A New Theory of Gravitation

Revised 05/07/2012

"We do not need a new theory because our present one explains everything".

Richard Feynman
  1. A New Theory of Gravitation
    1. Basic dimensions
    2. Other dimensions
    3. Most famous interactions
    4. Types of most famous forces
    5. Most famous questions
    6. Attractions and repulsions with simple to understand causes
    7. An old frame
    8. A new frame
    9. Inverse square coarsening
    10. Einstein's equivalence principles
    11. Objects, properties, events, messages, causes and coarsening
    12. Causality
    13. Interaction
    14. Gravitational lens
    15. Definition of the mass
    16. Stopping of the light
    17. A definition of the matter
    18. A weak definition of the mass
    19. The properties of the mass
    20. Does Gravity Travel at the Speed of Light?
      1. Introduction
      2. If the gravitation has a finite speed
      3. Isaac Newton
      4. Gerber's theory of gravity
      5. Albert Einstein
      6. Tuomo Suntola
      7. Le Sage types of the theory of gravitation
      8. Conclusion
    21. The speed of the light and Olber's paradox
      1. Olbers' paradox
      2. Supernovas and the speed of the light
    22. The simplicity and the hidden complexity
      1. Immanuel Kant and Moritz Schlick
      2. Stratified complexity
    23. Some invariance
      1. Some invariance in the Newton's physics
      2. Some invariance in the Einstein's theory of the special relativity
      3. A basic postulate of the Einstein's theory of the general relativity
      4. The effect of the invariance to the transformations
    24. The metric tensor
      1. A definition of the metric tensor
      2. The fundamental tensor
      3. The Cartesian fundamental tensor
      4. Lorentz-Minkowski space
    25. Is the gravitation time dependent
    26. Is the gravitation local or universal
    27. The classification of Toivo Jaakkola
    28. Newton's theory of the gravitation
      1. Equations
      2. A coarse explanation
      3. Wikipedia against the history of the theory gravitation
    29. Velocity-dependent theories of the gravitation
      1. Newtonian theories of the gravitation using the velocity of the gravitation
      2. Einstein's velocity-dependent theory of the gravitation
    30. Why no speech of the special theory of relativity?
      1. Can the gravitation become the source for additional gravitation?
    31. All theories of gravitation are wrong
      1. Dark matter
      2. Dark energy
      3. What theories of physics can not explain
    32. Alternative frames
      1. Gérard Berger
      2. Berger's results
      3. Tuomo Suntola
      4. Matthew R. Edwards
    33. Used mathematics
    34. The problem of the dark energy
    35. Daniel Sunhede's dissertation
    36. David Hume on miracles
    37. Moving body
    38. The definition of the place
    39. Energy
      1. The energy of the cosmos
      2. Proper energy and virtual energy
      3. The energy of the photon
      4. If explanations using red shift are true
      5. Is the discrete cosmos possible?
      6. Has a photon a mass?
      7. Which is the half-life of the photon?
      8. The formula E = mc2 is unverified
      9. The formula m = E/c2 is against our definition of the mass
      10. Photon has a micro-structure
      11. Dark matter and photons
      12. Reality is not a human construction
      13. Electron and positron
      14. Is there a field without mass?
      15. Quantum
      16. Is the mass a scalar?
      17. Redefinition of the linear momentum
    40. Possibility to make the difference between the mass and the energy
    41. Two axioms of Dr Tuomo Suntola
    42. Relations of the universal constants
    43. The theory of the electromagnetic radiation
    44. The Maxwell equations can be wrong
    45. Energy principles
    46. What intelligent Eisteinians think
    47. Structural explanations or causal explanations
    48. Are there necessities in the nature
    49. The nature of mathematics
    50. Hafele-Keating experimet
    51. Operational definition
    52. Straight line
    53. Einstein's vicious circle
    54. Why it is not intelligent to use a curved space in physics
    55. Space and field
    56. Newtonian or Einsteinian black holes
    57. Are Big Bangs possible
    58. Independent and dependent variables
    59. Are black holes elementary particles
    60. Waves in a vacuum
    61. A new problem: The physics confuses mass and energy
    62. Energy
    63. Is there pure energy
    64. Explanation of the mass
    65. Black holes
    66. Simple functions
    67. Functions with zero points
    68. Which is the speed of the strong force
    69. Which masses are real
    70. Quarks, leptons and other particles
    71. Cosmic microwave background radiation
    72. Neutral elementary particles
    73. The difference of the neutron star and the black hole
    74. Which is the cause of the inertia
    75. Action and reaction
    76. Einstein's distance d
    77. The thesis of Hartikainen
    78. Additive units
    79. Velocities of small and big masses
    80. Memory of acceleration
    81. The new clock paradox
    82. Definition of the timeTime
    83. Simultaneous cause and effect
    84. Curvature and torsion
    85. Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements
      1. Abstract
    86. Repulsion and attraction
    87. Manipulating the frequencies of the photons
      1. Different photons in, indistinguishable photons out
    88. How a single photon can stop the black hole
    89. Are the following pictures correct
    90. The neutrino theory of light
    91. Are neutrinos the main component of dark matter?
    92. Is the black hole a very big neutrino?
    93. Scattering
    94. Real attractive forces
    95. Coulomb's law
    96. Einstein's aether
    97. Problems of the explanations
    98. Tensions and tensors are problematic
    99. Why do objects fall at the same rate of acceleration?
    100. The changing of the coordinate system
    101. Local and universal
    102. Is there rotation and acceleration
    103. Redshift and blue-shift
    104. Proposal for the electromagnetic elementary particles
    105. Possible cause to the uncertainty
    106. Where do photons come from?
    107. Which is the size of the photon?
    108. Intrinsic equations of a space curve
  2. Space-independent time
  3. Lower bounds and upper bounds
  4. What we can observe with our instruments
  5. Is the big bang possible
  6. The falling of the rotating solid body
  7. Nothing in the special relativity theory is true
    1. The Growth of the masses?
    2. Where the distant galaxies are?
    3. Is the space expanding?
    4. Is there a space?
  8. Inertia
  9. If there was a black hole before the big bang
    1. If Hawkings's theory of black hole radiation is correct
  10. Is the known universe a closed system?
  11. Why we are in the center of the known universe?
  12. Pulling or pushing?
  13. David Hume on miracles
    1. The text
    2. The argument
  14. The miracle of the big bang
  15. Le Sage-type big bang
  16. Continues...

A New Theory of Gravitation

The General Theory of Relativity postulates that gravity is the result of a curvature of space-time in the presence of mass. But that tells us nothing about why gravity exists in the present context. It merely changes the question from "Why do objects attract each other?" to "Why do masses cause a curvature in space-time?"

Tom van Flandern [1] p. 29.

Basic dimensions

When I was a child, the basic dimensions were:
  • distance R
  • area A
  • volume V
  • time T??
  • mass M
  • distance 1 d = 2π m
  • area 1 a = π m2
  • volume 1 v = (4π/3) m3
  • time s??
  • mass kg

Other dimensions

When I was in the school, the basic dimensions were
  • length
  • height
  • width
  • time??
  • mass
with SI units.

Most famous interactions

  • gravitation
  • electromagnetic force
  • strong force
  • weak force
  • Casimir force

Types of most famous forces

  • gravitation: attractive
  • electromagnetic force: attractive or repulsive
  • strong force: attractive or repulsive
  • weak force: changes attractive forces to repulsive and so on...
  • Casimir force: attractive

Most famous questions

  • Which is the cause of the attractive force?
  • Which is the cause of the repulsive force?

Attractions and repulsions with simple to understand causes

  • A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. The explanation of the attractive forces is a complex area that is described by the laws of quantum electrodynamics.
  • Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation.

An old frame

The general theory of relativity is the geometric theory of gravitation by Albert Einstein in 1916.

It describes gravity as a property of the geometry of space and time, or space time.

In particular, the curvature of space time is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present.

The relation is specified by the Einstein field equations, a system of partial differential equations.

A new frame

  • There is no need to use the curvature of the space time.
  • The universe is independent of the human ability to make measurements.
  • The universe is independent of the human mathematics.
  • The gravity is a real force.

Inverse square coarsening

F = Gm2m2r-2

F = Keq1q2r-2
  • F is a force
  • G and Ke are constants
  • m1 and m2 are two masses
  • q1 and q2 are two charges and
  • r is a distance.

Einstein's equivalence principles

In one form the Einstein’s Weak Equivalence Principle (WEP) is defined as the equivalence of gravitational and inertial masses that is absolute and independent of any motion.

The strong equivalence principle (SEP) suggests the laws of gravitation are independent of velocity and location.

In our frame both equivalence principles are wrong.

We define that the gravitation is the force between masses. We assume that all particles (including bosons) have masses.

Inertia needs another explanation.

Objects, properties, events, messages, causes and coarsening

There are objects.

Human coarsening:
  • The object.
    • The property of the object.
      • The mass is a possible property of the object.
      • The charge is a possible property of the object.
  • The event.
    • The cause of the event.
  • The message.
    • The cause of the message.


Causality denotes a necessary relationship between one event (called cause) and another event (called effect) which is the direct consequence of the first.


Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction.

Gravitational lens

A gravitational lens is formed when the light from a very distant, bright source is bent around a massive object (such as a cluster of galaxies) between the source object and the observer. The process is known as gravitational lensing.

Orest Chwolson is credited as being the first to discuss the effect in print (in 1924).

Fritz Zwicky posited in 1937 that the effect could allow galaxy clusters to act as gravitational lenses. It was not until 1979 that this effect was confirmed by observation of the so-called "Twin QSO" SBS 0957+561.

Definition of the mass

Revised 10/12/2012

We define that the object has a mass is the gravitation has the effect to the object.

The gravitation is the cause of the bending of the light. The light has the gravitational mass. The electromagnetic radiation has the gravitational mass.

Stopping of the light

In June 1997, Hau and her co-workers finally cooled atoms enough to form a Bose-Einstein Condensate. “We were incredibly happy,” she said. “We had succeeded.” They were among the first people in the world to see those condensates.

After making the condensate, Hau and her co-workers began looking for ways to use it. They realized that if they massaged the condensate just right with laser beams, they could make light pass through the previously opaque condensate. And they found that the massaged condensate could slow light more effectively than any material ever discovered.

They used an electromagnet to suspend a cigar-shaped condensate, 0.2 millimeters (0.008 inches) long, inside a vacuum chamber. They first illuminated the cigar from the side with a finely tuned laser beam (the 'coupling' beam), and then shot a pulse of laser light along the long axis of the cigar. The pulse slowed down and compressed as soon as it reached the altered condensate. Hau worked late nights in the lab for a year, trying to perfect her experimental system for slowing light.

Finally, in March 1998, she began to see the light slow down. “I thought, 'gee, you are the first person to see light go this slowly,'” she said. That summer, when she flew to Copenhagen, she realized that she was traveling faster than her light beams. That fall, when she succeeded in getting light to travel at the speed of a bicycle, she decided to publish her results.

This year (2001), her group took its experiments a step further by getting light inside a Bose-Einstein Condensate to stop completely. While the light pulse was totally compressed and contained entirely within the condensate, the team abruptly turned off the coupling laser. This adjustment left the light trapped inside. When they turned the coupling laser back on, the original light pulse came out the other end. “We can park a light pulse in the cloud for a millisecond,” Hau said. “It might sound short to you, but it's really long - long enough for light at its normal speed to travel 300 kilometers - and there's no doubt that we can get the storage times up.”

American Physical Society ©2012
Which is the mass of the photon when it is stopped?

Einsteinians say that the photon is absorbed, but if the photon is practically in rest has it a mass?

A definition of the matter

Matter, strong definition: (Non Einsteinian definition): everything which can be influenced by the gravitation.

Matter, weak definition: everything which can influence or to be an object of the influence.

A weak definition of the mass

Revised 10/12/2012

Mass, existence
: An object has the mass if it the gravitation effects to the object.

The properties of the mass

The mass
  1. can be the source of an effect
  2. can be an object of the effect
  3. has an inertia
  4. can have energy (linear, rotational etc.)
  5. inertial mass is a quantitative measure of a body's resistance to being accelerated.
Mass is a problem for physics and cosmology. There are complicated models to try to compute the masses of the elementary particles but there is not much empirical support for the theories.

Does Gravity Travel at the Speed of Light?


To begin with, the speed of gravity has not been measured directly in the laboratory. The gravitational interaction is too weak, and such an experiment is beyond present technological capabilities.

The speed of gravity must therefore be deduced from astronomical observations, and the answer depends on what model of gravity one uses to describe those observations.

If the gravitation has a finite speed

Revised 10/10/2010

If the gravitation has a finite speed and if our meta-galaxy is expanding then the gravitation of the distant galaxies is not effecting us.

If the gravitation has a finite speed, we have same problems and paradoxes as with the special relativity theory of Einstein. Now we have no more general theory to solve the paradox.

Isaac Newton

In the Newtonian model gravity propagates instantaneously: the force exerted by a massive object points directly toward that object's present position.

For example, even though the Sun is 500 light seconds from the Earth, Newtonian gravity describes a force on Earth directed towards the Sun's position "now," not its position 500 seconds ago.

Putting a "light travel delay" (technically called "retardation") into Newtonian gravity would make orbits unstable, leading to predictions that clearly contradict Solar System observations.

Gerber's theory of gravity

Gravity propagates at the speed of light. See Walter Orlov, 2011.

Albert Einstein

In Albert Einstein's general relativity theory gravity "propagates at the speed of light"; that is, the motion of a massive object creates a distortion in the curvature of space-time that moves outward at light speed.

This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. In Albert Einstein's general relativity gravity is not a force, and a description in terms of speed and direction can be tricky.

Tuomo Suntola

Is the gravitational interaction is immediate (the velocity of the gravitation's is infinite, Suntola 2002, p. 276)?

Le Sage types of the theory of gravitation

The speed of the gravitational interaction is between the velocity of the light and infinite.


The minimum speed of the gravitational interaction is the speed of the electromagnetic interaction and the maximum speed of the gravitational interaction is infinite.

Some theories of gravitation suppose that there is no gravitation (the curvature of the space will explain the gravitation).

The answer depends on what model of gravity one uses.

The speed of the light and Olber's paradox

Revised 1/9/2010

Olbers' paradox

is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. It is one of the pieces of evidence for a non-static universe such as the current Big Bang model.

The argument is also referred to as the "dark night sky paradox" The paradox states that at any angle from the Earth the sight line will end at the surface of a star. To understand this we compare it to standing in a forest of white trees. If at any point the vision of the observer ended at the surface of a tree, wouldn't the observer only see white?

This contradicts the darkness of the night sky and leads many to wonder why we do not see only light from stars in the night sky.

The maximum speed of the light is not known.

The Einsteinian speed of the light is 299,792.458 m/s (definition, not a measurement).

The minimum speed of the light is 0.

Lene Vestergaard Hau (born in Vejle, Denmark, on November 13, 1959) is a Danish physicist.

In 1999, she led a Harvard University team who succeeded in slowing a beam of light to about 17 meters per second, and, in 2001, she was able to momentarily stop a beam.

She was able to achieve this by using a very cold super-fluid.

It is possible that there is such super-fluid in the space.

What happens when the sopped radiation begins to move?

Einsteinians say that the light is absorbed after stopping and emitted again after stopping. Do you believe this assertion?

Supernovas and the speed of the light

Soderberg's discovery of the supernova's shock breakout began on Jan. 9, 2008, when Soderberg and Edo Berger, also a Princeton/Carnegie Fellow, were using Swift to observe a supernova known as SN 2007uy in the spiral galaxy NGC 2770, located 90-million light years from Earth in the constellation Lynx. At 9:33 a.m. EST they spotted an extremely bright X-ray outburst that lasted for 5 minutes, and they quickly recognized that they were witnessing a new and unprecedented phenomenon that was occurring in that same galaxy.

In the paper to be published in Nature, Soderberg and 38 colleagues show that the energy and pattern of the X-ray outburst is consistent with a shock wave bursting through the surface of an exploding star, which gave birth to the supernova now known as SN 2008D.

A fascinating conclusion from the theoretical modeling of this outburst is that a thin outer layer must have been ejected at velocities up to about 70-percent the speed of light. This speed is much higher than previously known for the bulk of the stellar envelope, which moves at only up to 10-percent the speed of light," said Peter Meszaros, Holder of the Eberly Family Chair in Astronomy and Astrophysics and Professor of Physics at Penn State and leader of the theory team for Swift.

Which is the velocity of the emitted radiation?

See http://users.beotel.net/~svetlost/

The simplicity and the hidden complexity

Immanuel Kant and Moritz Schlick

Immanuel Kant (1724-1804, The Critique of Pure Reason) argued, that the space is an a prior form of the sensibility. That is, we can know the claims of geometry with a prior certainty (which we do) only if experiencing objects in space is the necessary mode of our experience. Kant also argued that we cannot experience objects without being able to represent them spatially. It is impossible to grasp an object as an object unless we delineate the region of space it occupies.

Moritz Schlick (18821936)studied physics at Heidelberg, Lausanne, and, ultimately, the University of Berlin under Max Planck. In 1904, he completed his dissertation essay, "Über die Reflexion des Lichts in einer inhomogenen Schicht" ("On the Reflection of Light in a Non-Homogeneous Medium").

Schlick was the founder of the logical empiricism. Finnish philosopher Eino Kaila (1890-1958) used first the words "logical empiricism".

Logical empiricism opposed Kantian philosophy.

Schlick was helping Albert Einstein to create the philosophy of the theory of relativity and gravitation in his book Raum und Zeit in der gegenwärtigen Physik (2nd ed. 1919; Space and Time in Contemporary Physics, 1920).

Albert Einstein
(1879-1955) writes in his book The Meaning of Relativity, 1921, p.2:

"The only justification for our concepts and systems of concepts is that they serve to represent the complex of our experience: beyond this they have no legitimacy. I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to intangible heights of the a prior. For even it should appear that the universe of ideas cannot be deduced from experience by logical means, but is, in a sense, a creation of the human mind, without which no science is possible, nevertheless this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympos of the a prior in order to adjust them and put them in a serviceable condition."

Stratified complexity

Paul E. Kustaanheimo (1924-1997) writes in his book Sovelletun matematiikan peruskurssi 1968 (The Basic Course of the Applied Mathematics):

We will take the field of the ordinary complex number coefficients C and we will form using these components and 2n symbols Ea, Fa (a = 1,2,...,n) all possible polynomials, it is, all expressions which are composed of the elements of the field C and the quantities Ea, Fa using finite number of additions, subtractions and multiplications. This set of the polynomials is a tensor ring and we will denote it

C[E1,E2, ... ,En, F1, F2, ... , Fn]

Used mathematics looks simple, and it is simple, but it is very hard to remember it. It is very hard to understand the connection between this mathematics and the reality.

Albert Einstein had difficulties to learn the concept of tensor.

Tensors are mathematical objects which are invariant in multilinear mappings.

If we will have much of invariant objects we can use mathematics which looks simple but has a stratified complexity.

Another possibility is to use really simple mathematics and to have less of invariance.

To avoid numerical parameters we can try to use more dimensions or the curved space.

The string theories and the relativity theory of PhD. Tuomo Suntola are using extra dimensions.

Albert Einstein is using curved space and some extra dimension (-ct).

It is possible to use both much of dimensions and curved spaces.

But we can not say, that the result is really simple.

Some invariance

Some invariance in the Newton's physics

  • time intervals
  • distances
  • masses

Some invariance in the Einstein's theory of the special relativity

  • time order (causality)
  • velocity of the electromagnetic radiation

A basic postulate of the Einstein's theory of the general relativity

  • inertial mass = gravitational mass

The effect of the invariance to the transformations

Different invariances will lead to the different transformations and to the different metrics.

The metric tensor

A definition of the metric tensor

In mathematics, the metric tensor is a symmetric tensor of rank 2 that is used to measure distance in a space.

The fundamental tensor

ui* · uj* = uj* · ui* = gij

where gij is a component of a second rank tensor is called the fundamental tensor.

The Cartesian fundamental tensor

gij = δij

where δij is Kronecker's delta symbol.
\delta_{ij} =
                  \left\{\begin{matrix} 1, & \mbox{if } i=j \\ 0,                  & \mbox{if } i \ne j \end{matrix}\right.

Lorentz-Minkowski space

The fundamental tensor differs from the Cartesian fundamental tensor in
g11 = -c2

i=1,2,3,4, j=1,2,3,4.

Is the gravitation time dependent

If the speed of the gravitation is infinite (immediate effect, Tuomo Suntola) then the gravitation is not time dependent.

F = f(m2,m2,r).

If the speed of the gravitation is finite, the gravitation is time dependent and the original equation needs corrections and the result has the form

F = f(m2,m2,r,t)

Is the gravitation local or universal

If the gravitation is local, the causes of the gravitation can be local.

If the gravitation is universal, the causes of the gravitation can be universal.

The gravitation can be both local and universal.

The classification of Toivo Jaakkola

Finnish astronomer Toivo Jaakkola (1941 – 1995) gives the following classification of the theories of gravitation (Apeiron 2, 1996 p.61):

"The problem of the character of gravitation is approached by discussing three main possible modes of action from the historical, theoretical and empirical standpoints.

The “Newtonian” mode of action -at-a-distance (AAAD)—in which Newton himself did not believe—is followed through three centuries, though the aim is not historical accuracy.

This approach includes several Weber-type theories of velocity-dependent action; these are found to be compatible with or transformable to the mode of the “material field local action” (MFLA).

The historical roots of the mode of relativistic local action (RLA) are sketched, and it is criticized on both conceptual and empirical grounds.

For the MFLA mode, a new theoretical framework is presented by giving a summary of equilibrium cosmology (EC) recently developed by the author.

In EC, gravitation is an equilibrium process providing energy balance in systems of baryonic matter, while electromagnetic radiation is the contrary effect.'

Gravitation on a body is a pressure effect of gravitational quanta (gravitons) conducted from the background field by the gravitation field of the body.

The formation of the field is outlined. Gravitons and photons interact via electrogravitational coupling (EGC), which causes the redshift effect and an analogous weakening of gravity, as well as the cosmic background radiation which is a re-emission equilibrium effect.

From pressure-induced gravitation and EGC, a dynamical theory (EGD) can be constructed which unifies the gravitation effects in systems on different scales; until now, numerous ad hoc hypotheses had been necessary to explain the effects.

When EGD is applied to the two-body problem, Newton’s law is obtained directly. In it the force is a sum of two equal terms which are due to the two fields of graviton flow into the bodies, which are mutually screened by the second body.

While gravitation is basically not an attractive
but rather a repulsive pressure force, the two-body attraction results from the screening effect.

The dilemma of a distant action versus a local action character of gravitation receives a simple but unexpected solution: both are true.

While the momentum due to the pressure of gravitons flowing towards the second body has a distinctly local character, the momentum obtained due to the screening of the body’s own field by the second body is an action at the distance of that body.

Both are expressions of a single interaction between the mass systems and the background field."

Newton's theory of the gravitation


Newton saw that the gravitational force between bodies must depend on the masses of the bodies. Since a body of mass m experiencing a force f accelerates at a rate f/m, a force of gravity proportional to m would be consistent with Galileo’s observation that all bodies accelerate under gravity toward the Earth at the same rate, a fact that Newton also tested experimentally.

Picture: Wikipedia
In Newton’s equation F is the magnitude of the gravitational force acting between masses m1 and m2 separated by distance r. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance.

The constant G is a quantity with the physical dimensions (length)3/(mass)(time)2; its numerical value depends on the physical units of length, mass, and time used.

The force acts in the direction of the line joining the two bodies and so is represented naturally as a vector, F.

The attractive force of a number of bodies of masses

Picture: Wikipedia

M1 on a body of mass M is where Σ1 means that the forces due to all the attracting bodies must be added together vectorially.

This is Newton’s gravitational law essentially in its original form.

A coarse explanation

(Toivo Jaakkola 1996 p. 72)

Consider two spherical bodies B1 and B2 with masses m1 and m2, radii R1 and R2 separated by a distance r.

The inflow of cosmic objects onto B1, which is partially blocked by B2, which covers a fraction A2/(2π) of the sky on B1; A2=(πR22)/r2 is the solid angle on B2 seen from B1.

This brings about B1 a change of momentum towards B2, i.e. a net force,

S1 = 2m1A2)/(2π) (η2m1R22)/(2r2).

Moreover, B1 shields the inflow of the gravitation onto B2, causing a further change of momentum toward B2,

S2 = 1m2A1)/(2π) =η1m2R12)/(2r2).

Coefficients η1 and η2 measure the power with which the bodies B1 and B1 absorb objects; evidently these are identical with the surface gravity η1 = (Gm1)/R12 andη2 = (Gm2)/R22. Altogether, the change of momentum to B1 is

F = S1 + S2 = (Gm1m2) /(2r2) +(Gm2m1) /(2r2) = (Gm1m2) /(r2)

This is identical to Newton's gravitation.

This is an Le Sage -type explanation but if you have a better explanation send it to me.

You can read the Le Sage Theory of Gravitation in English clicking here.

Georges-Louis Le Sage (1724-1803) used the physics of Democritus (c. 460 BCE – c. 370 BCE).

John Dalton's(1766-1844) theory of atoms was presented after the death of Le Sage.

Wikipedia against the history of the theory gravitation

Sensors are writing:

Le Sage's theory of gravitation was a good article nominee, but did not meet the good article criteria at the time.

Wikipedia has been religious and now it is Einsteinian.

Velocity-dependent theories of the gravitation

Newtonian theories of the gravitation using the velocity of the gravitation

It has been shown (2011) that Paul Gerber's velocity dependent Newtonian theory of gravitation is mathematically correct. See Walter Orlov, 2011.

Einstein's velocity-dependent theory of the gravitation

Field theories of gravity predict specific corrections to the Newtonian force law, the corrections taking two basic forms:

(1) When matter is in motion, additional gravitational fields (analogous to the magnetic fields produced by moving electric charges) are produced; also, moving bodies interact with gravitational fields in a motion-dependent way.

(2) Unlike electromagnetic field theory, in which two or more electric or magnetic fields superimpose by simple addition to give the total fields, in gravitational field theory nonlinear fields proportional to the second and higher powers of the source masses are generated, and gravitational fields proportional to the products of different masses are created.

Gravitational fields themselves become sources for additional gravitational fields. Examples of some of these effects are shown below. The acceleration A of a moving particle of negligible mass that interacts with a mass M, which is at rest, is given in the following formula, derived from Einstein’s gravitational theory.

The expression for A now has, as well as the Newtonian expression from equation (1), further terms in higher powers of GM/R2—that is, in G2M2/R4. As elsewhere, V is the particle’s velocity vector, A is its acceleration vector, R is the vector from the mass M, and c is the speed of light. When written out, the sum is

This expression gives only the first post-Newtonian corrections; terms of higher power in 1/c are neglected. For planetary motion in the solar system, the 1/c2 terms are smaller than Newton’s acceleration term by at least a factor of 10−8, but some of the consequences of these correction terms are measurable.

The first term is same as a Newtonian acceleration. Other terms have the velocity of the electromagnetic radiation c.

Is there something common in the electromagnetism and the gravitation?

Why no speech of the special theory of relativity?

Professor emeritus Ian McCausland (Department of Electrical and Computer Engineering, University of Toronto)proves in his article (A Question of Relativity, Apeiron, Vol. 15, No. 2, April 2008) that the special theory of relativity is non-verifiable and non-falsifiable.

He writes:

I suggest that scientists need to answer (Herbert) Dingle’s Question. Since the question was explicitly about the special theory of relativity, I suggest that the answer to the question should have the following properties:
  • it should provide a clear criterion to distinguish which of two clocks in relative motion the special theory requires to work more slowly, the applicability of the criterion to the case of the polar and equatorial clocks should be clear,
  • and the answer should not depend in any way on the general theory of relativity.
The world has been waiting more than thirty-five years for Herbert Dingle’s perfectly reasonable question to be answered.

If you did not understand what professor McCausland said you can read his article clicking here.

If you did not understand his article read all possible answers to professor Herbert Dingle (H. Dingle, “Dingle’s Question”, Nature 242, (6 April 1973), 423.) and think following:

  • Will the answers contain something which does not belong to the axioms or theorems of the special theory of relativity?
  • Will the answers contain something which is a part of the general theory of relativity but not a part of the special theory of relativity?
  • Why the different answers are very often in contradiction with the other answers?
  • Can you really understand the special theory of relativity?
  • Are you authoritarian personality?

Can the gravitation become the source for additional gravitation?

There are two answers:
  • If yes, why?
  • No.

All theories of gravitation are wrong

Dark matter

Dark matter is the name given to the amount of mass whose existence is deduced from the analysis of galaxy rotation curves using Newton's or Einstein's theories of gravitation but which until now, has escaped all detections. There are many theories on what dark matter could be. Not one, at the moment is convincing enough. It is possible that all theories of gravitation are wrong.

Dark energy

New evidence has confirmed that using Newton's or Einstein's theories of gravitation the expansion of the universe is accelerating under the influence of a gravitationally repulsive form of energy that makes up two-thirds of the cosmos.

Two-thirds of the cosmos is made of "dark energy" - some sort of gravitationally repulsive material.

The dark-energy story begins in 1998, when two independent teams of astronomers were searching for distant supernovae, hoping to measure the rate at which the expansion of the universe was slowing down.

The observations showed that the expansion was speeding up. In fact, using Newton's or Einstein's theories of gravitation the universe started to accelerate long ago, some time in the last 10 billion years.

It is possible that all theories of gravitation are wrong

What theories of physics can not explain

The dark matter component has much more mass than the "visible" component of the universe.

At present, the density of ordinary baryons and radiation in the universe is estimated to be equivalent to about one hydrogen atom per cubic meter of space.

Only about 4% of the total energy density in the universe (as inferred from Newtonian or Einsteinian gravitational effects) can be seen directly.

About 22% is thought to be composed of dark matter.

The remaining 74% is thought to consist of dark energy, an even stranger component, distributed diffusely in space.

Some hard-to-detect baryonic matter is believed to make a contribution to dark matter but would constitute only a small portion.

The vast majority of the dark matter in the universe is believed to be non-baryonic, which means that it contains no atoms and that it does not interact with ordinary matter via electromagnetic forces.

The non-baryonic dark matter includes neutrinos, which were discovered to have mass in recent years and unknown entities.

Unlike baryonic dark matter, non-baryonic dark matter does not contribute to the formation of the elements in the Einsteinian early universe and so its presence is revealed only via its gravitational attraction.

Alternative frames

Gérard Berger


Apeiron Vol. 15. No 3. July 2008 An Alternative Theory of Gravitation, Derived from the Fatio-Le Sage Theory Gérard Berger 14 Impasse des Carpeaux 94520 Périgny sur Yerres. France

It has been perhaps rediscovered by Bourbon (B. Bourbon, L’éther, Dunod, Paris (1948)), who did not mention any preceding authors.

Vacuum would be made up of gravitational corpuscles, several orders of magnitude smaller than the elementary material particles, moving with great speed and without mutual interactions.

An elementary material particle alone, surrounded by this medium which is supposed isotropic, would receive momentum from these corpuscles on all sides, and the resultant force would be null.

When there are two elementary material particles A and B, the resultant of the forces would be a mutual attraction, as shown by Le Sage: any point of B would be protected by the mass of A from the corpuscles circulating within the solid angle dω, that A subtends at a point of B, but would be subjected to the bombardment of corpuscles from the opposite solid angle.

The resultant of the momentum from corpuscles circulating in all other directions would be null. By reciprocity, B would protect the points of A from the corpuscles of the solid angle dω’, that B subtends at the points of A, and these points are then subjected to the action of the gravitation particles from the opposite solid angle.

Berger's results

Berger uses Fatio-Le Sage frame and demonstrates two formulas:
V2 = c2(1 + (4GM)/(rc2))
G' = G(1 + (4GM)/(rc2))
  • V is the speed of the gravitational corpuscles
  • r is the distance to the center of the body
  • M is the mass of the body
  • G is the common gravitational constant
  • G' is the gravitation constant for material particles.
  • c is the velocity of the electromagnetic radiation
  • the gravitation constant would be doubled when considering the gravitational interaction between a material mass and a photon
Berger's theory predicts the light deflection, the gravitational redshift, the Shapiro delay effect and the perihelion precession of Mercury but the last is too small.

Berger uses the Euclidean three-dimensional space.

Tuomo Suntola

Tuomo Suntola (Suntola, 2002, p. 162) has a correct value for the perihelion precession of Mercury but he is using four dimensions.

Matthew R. Edwards

Source: Apeiron, Vol. 15, No. 4. October 2008
Matthew R. Edwards Gerstein Science Information Centre University of Toronto Toronto, Ontario, Canada M5S 3K3
E-mail: matt.edwards@utoronto.ca

Assuming that the universe is not expanding and instead operating under conditions of general equilibrium, the author recently proposed that photons and gravitons are steadily being inter converted at fractional rates proportional to the Hubble constant, H0.

On the cosmic scale, the decay of photons was suggested to give rise to the cosmological redshift, while the decay of gravitons was linked to gravitation.

Used mathematics

Paul Kustaanheimo, late professor of applied mathematics and astronomy in University of Helsinki has written much of alternative mathematics. Part of his mathematics is published only in German. His theory of relativity (motor mechanics) is too complicated to be presented here.

The mathematics to transform curved spaces to linear spaces exists now.

My teacher, late professor of mathematics Raimo Lehti has been working with Paul Kustaanheimo. Raimo Lehti has supported the work of Dr. Tuomo Suntola.

Raimo Lehti asks in his book "Tieteen rannalla, 2004": "Is Einstein or Mandelbrot the prophet of the cosmos?" and answers: "Mandelbrot."

Mathematics is not the map of the reality. Mathematics is only a human tool. Professor Raimo Lehti tells in his book that it is possible to develop mathematics, which is completely different than human mathematics.

The paths of the electromagnetic radiation are often curved but we can not know that they are curved if we have no conception of what is a linear line.

The problem of the dark energy

The problem of the dark energy has been the most important problem in cosmology.

Teppo Mattson has made an enterprise to solve this problem using the Einsteinian frame in his academic dissertation Acceleration of the Cosmological Expansion as an Effect of Inhomogeneities, University of Helsinki, Finland, on March 27the, 2009.

He writes: (page 55)

The observations of light from various cosmological objects, in particular the type Ia supernovae, the cosmic microwave background and the galaxy distribution, seem to imply that the expansion of the universe has unexpectedly increased by a factor of 3/2 along our line of sight roughly during the latter half of the age of the universe.

Conventionally, the accelerated expansion has been ascribed to dark energy, a uniform fluid with large negative pressure that causes repulsive gravity.

However, it appears that accounting for the perceived acceleration by dark energy entails more questions than answers; most notably: how would the effects of the observed cosmic structures average out, why does the onset of acceleration coincide with the formation of voids and galaxy filaments, why would a quantum field arise at such an unnaturally low temperature T ∼ 4 K and why would Λ ∼ 10−123 G−1 and H0t0 ∼ 1 have such unexpected values.

In this thesis, we have studied the possibility that, instead of dark energy, the perceived acceleration of the expansion would be caused by the formation of nonlinear structures, ignored in the standard FRW cosmology.

We have identified three physical mechanisms as to how the inhomogeneities could explain the observations without dark energy:
  1. acceleration of the average expansion due to spatial variations in the expansion rate (often called back-reaction),
  2. faster local expansion rate due to a large local void and
  3. propagation of the detectable light mostly through the voids that expand faster than the global average.

(page 52)

Description Parameter Concor-
Transition redshift z0 0.35
Optical Hubble constant h 0.66
FRW Hubble constant _
Age of the universe to 14.8 Gyr
Baryon proportion _
Cold dark matter proportion _
Hot dark matter proportion _

Daniel Sunhede's dissertation


This thesis considers extended theories of gravity as a possible solution to the dark energy problem and in particular studies the impact of Solar System constraints on scalar-tensor theory and f(R) gravity.

The present observational status in cosmology and the basic properties of scalar-tensor theory and f(R) gravity are reviewed. The main work is then presented in four appended papers.

In summary, Solar System observations put strong constraints on both scalar tensor theory and f(R) gravity, in particular via the post-Newtonian parameter γPPN which is the main focus of this thesis.

The scalar-tensor theory discussed in the first paper is a model inspired by large extra dimensions. Here, two large extra dimensions offer a possible solution to the hierarchy problem and the effective four-dimensional theory is a dilatonic scalar-tensor theory exhibiting a cosmological behavior similar to quintessence.

It was shown that this model can also give rise to other types of cosmologies,some more akin to k-essence and possibly variants of phantom dark energy.

The observational limits on γPPN strongly constrain the scalar field coupling to matter, which together with the cosmological constraints nearly determine the model parameters.

The work presented in the three latter papers considered static, spherically symmetric space-times in f(R) gravity. The generalized Tolman -Oppenheimer -Volkoff equations were derived both in the metric and in the Palatini formalism of f(R) gravity.

By solving these equations for the configuration corresponding to the Sun, it was shown that metric f(R) gravity will in general fail the strong constraint on γPPN, whereas Palatini f(R) gravity will yield the observed γPPN ≈ 1.

However, the non-standard relation between the gravitational mass and the density profile of a star in f(R) gravity will constrain the allowed forms of the function f(R) also in the Palatini formalism.

Although solutions corresponding to γPPN ≈ 1 do exist in the metric formalism, a study of the stability properties of the spherically symmetric solutions reveals a necessity for extreme fine tuning, which affects all presently known metric f(R) models in the literature.

David Hume on miracles

'That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish....'

Moving body


If there is an electromagnetic background radiation in the space which is uniform in all directions it has an effect to the moving body.

It is well known that the energy of the electromagnetic radiation is proportional to the frequency of the radiation.

If the body is moving to different directions or if the body has different velocities, the radiation has different breaking effects.

When the velocity of the body is big the effect of the radiation to the body is big (the frequency of the radiation in the direction of the body will increase).

It is possible that the radiation can give to the accelerating body a constant velocity, if the body is absorbing or reflecting a big part of the radiation.

The definition of the place


There is no exact mathematical or physical definition of the place.



The energy of the cosmos

We use Dr. Tuomo Suntola's principle that the energy of the cosmos is zero.

Proper energy and virtual energy


There are several types of energy. We use the distinction
  1. Proper energy
  2. Virtual energy

The energy of the photon

Standard physics books tell us that the energy of the photon is

E = hν,

h is a constant and ν is an integer.

Niels Bohr found out in 1913 , that the light quanta or the photons have a spin, or an ability to rotate. Which is the energy of the rotation?

If explanations using red shift are true

If the source of the photon is moving away from us, ν decreases, and if the source of the photon is moving toward us, ν increases.

Then the energy of the photon can be arbitrary.

We can see only the photons coming toward us.

Is the discrete cosmos possible?

Some Finnish scientists said a half century ago that the discrete cosmos is possible, but now those scientist are dead.

Has a photon a mass?

Revised 10/12/2012

If we have no Einsteinian religion, we can easily see that the photon has a gravitational mass. The light is bending in gravitational fields was found in 1919.

The presumption that the photon has a mass is more simple than that it has no mass.

We are doing a new theory of relativity. We can change all Einsteinian postulates.

Photon can rotate because a mass can rotate.

Which is the half-life of the photon?

Einsteinian model says that photons does not feel a weak force which is the reason for the decay. We will not agree.

The formula E = mc2 is unverified

We have no reason to keep distance, time or mass as relative. Velocity and energy are relative.

The kinetic energy of the mass m and the velocity c can be
Ek = (mc2)/2

in a local frame but which is the amount of the other kinds of the energy is not known.

The formula m = E/c2 is against our definition of the mass

Last updated 1/1/2010

The article The Origin of Mass tells us that the origin of the mass is the energy. This is not true because m = E/c2 is not valid in our gravity theory.

The Einsteinian equation

E2 = mo2c4 + p2c2

is not valid in our gravity theory.

Photon has a micro-structure


Photon has a micro-structure and it is possible, that photon consists of several parts. Best known theory of several part photon says that photon contains neutrino and anti-neutrino.

Dark matter and photons


If there is dark matter with gravitation then the dark matter can change the direction of the moving of the photon.

Reality is not a human construction

Revised 10/12/2012

Mathematics is a human construction.

We can use different mathematics to make a coarsening of the reality. We have no real need to use curved straight lines or curved time.

The example of Dr. Tuomo Suntola has shown that it is possible to use mathematics which is simpler than the mathematics used by Albert Einstein.

Electron and positron

Electron–positron annihilation occurs when an electron and a positron (the electron's anti-particle) collide. The result of the collision is the conversion of the electron and positron and the creation of gamma ray photons or, less often, other particles.

There are only a very limited set of possibilities for the final state.

If the local energy of the particles is low, the most possible is the creation of two or more gamma ray photons.

If me is the mass of the electron and the mass of the positron is same, we have a local kinetic energy

Ek = (mec2)/2 + (mec2)/2

but this is not proving the formula E = mc2.

Is there a field without mass?

When I was young I was thinking that the change of the field can exist without masses in the neighborhood of the moving change of the field. Now I am thinking that the matter is hard, not soft. The hard core of the matter is the mass.


Written 12/27/2009

In physics, a quantum (plural: quanta) is the minimum unit of any physical entity involved in an interaction.

An example of an entity that is quantized is the energy transfer of elementary particles of matter (called fermions) and of photons and other bosons.

The word comes from the Latin "quantum", for "how much." Behind this, one finds the fundamental notion that a physical property may be "quantized", referred to as "quantization".

This means that the magnitude can take on only certain discrete numerical values, rather than any value, at least within a range. There is a related term of quantum number.

Distance, velocity and acceleration are not quantized.

The mass is quantized.

Energy is a manifestation of the matter and it contains the quantization of the mass.

The mass is not "a coefficient in the equation F = ma".

If there is a quantum of the mass, is the norm of the mass constant?

Is the mass a scalar?

Written 12/28/2009

If we write F = a m which is the difference to the formula F = ma?

Redefinition of the linear momentum

Written 12/28/2009

p = v m,

where p is the linear momentum of the body.

Possibility to make the difference between the mass and the energy

Written 1/27/2010

The frame of the physics must be able to make the difference between the mass and the energy.

The algorithms which does not do so must be rewritten. As my readers have said Einsteinian theories are circular.

Two axioms of Dr Tuomo Suntola

Written 7/16/2012

Two postulates of Dr. Tuomo Suntola (DU) are

"Distance and time are coordinate quantities independent of phenomena described."

There is no need to change these postulates.

The postulates of Einstein are too strong (See Einstein's Hidden Postulate, professor Robert J. Buenker, Apeiron, Vol. 19, No 3, July 2012).

Relations of the universal constants

The vacuum permittivity is today defined using equation

ε0 = 1/(c02 µ0)

where c0 and µ0 are defined maximum speed of the light and permeability of the vacuum.

In Tuomo Suntola's theory c0 is the speed of the expansion of the university. In my theory the universe is infinite.

It is possible that there is no maximum speed of the speed on electromagnetic radiation:

c0 = .

We know that in a very small scale this can be true.

The theory of the electromagnetic radiation

There is no good theory of the electromagnetic radiation.

We can begin with the light. We must make experiments with real spaceships. We can not use mirrors or lenses.

The problem is that the science does not believe to the necessity of such experiments.

The Maxwell equations can be wrong

Written 7/17/2012

It is possible that the Maxwell equations are wrong (see Apeiron, Vol. 19, No. 1, January 2012, Bringing Simultaneity Back to Life T. E. Phipps, Jr.).

Energy principles

If the radiating body is moving towards us, we will receive more energy than if it is moving away.

It is possible to measure both cases (using spaceships).

The amount of the energy will be different for simple Doppler effect and for Einsteinian Doppler effect.

What intelligent Eisteinians think

Written 7/18/2012

Late mathematics professor Rolf Nevanlinna was thinking that the simplicity of the theory is the reason for the selection of the space type, not empirical facts.

Different theories are under-determined.

There is no solution to the problem of simplicity.

Structural explanations or causal explanations

Written 7/19/2012

Einsteinian explanations are structural explanations. To be natural science physics needs causal explanations.

All explanations are human constructs.

Time is a human construct and we can choose how we will define time.

It we use time as independent variable we have no need to consider that the causality is broken.

Are there necessities in the nature

I agree wit David Hume that there are no necessities in the nature.

Logical necessities are human constructs to use coherent language.

Causality is not a necessity.

However we are waiting that the cosmology shall be a causal theory. To be a causal theory cosmology need physics, which is a causal theory.

The nature of mathematics

Mathematics is a human construction. Without interpretation mathematics tells nothing of reality. Human mathematics is stratified. No individual can make complicated computer programs using only binary language. (I have been four years SAS -programmer.)

Hafele-Keating experimet

In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory.

June 2010 the experiment was repeated, this time around the globe (London - Los Angeles - Auckland - Hongkong - London).

The result was that the different clocks in different environments were showing different times.

I have four rooms and a kitchen in my home in Helsinki. Clocks in different rooms will show different times.

I am not thinking that the time is different in different rooms.

The clock synchronization is easy. We have no need to define the time as a dependent variable.

Operational definition

An operational definition, also called functional definition, defines something (e.g. a variable, term, or object) in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman. One might use definitions that rely on operations in order to avoid the troubles associated with attempting to define things in terms of some intrinsic essence.

Properties described in this manner must be sufficiently accessible, so that persons other than the definer may independently measure or test for them at will.

The special theory of relativity can be viewed as the introduction of operational definitions for simultaneity of events and of distance, that is, as providing the operations needed to define these terms.

We will not use operational definitions. We oppose operational definitions.

Straight line

Written 7/22/2012

The Euclidean line is the only straight line.

The path of the photon is not a straight line.

The path of the photon is ellipse, hyperbola or parabola or anything else than the straight line.

In the everyday measuring the path of the photon is near the straight line.

Einstein's vicious circle

Einstein's elevator experiment is a vicious circle. Any force has the same effect than the gravity.

The cause of the popularity of the elevator experiment is the fact that the gravitation has an effect to all cells of the man.

Why it is not intelligent to use a curved space in physics

Written 7/24/2012

Computers can use complicated formulas but in a real world we will need information of the whole of the universe. Relativity theories split the reality to incompatible parts. There are infinite number of local spaces ( source: discussions with late professor of mathematics and astronomy, Paul Kustaanheimo).

The curvature can not explain the gravity.

The impossibility in the reality is different from the impossibility in logic.

Space and field

Space is a mathematical construction. The field is a part of the physical reality.

Newtonian or Einsteinian black holes

My opinion is that the Einsteinian black holes and the Einsteinian Big Bang are pseudo-science. There are no singularities in the nature.

Are Big Bangs possible

Revised 10/12/2012

The theory of the Big Bang does not explain why Big Bang happened.

If the Einsteinian theory of black holes is true, the Big Bang is impossible.

If black holes can explode then local Big Bangs are possible.

Big Bang believers think that the speed of the radiation was over the speed of the electromagnetic radiation in the beginning. This is an Anti-Einsteinian proposition.

We can define that the space is infinite. We can expect that the matter in the infinite space has an equilibrium.

If there was a big bang and if the black holes are very stable it is possible that there was black holes before the big bang (Black Hole Era 1040 years to 10100 years ).

Independent and dependent variables

We shall collect theory independent data of physics. We shall use statistics to determine which variables are dependent and which variables we can choose to be independent. We can use factorial analysis and some newer methods of the statistics - and expensive computer programs.

Are black holes elementary particles

Written 7/25/2012

If black holes have no other properties than Einsteinians say, the black holes are elementary particles. If so, there can be elementary particles with arbitrary mass.

Waves in a vacuum

This is functioning in a vacuum.

A new problem: The physics confuses mass and energy

Written 7/25/2012

It is not possible to find real masses of elementary particles. The physics confuses masses and energy.

It is very difficult to change the Einsteinian physics to the Newtonian physics. I have full competence to use mathematics and computers but it is very difficult to find the real data.


There is no good definition of the the energy. Einsteinian faith is now used in the teaching of mechanics.

Is there pure energy

It is possible that there is pure energy. If there is pure energy this energy can be electromagnetic radiation. But it is not necessary that there is pure energy.

It is possible (as several Non-Einsteinians think) that the photon has for example the mass mf and this has a kinetic energy (mfc2)/2 which is the energy which the electron is losing.

It is possible that the photon has several parts (neutrino and anti-neutrino).

It is possible that a photon has rotational energy and other forms of energy.

Explanation of the mass

Written 7/27/2012

Mass needs no explanation.

The graph of the strong force

There is no dark matter. Gravitation has same kind graph than strong interaction (if there is a strong interaction).

Additionally the gravitational field is not symmetric.

The problem is very complicated and it is difficult to make any Non-Einsteinian calculations.

There are no universal forces. The nature has independent parts.

Black holes

Written 7/28/2012

If the gravitation has same kind of graph than other interactions, there are no real black holes.

Simple functions

Written 9/12/2012

Very simple function which has a form of the graph of the strong force is

f(x) = a/x3 - b/x2.



f(x) = 1/x3 - 1.5/x2.

All rational functions

f(x) = - a1/x2 +a2/x3 - ... +a2n-1/x2n-1

have the same form.

The derivatives of the functions f(x) = - a1/x2 +a2/x3 - ... +a2n-1/x2n-1
have the same form.

To avoid the infinite repulsion we can replace x by ex.

If we will have some periodicity we can add some trigonometrical functions:

We can also add damped oscillation an we will get oscillating universe. To exclude the oscillating universe we must have an exact theory of gravity.

We have an infinite amount of the possible functions but we must find some explanation for the function. We will do it later.

Functions with zero points


If we will have zero pints at x = 1 and x = 3 we can use function (blue curve)

f(x) = k(x-1)(x-2)/x3.

Inverse cube will be found in the case of the dipole and the electric charge .

The nucleus of the proton is a dipole plus an electric charge.

Which is the speed of the strong force

Written 11/10/2012

If the strong force has a speed it is as problematic than the electromagnetic force (same paradoxes).

Which masses are real

Written 7/30/2012

Most calculations of the masses of the elementary particles are using Einsteins relativity theory.

We must make new calculations.

Quarks, leptons and other particles

There are people who say that there is no strong or weak force.

We can additionally suppose that quarks and leptons are not elementary.

If so we have no problem with fractional charges.

It is possible that there is only one fundamental force.

Cosmic microwave background radiation

Written 7/31/2012

Einsteinians tell us that the cosmic microwave background radiation radiation was emitted 13.7 billion years ago, only a few hundred thousand years after the Big Bang, long before stars or galaxies ever existed. Thus, by studying the detailed physical properties of the radiation, we can learn about conditions in the universe on very large scales at very early times, since the radiation we see today has traveled over such a large distance.

The calculations are made using Einstein's relativity theory.

The real sources of the radiation can be whatever else.

Neutral elementary particles

Photon, gluon, neutrino, Z0 boson, Higg's boson and graviton are without charge.

There is no evidence of the existence of the graviton.

The evidence of the existence of the Higg's boson is weak.

The standard model supposes that most of the neutral elementary particles are without rest mass.

We suppose that all elementary particles have a rest mass. It is possible, that supposed neutral particles have several parts which have charge. If so then the electromagnetic force between the parts is very strong.

It is possible that all fundamental forces are electromagnetic forces.

The difference of the neutron star and the black hole


Amount of mass.

Which is the cause of the inertia

Proposal: The acceleration of the body which has several parts produces internal energy to the system.

Problem: How the energy can survive in a moving body.

Action and reaction

The third of Newton's laws of motion of classical mechanics states that forces always occur in pairs. This is related to the fact that a force results from the interaction of two object. Every force ('action') on one object is accompanied by a 'reaction' on another, of equal magnitude but opposite direction. The attribution of which of the two forces is action or reaction is arbitrary. Each of the two forces can be considered the action, the other force is its associated reaction.

If we have a body with the mass m and if we divide it to two parts, we have masses m1 and m2 and if the parts are exploding to opposite directions, they will have kinetic energies

(m1v12)/2 and (m2v22)/2.

The energies are equal and the total energy is

m1v12 or m2v22

If we divide the body with mass m to equal parts and continue the dividing to infinity we will get series of energy of the parts:

mv2(1/2 + 1/4 + 1/8 + 1/16+ ... ) = mv2.

Einstein's distance d


s is the distance, (x,y,z) is the place, c is the speed of the light and t is the time.

ds2 = dx2 + dy2 + dz2 - c2dt2

Source: Relativity: The Special and General Theory © 1920
Publisher: Methuen & Co Ltd
First Published: December, 1916
Translated: Robert W. Lawson (Authorised translation)

If we put

ds2 = dx2 + dy2 + dz2 + dt2

then dt2 has a wrong dimension. The time t is not a dimension.

If we divide the equation

ds2 = dx2 + dy2 + dz2 - c2dt2

by dt2 we will have the equation
ds2/dt2= dx2/dt2 + dy2/dt2+ dz2/dt2- c2

This equation says that the speed of the light is the maximum speed. As we know this supposition leads to the infinite amount of local spaces (I agree with the late professor of mathematics and astronomy Paul Kustaanheimo).

In our reality we need only one space. We will need no acrobatics with complicate mathematics.

The thesis of Hartikainen


It is possible to construct a clock which is independent of the gravitation.

Additive units


Distances are not additive. Velocities (v), accelerations (a), forces (F) etc. are additive (vectors).

Velocities of small and big masses


A body with a big mass need much of energy to have a high speed.

It is the task of the experimental physics to find out which is the highest possible speed and why it is the highest possible.

Memory of acceleration

Which kind of body has a memory of its accelerations?

The new clock paradox

If we have a clock which can slow down when the speed is increasing we have a new clock paradox.

Definition of the timeTime


Let x = (x1, x2, x3,...,xn) be a continuous vector-valued function defined on an interval [a,b]. The image of [a,b] under x is a curve Γ.

Let a parametric representation of x be x(t).

We call the parameter t time.

Simultaneous cause and effect


I have no money to read new scientific journals. I can only read scientific news.

If the news are correct, the situation now (9/29/2012) is following:

  1. It is possible to separate a single photon.
  2. It is possible to double a single photon.
  3. It is possible to change the state of the single photon.
  4. The other of the two new photons will have the same new state.

If all of this is true, we have simultaneous cause and effect.

Curvature and torsion


At the regular points of Γ we define the unit tangent T as follows:

A point x(t) is called a regular point of Γ if the derivative x'(t) exists and is non-zero, in which case x'(t) is called the tangent vector at this point. Points where x'(t) fails to exist or where x'(t) = 0 are called singular points of Γ.

At the regular points of Γ we define the unit tangent T vector as follows.

T(t) = x'(t)/|x'(t)|.

The non-negative function κ defined by equation

κ(t) = |T'(t)|/|x'(t)|

is called a curvature of the curve.

At those points of Γ for which t'(t) ≠ 0 we define the unit principal vector N by the equation

N(t) = T'(t)/|T'(t)|.

The length of arc is s(t) = ∫a t|x'(u)| du.

T'(t) = κ(t) s(t) N(t).

The unit vector B defined by the equation

B(t) = T(t) X N(t)

is called binormal vector.

It is easy to verify that B'(t) is a scalar multiple of N(t).

The real valued function τ defined by the equation

B'(t) = - τ(t)s'(t)N(t)

is called the torsion of the curve.

Einsteinians speak of the curvature of the four dimensional space. Is there the torsion of the space?

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements


Phys. Rev. Lett. 109, 100404 (2012) [5 pages]


Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg
Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, 60 St. George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7

[Selected for a Synopsis in Physics] [Editors' Suggestion] Received 4 July 2012; published 6 September 2012

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as “Heisenberg’s uncertainty principle,” Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create.

Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle.

Here, we experimentally observe a violation of Heisenberg’s “measurement-disturbance relationship”, using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus.

Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.

© 2012 American Physical Society

Repulsion and attraction


To explain repulsion all you need to do is draw a Feynman diagram with two electrons swapping a photon. The photon conveys momentum between them.

There simply isn't any good explanation for electromagnetic attraction.

If we assume that there are two kind of photons (and two kinds of other same type of particles), we can explain the attraction without uncertainty principle.

My opinion is, that the uncertainty principle is not an explanation.

In the 20th century, the Fatio-Lesage concept of gravity attracted the interest of Richard Feynman, who used it more than once to illustrate various aspects of theoretical models. For example, in a series of public lectures given in 1964, published as “The Character of Physical Law” in 1965, Feynman described Fatio’s model as an example of the kind of theory that might satisfy someone’s desire for an “explanation” – rather than just a description – of gravity. Feynman’s notion of a mechanism was something that “gets rid of the mathematics”.

Manipulating the frequencies of the photons

Different photons in, indistinguishable photons out

A recent experiment demonstrates that nonlinear optics can erase frequency differences in photons emitted by solid-state devices.

See http://www.physicstoday.org/daily_edition/physics_update/different_photons_in_indistinguishable_photons_out

September 17, 2012

Published: September 17, 2012

Device fabrication being an imperfect art, single photons from solid-state systems such as quantum dots are not identical; a collection of dots designed to emit at nominally the same frequency will actually produce a range of frequencies. That phenomenon, called inhomogeneous broadening, is an obstacle to experimentalists who need a stream of identical photons—say, in applications requiring entanglement.

One way to overcome the obstacle is to tune the solid-state devices themselves; applying appropriate strains, for example, can change the internal structure of the devices so they all give off photons of the same frequency. Now Kartik Srinivasan of NIST, his postdoc Serkan Ates, and other collaborators have demonstrated an alternative approach: Let the devices emit as they will, but use nonlinear optics to convert the frequencies of the resulting photons. When a source photon and light from a pump laser interact in a nonlinear crystal, the result could be a photon whose frequency is the sum of source and pump frequencies.

As schematically indicated in the figure, with carefully tuned pump-laser frequencies ωp1 and ωp2, Srinivasan and colleagues produced photons with the same frequency ωc from input photons of different frequencies ωs1 and ωs2. The research team established that the output photons were indeed identical by observing their telltale interference. In the future, such frequency conversions may enable photons to communicate between the nodes of a quantum internet. (S. Ates et al., Phys. Rev. Lett., in press.)—Steven K. Blau

How a single photon can stop the black hole

If we suppose that there is background radiation everywhere in the space and if we suppose that the energy of the photon is inversely proportional to the photons wavelength then a single photon from the background radiation will prevent every material body to move with the speed of the background radiation.

If we will move faster we must find a place without electromagnetic radiation.

This means that the background radiation will limit the speeds of the bodies. The background radiation forms the "absolute space".

Locally we have much more radiation and local limitations of the speed of the material bodies will vary.

Are the following pictures correct


π0 → 2 γ

π0 → γ + e + e+

If this is correct, can we say that the matter is photons and neutrinos?

The neutrino theory of light

The neutrino theory of light is the proposal that the photon is a composite particle formed of a neutrino-anti-neutrino pair.

The main argument against the neutrino theory is: Since mass-less neutrinos are needed to form a mass-less photon, a composite photon is not possible.

We have said earlier that the photon has a mass.

If this is correct we can say that the matter is neutrinos.

Are neutrinos the main component of dark matter?

There is a large debate right now in the physics community about whether neutrinos are the main component of the dark matter of the universe. And the idea that neutrinos can explain dark matter is starting to pick up in the physics community.

Is the black hole a very big neutrino?


Is this the attraction?

Real attractive forces


It is verified that there is an attractive force between the electron and the proton.

The proton of the standard model.

The proton of the alternative physics.

Now we have a problem of the attractive force in the proton.

Coulomb's law


William Watson and Benjamin Franklin introduced the one-fluid theory of electricity independently in 1746.

Henry Cavendish attempted to explain some of the principal phenomena of electricity by means of an elastic fluid in 1771.

Not contented with the above mentioned one fluid theory of electricity, du Fay, Robert Symmer and C. A. Coulomb developed a two-fluid theory of electricity from 1733 to 1789.

John Bernoulli introduced a fluid aether theory of light in 1752. Euler believed that all electrical phenomena is caused by the same aether that
propagates light.

In 1821, in order to explain polarization of light, A. J. Frensnel proposed an aether model which is able to transmit transverse waves. Inspired by Frensnel’s luminifeous aether theory, numerous dynamical theories of elastic solid aether were established by Stokes, Cauchy, Green, MacCullagh, Boussinesq, Riemann and William Thomson.

In 1861, in order to obtain a mechanical interpretation of electromagnetic phenomena, Maxwell established a mechanical model of a magneto-electric medium.

Maxwell’s magneto-electric medium is a cellular aether, looks like a honeycomb. In a remarkable paper published in 1864, Maxwell established a group of equations which were named after his name later.
In a remarkable paper published in 1905, Einstein
abandoned the concept of aether (A. Einstein, Ann. Phys. 17, 891 (1905)).

Xiao-Song Wang writes:

"We speculate that the universe may be filled with a continuum which may be called aether. Based on a spherical source and sink model of electric charges, we derive Coulomb’s law of interactions between static electric charges in vacuum by methods of hydrodynamics. A reduced form of the Lorentz’s force law of static electric charges is derived based on a definition of electric field."

Xiao-Song State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China (Dated: February 2, 2008)

Wikipedia says:

Coulomb's law states that the magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them.

F21 = (q1 q2/4π ε 0 r2)r21

No explanation.

Why Einstein stopped all explanations?

Einstein's aether

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

Albert Einstein, An address delivered on May 5th, 1920, in the University of Leyden

Problems of the explanations

Human explanations will always be restricted. We can not know where are the borders of the explanations. My opinion is that the Einsteinian borders are too strong.

If we are using hydrodynamics (Xiao-Song) the problem is that we have only a set of equations.

It is possible that the particles are (as Einstein said) fields, but I think that we must use particles as much as we can.

Tensions and tensors are problematic


Both Einstein and the representatives of new aether theories are using tensors in the theory of the gravity.

Dr. Tuomo Suntola does not need tensors in hist book Dynamic Universe. He is using vectors and vector fields.

I agree with Dr. Suntola in many points. The only problems of his theory are infinity points and the complex fourth dimension (it is not the time). He knows that they are problems.

Why do objects fall at the same rate of acceleration?

Revised 10/10/2012

Democritus (Greek: Δημόκριτος, Dēmokritos, "chosen of the people") (ca. 460 – ca. 370 BCA) was an Ancient Greek philosopher born in Abdera, Thrace, Greece.

Democritus was not Einsteinian.

The atomists held that there are two fundamentally different kinds of realities composing the natural world, atoms and void.

The gravitation is the force which has the same effect to the particles of the same mass.

electron mass = 9.10938188 × 10-31 kg
proton mass = 1.6726 x 10-27 kg
neutron mass = 1.6749 x 10-27 kg

In practice all bodies are formed of protons, neutrons and electrons.

In the scale of the galaxy there is no good theory of the gravitation (the problem of the dark materia).

In the scale of the atom the other forces are stronger that the gravity.

We have no cause to change the conception of Democritus.

If the photons fall with the dirrent rate than the other objects the Einsteinian equivalece principle is wrong.

(All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass.)

The changing of the coordinate system

The changing from the linear coordinate system to the curvilinear coordinate system will not change the object.

My main argument against Einstein is that the use of the curved space will not give different results than the use of the linear space.

The use of the path of the photon as a basis of the mathematics will not change the physical objects. If we will we can always use Euclidean space.

If the physicists will get different results with different coordinate systems they are calculating wrong.

Local and universal

I think that Einsteins theories can not make the separation of the local space and the universal space. In this I agree with Dr. Tuomo Suntola.

Is there rotation and acceleration

Mach was thinking that it is not possible to observe the rotation in a completely empty space. I think that we can observe both rotation and acceleration.

Redshift and blue-shift

In physics (especially astrophysics), redshift happens when light seen coming from an object that is moving away is proportionally increased in wavelength, or shifted to the red end of the spectrum. More generally, where an observer detects electromagnetic radiation outside the visible spectrum, "redder" amounts to a technical shorthand for "increase in electromagnetic wavelength" — which also implies lower frequency and photon energy in accord with, respectively, the wave and quantum theories of light.

The relativistic redshift is different than the classical redshift.

If we use the classical redshift we observe that the galaxies are moving away in proportion to the square of the distance (it is easy to calculate this using observational material for schools).

There are few galaxies that have a blue-shift.

Proposal for the electromagnetic elementary particles

The standard model of the physics has no masses.

There is no experimental material for electromagnetic elementary particles, but we can speculate.

We define:

e- = e- + e- + e- + e- + e+ .

I will call e- as negattiny (© Erkki Hartikainen) and e+ as posittiny (© Erkki Hartikainen).

The form of the e- is a tetrahedron.

We define:

e+ = e+ + e+ + e+ + e+ + e- .

The form of the e+ is the tetrahedron.

We define:

p+ = (e+ + e+) + (e+ + e+)+ e- .

We define:

n0 = (e+ + e+)+ e- + e- .

Possible cause to the uncertainty

It is possible that the proposed electromagnetic substructure of the electron is the cause to the apparent uncertainty of the place of the electron.

Where do photons come from?

The electron can emit and absorb photons. It is possible that the micro-structure of the electron will explain the origin of photons.

Which is the size of the photon?


When I was a child we were using radio waves with the wavelengths of several kilometers.

Try to ask the explanation for the big size of the particle. I expect that you will get no explanation.

Intrinsic equations of a space curve


For a particular curve C, the curvature κ and torsion τ are functions κ(s) and τ(s) of arc length s as measured from some fixed point on C.

As we move along curve C the tangent is turning in the direction of the normal at a rate determined by the curvature κ(s) while the osculating plane rotates around the tangent with a speed determined by the torsion τ(s).

It can be shown that two curves with the same curvature and torsion as functions of arc length are identical except for position and orientation in space (i.e. one of them can be rigidly moved so as to coincide with the other).

Thus the curvature κ(s) and torsion τ(s) describe all the essential, invariant properties of the curve. The equations

κ = κ(s)

τ = τ(s)

are called the intrinsic or natural equations of the curve.

Example 1:
the circle equation is

κ = 1/r,

τ = 0.

If we will add some Einsteinian physics we define the time t as follows:

t = t(s).

Example 2:

t = 2s,

dt = 2ds,

ds/dt = ½ = v = velocity.

Example 3:

t = s½ ,

dt = [1/(2s½)] ds,

ds/dt = 2s½ = v.

Space-independent time


In this book we define that the time is independent of the place and of the speed.

The speed v is dependent of the time and of the distance:

ds/dt = v.

The time is not the speed of the clock.

Lower bounds and upper bounds


Are there physical lower bounds or/and upper bounds.

The absolute zero temperature, -273,150C is a sensible lower bound but are there other lower bounds or upper bounds.

Einsteinians argue that there are the zero mass and the maximal speed.

The vacuum has the zero mass but are there particles with zero mass? Einsteinians argue that the particles of the electro-magnetical radiation has the zero mass.  I disagree.

Einsteinians argue that the speed of the electro-magnetical radiation is the upper bound of the speed. I disagree.

Which is the speed of the vacuum?

We must consider the cause of the speed of the particle in a system. There are different causes for the accelerations. For example:
  • the collisions of the particles
  • the scattering of the particles
  • the radiation (of the particles?)
The velocities are dependent of the properties of the particles.

Can we divide photons or can the photons scatter?

What we can observe with our instruments


If we have a rotating solid body in the space between galaxies we can observe the rotation and the axis of the rotation. This rotation defines the internal time of the body.

We can not observe the constant linear acceleration of the body. We can only observe the change of the acceleration of the linear movement of the body.

If we are falling free we have an acceleration but we can not observe it.

Is the big bang possible


It is not logically impossible. But it is physically impossible. Very big masses form black holes. We do not know a single black hole which has exploded.

Philosophically the big bang is only a hypothesis that there is one black hole which has exploded.

The falling of the rotating solid body


If we are using the rotating body as a clock we can test relativity theory as follows.

We will send several rotating solid bodies with  much of speed to the space. The body has an instrument which measures the angular speeds and sends the results to the earth.

We can make generalizations using computers.  

The test is not deciding which of the relativity theories is true but it will test if the rotating solid body is a good clock.

Nothing in the special relativity theory is true

The Growth of the masses?


There are discussions in Internet which talk over the growth of the masses of the distant galaxies. The physicists say that the special relativity is not true in the cosmology. Masses of the distant galaxies are not bigger than the masses of the near galaxies.

Where the distant galaxies are?


We do not know. Our last information is about 13 billions of years old. It is not sure that the distant galaxies still exist.

We do not know. Our last information is about 13 billions of years old. It is not sure that the distant galaxies still exist.

Is the space expanding?


It depends on the what we mean with the word "space".

My opinion is that the space has not the property of expand.

Is there a space?


The space is a mathematical abstraction. The stretching is a physical abstraction.

The stretching of the scale will not cause the redshift  or the change of the gravitational fields. Only the real motion will cause the redshift.



I do not know any good explanation for the inertia. 

My opinion is that the Le Sage-type gravitation can explain both inertia and in-determinism.

If there was a black hole before the big bang

If Hawkings's theory of black hole radiation is correct


If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time because they lose mass by the emission of photons and other particles. The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.

Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrink.

To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole needs to have less mass than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter.

If a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. 

If there was no cosmic microwave background radiation before the big bang then the black hole had an infinite time to evaporate. 

So the black hole did not explode because there was no black hole.

Is the known universe a closed system?


This is impossible to prove.

Why we are in the center of the known universe?


We have shown that the space is not expanding. The the origin of the redshift is the motion or the property of the light. It the distant galaxies are near of the border of the known universe, we are near of the center of the universe. 

If the known universe is not a closed system it is possible that we are not in the center of the real universe.

Pulling or pushing?


The pushing is easy to explain but what is the pulling? The pulling is not easy to explain in an atom and it is much more difficult to exlain in the space.

David Hume on miracles


The text

In the 19th-century edition of Hume's Enquiry (in Sir John Lubbock's series, "One Hundred Books"), sections X and XI were omitted, appearing in an Appendix with the misleading explanation that they were normally left out of popular editions. Although the two sections appear in the full text in modern editions, chapter X has also been published separately, both as a separate book and in collections.

The argument

Hume starts by telling the reader that he believes that he has

"discovered an argument [...] which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion".

Hume first explains the principle of evidence: the only way that we can judge between two empirical claims is by weighing the evidence. The degree to which we believe one claim over another is proportional to the degree by which the evidence for one outweighs the evidence for the other. The weight of evidence is a function of such factors as the reliability, manner, and number of witnesses.

Now, a miracle is defined as:

"a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent."
Laws of nature, however, are established by

"a firm and unalterable experience";
they rest upon the exception-less testimony of countless people in different places and times.

"Nothing is esteemed a miracle, if it ever happen in the common course of nature. It is no miracle that a man, seemingly in good health, should die on a sudden: because such a kind of death, though more unusual than any other, has yet been frequently observed to happen. But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country."

As the evidence for a miracle is always limited, as miracles are single events, occurring at particular times and places, the evidence for the miracle will always be outweighed by the evidence against — the evidence for the law of which the miracle is supposed to be a transgression.

There are, however, two ways in which this argument might be neutralized. First, if the number of witnesses of the miracle be greater than the number of witnesses of the operation of the law, and secondly, if a witness be 100% reliable (for then no amount of contrary testimony will be enough to outweigh that person's account).

Hume therefore lays out, in the second part of section X, a number of reasons that we have for never holding this condition to have been met. He first claims out that no miracle has in fact had enough witnesses of sufficient honesty, intelligence, and education. He goes on to list the ways in which human beings lack complete reliability:

  • People are very prone to accept the unusual and incredible, which excite agreeable passions of surprise and wonder.
  • Those with strong religious beliefs are often prepared to give evidence that they know is false,
"with the best intentions in the world, for the sake of promoting so holy a cause".
  • People are often too credulous when faced with such witnesses, whose apparent honesty and eloquence (together with the psychological effects of the marvelous described earlier) may overcome normal skepticism.
  • Miracle stories tend to have their origins in "ignorant and barbarous nations" — either elsewhere in the world or in a civilised nation's past.
  • The history of every culture displays a pattern of development from a wealth of supernatural events – "[p]rodigies, omens, oracles, judgements" – which steadily decreases over time, as the culture grows in knowledge and understanding of the world.
Hume ends with an argument that is relevant to what has gone before, but which introduces a new theme: the argument from miracles. He points out that many different religions have their own miracle stories.

Given that there is no reason to accept some of them but not others (aside from a prejudice in favour of one religion), then we must hold all religions to have been proved true — but given the fact that religions contradict each other, this cannot be the case.

The miracle of the big bang

The einsteinian theory of the big bang is an extrapolation towards a state (a black hole) which can not explode.

We mus compare the two alternatives:

  1. There was a miracle.
  2. The extrapolation is wrong.
If we will accept Hume's article on miracles, we must accept the second alternative.

Le Sage-type big bang

If we will accept the Le Sage-type gravitation the big bang is possible.

If the very big black hole moves to the place where there are no Le Sage-type particles the black hole begins to expand and it is possible that it will explode.