then you use predictions (preferably quantitative) to test how good is that explanation.

Say we can have some empirical data and do some curve fitting using that data. Now we can make predictions using untested parts of that curve (we interpolate or extrapolate empirical data). This is not a theory as it lacks explanatory part, right?

For me explanation is the theory. If we have equations with very direct connection to physical observations I would probably call it something like "empirical theory".

The problem with this is that your idea of a scientific theory cannot be tested with the scientific method. The only part which can be investigated by the scientific method is what you call an "empirical theory".