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Appendix A: Velocity Addition and Unlimited Energy
Consider a body with an Internal Force Engine in outer space. We shall discuss the engineering aspects of such engines in later chapters. For now let us say that with a hit (an internal collision creating a quantum change in velocity, see Appendix B for more details), the speed of the body increases by v. The energy required doing that is E, and the total mass of the body is m. The kinetic energy gained by the body as a result of the first hit is 0.5*m*v2, following the well-known formula. Let us expect E to be rather greater than 0.5*m*v2 , as internal losses are involved. So let:
E = k * 0.5*m*v2
In outer space, there are no forces to retard the motion of the body. We assume that after another hit of same intensity, the velocity of the body increases by v with respect to its moving reference, and 2v with respect to its rest state.
This is a most major assumption, this one about velocity addition. It is justified by our current understanding of physics. After attaining the velocity v from the first hit, the body is at rest with respect to the inertial reference frame moving at velocity v with respect to the earlier (zero velocity) reference. A second hit will increase this velocity by v with respect to that inertial reference frame moving at velocity v, or 2v with respect to the rest state.
After N hits, the velocity will be N*v. The kinetic energy of the body will be
0.5*m*(N*v)2,
while the total input energy required to bring it to that state will be
0.5*N*k*m*v2, as a result of N continuous hits.
The difference in input and output energy will be
0.5*N*m*v2*(k - N).
Now N can be unlimited, as we may have as many hits as required or mechanically possible. Whereas k is finite. So there is a negative energy output, which means that more energy is being created in this setup than lost. Which means the energy is being created by this particular engineering method, out of nothing. So, the law of conservation of energy is not correct, where bodies driven by internally generated forces are concerned.
This is a small paper that deals with the collision of two perfectly elastic bodies. Elastic in the physical sense, meaning that no energy losses are involved in the actual impact. This is an assumption. In practice, one expects to minimise the actual energy losses of heat and sound.
Examples of such collision may be found in such board games as billiards or carrom. In carrom, we have a striker, which is a thin cylindrical object, sliding on a smooth surface, hitting a coin of similar nature but lighter, usually with the idea of pocketing the coin.
The after velocities of the two colliding bodies may be found if their masses and initial velocities are known, applying the law of conservation of linear momentum and the law of conservation of energy. If:
- m1, m2 are the masses of the colliding bodies (let us consider m1 heavier and hitting the stationary m2)
- v1, v2 are the initial velocities of masses m1 and m2 respectively
- v3, v4 are the final velocities of masses m1 and m2 respectively.
Then, m1*v1 + m2* v2 = m1* v3 + m2* v4.
And, m1*v1* v1 + m2* v2* v2 = m1* v3* v3 + m2* v4* v4.
Let
- c1=
- c2=0.5*( m1* v1* v1 + m2* v2* v2)
- c3=c2 0.5*(c1*c1/ m2)
- c4=0.5* m1*(1 + m1/ m2)
- c5=c1*m1/ m2
- c6=-1*c5/c4
- c7=-1*c3/c4
Then
v3=0.5*(-1*c6+sqrt(c6*c6 4*c7))
v4=(c1 m1*v3)/m2
A small worksheet program could give the results of the final velocities of the colliding masses. Knowing m1, m2, v1, v2 we can work out c1, c2,… c7 and then v3 and v4. By playing around with the values of m1, m2, v1, v2 we can design Internal Force Moved Bodies.
Note: The following article was posted in Usenet, in such scientific newgroups as sci.physics.electromag and sci.physics.energy. These newsgroups are read by graduate students, researchers and professional engineers. (Usenet is a world-wide electronic bulletin board covering many thousands of topics anyone from anywhere can post there.) It was a greatly daring thing to do, for Usenet is the ultimate coffee-shop, or public house of ideas. Most traditional researchers avoid putting their original ideas in Usenet, as anyone can tear them into pieces, figuratively speaking. It is safer and conventional to publish in acclaimed journals, or build a web site over which they can have control.
It was with trepidation that I ventured to see the result of my action. I was elated to find no response at all to the article in the newsgroup that really mattered, sci.physics.energy. In the other newsgroup, there were three responses, to which I replied as shown below. To my responses, there was no further reaction.
I also submitted the article to some scientific journals and magazines. I am still waiting for any reply pointing out any flaw in my approach. So it seems that if I am in error, it is of a new nature, and so, in that sense, remarkable. But if I am right, I have truly set the human race to the stars!
Since I published my paper in end January 2000, I have been on the lookout for responses in Usenet. I publish many writings there, on a variety of subjects, and do indulge in vigorous debate. People who disagree with me know about the following article and at times strike a sarcastic note regarding it, but I am glad to say that upon challenge they are unable to provide any evidence to discredit my theory about unlimited energy. In this give-and-take, some impartial personalities noted that Heinlein apparently did write somewhere that a rocket ship accelerating at 1g for a year would exceed the speed of light, disproving Einstein thereby, as I have said in my book. I must admit that the idea of walkways moving at different speeds came to me from one of Dr Isaac Asimov's science fiction novels, as also from my daily trips on the subway.
Mathematical Derivation and Machines for Unlimited Energy
Arindam Banerjee
31 January 2000, Melbourne
*****
Mathematical derivation for unlimited energy, or showing that the law of conservation of energy is invalid for mass transfers across relativistic systems.
*****
Energy is force multiplied by the distance over which the force is applied. Thus if force F=Ma is applied over time T, at the end of which the body Mgets velocity V after travelling distance S, then the energy content of thebody increases by MaS which by Newtonian mechanics is Ma0.5aTT, or0.5MaTaT, or 0.5MVV. This is assuming that the body initially was at restwith respect to some inertial reference frame.
Now consider a system of initial reference frames, at velocities 0, v, 2v, 3v, etc. (This can be visualised as moving walkways, such as exist in airports.) These reference frames are located such that mass M can be moved from the initial reference frame at velocity 0 to one at velocity v, from that at v to another at 2v, from that at 2v to another at 3v, etc.
Let the body of mass M be moved from the initial reference frame of velocity 0 to the reference frame of velocity v. (This is equivalent to a person stepping on an escalator.) As soon as M touches the higher velocity reference frame, it has a velocity -v with respect to a point on the higher velocity frame. After a time t, mass M will attain the speed of 0 with respect to the new reference frame, and v with respect to the earlier reference frame. This will be due to the frictional or other forces involved, acting over the time t. Let this frictional force have the acceleration value a. The energy gained by the mass M, following the above derivation, is 0.5Mvv, obtained by travelling the distance 0.5att. That is, the work done by the system to give it this extra energy is 0.5Mvv.
Once the mass M has reached the velocity v, let it be moved to the next reference frame of velocity 2v. As soon as it touches this reference frame, it will have a speed of -v with respect to a point on the higher velocity frame, exactly as earlier. Following the earlier derivation, work of 0.5Mvv will be required to bring body M to same speed as any point on this reference frame with velocity 2v. But the kinetic energy of the body M, travelling at velocity 2v with respect to the initial zero velocity reference, is 0.5M(2v)(2v).
Proceeding similarly, we shall find that to bring the body M to speed 3v in the next reference frame will require work done of 0.5Mvv, but the kinetic energy of the body will be 0.5M(3v)(3v).
Let there be N reference systems, and let the final velocity be V=Nv. Then the final kinetic energy of the mass M is 0.5MVV or 0.5MNNvv.
But the work done by this system to raise the the kinetic energy to that level is only N*0.5Mvv.
So the extra energy obtained from this setup is 0.5MNvv(N-1). (If N=1, it is zero, as we find, normally.)
This shows that the law of conservation of energy is invalid for this system involving mass transfers across reference frames with ascending relative velocities. It also indicates how energy can be obtained from nothing. It challenges all established engineering concepts, and gives the theoretical basis for perpetual motion engines that will not need any fuel nor create environmental degradation.
Perpetual Motion Engines
The above derivation implicitly indicates the technology for perpetual motion engines, that is, say, a generator that will produce electricity without need for any kind of fuel, or external source of motion.
We have a system of moving "walkways" of velocities v, 2v, 3v,...Nv. A body of mass M is dropped from zero velocity to the walkway of velocity v. As soon as it reaches velocity v (by frictional forces involving drag or work done by the motor powering this reference frame) it is shifted to the higher speed walkway of velocity 2v, and so on, till it reaches the velocity Nv. From the earlier derivation, it has more kinetic energy than the work required to make it acquire same.
(One may think of walking across such a system of walkways - what a terrific amount of kinetic energy we can have by simply keeping on stepping from one to another!) The kinetic energy should be converted into electrical energy. Conversion of kinetic to electrical energy is what electrical power generation is all about. Some kind of turbine may be devised so that blades are turned by the high speed mass, such turning blades then producing electricity using a generator. We could think of a stream of sand-like high speed particles used for such energy generation. If extra energy is produced, after taking care of the energy required to run the reference systems, then we indeed have a generator not needing fuel.
Or we could think of a reverse rail gun. In a rail gun a projectile is accelerated by a heavy current passing down rails and through the projectile in the presence of a strong magnetic field. In the reverse rail gun, the high speed mass is popped into such a rail gun. By breaking the magnetic lines of force at high speeds, with proper electrical contacts it generates very heavy current, and also decelerates. This I speculate should be a highly efficient way of generating electricity.
*****
(Responses from the Usenet newsgroups readers follow.)
From: "Arindam Banerjee" <a.banerjee@trl.oz.au>
Newsgroups: sci.physics.electromag
References: <mLfl4.3231$VJ1.6023@newsfeeds.bigpond.com> <3895D26D.30C017FA@cern.ch>
Subject: Re: Mathematical derivation and machines for unlimited energy
Date: Mon, 7 Feb 2000 08:31:48 +1100
Lines: 56
X-Newsreader: Microsoft Outlook Express 4.72.3110.5
X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3
(Name of author deleted) wrote in message <3895D26D.30C017FA@cern.ch>...
>Arindam Banerjee wrote:
>>
>> Mathematical Derivation and Machines for Unlimited Energy
>
>You're claiming that accelerating something from speed 0 to v requires the same energy as
>accelerating it from v to 2 v. That's simply wrong!
Yes, you are right, for a single reference frame. I acknowledged that straight off in my paper.
But (and here is the great conceptual leap which will give us unlimited energy) for multiple reference frames moving at v, 2v, 3v, 4v, etc, mass transfer from one to next, 3v to 4v say, takes the same energy as for 2v to 3v, or 10v to 11v. This is because exactly as you say, we are accelerating the body of mass m from 0 to v, in all cases.
Imagine a series of conveyer belts, moving at v, 2v, 3v, etc. You step across them, till you reach the velocity Nv. (I gave this example in my paper.) You have a very high kinetic energy, but the energy required to make you acquire that is much lower. The difference, minus all losses, should give us sweet energy without external sources such as fuel, water, sun etc.
Of course, only experiment can prove me right or wrong. I wish I had the means to follow up on my idea. I would welcome anyone to try.
Successful outcome would mean many trillions of dollars worth of business. All power plants could run without fuel, as could ships, trucks, homes, cars, even appliances. The pollution problem would be wiped out. All building industries would get a tremendous boost. Deserts would be greened, people could live in any corner of the universe they chose to...
Worth a try. A dogmatic no based upon worship of "conservation laws" is unworthy of those with scientific background.
In any case, I am very very glad to know that I am the first to have proposed this new idea. I posted this to sci.energy as well, and there has been no response, which indicates that this idea was original - no one published it before.
Arindam Banerjee
From: "Arindam Banerjee" <a.banerjee@trl.oz.au>
Newsgroups: sci.physics.electromag
References: <mLfl4.3231$VJ1.6023@newsfeeds.bigpond.com> <3896F477.F7E0DD23@tripoint.org>
Subject: Re: Mathematical derivation and machines for unlimited energy
Date: Mon, 7 Feb 2000 08:38:23 +1100
Lines: 26
(Name of author deleted) wrote in message <3896F477.F7E0DD23@tripoint.org>...
>> *****
>> Mathematical derivation for unlimited energy, or showing that the law
>> of conservation of energy is invalid for mass transfers across relativistic
>> systems.
>> *****
>
>You've never heard of "Special Relativity" have you?
Certainly Mr ***,
My paper was based upon appreciation of the correctness of the first postulate of Einstein's Theory of Special Relativity. Since you seem to be aware of that, I see no point in posting it. It is surprising though that you seem unable to appreciate that that postulate may be seen as a key basis for my scientific breakthrough.
Arindam Banerjee
From: "Arindam Banerjee" <a.banerjee@trl.oz.au>
Newsgroups: sci.physics.electromag
References: <mLfl4.3231$VJ1.6023@newsfeeds.bigpond.com> <38970EA1.DA9B042@mmm.com>
Subject: Re: Mathematical derivation and machines for unlimited energy
Date: Mon, 7 Feb 2000 08:45:11 +1100
Lines: 45
(Name of author deleted) wrote in message <38970EA1.DA9B042@mmm.com>...
>Arindam Banerjee wrote:
>
>> Thus if force F=Ma
>
>that is the small velocity approximation.
>
>Newton wrote it this way:
>
>F = d(Mv)/dt
>
>Newton was a careful scientists and realized
>that he could not assume M was a constant.
Quite true, but I was taking M constant. And since I wanted laymen to understand my paper for its scientific value, I avoided derivatives.
When M is a function of time, as v, then
F = v*d(M)/d(t) + M*d(V)/d(t)
the formula you use when designing rockets where M is a function of time.
As M remains constant in my paper,
d(M)/d(t) = 0
So F = M*d(V)/d(t)
or F=Ma
If I wanted to confuse people with mathematics, believe me, I could do so. I choose to be as clear as possible, instead. Heightening the poetic aspects, that is.
Arindam Banerjee
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