In this chapter the concept of how we prove something is discussed linked with the following topics:


In the previous chapters a description of the reality is shown. In particular the movement of the planet is described. The first question is: is this description correct i.e. how can we prove this.

As I already have indicated we cannot prove the reality. The reality is. The only thing what we can do is to describe the reality as accurate as possible. The question now becomes: how accurate is this description.

In order to evaluate the accuracy of our description we do as follows: When the prediction is correct we are satisfied (temporary).
When the prediction does not match with the reality we have to modify our description and repeat the three steps.


In order to see how accurate our description (model) is let us assume that the reality consists of four objects m1, m2, m3 and m4. The mass m of each object is not known.

The first step what we have to do is to measure the position p (x,y,z) in absolute space for each object at three equally spaced moments t0, t1 and t2.

Next we calculate v0.5 and v1.5 at t0.5 and t1.5 and the acceleration a1 at t1 for each of the four objects.

	       p1 - p0   p1 - p0                    p2 - p1   p2 - p1
      v0.5 = ------- = -------             v1.5 = ------- = -------
	       t1 - t0   delta t                    t2 - t1   delta t

v1.5 - v0.5 v1.5 - v0.5 a1 = ----------- = ----------- t1.5 - t0.5 delta t

Each of those values is a vector in absolute space.

Next we are going to calculate the mass of each object. In order to do that we are going to use Newton's Law. Newton's Law states that the acceleration an object is caused by the mass of each of the other objects. More specific that the acceleration of an object is equal to the sum of the mass of each object divided by the distance squared. (The factor of G is not important)

                   m2     m3     m4
      a1 of m1 =  ---- + ---- + ----              (1)
                  r12   r13   r14

m1 m3 m4 a1 of m2 = ---- + ---- + ---- (2) r21 r23 r24

m1 m2 m4 a1 of m3 = ---- + ---- + ---- (3) r31 r32 r34

m1 m2 m3 a1 of m4 = ---- + ---- + ---- (4) r41 r42 r43

r12 = r21 is the distance between m1 and m2 at t1 etc.

Equation 1 should be read as: vector a1 (of m1) is the sum of three vectors:

       m2    m3       m4
      ----, ---- and ----          
      r12  r13     r14

Those 4 equations can be solved.

The result is a value of the mass of each object as a function of:

p1, p2, p3, p4, t0, t1 and t2

Using more or less the same method you can now calculate

the acceleration a2 of m1 at t2,
the velocity v2.5 of m1 at t2.5 and
the position p3 of m1 at t3.

The result will be the position p3 as a function of:

p1, p2, p3, p4, t0, t1 and t2 (mass and G are not included)

The prove of the pudding now becomes to compare the position p3 of m1 at t3 with the measured position at t3.

To get a feeling about this problem perform the following test: 2OBJECTS.TXT 2.17 MASS CALCULATION TEST


The measured value will only be equal to the predicted value when the description of the reality is correct.

One of the first reasons why the prediction is not correct is because not all the objects are included that influence the position of the predicted object.
If we want to predict the position of Mercury then at least we have to take into account:

The planets (Except Pluto, Charron etc. ?)
The Sun
Our Galaxy
The Speed of our Galaxy in space (Substitute for Local Group of Galaxies)

In chapter 4 I have indicated that the shape of the object has to be taken into account. When the shape is round the distance between the two objects is the distance between the center of each object. When the shape is not round this is not true.

In chapter 4 I have also indicated that the direction of the acceleration is not towards the position where the object is now but towards a virtual position i.e. the position of the object a time delta t ago. Delta t is the distance between the object and the speed c of gravity.

In order to calculate the speed of gravity the equations 1,2,3 and 4 have to be modified (c has to be included) and solved. This will result in a new value for the mass of each object and a value for c.

With those new values you can calculate a new predicted position p3 of m1 at t3.
This new position is a function of:

c, p1, p2, p3, p4, t0, t1 and t2 (mass and G are not included)
When the difference between the predicted value and the real position at t3 becomes less then you know you are on the right track.

It is very important to understand that probably each (new) description results in new values of the mass of each object.
When a book for example gives the mass of the Sun, then it should also indicate how this mass has been calculated.

Two other parameters also have to be considered: For each the question is how.


A very important aspect is accuracy of our prediction i.e. how to get the highest accuracy. This is a very difficult subject.

The first general rule is (?): The further away an object is the more inaccurate you can measure its distance. Uncertainty in distance increases linear with distance.

The best way to calculate acceleration of an object is to measure its position at 3 equally spaced moments, as short as possible together.


80% of all the matter in the universe is cold and dark i.e. not visible. (See Literature 38 page 60)
The visible disk of our Galaxy (!) is embedded in an extended dark halo, perhaps ten times as massive as the visible stars. (See Literature 33 page 602)

The first question that pops up is: how did one calculate those huge amounts. What value for the speed of gravity propagation did one use?
The second question is: this invisible mass does it also influence the movement of the planets around the Sun.


The first method to calculate the amount of dark matter is two study the behaviour of two galaxies with equal mass.

Perform the following test: MERCURY.TXT 8.1 TEST 6

What this test shows and calculates is the speed and revolution time of two galaxies as a function of:

distance, and mass.

The same test can be repeated for a different values of mass, each of which will give a different speed. The results can be plotted in a curve.

If your observations of a binary galaxy are not distance and mass but distance and speed then the previous plot will give you the mass.

The problem is I have no results of such an observation so I don't know how much extra mass there is in a galaxy based on this methodology.


There are two ways to calculate the rotation curve of a galaxy:
  1. Assuming that all the mass is concentrated in the center.
  2. By taking the mass distribution into account.

This calculation is performed in the following test: SUNRAD.TXT 9 SPEED OF OUR GALAXY CALCULATION

The above test also shows the rotation curves.

In order to see a picture of the galaxy in 3D see the following figure: FIGURE.TXT 2.8 OUR GALAXY IN 3D

What does this simulation tells you: there exist almost no dark matter and may be even nothing.

To understand this you must compare the calculated curve with the observed curve of the book UNIVERSE page 492 fig 25-15: the two are identical.

Next you must compare the shape of the galaxy with the shape on page 487 fig 25-7.
In this figure the radius of the visible galaxy is 40000 lightyears.
In the calculation the radius of the visible galaxy is 60000 lightyears.

M0 = mass of the Sun = 2 * 10^30 Kg.
The amount of mass within 40000 lightyears is 3.70 10^41 = 1.85 * 10^11 * M0
The amount of mass within 60000 lightyears is 5.11 10^41 = 2.55 * 10^11 * M0

Accordingly to the book UNIVERSE page 492 the rotation curve requires a mass of 6 * 10^11 * M0.

The simulation is not in agreement with this claim.


In NATURE of 14 October 1993 there are two articles which describes what has been observed when dark matter passes in front of a visible star: the visible star brightens 10 fold.

What should have been observed see the following figure: FIGURE.TXT 2.6 GRAVITATIONAL MICROLENSING AND DARK MATTER

What the figure shows is, assuming that all dark matter is concentrated "in a compact body" (like a planet), that a star with a certain intensity, first dims, then brightens, then dims again and at the end returns back to its original intensity.

The two articles in NATURE only show that the light brightens. As such I'm of the opinion that there should be a different explanation for the observed phenomena; it is not microlensing around dark matter.

The mathematics behind the previous figure is explained in the following text: FIGURE.TXT 2.7 DARK MATTER CALCULATION


This paragraph discusses an article (or abstract) in New Scientist of 17 September 1994 page 14 with the same title.

First in this article is written: "A third of all quasars may be visible only because their light is lensed by the gravity of galaxies between them and us". The problem with this article is that it does not show in a picture how this works.

In principle a galaxy can bent light and serve as a lens. However (and we all know that from the Hubble space telescope) it is very difficult to get a clear picture.
In paragraph 3.3 I demonstrate what happens when all mass is concentrated "in a compact body", however this is not the case for a galaxy where mass is not equally distributed. For me the chance that quasars are brightened by the gravity of galaxies is extremely small.

There is an other problem: where does this light comes from? What could be the case that some are brightened (which again I doubt) but then definitely others should be dimmed.

Second in the same article is written: " They examined 63 quasars and the results show a significant excess (a sixth) of quasars in the vicinity of galaxies". This will be music in the ears of H. Arp. (See Literature 12). Unfortunate the article does not indicate the speed of the galaxies and the accompanying quasars.

Paragraph 3.3 is based that the distance between the visible star and dark matter is large. When the visible star (or quasar) is close to the dark matter (or galaxy) I don't believe that microlensing is possible.

Third next in the article is written: " This (the) discovery, as well as confirming the existence of large amounts of dark matter associated with galaxies, also means etc." I don't understand how so little information can prove (?) so much.

In New Scientist of 10 September Webster writes that: most quasars are actual hidden from us by dust. This is completely the opposite point of view. I my opinion you can only "prove" such a claim when all the quasars (at the same distance (?)) are identical.

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When I was at high school the subject of the fourth dimension (time) in relation with the relativity theory was discussed. The question was how to prove that the fourth dimension was something (almost?) identical as the other 3 dimensions.

The proof of the fourth dimension goes in two steps:
  1. First you prove the third dimension
  2. Next you prove the fourth dimension.

Starting point of the proof of the existence of the third dimension is a two dimensional world with a two dimensional creature. This creature crawls on a two dimensional (flat) surface.

On this two flat surface he or she can do the following:

This path of a square is only possible on a flat surface.

Now suppose the creature in actual fact observes the following:

Is this path of a triangle possible?

The only explanation for the creature is that he did not move over a flat surface but over the surface of a sphere (with for example A and C at the equator and B at the North pole) i.e. there exists a third dimension.

The same argumentation can now be used to prove the fourth dimension.

My (highly regarded) teacher did not tell what to test.


Is this proof of the third and fourth dimension correct?

I don't think so.

In my opinion you cannot use the same argumentation to prove that the fourth dimension exists i.e. that time exists.

Even stronger: you cannot prove that time exists


This paragraph is largely based on Literature 49.

In Zeno's third paradox the flight of an arrow is studied at a certain moment t. The problem is that at that certain moment the arrow is not in movement. This is also true for any moment. Ergo there is never any movement.

The problem with the third paradox is the same when you observe a photograph from a flying aeroplane. Such a photo is strange because the aeroplane does not move but stays in the air. The reason is because a photo is not a correct representation of the reality. A photo does not capsulate time. Reality is indismissible linked with time (a duration).

My grandmother owned a painting, which showed a lady emptying a pitcher. Every time when I visited my grandmother the lady was still emptying this pitcher. Many people asked the same question: is it possible the lady becomes ready and finished and that the pitcher is empty.

In Literature 49 mathematics is used to solve Zeno's third paradox. In that article infinitesimal (very small) intervals are introduced which are so small that they remain forever beyond the range of observation and can never be monitored.
When people start to include concepts which are beyond observation then you have to be very careful. (It is easy possible that the Universe is much larger then we can ever observe, even if we use the most powerful telescope.)

What is true that physical there is a smallest distance (the size of an atom ?) when you want to move something.
For example if you ask someone, in the game of golf, what is the maximum number of strokes possible that the ball goes into the hole then the number is always finite, assuming that with every stroke the ball moves in the direction of the hole. The decrease in distance towards the hole can be "observed" or measured using a laser beam.

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