Can one measure one's speed based on how much energy it takes to accelerate?
For instance, in Newtonian Physics, increasing speed by a certain amount (say, 1 m/s) took a certain amount of energy for a certain amount of mass. In relativity, it takes more energy the higher speed you are at.
One might be able to use a measurement of this increase in necessary energy to calculate a seeming "absolute speed". For example, x J per 1 m/s compared to x + y J for 1 m/s at a higher speed.
With this in mind, one could calculate one's speed by measuring the amount of energy needed to increase speed by a certain amount. Plugging this energy into an equation that creates a graph of speed vs necessary energy needed to increase speed should show what speed one has compared to light, but in the way of creating it absolutely, because it is being compared to a constant state of speed (and thus, rest) found in nature, c.