Look at the following example.

An object’s initial speed is 10k/h (ten kilometers per hour).  The formula for how far that object will go in its present environment could be: D(distance) = iS (initial speed) x T(time).  Therefore, if nothing changed after 1 hour the object should have gone D = iS x T = 10k/h x 1h = 10k.  But it is observed that the object only went 9k after one hour.  Consequently, if you want your equation for the distance which that object will travel in its present environment to reflect the reality you will have to adjust your equation.

The adjustment could be D = iS x T – 1k/h x T.  Distance = initial Speed x Time minus 1 kilometer per hour x Time).

Then you would get D (distance) = 10k/h x 1h -1k/h x 1h = 10k – 1k =9k, which answer now agrees with the observed result.

But what if it was observed that after half an hour the object went 5k, and that after one hour the object went 9k ?  Then the above modified equation would give you the wrong answer at the half hour point, so you have to come up with a different modified equation.

For example:  D = iS x T – (T > 0.5) x 1k/h.
At the half hour time T would not be greater than 0.5, hence there is no T > 0.5, which means that the 1k/h is being multiplied by nothing (ie. by 0), 0 x 1k/h = 0, hence the distance would simply be D = iS x T = 10k/h x 0.5h = 5k.  In other words at times less than a half an hour the modified equation simplifies down to the original equation of D = iS x T.

Then at the hour point, because T would be greater than 0.5, after one hour the equation would turn into: D = 10k/h x 1h – 1h x 1k/h = 10k – 1k = 9k, which is the correct answer for the one hour time period.

Accordingly the second modified version of the original equation worked for both the half hour result and for the hour result.  What does that mean ?  It means that if you know the result you are looking for you can write an equation to get that result.

However, the equation which gives you the correct result does not tell you why the thing happened.  A person can postulate theories which are consistent with the equation, but that does not mean the theories explaining the result are correct, it just means that they could be correct as they are in agreement with the equation.  One theory is that after half an hour the object’s mass increased, therefore it was moving slower after the half hour point as having become more massive it was now heavier and as no extra energy was added to keep the now heavier object moving at 10k/h it slowed down.  Or is the theory that after the half hour point the object was now passing through a denser medium and hence it was slowed down by the denser medium, like if a heavy boulder is rolling along the ground and then rolls into water, it will now roll slower in the water which is a denser medium than air.  Or is the theory that at the half hour point the object was at a location where there was now a force pulling it back toward that half hour location, but that the force pulling it back was not strong enough to cause it to reverse its course, that force was only strong enough to slow down the object.  Or whatever other theory a person can come up with.

The modified equation works equally well with any of the above theories, and could work equally well with many other theories.  The equations are not the physics.  For known paths of motion a person can write equations which model that motion.  However, just because equations model known motion does not mean that they can be used to interpret the meaning of motions of unknown entities or in unknown environments.  Space is an environment for which there is no evidence of uniformity and for which there is great evidence of variance.

What would the above equation predict for how far the object would go after ten hours ?

At the ten hour point, because T would be greater than 0.5, after 10 hours the equation would turn into: D = 10k/h x 10h – 10h x 1k/h, hence the equation would predict that after ten hours the object would go:100k – 10k = 90k, but if many years later it was observed that the object actually went 125K after 10 hours, then clearly the equation's prediction was wrong, which means that the physics on which the equation was based was wrong.

The point is that if a person writes an equation to produce correct results for known facts (eg. the orbit of Mercury) it does not mean that the equation is good for predicting unknown facts.  It also means that if the equation's predictions for unknown facts are found to be wrong when those unknown facts have been able to become known, it is strong evidence that the theory on which the equation was based was wrong.

Click here to return to the
Einstein Theory of Relativity Misconceptions and Errors paper.