I believe that Newton made some very basic errors early on when founding his physics and that these errors have never properly been recognised by modern physicists and therefore corrected.

The first fundamental error in my opinion concerns the equation pertaining to Work Done:

Work Done = Force x Distance.

The equation appears so straight forward that at first sight it would hardly seem possible it were wrong.

But consider the following. A man pushes a given weight with a set, unchanging force of ‘F’ through a distance of ‘D’ therefore carrying out work in the process. Next the same man pushes a weight which is twice as heavy as the first with the exact same unchanging force of ‘F’ through the exact same distance of ‘D’.

Since he has pushed both weights with the same force of ‘F’ through the same distance of ‘D’ then Newton would tell us that in both instances he has performed the same amount of work because Work Done = Force x Distance. But how could he? In the second instance he pushed a weight which was twice as heavy as the first through the same distance and pushing with the same force of ‘F’ it would have taken him longer so surely he would have carried out more work in the process?

If the equation concerning Work Done is in error as we have just indicated then an equation that is ultimately derived from it, that for Kinetic Energy, would also therefore be wrong.

The equation in question is of course is K. E. = ½ mv².

Again this equation would seem fairly straight forward. If the mass is constant then the Kinetic Energy is proportional to the velocity squared.

But consider that if the Law of Conservation of Energy is to apply the energy supplied to an accelerating body causing it to accelerate must always equal the Kinetic Energy obtained. If it didn’t then conservation would be defied.

I would like you to picture a rocket accelerating in the frictionless environment of space. As the rocket engine burns fuel at a constant rate a constant acceleration is produced. The same amount of fuel therefore would be burnt accelerating from 0 to velocity ‘v’ as it would having accelerated from ‘v’ to ‘2v’. In both cases the increase in velocity is ‘v’.

However if you look at the Kinetic Energy obtained by the rocket having reached a velocity of ‘v’, it is obvious that its Kinetic Energy would be proportional to ‘v²’. However having obtained a velocity of ‘2v’ the rocket’s Kinetic Energy would now be proportional to ‘4v²’.

In other words after its velocity has doubled, the Kinetic Energy of the rocket would have quadrupled. This is simply because the Kinetic Energy is proportional to ‘v²’.

But surely the rocket would have burnt the same amount of fuel accelerating from 0 to ‘v’ as it did accelerating from ‘v’ to ‘2v’? So where has the extra energy come from if its Kinetic Energy is now four times as great even though the velocity has only doubled?

Something must surely be wrong? The energy supplied by the rocket engine should always equal the Kinetic Energy obtained by the rocket but in this example it clearly doesn’t.

This equation for Kinetic Energy, K. E. = ½ mv², is still used today in Quantum Physics and Relativity.