The Law of Conservation of Energy says that energy cannot be created or destroyed - it can change its form (from say electrical to mechanical). After Einstein, it has been modified. We now have a joint Law of Conservation of Mass and Energy, following Einstein's famous equation, e=mc2. For non-nuclear cases, the Law of Conservation of Energy holds.
Mathematically, the fact that Newton's First Law of Motion is too specific means that the equally hallowed Law of Conservation of Energy is wrong.
Which is very good news, because that means we can create energy from nothing. There is an inexhaustible source of energy we can tap just like that, if we only know how.
Let us see how.
I had earlier put the mathematical bits right here, but Durba, after reading the draft, disapproved. "I did not understand them. They put me off. You do not want that kind of effect upon your reader. Put all the difficult stuff elsewhere." I took her advice. If you want to get into the mathematical expressions and physics concepts, please go to the Appendix A. They are really not difficult, if you have some high school knowledge of mathematics and physics.
What is most important in the mathematical derivation shown in Appendix A, in the physical sense, is the concept of incremental velocity addition. It leads to an overall very high velocity meaning high kinetic energy for the body, with much lower input energy given incrementally from outside. Since as a result you have a body having more energy than you put in it, you have violated the law of conservation of energy. Some examples are:
1) Take a simple toy car, and give it a tap. It will start to move. While moving, give it another tap. It will move faster. With continuous light taps of same power, it can reach a fairly high speed, limited by whether you can catch up with it for the tapping process.
2) Go to the streets of India, and see a small boy running beside a vertically moving wheel (often the rim of a bicycle wheel), and accelerating it from rest by small taps with a stick. If you consider just the energy involved in the continous taps (and not the boys running) to the wheel, you should find that the final energy of the wheel is more than that of the sum of the energy involved in every tap.
3) This is rather like Example 2 given above, that of the small boy accelerating a bicycle wheel. Go to a carousel in a fun park. You give a sharp jerk on one of the objects that go round and round. You start the whole carousel moving, that way, if it is not too heavy. Running on the sidewalk beside the carousel, you keep on pushing, in small jerks, till the carousel moves at fair speed. Stopping the carousel, by just standing on one spot, will not be so easy!
This experiment shows the principle of how we can get unlimited power. Internal force will move a body such as a carousel, external force will stop it. We have seen mathematically (Appendix A) that getting a body to move at high speed using internal force needs much less energy than getting it to stop using external force.
4) A practical example, now. To show velocity addition, I put the lunch box system on our coffee table. Using some books as support for one end, I inclined the table till the lunch box was just able to slide. This way, I used gravity to mitigate the frictional effects. Then I used the remote control to move the lunch box. After one hit, the box would not just stop it would continue to move. As it moved, I caused another hit. It moved faster. If I had a very long and very smooth coffee table, the kind richer people do have, I could have gone in for more hits. It would have been better if I had a laboratory with assistants and a fat budget, of the kind say fusion researchers had.
But I am a poor man. The kind who works hard on a hot day and then expresses his desire thus:
Beaded bubbles winking away - nice but too expensive.
Today I feel not like John Keats, even though Im pensive.
Beer, girl, beer I want, with all the strength, the froth.
Cold liquid gold down the hatch, for this thirsting moth.
Beer in pot or can or bottle, bring it any way.
Beer is what I want, on this hot, horrid, day.
Maybe the physics behind beaded bubbles, the motion of fish, the sub-atom and the universe, may be better understood one day with newer fundamental conceptions. Enormous kinetic energy must be involved in solar flares and the solar wind to escape the tremendous gravity of the sun. It is now known that extremely strong magnetic fields exist in the sun. As we shall see later, strong magnetic fields will drive interstellar spaceships. The effects that will impart the enormous kinetic energy needed for the interstellar spaceship drive, may be taking place naturally in the sun.
Perhaps we should reconsider what Leonardo da Vinci had to say about the basic nature of force in his notebooks: