Sampling Universe Theory

Expansion of the Universe and its acceleration

The Sampling Universe Theory provides a natural and simple explanation for the expansion of the universe and its acceleration. In a sampled universe, the forces of gravitation are cancelled past a critical distance. But particles can travel in empty space without limit, so that over long distances the radiation pressure from the stars prevails and is causing the expansion of the sampled universe.

3. Current facts: the red shift, the expansion of the universe and its acceleration

By using spectrometers, astronomers can observe the individually colored components of the light we receive from stars and galaxies. The spectrometer is producing some kind of a rainbow which is called a spectrum.

When looking at the spectrum of the Sun, we see a pattern of dark bands which are the signature of its chemical composition. When looking at the spectrum of a distant galaxy, wee see the same pattern of dark bands, but shifted towards the red part of the spectrum. This means that:

1. Distant galaxies are made of the same matter as our Sun

2. The frequency of the light from distant galaxies is lowered

Consequence : homogeneous universe and isotropic expansion

The only way to explain these lower frequencies is to consider that the galaxy is receding. The frequency of the light is lowered, like the sound of a car moving away from us. As the red shift is increasing with distance, this means that our universe is expanding.

After measuring thousands of galaxies, it has been discovered that this expansion is isotropic (the universe looks the same way in all directions) and that the universe is homogeneous (the universe has roughly the same smooth mixture of material at every location.) That is important to consider these two facts when trying to build a theory.

Acceleration of the expansion

1998 was a year of great surprises for cosmologists. According to theories of the times, the universe should eventually collapse under the effect of the forces of gravitation. But it was discovered by an international team of astronomers that the expansion of the universe was in fact accelerating. Cosmologists had to invent a new kind of energy, the dark energy, in order to explain that acceleration.

So, in brief, the observed facts are:

The spectrum from distant galaxies is red shifted
The universe is expanding
The expansion is isotropic
The expansion is accelerating

These facts are simple enough, but that is more difficult to build a satisfying theory.

1. The forces of gravitation become null over long distances

The statement that the forces of gravitation become null over long distances is not part of classical gravitational theories. But that would be a natural consequence of the sampling hypothesis, which is itself a logical consequence of quantum mechanics.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well confirmed by observations. Hence we are using it as our start point.

Space-time bending

According to General Relativity, the presence of matter changes the geometry of spacetime, and this curved geometry is causing gravity.

The picture to the left represents a two-dimensional analogy of the space-time distortion caused by a massive body. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity.

The light follows the curvature of space and is
bent by the gravitational field.

Sampled curvature

According to the sampling universe theory, space is sampled (the length of Planck being the sampling resolution), so that the curvature of space is sampled too.

This means that when we are far enough from the mass causing the curvature, the curvature of space becomes smaller than the length of Planck, hence it becomes in fact null and gravity is cancelled.

4. Current theories: Big Bang, Cosmic Inflation and Dark Energy

Appendix:
Evaluating the radiation pressure from our local group of galaxies on another galaxy

2. Radiation pressure is strong enough to cause the expansion

The example of comets

Radiations from the stars exert a pressure when they encounter a body.

For example radiation pressure from the sun is creating the tail of comets. The picture to the left shows the Hale-Bopp comet in March 1997:

Spatial Distortion grid

Sampled curvature

Classical continuous curvature

Spatial grid

Spatial resolution

Critical distance

Null gravity

Curvature

The figure above is comparing the classical curvature with the sampled curvature.

With the formulas of classical general relativity, the curvature (blue curve) is a continuous function of space, time and mass and is allowed to become infinitely small.

With the sampling hypothesis, space is discrete, so that the curvature of space (in green) cannot become infinitely small: when it becomes smaller than the length of Planck, it is cancelled, hence gravity is cancelled.

Why is the body of a comet not repelled by radiations, but its tail is?

The answer is very simple: the acceleration from radiation pressure increases as the size of the body decreases. When applied to dust and gas, radiation pressure becomes quite noticeable.

Basic formula

When radiations encounter a body, they exert a pressure which is communicating an acceleration to that body, according to the formula:

Acceleration = (Pressure x Surface) / Mass
When the diameter of the body is divided by 2, its surface is divided by 4 but its mass is divided by 8, hence the acceleration is multiplied by 2.

Dust and gas repelled by radiation pressure are forming the tail
The main body of the comet is not affected by radiation pressure

Now we have to consider a very important feature of the universe:
98% of the mass of galaxies is made of hydrogen and helium, in molecular and dust form.

So galaxies are very sensitive to radiation pressure, even over intergalactic distances. As gas and dust form 98% of the total mass of galaxies, they attract the remaining 2% which are stars and planets. Eventually the whole galaxy is propelled by radiation pressure.

In brief, over intergalactic distances, past a critical distance, the forces of gravitation are cancelled when the acceleration from radiation pressure is strong enough to propell galaxies. Hence the universe is expanding.

Now we can compare this result with current facts and theories.

The following section is providing an estimation of the acceleration exerted by our local group of galaxies on another galaxy placed at the level of the critical distance between attraction and repulsion.

That is a rough estimation only, as we are interested only in order of magnitudes, in order to check whether actual accelerations from radiation pressure are strong enough to propel galaxies.

Principle of a quantitative evaluation

The assumptions made are in agreement with the generally accepted data from current cosmology.

1. We consider the example of our local group of galaxies
2. The local group is the "source", the radiation emitter
3. We assume that the local group includes 700 billion stars
4. We consider that the main mass of each galaxy is made of dark matter
5. We consider that dark matter is made for the main part of gas
6. Hydrogen is the dominant gas in the universe
7. So we place atoms of hydrogen at the zero acceleration limit
8. We calculate the acceleration of gas caused by radiation pressure
9. We compare it with the acceleration of the expansion of the universe

Eventually we find that the acceleration from radiation pressure is similar to the acceleration of the expansion of the universe.

We are using the example of our local group of galaxies, as the zero acceleration limit has been accurately measured. This limit separates the inner region, in which the gravitation of the galaxies dominates, from the outer region, in which the expansion of the universe dominates.

If now we assume that at the zero acceleration limit, in the frame of the theory of the sampled universe, the forces of gravitation are too weak to exist, the pressure of radiation is sufficient to explain the expansion of the universe.

Basic units and symbols

* Is the symbol of multiplication (from C language)
Pa = Pascal = unit of pressure
Distance from Sun to Earth = Astronomical Unit (Symbol AU)
1 Megaparsec (symbol Mpc) ~ 2.0 * 10¹¹ AU
Basic data from current observations of the universe
(1) Radiation pressure from Sun to particles ~ 2.2 * 10^-5 Pa
(2) Zero acceleration limit for our local group of galaxies ~ 2 Mpc
(3) Number of stars in our local group ~ 700 billion
(4) Size of an atom of hydrogen ~ 10^-10 m
(5) Mass of an atom of hydrogen = 1.7 * 10^-27 kg
(6) Hubble acceleration (expansion rate) ~ 6.9 * 10^-10 ms^-2

Formulas

1) Radiation pressure at a 2 Mpc distance

1a) Radiation Pressure from the Sun at a 2 Mpc distance (RPS):
Radiation Pressure obeys the inverse distance square law, hence
RPS = (2.2 * 10^-5) / (4 * 10¹¹)² = 1.4 * 10^-28

1b) Radiation Pressure from the local group of galaxies at a 2 Mpc distance (RPG):
The local group of galaxies includes 700 billion stars, and we assume that the mean value of the radiation pressure from the stars is similar to the radiation pressure from the Sun. Hence:
RPG = (1.4 * 10^-28) * (7 * 10¹¹) = 9.8 * 10^-17

2) Acceleration of gas at 2 Mpc distance (AG)

We consider a gas made of atoms. We take as an example hydrogen, the dominant interstellar gas
By using the formula : Acceleration = (Pressure * Surface) / Mass
Surface of an atom of hydrogen = 7.9 * 10^-21
AG = (9.8 * 10^-17) * (7.9 * 10^-21) / (1.7 * 10^-27) ~ 4.5 * 10^-10

3) Comparing the results

Hubble acceleration:
6.9 * 10^-10 m / s²

Acceleration of hydrogen at a 2 Mpc distance caused by radiation pressure:
4.5 * 10^-10 m / s²

The two numbers are similar, of the same order of magnitude.

If gravity forces are cancelled at a 2 Mpc distance, as they are below the sampling resolution limits, this means that the acceleration from radiation pressure is strong enough to cause the acceleration of gas and dust.

As 98% of the distant galaxy is made of hydrogen and helium, in molecular and dust form, 98% of the galaxy is accelerated, then stars and planets follow as they are bound to gas and dust by gravity.

Sun

Spectrometer

Spectrum of the Sun

Spectrum of the Galaxy

Distant Galaxy

Currents theories are:

Big Bang theory, to explain the expansion

According to the Big Bang theory, there was an original explosion which propelled all matter from a very small point. The expansion comes from the original impulse of the explosion.

Cosmic Inflation, to explain the isotropy

With the theory of the explosion, the universe would not be homogeneous. So cosmologists added a new theory: the cosmic inflation. Cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density, caused by a new particle, the Inflaton.

Dark Energy, to explain the acceleration of the expansion

The acceleration of the expansion is explained by the existence of a new kind of energy, the dark energy.

These theories create several problems

Problems with the Big bang theory

When claiming that the universe was born in an explosion, the Big Bang theory does not explain from where this huge energy and impulse are coming. That sounds like magic: something appears suddenly from nowhere without any rational explanation.

Moreover with a single original explosion, the universe would not be isotropic: it was necessary to add the theory of cosmic inflation.

Then, as the expansion apparently is going to continue forever, this means the production of a continuous energy, as in order to move away a galaxy forever, you need to apply a never ending force on that galaxy. That is difficult to explain how the production of an infinite energy can be embedded in a single original explosion.

Problem with cosmic inflation

The theory of cosmic inflation is supposing the existence of a new particle, the inflaton, which has never been observed.

Problem with dark energy

Dark energy has never been directly observed, and currently it cannot be explained by current theories of matter and energy.

5. Problems with current theories

Version 2
April 5, 2007

distance

7. Comparing current theories with the Sampling Universe Theory

Current theories are based on arbitraries assumptions: the Big Bang, the Inflaton, dark energy. These assumptions allow explaining the observed facts, but any other hypothesis explaining the same facts is acceptable as well.

The Sampling Universe Theory is explaining the same facts by using the basic assumption that space and time are discrete. This assumption makes sense when considering that Quantum mechanics demonstrated that matter and energy are discrete, and that time cannot be smaller than the time of Planck and that space cannot be smaller than the length of Planck.

So the Sampling Universe Theory does not introduce any new component really, it is just considering the natural consequences of an application of both Quantum Mechanics and General Relativity.

Hence the Sampling Universe Theory is less arbitrary than current theories.

6. An explanation for the expansion of the acceleration

We have seen at the beginning of this article that the universe is evolving under the influence of two main forces: the forces of gravitation, and the forces exerted by radiation pressure.

But how to explain that the expansion is accelerating?

By rewinding the film of the expansion, we have apparently a point, 14 billion years ago, where all matter was concentrated in a single point, hence the theory of the Big Bang.

But with the sampling hypothesis, there is a difference: as expansion comes from the light and radiations emitted by stars and galaxies, eventually we come back to a point where there are no galaxies, hence there is no expansion.

When rewinding the film, there are less and less galaxies, thus the expansion is slower and the universe could be much older than 14 billion years.

This scenario explains why the expansion of the universe is accelerating: as more and more stars are formed from hydrogen and dust, the amount of radiation in the universe is increasing, so the expansion is accelerating.

Currently there are several theories proposed to explain the acceleration of the expansion: dark energy, vacuum energy, etc. There is not yet a general agreement amongst cosmologists about the cause of that acceleration.

The sampling hypothesis is explaining that acceleration quite well.

The figure above illustrates spectrum analysis, one of our main tools to observe the universe. This technology is so simple and accurate that the expansion of the universe is almost a certainty, when current theories are not so certain.

Spectrum analysis of the light from distant galaxies

Time

Singularity

The picture above (from Wikipedia) represents the Big Bang and the expansion