Unified Theory Foundations

Engineer Xavier Borg - Blaze Labs Research

Science tail chasing
... the mechanism that guarantees getting to nowhere

The space-time conversion table shown in the previous page, is a great leap towards unification, and makes obvious the redundancy of the conventional scientific laws just by a general approach to its foundations - its measuring system. If the measuring system of a science is full of redundant units, then, it surely means that much of the laws based on those units are redundant or circular.

The notion of redundancy of the scientific laws has been well expressed by the late Professor JL Synge and made public in the series of lectures at the Dublin Institute of Advanced Studies delivered in 1949. Quoting Synge in the following passage:

..... Thought is difficult and painful. The difficulties and pain are due to confusion. From time to time, with enormous intellectual effect, someone creates a little order - a small spot of light in the dark sea of confusion. At first we are all dazzled by the light because we are used to living in the darkness. But when we regain our senses and examine the light we find it comes from a farthing candle - the candle of common sense. To change the metaphor, the sages chase their own tails through the ages. A little child says 'Gentlemen, you are chasing your own tails.' The sages gradually lose their angular momentum, and, glancing over their shoulders, see what they are persuing. But most of them cannot believe what they see, and the tail chasing does not die out until a generation has passed.....

Forty years ago Schroedinger wrote (in his article recently reprinted in the Special Issue 1991 of Scientific American, "Science in the 20th century", p.16):

"Fifty years ago science seemed on the road to a clearcut answer to the ancient question which is the title of this article [Our Conception of Matter]. It looked as if matter would be reduced at last to its ultimate building blocks - to certain submicroscopic but nevertheless tangible and measurable particles. But it proved to be less simple than that. Today a physicist no longer can distinguish significantly between matter and something else. We no longer contrast matter with forces or fields of force as different entities; we know now that these concepts must be merged... . We have to admit that our conception of material reality today is more wavering and uncertain than it has been for a long time. ... Physics stands at a grave crisis of ideas. In the face of this crisis, many maintain that no objective picture of reality is possible. However, the optimists among us (of whom I consider myself one) look upon this view as a philosophical extravagance born of despair. We hope that the present fluctuations of thinking are only indications of an upheaval of old beliefs which in the end will lead to something better than the mess of formulas that today surrounds our subject."

It is astonishing, but also frustrating, to see how topical are the remarks still today. Weinberg, Feynman, Wolff and certainly other well known science explorers, have more than once drawn our attention to the same inadequate foundations for natural laws.

In my ST table together with the description of the fractal model of the atom described in the particle section, I tried to show the head and tail of science. As you should have followed, the units candela, Kg, mole, Ampere and Kelvin are the teeth holding tight the tail of science. Our present science knowledge books and lectures are the force driving the circular motion of the tail chasing. The conversion table stops this vicious loop in quite an abrupt way and attempts to put back some order.

Of course, most of you do not like what they see, and argue that the tail they are chasing is not theirs. But let's stop with metaphors, and try to explain it with some elementary physics.

What looks so unconventional in the ST unification table is the fact that matter is a 3D version of energy, and that energy or 1D mass, is the inverse of velocity. Once cleared these two weird links, it becomes immediately clear that the ST table should be the real fundamental measuring system of science.

Let's start from what everybody should know: 1D space dimension S is a unit of length, and 1D time dimension T is a unit of time. It also follows that the unit of velocity should be S/T and that of acceleration is ST-2. Also the second dimension of space is not 2S but S2. Now, anybody who tried out known equations and worked out their dimensions according to the ST table, would agree, that the rest of the table is to say the least SELF COHERENT, but the link between length, time, velocity or acceleration to energy and all the rest of the parameters may not be obvious. For this analysis I've used the quite elementary yet powerful equations of motion given by Jeans J. in his introduction to the Kinetic Theory of gases, and will try to derive the mass unit in its one dimensional form, in terms of length and time.

We will here consider the impact of two elastic bodies masses m1, m2 in a simple 1 dimensional space. The velocities before impact are u1, u2 respectively. The velocities after impact are v1, v2. Since we will consider mass in one dimension (a point moving along a line), we will assume movement is taking place only in the x-direction, to the left and right. You can choose any x-direction of motion to be positive velocity and the other will be the negative.

Energy is Inverse velocity (T/S)

The following is taken from the mathematical work of Jeans J, from 'An introduction to the Kinetic theory of gases', Cambridge Univ press 1960. We'll here consider a totally isolated system, in which we know that total system momentum is conserved. The momentum lost by one object is equal to the momentum gained by another object. For collisions occurring in an isolated systems, there are no exceptions to this law.

momentum before impact = momentum after impact

m1u1 + m2u2 = m1v1 + m2v2 .....(1)

Looked at hierarchically, velocity may be viewed as existing at two levels, a high order velocity V averaged over equal intervals of time before and after impact and defined by the equation:

V = 1/2 (u1 + v1) = 1/2 (u2 + v2) .....(2)
and low order velocities obtained by subtracting the high order velocity, V, from the individual velocities, u1, u2, v1, v2:

μ1 = u1 - V .....(3)

μ2 = u2 - V .....(4)

τ1 = v1 - V .....(5)

τ2 = v2 - V .....(6)

From equation (2):

μ1 = -τ1 .....(7)

τ2 = -μ2 .....(8)

The individual velocities can now be seen as the sum of the low order, 'within batch' velocities μ1111 and the higher order, 'between batch' velocity V. Now from equations (3) to (8):

u11 + u2/(-μ2) = v1/(-τ1) + v22 .....(9)

Substituting from equations (7) & (8) and re-arranging:

(1/μ1) u1 + (1/τ1) u2 = (1/μ1) v1 + (1/τ1) v2 .....(10)

Equation (10) is isomorphic to the equation of conservation of momentum, equation(1):

m1u1 + m2u2 = m1v1 + m2v2 .....(1)

The 1D masses m1 and m2 have been replaced by the reciprocal internal 1D velocities (1/μ1) and (1/τ1). Numerically, these reciprocal terms will differ from the mass values in Kg units, for the reason that the kg SI unit is an arbitrary unit defined in 3D, whereas the reciprocal terms are in seconds per metre units. This implies that the 1D form of mass has dimensions (S/T)-1 or T/S. The concept of 3D mass can thus be replaced by the concept of reciprocal 3D internal velocity both at the macro and the micro scale, leading to a 3D mass dimension of T3/S3. The concepts of stepping up dimensions can be easily understood when one considers any spacetime unit to be a ratio of two spatial dimensions. We can easily understand that 2D space is S2, 3D space is S3. This rule applies to the spatial time dimension as well as to combination units as velocity, and mass. For example, the nth dimensional unit of a spacetime parameter SxTy will be equal to SnxTny. Thus units for different dimensions of mass will be of the form Tn1S-n1 all being the same entity in different dimensions. The Newtonian Kg is just one of these entities for the condition n=3, giving the 3D version of mass, spacetime dimension T3/S3.

From the kinetic energy equation E=1/2mv2, we get E= T3S-3*S2T-2= T/S, re-confirming Einstein's statement : 'It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind'. One could easily replace the Kg by Joules3 by simply introducing a conversion dimensionless factor between the two units. It is quite impressive, that we arrived to the same conclusion, without reference to Einstein's equations or special theory of relativity. All we did was in fact equating velocities in the elementary equation of conservation of momentum.
From the above we have proved that energy is a one dimensional form of mass, and that it has dimensions T/S, which are those of inverse velocity!

Replacing SI with ST units

Other ST units can be easily derived using our present knowledge as follows:

Planck constant h= E/f = T/S * T = T2/S

From E=mc2, m = E/c2 = T/S * (T/S)2 = T3S-3

For momentum = mv = T3/S3*S/T = T2S-2

For angular momentum L = mvr = T3/S3*S/T*S = T2/S ... same as Planck constant

For Moment of Inertia I=L/w = T2/S * T = T3/S

From F=ma, we get Force= T3S-3*S T-2= TS-2

Electromotive force (Voltage) = TS-2

For power, P=Fv, we get P=TS-2*S/T = S-1

For current, I= P/V = S-1/(TS-2) = S/T

For resistance, R = V/I = TS-2/ (S/T) = T2S-3

For mass flow rate mdot = dm/dt = (T3S-3)/ T = T2S-3

For Pressure = F/A = TS-2*S-2 = TS-4

Frequency = v/l= S/T*S-1= T-1

Temperature = E/k = T/S * 1 = T/S

For charge q=It = S/T * T = S

For Capacitance C = Q/V = S/(TS-2) = S3T-1

From V=L(dI/dt), Inductance L= TS-2 * T * T/S = T3/S3...same as mass!

Interesting things to note:

Newtons law: F=ma=m(dv/dt)

Comparing with V= L(dI/dt), where voltage has the same dimensions of force, Inductance the same dimensions of mass and current same dimensions of velocity. It is clear that the equations are actually the same, and that V=L(dI/dt) is actually Newtons law of motion.

Power = Force * Velocity

Comparing with Power = V*I, where voltage has the same dimensions as force, and current has dimensions of velocity. Again it's the same equation.

Kinetic energy = 1/2mv2

Energy stored in inductor = 1/2LI2, where L has dimensions of mass and I of velocity.

Work (Energy) = Force * distance
Compare with Energy = Vq, where voltage has dimensions of force, and charge dimensions of length.

Now compare the time constant of a simple pendulum given by (L/g)1/2
If we replace pendulum length L by charge (dimension S), and gravitational acceleration by (a=dv/dt=dI/dt) current acceleration, we have:
Time constant = (qT/I)1/2... but q=CV and R=V/I so:
(T)1/2= (RC)1/2
T=RC... time constant for RC circuit...derived from mechanical pendulum

From Force = Rate of change of momentum = m (dv/dt)
Compare to EMF = L (dI/dt)... means that product LI is in fact the momentum of the electrical system.

Energy = Force * distance
Energy = ma * d
E = mvd/t .... but mvd is momentum*distance which has the same dimensions as Energy*time same as the well known quantum of action : Planck constant h, so:
E = h/t .... 1/t= frequency, thus
E = hf

From rocket equation : Thrust = Velocity * Mass flow rate

Replacing Thrust (force) by voltage, velocity by current, and mass flow rate by resistance, we get Ohms Law:
V = IR .... so, Ohms law is nothing more than the rocket thrust equation and shows that a resistor controls MASS flow rate NOT charge flow rate. This clearly shows one of the major misconceptions of the present electrical theory, in which it is assumed that a resistor has an effect on charges, which is clearly not the case. Resistance is in fact acting on the MASS of the flowing electrons and not on their charge.

From linear drag equation : Viscous force = Velocity * b(drag constant)

Replacing Force by voltage, and velocity by current, we get:
V = Ib .... so, from Ohm's law, we find out that the drag constant is nothing but the analogue of electrical resistance.

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