A New Look towards the Princples of Motion - Section 2

[Arindam Banerjee]

A New Look towards the Princples of Motion

A book for keen and fresh young minds: ew physics leading to superior technology and better understanding of the universe's workings.

Section 2

The Creation and Destruction of Energy

The Effect of Masses Transitioning Across Contiguous Inertial Reference Frames


We repeat our earlier definition for the inertial reference frame: an inertial frame of reference is a specified point, line, area or volume such that all points that are fixed on that particular frame of reference do not move with respect to each other; and such an inertial frame of reference is not accelerating away from another such inertial frame of reference.

Let us now consider examples of contiguous inertial reference frames, from Nature. The ground is of course the obvious inertial reference frame. Contiguous inertial reference frames, with respect to the inertial reference frame of the ground, are: steady winds, steady sea or river currents, steady flow of lava from a volcano, the steady movement of a cart or train, the steady flight of a bird or airplane, and so on… There could be contiguous layers or such inertial reference frames, such as winds increasing in speed with altitude, river currents increasing in speed as we reach the centre of the stream, stronger flows of lava on top of each other, flocks of birds flying at different speeds, car streams in adjacent lanes moving with different speeds with respect to the adjacent lanes.

Earlier, in our consideration for the dynamics of the internal force moved object, we had considered the effect of moving a body of mass M across N travelators, situated side by side, and moving at speeds v, 2v, 3v,…. Nv with respect to the ground, which is let us say the 0v or rest inertial reference system. We had found that each inertial reference system had to spend an equal amount of energy upon the mass M, to accelerate it from its earlier position in the one-step-lower-velocity inertial reference frame. The net energies thus spent upon the mass by each inertial reference frame, when summed, come out lower than the kinetic energy of the mass with respect to the 0v inertial reference frame, and that difference is the “free energy” or energy created.

We will now consider the mathematics involved in a greater detail, and with a different angle, taking the natural inertial frames of reference (currents of wind or water or lava at different speeds along different contiguous layers) into consideration. Now we are not interested in propelling a ship with internal force; we are interested in showing how the Sun and the Earth create energy.

The Travelator Analogy – Again.

As before, let there be N heavy travelators (flat moving platforms, of the type commonly found in modern airports for faster passenger movements) running side by side, with speeds v, 2v, 3v and so on with respect to the Earth – but are actually connected to the Earth. They are from our assumption effectively like long spaceships, N in number, and flying side by side, parallel, with speeds, v, 2v, 3v, ,,, Nv.

Let a person of mass M jump from rest (the 0v inertial reference frame) to the travelator running a speed v (the 1v inertial reference frame). The travelator will accelerate him to the speed v in time t. When it will reach that speed v, the kinetic energy of the body with respect to the earlier inertial frame of reference (the rest frame, or 0*v frame) is 0.5*m*v*v.

Then after he has attained balance, he jumps to the next travelator running at 2*v. Does the travelator running at 2*v spend exactly E = 0.5*m*v*v amount of energy, with respect to the earlier 1*v frame, in raising the speed of the body from v to 2v, or does it spend rather more as it now has to push the mass over a longer distance to make it reach the 2v speed? We have earlier seen that the former is the case, when the inertial frames of references are free.

Thus when the travelators are not fixed to the earth, that is to say, the earth (nor the air nor water, as for airplanes and ships) can not provide a reaction, then: When the person steps on the first travelator from the inertial rest frame, he gains the acceleration from the force exerted upon him by the travelator. As the travelator is not fixed to the earth, this means that its (the travelator’s) own velocity reduces very slightly – depending upon its mass with respect to the person who boards it. This drop in speed (v_small) can be found from the law of conservation of momentum. Here MT denotes the mass of the travelator.

So, MT*v + M*0 = (MT + M)*(v – v_small)
or MT*v = MT*v – MT*v_small + M*v – M*v_small
or v_small = M*v/(MT + M)

This happens with the velocities taken with respect to the rest or 0*v inertial frame of reference.

Instead of going back to the 0v reference, the person jumps to the 2v reference. This time, we do not assume that internal force has increased the velocity of the 1v reference from v-v_small to v. It remains at v-v_small. Then, taking the fall in velocity of the 2v reference as v_small_2, by applying the law of conservation of momentum we have:

MT*2*v + M*(v – v_small) = (MT + M)*(2*v – v_small_2), or
MT*2*v + M*v – M*v_small = MT*2*v + M*2*v – v_small_2*(MT + M), or
v_small_2*(MT + M) = M*(v + v_small) = M*v + M*M*v/(MT + M), or
v_small_2 = v*(M + M^2/(MT + M))/(MT + M), or
v_small_2 = v*(M/(MT + M) + M^2/(MT + M)^2).

If MT >> M, which should be the case for natural phenomenon, then the second term in the RHS becomes very small indeed. Thus v_small_2 is almost equal to v_small, when MT >> M.

When the man moves laterally from the 2v reference to the 3v reference, similarly we have:

MT*3v + M*(2*v – v_small_2) = (MT + M)*(3*v – v_small_3), or
MT*3v + M*2*v – M*v_small_2 = MT*3*v + M*3*v – v_small_3*(MT + M), or
v_small_3*(MT + M) = M*(v + v_small_2) = M*v + M* v*(M/(MT + M) + M^2/(MT + M)^2),
or
v_small_3 = M*v + M* v*(M/(MT + M) + M^2/(MT + M)^2)/(MT + M), or
v_small_3 = v*(M/(MT + M) + M^2/(MT + M)^2 + M^3/(MT + M)^3).

Again we find that if MT >> M, then v_small_3 is nearly equal to v_small_3 which again is nearly equal to v_small. However, when MT is not that much bigger than M, then these higher order terms start becoming more significant. Meaning, that the faster layers become increasingly slower relative to the slower layers.

More energy is now getting created in the system than existed before, as shown earlier in the last section. The loss in kinetic energy of the N travelators, is compensated by the increase in kinetic energy of the mass M.

This difference, call it extra or free energy, or energy created EC, is (0.5*M*N*N*v*v - 0.5*k*N*M*v*v), or 0.5*M*N*v*v(N – k). Thus

Energy created (EC) = 0.5*M*N*(N – k)*v^2.

The Natural Expression of Free Energy, or Heat

We have seen that the extra energy that is now in the system exists in the kinetic energy of the mass now in the fastest travelator. How may this extra energy be destroyed?

Let the man fall off the Nv travelator to the 0v (the inertial reference frame at rest, from where he started). He will roll on the 0v frame of reference for a very long distance, and work corresponding to his large kinetic energy (0.5*M*(N*v)^2) will have to be done on him to bring him to rest. Thus if the surface has friction, the distance would be (0.5*M*(N*v)^2) /F, where F is the constant frictional force. Since the inertial reference frame is earth, the frictional force F would be equal to M*g*k, where g is the acceleration due to the Earth’s gravity, and k is the coefficient of friction for the surface. If no effort is made to harness the extra or free energy that he had into some other kind of energy, all this extra energy will be ultimately converted into heat energy, since frictional forces always create heat. In other words, the system will now become more hot, or have a higher temperature. With time, there will be cooling, and so the energy will be destroyed as it was created.

So heat energy, is the ultimate natural expression of free energy. That free energy that was created, is spent as heat.

However, it is not necessary that the free energy has to be destroyed as only heat. It can be lost the way it was created, and we shall see how in the next few paragraphs.

The Heat-less Destruction of Free Energy

Let the man of mass M move the other way – from the high speed travelator at speed N*v to the lower speed travelator, at speed (N-1)*v. We will find the speed of the (N-1)*v travelator has increased by v_small, by applying the law of conservation of momentum.

M*N*v + MT*(N-1)*v = (M + MT)*((N-1)*v + v_small), or
v_small = v*M/(M + MT).

The loss in kinetic energy now is, with reference to the 0v inertial frame of reference, 0.5*M*(N*v)^2 – 0.5*M*((N-1)*v)^2 or 0.5*M*v^2*(2*N – 1) for the mass M. Whereas, the (N-1)v reference frame has gained energy (with respect to its own frame of reference) of value 0.5*M*v^2. Thus the net loss of free energy with the transition of the mass from the Nv inertial frame of reference to the (N-1)v inertial frame of reference is

(0.5*M*v^2*(2*N – 1)) – (0.5*M*v^2) or M*V^2*(N – 1).

This loss of energy takes place without generation of heat. Thus when mass M transitions from the Nv frame of reference to the (N-1) frame of reference, the mass associated with the (N-1)v inertial frame of reference gets an addition of energy, raising it to the (N-1)(v + v_small) inertial frame of reference. All the free energy generated vanishes when the mass returns to the 0v frame of reference – however all the frames of reference have been incremented in velocity, of the order of v_small. If the mass M once again makes all the N transitions from the 0v (rest inertial frame of reference) to the Nv inertial frame of reference, all the v_small components would vanish. This effect is similar to the interchange between the potential and kinetic energies, seen earlier, that led to the development of the law of conservation of energy. Here, too, we see that there is conservation of energy, so long as there is no collision involved at some high-speed frame of reference, that will lead to the generation of heat.

The Burning of Fossil Fuel

Fossil fuel represents the storage of solar energy, over time. When energy that has been absorbed and stored over millions of years is released as heat, it is inevitable that local temperatures will increase steadily, beyond the normal patterns. If it could be radiated away to outer space, effectively, then no great harm need happen. However, when this process is affected by the presence of gases that cause the reflection of radiation back into the Earth (popularly known as the “Greenhouse Effect”), then there is no stopping the increase of temperature, also known as “Global Warming”. The impact of this phenomenon is already being felt, all over the world. To reduce the carbon and other greenhouse emissions through the burning of fossil fuel, and to cultivate more greenery to absorb the Carbon Dioxide produced, is now increasingly being felt as an international imperative. A great deal of political will is required to make this happen. A roadmap to a cleaner, greener world is required. Appendix B deals with the “Hydrogen Transmission Network” which has been described as a breakthrough in this area. It will make the Hydrogen Economy viable, and the Hydrogen Economy will provide clean water and energy for all time to come.

Conclusion of Section 2

It should be obvious by now that the law of conservation of energy is at best a very special case, and that the thermodynamic concept of entropy was invented because it was not known even as a matter or theory that energy is continually getting created, and destroyed. We will touch upon this important subject once again, when we will discuss the nature of the explosion.

[pnal...@gmail.com]

On Wednesday, May 29, 2019 at 7:37:53 PM UTC-7, Arindam Banerjee wrote:

> It should be obvious by now that ...

... Banjo-Boy is still bat-shit crazy...