The mathematics used in deriving the Lorenz Transformation, using his view of the universe, is straightforward and correct, but a concrete example shows that the physics is invalid.
The prevailing belief of physicists at the end of the 19th and beginning of the 20th century was that light is carried by a medium, called the ‘aether’. Further, that the aether is stationary in the universe with the sun at the center. So that an experiment with two points on earth, and a mirror at the second point, so oriented as to let the light travel in the direction of the motion of the earth, and return in the opposite direction, will show the total time of travel, call it t(v) to be
t(v) = L/(c-v) + L/(c+v)
using the fact that time = distance/velocity.
This can then be written as
t(v) = 2Lc / (c-v)(c+v) = 2Lc / c2-v2
where L is the distance between the mirrors and v is the orbital velocity of the earth.
In the alternative model where there is no carrier the time is the same in both directions and the sum is given by
t(0) = 2L / c
The ratio of these is a pure number
t(v) / t(0) = c2 / c2– v2
This is the square of what Lorentz calls gamma. It can also be written as:
t(v) / t(0) = 1 / 1-(v/c)2
So the square of gamma is the correct comparison of these two models.
If we then use the largely negative results from various attempts at duplicating the results of the Michelson-Morley experiment, we come to the conclusion that the ratio is most likely one – that there is no carrier for light.
As a concrete example: We know that the velocity of a plane is measured with respect to the air stream through which it moves. If we fly from, say, San Francisco to New York and back and the air is still, it will take six hours each way, a total of 12 hours, at 500 miles per hour. If the air is moving at 100 miles an hour, from west to east, and the plane flies at 500 miles per hour, with respect to the air stream, the distance of about 3000 miles is covered in five hours (at 500+100 miles per hour) and the return trip takes 7.5 hours (at 500-100 miles per hour). So the total time is not 12 hours but 12.5 hours! The gain and loss, due to the movement of the air, don’t quite balance out. Analogously, that would be the situation if the velocity of light is measured with respect to the aether, and the earth moves through the aether.
Here c=500, v=100, and L=3000, so the ratio t(v)/t(0) = 1.04
It is easy to show that if the round trip distance is reduced by 240 miles, or the distance between SF and NY by 120 miles, that is, by one-half this amount, it takes about 4.7 hours going, 7.3 hours returning, and the total time will be 12 hours – the same as it would be if there were no jet stream.
We cannot use the square root i.e. the Lorentz Transformation, since it would reduce the distance by about one-half this amount – not enough to bring the time back to 12 hours.
The point to notice, from this example, is that even if the sun were the center of the universe, and the aether exists and is stationary in that universe (as Lorentz believed), taking the square root is unjustified and leads to a false conclusion.
Einstein derived the Lorentz Transformation, not by assuming that light is carried and has the speed c in the coordinate system in which an ‘aether’ is at rest, but that it has the speed c in all coordinate systems that are in relative motion. Einstein believed that any observer measures the speed of light to be the same constant, c, even if the source is in motion relative to the coordinate system in which the observer is at rest.
This hypothesis leads him to the same expression, gamma, but it has a different meaning! Einstein’s view is that time is relative – observers in relatively moving coordinate system will not measure ‘time’ the same way. His ‘proof’ is unconvincing since his idea of relative time is itself not justified.
Einstein’s argument is based on his conviction that time is relative because clocks on bodies in relative motion cannot be synchronized. But using the Doppler effect it is easy to show that this conviction is false. Observers on different bodies in relative motion need only each note the event when the two bodies are at minimum or maximum separation. At this point both will see a reversal of the Doppler effect and can both use this to synchronize their clocks – without the need of signaling this event to each other in ‘real’ time.
So, for both Lorentz and Einstein, the square root should never have been taken. We can conclude that the ‘gamma’ of the Lorentz Transformation is physically, but not mathematically, wrong.
All this, and more is covered in my web site: www.relativityunraveled.net
I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. (Lorentz, 1906)
Indeed one of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms, or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest. (Lorentz, 1906)
December 25, 2013:
Two weeks have gone by since I wrote the above, and I have taken the ‘time’ to look at Einstein’s treatment of 1905. Here is a quote:
“1. Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body. Hence
velocity= light path/time interval
We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established for the synchronization of two clocks. [What does that last sentence say??] Let a ray of light depart from A at the time4 , tA, let it be reflected at B at the time tB, and reach A again at the time t’A. Taking into consideration the principle of the constancy of the velocity of light we find that
[So for the round trip we have the same formula as Lorentz!]
where rAB denotes the length of the moving rod—measured in the stationary system. [What can that possibly mean??] Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous [This needs translation or clarification!].
So we see that we cannot attach any absolute signification to the concepts of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.” [What is THAT system? And what is the system that is in relative motion to THAT system?]]
It is clear that both Einstein and Lorentz start with the same equation, and end with the same quandary – only their reasoning is different in that Lorentz ‘blames’ space and Einstein ‘blames’ time (i.e. simultaneity). Both take the square root and end up with the same wrong formula – (maybe a coincidence, maybe not). But it is the absolutism about space and the movement of bodies and light in that space which unites their vision – and gets them to the same wrong formula. That they both took the equation to the square root may be a coincidence – but I doubt it.
What we can take away from this discussion is that there is no absolute space in which events can be placed. The source should be seen as the origin, the linear distance to the reflector can define the x axis in which L is measured, the return trip is in the same coordinate system, and the time of the round trip is :
t = 2L/c. As Observed, End of mystery.
But what if the source of the light, or the rod, begins to move in the course of the experiment? Then the light pulse can’t find its way back – there is no round trip – end of the experiment, of equations, and of physics.
January 9, 2014:
The 19th century needed the existence of the ’ether’ to try to get around the problem of action at a distance, and to ‘justify’ that light is ‘carried’ through space. Maxwell, for all his insight into mass and energy, accepted the ether as real – in so far as the propagation of light is concerned. (The complete radiation spectrum remained to be discovered long after his death.) Einstein conceived the dogma that light has no mass and travels through space at the constant velocity c – independent of the motion of the source. He also had no clue about radiation other than ‘light’.
Light, as we now know, occupies a small region of the radiation spectrum. Radiation itself has a wide range of attributes –more wave-like in the region below the wavelengths of visible light, i.e. longer wavelengths, and more particle-like in the region of x-rays and gamma rays.
Action at a distance – gravity – or attraction and repulsion of charges – these are facts that have no mechanistic basis – as we now understand and use mechanics. But we know and appreciate the fact of attraction, and its opposite, in human (and animal) interactions – a reality that physics cant deal with. But that only means that we cant make physics, as practiced today, the basis for understanding the universe. Furthermore, action at a distance is not really a problem if there is no universal upper bound to speed – it is simply a speed so fast that it is not measurable.
I have come to the view that radiation has a velocity, in space, inversely proportional to it frequency, and a mass proportional to its frequency, and that there is no absolute limit, c. ‘c’ is, at best, the speed limit, in empty space, in the visual region of the spectrum. But the evidence from supernovae observations points to a slower speed for ultraviolet and X-ray radiation reaching us, than for radiation in the visible region.
One experimental fact that reinforces the idea that radiation has mass is the difference in dispersion of light using a prism and using a grating. With a grating the red light is dispersed at a greater angle than is blue light. The opposite is true with a prism, where the blue light is deviated to a greater extent than the red. This is easily explained if we notice that a grating operates on the wave character of light, in which the longer wavelength of the red light favors the dispersion of a grating. In the case of a prism the dispersion is most likely due to the interaction of the mass of the light with that of the prism – and that favors the blue region!
~ Hans J. Zweig (email@example.com)