The Lorentz Transformation

The question as to the character of both time and light has been the most vexing problem for physicists since the nineteenth century. Shedding ‘light’ on this problem was the ultimate objective of both Lorentz and Einstein. Here their results are summarized and reevaluated.

The following argument, using only simple algebra, shows that the Lorentz factor, gamma, is a pure number, comparing the time of travel of light under two models of physical reality -and it is not necessary or correct to use a square root in calculating this factor.

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 to be

t(v) =       L/(c-v)  +   L/(c+v)

by 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.

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 instead, 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.

Furthermore, his argument starts with the assumption that at time t=0 (whose time?) the light pulse is ‘simultaneously’ at two different coordinate points, x=0 and x’=0 (for different observers, in different coordinate systems) and moves at the same speed c to two different coordinate points (for the two observers) – to x at time t and  to x’ at time t’, before returning to the ‘origin’.  This is the same light pulse.  But if time is relative, how can the two observers have a common origin t=0, and agree what happens at the ‘time’ when the light pulse returns? His concept of the relativity of time prevents his being clear about THE ‘time’, or about ‘simultaneity’, for the two observers in his equations.

Nothing is wrong with his mathematics, but nothing is physically clear.  He gets to the square of gamma, and like Lorentz (most likely by imitating him) he feels compelled to take the square-root.

Note:  It is easy to construct examples of good math producing bad physics – see “Undoing Math”.

ADDENDUM TO ‘LORENTZ”:

The Character of Light
(a foray into pure speculation)

20th Century Physics was a period of intense speculation as to the character of the universe and the ultimate nature and constituents of matter and the elements. The leading lights among physicists can be counted using our ten fingers:  Lorentz, Einstein, Bohr, Heisenberg, Plank, Dirac, Schroedinger, (leaving a few fingers free for others to add to this list).

The question is not ‘who got it right?’ but  ‘who asked the right question?’

The answer is none of the above.  The right question was answered years earlier by James Clerk Maxell – about ‘energy’:  “There can be no energy without matter!”.  The right question was “what is energy?”

It is tempting to extend the thoughts about the fundamental characteristics of light beyond what is presently believed.

At present we think of radiation as having the same character throughout the spectrum.  In terms of present concepts:  radiation consists of pure energy, traveling at the same speed c in free space, in the form of photons that are indivisible.

We have already challenged the notion that the speed is constant for all types of radiation.  Here we go a step further – we challenge the notion that the mass is zero, and that the photons are indivisible – at least ‘not so’ in some regions of the spectrum.

For high-energy radiation – x-rays through gamma rays, it seems plausible that the mass is large enough so that some energy can be given off  [To make it clear and explicit: energy, and therefore matter are proportional to frequency!]– In some interactions the ‘photon’ could split and the remaining photon (or photons) could move down the line – to a different ‘color’ or frequency – and to less energy.

That such a thought is not entirely wild came to me recently in reviewing some research I had done in my twenties and thirties while working in the Physics Research Laboratories of Eastman Kodak.

A paper I published in the Journal of the Optical Society of America, vol. 49, number 3, March 1959, deals with the granularity of black and white photographic emulsions.  In one experiment the granularity of exposed and developed emulsions was compared using visible radiation and using X-ray exposures.  It turns out that in the latter case there is an increase in the apparent ‘graininess’ and measured granularity – a clumping which suggests that several grains may have been made developable by a single x-ray photon!

It is the only case I know where a photon may have split into fragments, (or perhaps bounced around, giving up energy in small doses, before exiting the photographic emulsion).  I suspect that in particle physics there are many bubble chamber experiments that point to a situation where one entity – a gamma ray, for example- ‘disappears’ and two or more ‘entities’ move forward in different directions, (that are called out as being short lived ‘particles’).  [See for example “The Particle Hunters” by Yuval Ne’Eman and Yoram Kirsch, Cambridge University Press, 1986]

If mass is divisible, for example by transforming elements through fission, perhaps it is not such a wild idea to allow the identity of photons to be changed through a similar process, especially for the more massive photons in the x-ray region or above. The implications of this for particle physics are mind-boggling.

But once we question the Lorentz Transformation we open the door to new ways of dealing with ‘elementary’ particles.

We still have a lot to learn. The universe gives up its secrets very reluctantly.

Conclusion: energy is matter in motion – without speed and without mass you don’t get ‘energy’.  ‘Potential  energy’ is energy waiting to be released.  Taken one photon at a time; blue light has potentially more energy than red light.

The consequences of these deliberations for contemporary cosmology and for contemporary particle physics are considerable and far reaching.

See also www.lorentztransformation.com for an earlier, more extended critique.