RELATIVITY UNRAVELED

APPENDIXES

INTRODUCTION & SUMMARY

Mathematics and logic are the indispensable cornerstones of science, but even the ‘best’ of scientists have been guilty of misusing them, or failing to understand their relation to physical phenomena. Some of the problems this has generated for contemporary physics are here examined. They are surprising - and almost unbelievable.

This is the story of modern physics and how it has colored our view of time and the universe - how it has led us to beliefs such as the relativity of time, the absolute constancy of the speed of light, a one time creation, the big bang, and further, a belief in an unending expansion of the universe, leading to a cold death of the cosmos, sometime in the distant future, ten or twenty billion years from now.

I want to explain how these conclusions, that I believe are false, were arrived at by theoretical physicists and cosmologists, as a result of errors in reasoning, errors in mathematics and errors in interpreting experimental results.

That Einstein’s Special Relativity Theory (SRT) is invalid can be shown using several distinct approaches: (1) through a logical analysis of the important concepts and thought experiments, (2) through recently available empirical results in astronomy, and (3) through a physical/mathematical analysis of the foundation of SRT.

Logical analysis of concepts and conclusions reveals that the key concepts of SRT are vague and ambiguous, and that Einstein’s conclusions, derived from badly formulated thought experiments, are false. Empirical data, obtained from recent supernovae observations, point to the fact that the velocity of light is not constant across the radiation spectrum. But the most convincing argument against SRT comes from the fact that it is based on the Lorentz Transformation (LT) that will be shown to be invalid. All three approaches are developed in the chapters below.

Using mathematics uncritically in physics leads to more severe errors in theory than one could have imagined. Appendix IV has been added to call attention to this fact. Here, it is also shown that the principle that motion is relative is inconsistent with Einstein's belief that the speed of light is independent of the movement of the source.

TIME

Einstein’s logic, as developed in his original work, in 1905, is questionable.

He begins by questioning the idea that time is universal. He wants to show that time is local and that clocks which are separated in space, and on different bodies that are in motion, cannot be synchronized, and that time "flows" differently, as seen from one body, to the next. Here is the beginning of his argument:

". . . a ray of light proceeds from A at time tA towards B, arrives and is reflected from B at time tB and returns to A at time tA’. According to the definition both clocks are synchronous if tB - tA = tA’- tB. We assume that this definition of synchronism is possible without invoking any inconsistency. . ." (Einstein 1905, my translation)

The deceptively basic equation, in this citation, expresses the fact that the time in which the light travels from A (on one platform) to B (on a different platform) is equal to the time required for the return path. It is true that IF that equation defines what we mean by synchronized clocks, then it follows, from elementary logic, that if these times are not equal, the clocks are not synchronized. But the converse is not true. If the times of travel are not equal the clocks may in fact be synchronized, but other factors are responsible for the fact that the times of travel are not equal. We cannot use this equation as a valid definition of synchronization.

As regards simultaneity: in Einstein's 1917 book, his attempt to justify the relativity of time rests on his ‘analysis’ of the concept of simultaneity. He maintains that it is the relativity of "simultaneity" that leads us to a different view of reality, and to the concept of the relativity of time and space, as opposed to the absolute nature of time and space.

But Einstein does not realize that there are two distinct and independent types of "simultaneity." One type occurs when a single observer is aware of two distinct signals simultaneously, for example, hearing a doorbell and a siren at the same time. We can call this e-simultaneity, i.e. one observer, two events. The other type occurs when two observers become aware of one event at the same time, such as an explosion or an earthquake. We can call this o-simultaneity, two observers, one event.

"Relativity" is true only for e-simultaneity, and means that different observers, because of their different locations, may not agree that two events or signals are simultaneous. This type of simultaneity does not require a clock. Each observer simply needs to notice when two events are concurrent - and two observers may disagree, because of their different location with respect to the two events.

But it is the other type of simultaneity that is needed for his theory. In that case, the simultaneity is determined by the clock time, which must be the same for both observers, (o-simultaneity). They can infer that they noticed the event at the same time by comparing the readings of their watches - assuming these were synchronized in advance. The idea of relativity does not apply to this type of simultaneity. His argument does nothing to justify Special Relativity Theory (SRT).

C

There is evidence, based on the arrival time of radiant energy from supernovae, that the speed of light is not the same for ultraviolet and x-ray radiation. From this it follows that the speed of light, c, is not a universal constant.

There is a NASA web site that contains an image that shows “a supernova remnant - the remains of a star that exploded in a nearby galaxy known as the Small Magellanic Cloud.”

Small Magallanic Cloud

ATCA radio image by Shaun Amy; X-ray:NASA/CXC/SAO; Optical: NASA/HST
Source: outreach.atnf.csiro.au/images/astronomical/e0102-723.html

"This is a colour-composite image of E0102-72.3 - a supernova remnant in the Small Magellanic Cloud. The Chandra X-ray image (blue) shows gas that has been heated to millions of degrees Celsius by a shock wave moving into matter ejected by the supernova. This gas is rich in oxygen and neon. The radioimage (red) made with the Australia Telescope Compact Array, traces the outward motion of a shock wave due to the motion of extremely high energy electrons. The optical image (green) made with the Hubble Space Telescope, shows dense clumps of oxygen gas that have 'cooled' to about 30,000 degree Celsius.

The image shows, in false colors, what the supernova remnant looks like, at this point, here on earth, in the x-ray, visible, and radio regions of the spectrum. An outer circle is the radio region, just a little smaller circle represents the x-ray region, inside both circles is the visible region! The outer region corresponds to a later epoch in the evolution of the explosion (it therefore takes less time to get here). This implies that c is not constant. Fortunately for us visible ‘light’ travels faster, so we know where to point the receiver to detect x-ray and radio frequencies. Note that most of the visible radiation had already passed us at the time this image was taken - the center is essentially blank.

MICHELSON-MORLEY and LORENTZ

The prevalent belief in the nineteenth century was that light is a wave, carried by a subtle medium, the aether, which is at rest in the universe. The sun is at rest, in the center of the universe, and the earth moves through the aether and around the sun at about 30 km/sec. The Michelson-Morley (M&M) experiment was designed to verify this belief.

This experiment, first performed in 1881, repeated in 1887, and often thereafter, could find no indication of the aether. But the belief could not be shaken.

Lorentz was willing to have matter, even time, deform rather than give up the idea of a carrier of light. That his mathematics contained a fatal flaw was even more unfortunate than his inability to give up the idea of a carrier of light.

Einstein was courageous enough to abandon the idea of the aether, but in so doing, he invested photons with the ability to determine their own speed, (he even made c into a universal constant) and in addition postulated that the speed was independent of the movement of the source, his second principle of Special Relativity.

Einstein did not see the connection of this principle with the idea of the aether. But this principle invests photons with a capacity to generate motion, much as the air has that capacity for sound. The second principle emancipated the movement of light from the movement of the source. This is comparable to making the movement of a bullet independent of the movement of the gun from which they are fired.

Reviewing Einstein’s proof of the Lorentz Transformation, it appears that he confuses mathematical and physical simultaneity.

Mathematically, two linear equations that are both true can be added or subtracted; but physically light cannot simultaneously move in two opposite directions - especially at different rates. Consequently to combine two equations that represent such alternative possibilities is not physically meaningful. Lorentz adds the back and forth movements of light. The two movements are presumed not to be identical because the earth moves through the aether. Einstein’s equations 3 and 4, in his appendix 1, suggest that light simultaneously has different speeds in opposite directions - without the aether.

That is the fundamental mistake! Without the aether to carry it, light propagates at the same rate in all directions - in the coordinate system of the stationary source.

E/M

Aside from the mathematical error in the derivation of the Lorentz Transformation, the belief that mass increases with velocity has become the ultimate justification and vindication of SRT. It is ‘verified’ in each construction of particle accelerators.

The belief that mass increases with velocity can be traced back to an almost forgotten experiment published in 1901 by Walter Kaufmann. Kaufmann showed that when electrons are accelerated to velocities close to the speed of light the ratio of charge to mass, e/m, does not remain constant, as had been expected, but decreases. He, and others jumped to the conclusion that a variation in m, not in e, must be responsible. Kaufmann found that e/m decreased more rapidly with velocity than predicted by the Gamma Factor of SRT, and this was initially interpreted as evidence that Einstein’s theory was false.

From this view, as codified in SRT, it follows that light can have no mass, since any entity having mass becomes infinitely ‘heavy’ if it moves at the speed of light.

All this should have been a warning that physics was perhaps moving down the wrong path, but no one entertained the idea that the ratio e/m decreases because the charge of the electron, e, decreases with increasing velocity. If e decreases, it means that particles tend to become electrically neutral as they approach the speed and character of ‘light’.

This point of view can explain many troubling aspects of particle physics. The notion that two oppositely charged electrons, at high velocity, can collide and transform into gamma rays, replaces the idea that they are destroyed but generate radiation out of ‘thin air’. The appearance of short-lived exotic particles can be interpreted as transitional times and states between states of stable entities - particles losing or gaining charge and mass, along with changes in velocity, as they take on another identity, and as they collide with, or break lose from other particles. If atoms can change their nature in this way, why not allow the constituent parts of atoms to behave in the same manner.

At the beginning of the twentieth century the sub-atomic nature of matter was not yet clearly understood (is it now?); the nature of radiation was a total mystery (X-rays had just been discovered, and it was known that radium emitted two types of ‘radiation’, alpha and beta rays). Since atoms turned out not to be the fundamental, basic, indivisible building blocks of nature, as had been believed, it was easier to deal with mass as the variable, and e as the constant, in the inseparable connection e/m.

THE DOPPLER EFFECT

The Doppler effect, in all standard textbooks, is treated as though it applied only to waves - whether of light or of sound. But it applies equally well to pulses, and is much easier to comprehend and to characterize mathematically.

The Doppler effect for light is symmetric (it doesn't matter if the source is moving or the receiver), and depends only on the separation rate between the source and receiver. In the case of sound, where there is a carrying medium, the effect is asymmetric.

For sound, if the source is in motion with respect to the air, the spacing is (1+v) seconds at the receiver, when pulses are sent 1 second apart (where v is the ratio of the speed of separation of source and receiver, divided by the speed of sound).

In the case of light, if we assume the source is moving at v = .5 light-seconds per second, we cannot argue that it will take 1.5 seconds for the light pulse to reach the receiver. We know from the M&M experiment that there is no medium as carrier so the situation is different. But if the source is stationary, or is stationary with respect to the air or the aether, the magnitude of the Doppler effect will be the same for both light and sound, so we can analyze this case by putting the source at the origin and the receiver in motion. The general formula now becomes 1+v+v2+...= 1/(1-v) for the spacing between pulses, that is to say, with v = 0.5 the spacing is doubled. The received frequency is one-half the emitted frequency. If blue light was emitted, red light is received. The same result applies to sound. In the case of light we can use Einstein’s first principle, to declare that we will get the same result if the source is in motion - but not so with sound!

To make the case for symmetry it is better to think of two spacecraft in outer space that try to determine whether the distance between them is fixed, or whether they are separating. Neither spacecraft can be said to be preferred. They can establish their relative motion by noticing if the signal sent out by the other is getting weaker, or by sending out pulses that bounce off the other and return.

If the spacing of the returned pulses remains constant and equal to the spacing with which the pulses were sent, the spacecraft are at constant distance. If the spacing remains constant over time, but larger than sent, the spacecraft are separating at a constant rate. The Doppler effect, as inferred from the spacing, must be symmetric as long as there is no other body in terms of which motion or rest can be defined.

Physicists usually use the concept z, called the Doppler shift, and defined as the difference between the sent and the received frequency divided by the received frequency. On the other hand, the quantity z+1 represents the ratio of the sent to the received frequency. This is the quantity that can be treated under multiplication, and that can be "averaged" (in the sense of a geometric mean) by taking the square root of the product. Here we call the ratio z+1 the Doppler factor.

There are type 1A supernova data, published in 1998, which show that z is always less than one in the visual region. This implies, (without invoking SRT) that even the most distant and fastest moving stars never exhibited a velocity greater than one-half the speed of light.

THE AGE OF THE UNIVERSE

Supernovae, and in particular, type 1A supernovae, give us some insight into the age of the universe, as well as its rate of expansion. A supernova is a rapid explosion of a star at the end of its normal life. Type 1A refers to those supernovae which lack hydrogen in their spectra. This differentiates them from other stars and supernovae, and suggests that they originated near the very beginning of time.

These supernovae give us the only view into the very distant past based on individual stars. All other, similar, astronomical observations have been limited to a relatively short time, in the past, far less than a billion years, and correspondingly, distances of less than a billion light years (excluding radio astronomy where the interpretation of the experiments will take more time.).

It turns out that the smaller the star, (but at least 1.4 solar masses), the longer it can burn before exploding as a supernova. Those with a mass near 1.4 solar masses have a life-time of about three billion years. Stars that have a smaller mass do not end as supernovae. The small stars are those that lasted the longest and whose supernovae are still visible at present, the larger ones would have exploded and been seen much earlier.

One thing is clear. If the type 1A supernovae come from stars created near the beginning of time then the arithmetic which combines their life time (about three billion years) with the time until the light from the explosion reaches us (also about three billion years) gives us an estimate of the age of the universe of about 6 billion years. That is less than one-half of the 12 or 13 billion years that is currently believed. There is no way around this. Current estimates of the age based on Hubble's Law, based in the end on relativity theory, cannot be reconciled with these numbers.