Category Archives: Science

Comment on Newton’s First Law 

February 15, 2023 – 12:01 PM

Reference: KHTK Key Words: Dynamic 6

Please consult the above reference for the definitions of CONSISTENCY and INERTIA.

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Inertial Frame of Reference

  1. It is a frame of uniform velocity and zero acceleration.
  2. This frame is tied to the consistency of substance.
  3. Accelerations in this frame means changes in the consistency of substance.
  4. Accelerations of mass objects means undetectable infinitesimal changes in mass.
  5. Relativistic changes in mass occur only at very high accelerations (not velocities).
  6. Elementary particles of different masses and quanta have different frames of reference.
  7. The inertial frame of reference of Newton is applicable to material particles of relatively low velocities.
  8. Einstein’s relativity points out slight changes in the inertial frame of reference due to celestial accelerations.
  9. Thus, there are Lorentz transformations of velocities of mass particles in Inertial Frame of reference.
  10. On a large scale, the paths of mass particles in uniform motion are only as straight as their motions.
  11. The lower is the consistency, the higher is the velocity, and the straighter is the path.
  12. The greater is the consistency, the slower is the velocity, and the more curved is the path.

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Newton’s First Law

Newton’s first law of motion says,

“Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.”

This law may be modified slightly as follows:

“Every object will remain at rest or in uniform motion “in a curvature based on its consistency” unless compelled to change its state by the action of an external force.”

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By vinaire | Comments (0)

The Spectrum of Substance (old-4)

February 15, 2023 – 10:47 AM

Reference: Fundamentals of Physics

In classical mechanics, substance is recognized by its mass. But since Einstein’s 1905 paper on “light quanta,” substance has taken a wider significance. Light has force and momentum, therefore, it is substantial. Substance is anything that is substantial enough to be sensed.

Since term “mass” is recognized only in the context of matter, we need a broader term equivalent to it in the context of substance. Such a term is “consistency.” For example, light does not have mass, but it has consistency.

MASS represents “atomic substance” only. CONSISTENCY represents both atomic and non-atomic substance. When consistency is very high, as in the nucleus of an atom, it is recognized as mass.

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Consistency (Thickness)

The consistency of substance is defined as follows:

Consistency is the degree of substantiality of substance. It is recognized as density, firmness, or viscosity of the substance. For example, “Honey has higher consistency than water.” For radiant energy, consistency is measured per quanta, where quanta is determined by frequency. For matter, consistency is measured by the mass of its elementary particle, such as, proton or neutron, where the elementary particle is determined by its smallest discrete inertia. The quanta and the mass of elementary particle may be measured by the same unit. Thus, substance can have a gradient of consistencies.

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Measure of Consistency

The consistency may be measured in terms of doubling of frequency as follows:

Consistency (C) = log f / log 2

We may calculate the consistency of electromagnetic substance from its frequency. This may be listed as follows:

We may assume the consistency of matter to be very close to 77.6.

The planets and stars may also have consistencies close to 77.6. But we may calculate their “relative consistency” based on their momentum as follows

De Broglie Equation,       λ = h/p,

where h is Planck’s constant, and p is momentum of the object, which is made up of many particles.

Frequency:                      f = c/λ = (c/h) p = 4.528 x 1041 p

Total Consistency:         Ctot = (log f) / (log 2) = 138.4 + 3.322 log p

Thus, knowing the mass and velocity of Earth, we may calculate its total consistency as follows,

ME = 5.972 x 1024 kg, VE = 3 x 104 m/s, and  p = ME VE = 1.79 x 1029

Ctot (Earth) = 138.4 + 3.322 log (1.79 x 1029) = 235.6

Similarly, we may calculate, Ctot (Sun) = 256.6

In terms of relative consistencies, we may say,

Crel (Earth) = 1

Crel (Sun) = 1.089

This means that the Sun is a bit more fixed in space than the Earth.

The Black holes may have much higher consistencies. Their absolute consistency (consistency per particle) may be higher than the consistency of the neutron. As a result they are much more fixed in space. We may, therefore, expect to find the Black holes at the center of the galaxies.

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What is Light?

February 15, 2023 – 9:10 AM

Reference: KHTK Key Words: Dynamic 6

Please consult the above reference for the definitions of CONSISTENCY and INERTIA.

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What is Light?

A wave in pond travels within the pond. The pond itself does not move. The speed of this wave depend on the density and bulk modulus of water.

Similarly, light travels within the space. The space itself does not move. The speed of light depends on the permittivity and permeability of space.

Light is not a wave. It is only analogous to a wave. The frequency of light is very likely its consistency as a substance. The wavelength of light is probably the “tension” of the light substance in space. Velocity is probably how fast a disturbance in the tension of light spreads.

Light substance is not made up atoms. It is actually made up of force. Faraday approximated it as “lines of force.”

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Conjectures on Motion

The measured speed of light is constant only within a certain limit of precision.The speed is limited by the inertia of the electromagnetic fields in spacetime. The spacetime represents the gravitational field.

Therefore, inertia of light comes from its interaction with the gravitational field. Absence of inertia would mean unrestrained acceleration and infinite speed.

Uniform finite velocity of light means that its acceleration is balanced with its inertia. The amount of resistance to “change in velocity” gives a sense of consistency of substance. A speed greater than ‘c’ will exist if and only if the consistency of substance is less than the consistency of light.

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Speed of light and Inertia

On the Spectrum of Substance, the motion of substance decreases as consistency increases. We may suppose that on a very large scale motion is inversely proportional to inertia. We may check this out as follows:

Ratio of speed of light to speed of matter (approximately) = 3 x 108

From Relative Consistencies of Substance:

Ratio of consistency of matter to consistency of light = consistency of proton/consistency of light

                                                                                    = 277.6 / 249

                                                                                    = 228.6

                                                                                    = 4 x 108

This is of the same order of magnitude as the approximated ratio of the speeds of light and matter. This value is higher because the consistency of neutron is slightly higher than the average consistency of matter. Therefore, it is quite possible that the consistency and motion (or, inertia and speed) are inversely proportional to each other.

In other words, the product of consistency (inertia) and motion (speed) shall give us a new universal constant. This has to be worked out carefully.

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Einstein: 1905 Paper #2 on Molecular Dimensions

February 11, 2023 – 10:44 AM

Reference: Fundamentals of Physics

Doctoral Thesis completed in April 1905 and revised in 1906.
Published in Annalen der Physik 19 (1906) 289-305
A New Determination of Molecular Dimensions
Highlights in bold and comments in color by Vinaire

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Summary

In this paper Einstein explores a new theoretical method to calculate the molecular dimensions through the observation of physical phenomenon in liquids. The main part of the thesis involves hydrodynamics and the relation between coefficients of viscosity, followed by a determination of diffusion-coefficient from fundamentals.

Einstein’s thesis serves to validate his theoretical approach and the fundamental expressions derived for the viscosities and the diffusion coefficient.

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Some of the mathematical symbols used by Einstein in his thesis are as follows:

k: coefficient of viscosity of the solvent
k*: coefficient of viscosity of the solution
x, y, z, t: the coordinates and time
x0, y0, z0: an arbitrary point (center of the molecule; molecule has a contact layer)
u, v, w: velocity components of the solvent
u0, v0, w0: dilation motion in the absence of the sphere—a particle of solute (at infinity)
u1, v1, w1: dilation motion in the presence of the sphere—would have to vanish at infinity
p: hydrostatic pressure (Section 1)
G: small region around this arbitrary point x0, y0, z0
P: radius of the rigid sphere
R: a sphere of radius R, where R is indefinitely large compared with P
Xn, Yn, Zn: the components of the pressure exerted on the surface of the sphere of radius R
n: the number of solute molecules per unit volume
W: mechanical work done on the liquid (per unit of time) in the liquid lying within the sphere R = the energy which is transformed into heat
ds: surface element
ϕ: the fraction of the volume occupied by the spheres.
s: specific volume of the sugar present in solution
p: the osmotic pressure of the dissolved substance (Section 4)
ρ: grams of solute in a unit volume (section 3)
m: molecular weight of the solute
N: the number of actual molecules’ in a gram-molecule (Avogadro’s Number)
P: the hydrodynamically-effective radius of the solute molecule (Section 3)

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Here is a summary of the steps taken by Einstein in his thesis:

1. When a very small sphere is suspended in a liquid, how does it effect the motion of that liquid? 

  • Set up hydrodynamical equations for viscous fluids for random motions in the liquid.
  • Solve it using the method given by Kirchhoff getting expressions for p (hydrostatic pressure) and for u, v, w (the velocity components of solvent). 
  • These solutions are unique for the boundary conditions at the surface of the sphere (a particle of solute).
  • Use these solutions to calculate the mechanical work done in the liquid (per unit of time).
  • The energy expression is obtained in terms of the viscosity of the solvent when the sphere is present.
  • Obtain the energy expression when the sphere is absent. There is a lot of mathematics and simplifying assumptions.

2. Calculation of the viscosity-coefficient of the liquid in which a large number of small spheres are suspended in irregular distribution.

  • Use the results from above to calculate the energy for a large number of spheres suspended in the liquid.
  • Express the energy in terms of the parameters for the solution in a manner similar to above.
  • Compare the energy expressions for the solvent and the solution, to determine the ratio of their viscosities.
  • This ratio of viscosities is obtained in terms of the total volume of the solute present in the solution per unit volume.
  • Conclusion: If very small rigid spheres are suspended in a liquid, the coefficient of internal friction is thereby increased by a fraction which is equal to 2.5 times the total volume of the spheres suspended in a unit volume, provided that this total volume is very small.

3. On the volume of a dissolved substance of molecular volume large in comparison with that of the solvent.

  • Einstein applies the above conclusion to the viscosity data for dilute solution of sugar in water.
  • A gram of sugar dissolved in water has the same effect on the viscosity as small suspended rigid spheres of total volume 0.98 cc. 
  • But a gram of solid sugar has a volume of 0.61 cc.
  • Einsteins reasons that the sugar molecules present in solution limit the mobility of the water immediately adjacent, so that a quantity of water, whose volume is approximately one-half the volume of the sugar-molecule, is bound on to the sugar-molecule
  • Using the molecular weight of sugar, Einstein calculates the volume of a sugar molecule in terms of the Avogadro’s number.

4. On the diffusion of an undissociated substance in solution in a liquid

  • Use Kirchhoff’s equation to calculate the diffusion-coefficient of an undissociated solution.
  • In this calculation osmotic pressure is treated as a force acting on the individual molecules.
  • This expression of diffusion-coefficient includes “the product of the number N of actual molecules in a gram-molecule and of the hydrodynamically-effective radius P of the molecule. 

5. Determination of molecular dimensions with the help of relations already obtained

  • The expressions of the ratio of viscosities and the expression of the diffusion-coefficient give us two equations in “N” and “P”.
  • Einstein solves these equations for the aqueous sugar solution.
  • The values of “N” and “P” are found to have the same order of magnitude as determined by other methods.

Einstein’s thesis serves to validate his theoretical approach and the fundamental expressions derived for the viscosities and for the diffusion coefficient.

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Other references to this Paper:

  1. Something Interesting about Albert Einstein’s Ph.D. Thesis
  2. On Einstein’s Doctoral Thesis
  3. Einstein’s PhD thesis

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Newtonian Concepts for Quantum Age

February 8, 2023 – 5:20 PM

Reference: Fundamentals of Physics

Newton defined momentum as the product of mass and velocity. But then we find that light has quanta (amount) in addition to velocity, and it also has momentum. Light has no mass, but the light quanta must have some property very similar to mass. The property common to mass and quanta has to be inertia (resistance to motion). In the absence of inertia, the velocity would be infinite. The finite velocity of light tells us that it must have inertia.

Let’s call the mass-like property of light quanta as its “consistency”. The English dictionary defines “consistency” as a degree of density, firmness, viscosity, etc. For example, we notice honey to have a thick consistency. The light quanta is not made of atoms like honey is. So, its consistency is extremely small. But the light quanta can coalesce with each other much like the drops of honey can. Therefore, photons will act much like fluid in that they can split and coalesce together as we see them do in the double-slit experiment.

Momentum provides us with the feeling of impact. It is this impact that underlies our sensations. Sensations make up our sense of reality. In Newton’s time we associated momentum with mass only because Newton mostly dealt with matter. But since then, we have been able to detect the momentum of light through very fine instruments. We have found that light can exert pressure. Even though this pressure is too small to be sensed by us; still, it puts light in the category of substance like matter.

In case of electrons, the consistency is much higher than that of light. In the atom, the consistency of electrons has been measured as 1/1836 of the mass in the nucleus. Up to this point, we have defined all the sub-atomic properties mathematically only. Now the concept of consistency brings all those mathematical interpretations closer to reality. We can visualize the electrons within the atom as forming layers of thin shells of slightly different consistencies.

We can now identify mass as the property of very high consistency. We can now see nuclear material, electrons, radiative energy and gravity forming a spectrum of decreasing consistency. We may find a direct relationship between consistency and frequency on this spectrum. We may call this spectrum—the spectrum of substance. 

On this spectrum, momentum may now be defined as the product of consistency and velocity, rather than mass and velocity. This explains the momentum of light in the absence of mass.

On this spectrum, inertia may be associated with consistency in a more generalized sense. This explains why the speed of light is large but still finite. Absence of inertia will inevitably lead to infinite velocity. 

On the spectrum of substance, we notice that the lighter (thinner) is the consistency, lesser is the inertia, and the higher is the natural velocity. There is an inverse relationship between the consistency of substance and its velocity. So there is an undiscovered universal constant that is more basic than the speed of light.

We may form a hypothesis that the speed of light ‘c’ varies infinitesimally with frequency of light, but it is virtually a constant when viewed in the inertial frame of reference of mass. Similarly, the inertial mass of objects changes infinitesimally with changes in their acceleration, but it is impossible to detect.

The “rest mass” of an object is measured when it is moving at a constant velocity (zero acceleration). This applies to material objects only. Subatomic particles and light quanta of all consistencies are always accelerating because their paths are always curved. They all are part of whirlpools, at the center of which are the nuclei of atoms.

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