Background

In the seventeenth century Isaac Newton developed his theory of gravity and defined various laws of motion, which appeared to define perfectly the movements of planets through the heavens. In the nineteenth century however, more powerful telescopes and more precise measuring implements suggested that the results were after all, not quite perfect, and that the model needed some additional factor that Newton had missed.

Early twentieth century Albert Einstein found that if one further equation was added to Newton’s model, then the model went back to perfection in its ability to forecast the movements that were actually seen. This further equation was the assumption that if an object travelled through space with a velocity v, then it would be reduced in length longitudinally in the direction of its travel, by an amount y, where y equalled the inverse square root of 1 minus v squared over c squared, c being the speed of light.

That mathematically the y equation described above made the model produce the right results was not in doubt. What was still a very large assumption however was that this reduction in length was actually happening. Einstein made this assumption and then began to develop other conclusions from it.

Relativity

If a car is driven at sixty miles an hour then the precise definition of its motion is that it has a velocity of sixty miles per hour relative to the surface of the earth. The earth is also spinning and circling the sun and so if the car is looked at relative to the solar system its velocity would be different, though measurable. As the solar system is also moving within a moving galaxy the absolute motion of the car is different again and is probable immeasurable. As an important definition of terms Einstein began by rejecting the notion of absolute velocity and stating that velocity could only ever meaningfully be expressed as the velocity of an object relative to another object.

The Theory

Einstein described a log flying through space. At the back of the log was a mirror. At the front of the log pointed towards the mirror was a lamp. Flying above the log was a space ship on which the crew studied the state of the log and timed events upon it. Meanwhile on earth teams of scientists used ultra powerful telescopes to themselves observe and monitor the log.

At a distinct moment in time T1 the lamp switches on. At a distinct later moment T2 the light from the lamp is reflected in the mirror. The log has no motion relative to the space crew flying above it and the log is ten metres long so the time between T1 and T2 viewed from the space ship is the time taken by light to travel 10 metres. The log has a velocity relative to the earth which is a significant fraction of the speed of light. In accordance with the y equation for those watching from earth the log not only appears to be less than 10 metres in length but actually is less than 10 metres in length. Thus for those watching from earth the time between T1 and T2 is the time for light to travel less than 10 metres. Light – so Einstein assumed – always travels at a constant speed and so if light has travelled a shorter distance less time has gone by. Thus on earth less time has elapsed between T1 and T2 than elapsed between those moments for those on the space ship. T1 is the same moment for those on the space ship as for those on earth and T2 likewise. If time has got from that one distinct moment to the next in a shorter time interval on the earth than on the space ship then time on the space ship must be running slower than on the earth. Thus Einstein concluded that for an object travelling at near light speed time is slowed down. This led to the idea that if a crew went on a two year round trip through space at near light speed they might find that sufficient time had past whilst they were away for apes to have taken over the planet.

Negative Time

Einstein also used his equations to show that if v was in fact greater than c then the interval between T1 and T2 for those on the space ship would in fact be negative. Einstein tended to assume that this could not actually happen and so suggested that speeds in excess of the speed of light would be impossible. It is others who have developed this idea to look at what might happen if speeds above light speed could actually be reached. The normal interpretation is that if a negative value of time has passed then you would have gone backwards in time. However the illustration begins by looking at the two distinct moments T1 and T2 and what passes between them. Regardless of what passes between these moments the distinct moment when the experiment ends is time T2. If negative time has passed in getting to T2, the time at which you arrive is still that moment T2, the correct implication however is that you would have grown younger getting there.

The above is very much a theoretical distinction that only actually matters if the main body of the theory is correct in the first place.

Earth Relative to a Space Ship

All definitions within Einstein’s model are of the velocity of object A relative to the velocity of object B. No distinction is made regarding the relative masses of objects A and B as the y equation is held to apply to all objects moving through space regardless of their mass. Thus the rule would equally apply if we considered the mass of object B relative to that of object A. To be more specific, if Einstein’s rule in fact held then we could consider the velocity of the earth relative to the velocity of the space ship and conclude that because the earth was moving at a significant fraction of the speed of light relative to the space ship then time on the earth would be slowed down relative to time on the space ship. The effects would be mirror images of each other and would cancel each other out. As both the earth and the space ship are moving at high speeds through space anyway and it is only relative velocity that is being considered, the impression of our staying where we were while the space ship undertook a journey would simply be an impression and of no relevance to the theory being considered.

That in Einstein’s conclusions these two effects do not cancel each other out suggests there may be something he has missed.

The Time Delay of Vision

A log twelve metres long has a front defined as A and a back defined as B. The log moves away from those watching it with a velocity of half the speed of light. Because the log is moving so fast by the time we see it at one point it will in fact already have moved further away than that particular point. If at an instant T1 we see point B as being 40 metres away then by the time that image reaches us it will have travelled half that distance again and so at moment T1 point B will be 60 metres away. As we know the object to be twelve metres long we know that at time T1 point A will be 72 metres away. However as illustrated with point B we know that point A will only be seen to be two-thirds as far away as it really is. Thus at moment T1 point A will appear to be 48 metres away. Point A will appear to be 8 metres further away than point B and the log will thus appear to be 8 metres long.

Thus the foreshortening of objects moving through space is an illusion that we would expect to see and again we would expect the extent of that foreshortening to be proportional to the fraction of the speed of light at which the object travelled. Einstein in fact found the effect to relate to the square root of that fraction’s square, although this is a similar concept and reflects the fact that he was studying objects moving in curved lines.

Thus Einstein by making no allowance for the time delay in light reaching the earth reached conclusions about objects travelling through space which are exactly those that would be expected to be observed for objects travelling through space away from us, without there actually existing. The key point is that this illusion is only created for objects moving away from us. If the log was moving towards us then by the same reasoning we would actually see it as longer than it really is. Einstein’s results only find objects reduced in length and so as in part 5 we seem to be missing the mirror image of the results when looked at from another perspective.

Square Roots

Velocity is speed in a stated direction. Relative velocity is velocity either towards a given object or away from it. If relative velocity is measured relative to a particular spot on the earth from which an object is monitored then relative velocity will be either its velocity towards the earth or away from it. If the measure used for a set of observations is velocity towards the earth then when the object is moving away from the earth the value of its velocity will be negative. If a space ship goes on a round trip from the earth its average velocity relative to the earth will be zero. The negative velocity will exactly cancel out the positive velocity.

From 6 above the apparent size of the object could be distorted if it has high enough velocity but the distortion would be positive in one direction and negative in the other. In Einstein’s model however the assumption is that the object is reduced in length whatever the value of its velocity. The way this effect is achieved, is that in the y equation v is squared and the resulting value is then square rooted. Thus negative velocity and positive velocity lead to exactly the same result. The logic would suggest that in fact if the velocity is negative then in fact the negative square root should be selected. However Einstein having stated that a length is reduced by a value which is the result of a square root calculation, then simply takes for granted that the length will be shorter. In reality if it is reduced by a negative value then it will be longer.

Conclusions

Newton’s model of the universe probably is still perfect. The results that appear to show faults in the model can in fact be explained by the movements of objects during the time in which their image travels to us. Einstein doubled up distortion effects that would naturally cancel each other out by ignoring the fact that numbers have negative as well as positive square roots.