Introduction

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A careful analysis of relativity theory reveals that one of the conclusions of special relativity, namely that a moving object has shrunk in the direction of motion by the Lorentz factor g, is based on a fallacy of Einstein's. To understand this, we must apply what I call the fundamental law of physics. We can formulate this as: There is only one physical reality. This means that all observers of a physical event will describe it in such a way that their descriptions agree. Of course, they must correct their observations for the circumstances under which the observation was made.

Ø An event here is understood as a change in the arrangement of material entities, whereby it is assumed that the emitted light that we observe from the event also owes its origin to a change in the arrangement of particles at the place where the light originates.

The event may occur in a different time period for one observer than for another, but the event remains identical. Based on this principle, one can demonstrate that the contraction of a moving object, the Lorentz contraction, is an error. This is discussed in detail in my book "Time and Cosmos," subtitled "A New Cosmological Worldview" (abbreviated to "T&C") (see "T&C" pp. 141-149). We will not repeat this evidence here, as it distracts too much from our search for the anomalous orbital motions of the Pioneer 10 and 11 space probes, which are traveling at large distances from the Sun, and of Comet Oumuamua.

Einstein's derivation showed that time in the system moving with velocity v is g times slower than time in the observer's frame. The derivation and the result are completely correct. The magnitude of the Lorentz factor g is given by: .

For the case that the speed is much smaller than the speed of light, so v<< c, we may write g≈1+½v²/c² as an approximation for the Lorentz factor.

However, instead of the Lorentz contraction, something else is going on: the velocity of a moving object, to which we assign the value v by measuring the time it takes over a distance between a starting point and an end point, turns out to be greater from a single observer by the Lorentz factor g to the fourth power.

For the latter, we can write: .

So, if we have found the value v for the velocity of an object between two points by dividing the distance by the time difference on the clock at the arrival point and the clock at the starting point, then the actual velocity is v*=g⁴ v m/sec.

Ø The concept of speed is in need of revision.

The above has also been proven in the book mentioned, although we mistakenly wrote down the result as v*=g² v m/sec. The formula for actual velocity will be clarified in the next section.

Furthermore, this analysis has led to a new insight in natural philosophy that has led to a refinement of Newton's formula for gravity. When we consider what influence a mass in the cosmos can have on an object at a distance r in space, the first finding is that that mass is simply there. We can see it. But at the same time, we cannot see what lies behind that mass.

The masses don't need to exert any forces on each other for this to happen. But if we calculate the relative solid angle occupied by the portion of space we can't observe, we get a number that is exactly equal to the time dilation (TDL) that Einstein calculated for that mass at the distance r, namely sec/sec.
This means that time is closely related to the visibility, the perceptibility of space.

If one knows that the time dilation of the gravitational acceleration around a mass is found by differentiating it with respect to r and multiplying by c², then we see that the gravity and the mass become more meaningful.

Naturally, time-velocity differences exist across the object because the solid angle subtended by the mass is larger from the front of the object than from the back. For natural-philosophical reasons, we assume that a freely moving object will always move in such a way that there are minimal differences in the time-velocity across the object. The acceleration an object experiences in the gravitational field of a mass minimizes time-velocity differences. In this way, two identical, freely moving objects will remain as identical as possible.

This leads to a new understanding of the gravitational field around a mass. The state of motion that a freely moving object possesses near another mass is the natural motion it copes to cancel out the time-velocity differences across the object. In an empty space without physical properties – as we assume – no force is needed to give the object its acceleration; only a force is needed to stop the object in its natural motion.

This is simply: gravity.

When we consider gravity in this way, we get a formula for gravitational acceleration that differs from the classical formulas of Newton and Einstein. We call the resulting new theory the Obstruction Theory.

The formula in the obstruction theory for gravity leads to higher values at close distances from the mass—considered a black hole—than Newton's law predicts. At very large distances, however, they coincide. At distances relevant to the solar system, we can observe small deviations in gravitational acceleration.

In §3 we will discuss this in more detail, because this improvement of the theory – together with the results found with the actual speed (§4) – can explain the deviating speed behaviour of the Pioneers (§6).

Finally, the new theory concludes that the gravitational acceleration an object experiences is determined by the location of its mass as observed from the object. Consequently, the acceleration is defined by the subjective distance at which the mass was located when the light reaching the observer was emitted from it.
This new view deviates sharply from the traditional view in which the gravitational field is a rigid physical entity attached to the mass and rotating and moving with the mass, with the magnitude of the acceleration experienced by an object at any given time depending solely on its objective or actual position from the center of gravity of the mass at that time.

This means, for example, that an object passing a mass will perceive and experience the mass in a slightly different location than an object stationary at that same point or moving in the opposite direction relative to that mass. This plays a key role in the anomalous behavior of Comet 'Oumuamua (sections 7 and 8) and also in solving the dark matter problem.

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