Einstein’s Special Relativity Theory (SRT) attempts to solve the problem, but it is invalid, as 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.
Einstein 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, with other factors being responsible. This equation is not 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 event-simultaneity (e-simultaneity), i.e. one observer, two events. The other type occurs when two observers, separated in space, become aware of one event at the same time, such as an explosion or an earthquake. We can call this observer simultaneity (o-simultaneity), two observers, one event. "Relativity" applies only to e-simultaneity, and means that two different observers, because of their different locations, may not agree that the two events or signals in question are simultaneous. This type of simultaneity does not require a clock. Each observer simply needs to notice whether two events are concurrent for him - 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. Relativity does not apply to this type of simultaneity. Einstein’s thought experiments are confused and confusing and do nothing to justify or clarify Special Relativity Theory (SRT).
Einstein derives his most important formula, E = mc², in a short sequel to his June 1905 paper on special relativity. Energy, in so far as it is classical kinetic energy, relates to mass and motion. He invokes his ‘relativity principle’. In trying to understand his relativity principle consider this: Suppose we have a gun at rest on the earth that we want to fire at a target ten feet away. But now we want to relate this situation to a train moving at twenty feet per second from left to right. Are the gun and the target to be now considered to be on the train, or is the train, with the observer in it, just going by and we are observing the situation while seated on the train? Which situation represents his relativity principle? He never clarifies this issue.
In the case of a gun at rest on the ground we would have to know the velocity v of the bullet with respect to the target and the mass of the bullet, and then we could compute mv². But we still would need to know which scenario to use in the case that we are on a moving train. Nothing in his math that follows his remarks clarifies the scenario.
If a body is at rest, and we want to associate with it some quantity or type of energy, independent of its movement or relationship to another body, it is not its mass but its atomic or nuclear character that can yield such energy or energies. To the extent that a substance is destroyed and its mass, m, is carried off by radiation and nuclear fragments moving at close to the speed of light, to that extent we can hope to generate classical kinetic energy approaching ½mc², but that will not happen to a mass of clay or iron, so it is the nature and character of the mass that is relevant. We are outside the domain of classical physics — and outside the domain of special relativity.
Einstein speaks of a body at rest in one system as emitting light energy. What is the meaning of the phrase ‘to emit light energy’? In classical physics we transfer energy from one body to another by means of matter — for example from the bullet to the target. So what is the light energy that is ‘emitted’? According to Einstein there is energy residing in the light — but also, according to Einstein, light has no mass.
But energy requires, and is coupled to mass. So there is an internal contradiction in his calculations and concepts, and it appears his idea of energy is clouded or confused.
Einstein was right in his intuition that there can be an energy associated with an object at rest. That recognition is the fact that pulled physics into the atomic age. But this is a new kind of energy, or better, a new family of energies and forces that were not suspected before the discovery of radioactivity.
[Note: That mass might change due to speed was under intense discussion in 1904. The Kaufmann experiments indicated that as the speed of electrons increases e/m decreases. Einstein’s results favored an increase in mass instead of a decrease in the effect of charge. That became the prevailing view. Whether Einstein was aware of these experiments is not clear, but highly probable.]
No amount of math can hide the absurdity, or contradiction — on the one hand, mass retains its quantity and its identity in the classical concept of kinetic energy, even as the velocity, v, of its impact increases and gets close to the velocity of light; but on the other hand the mass increases and becomes infinite according to special relativity (not to mention one interpretation of the Kaufmann experiments), but on the other hand (assuming a third hand), on reaching the velocity of light, it vanishes, and turns into energy (of some sort or other) — the meaning of the term ‘energy’ is left to the imagination of the reader.
An example from a different context may help in understanding the concept ‘energy’: If I am making pancakes I take water from one container and flour from another and combine them in a third container that then contains a mixture from which I can make pancakes. But in the case of ‘energy’ we don’t have a container of mass and a container of motion that we can combine to make a third and separate entity called ‘energy’. Kinetic energy IS that combination of mass and velocity — it is not just ‘equal’ to that combination. What the word ‘energy’ can mean apart from ‘mass times the square of the velocity’ was not clearly defined by Einstein or other physicists of that time.
"Energy cannot exist except in connection with matter."
(James Clerk Maxwell, 1877, "Matter and Motion" Chapter 6 paragraph 108)
The Michelson-Morley (M&M) experiment was designed to verify this belief. If light is sent back and forth on earth, in the direction of the earth's movement, then the round trip should take longer than it would if there were no aether. It should also take a little longer, but not as much as in the parallel direction, for light moving back and forth in the direction perpendicular to the earth's movement. The M&M experiment used two identical rods perpendicular to each other along which the light moved back and forth.
This experiment, first performed in 1881, repeated in 1887, and often thereafter, could find no indication of a difference. But the belief could not be shaken, and Hendrik Lorentz, in 1895 and again in 1904, thought the explanation could possibly be that the rod placed in the direction of the earth's movement might contract due to the earth's movement, just enough to make the round trip time equal to the case when there is no movement. The equation he developed is known as the Lorentz transformation (LT).
To understand the challenge, and the significance, of the Michelson-Morley (M&M) experiment, and explain the mathematical error, we can look at an analogous situation. 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 (a distance of 3000 miles each way) 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.
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 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 reduce the distance between NY and SF by the square root of 240 or about 16 miles, since that would not be enough to bring the time back to 12 hours.
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.
Simply put, the mathematics of the Lorentz transformation, the last step of taking the square root as pertaining to the time for one leg of the journey, is pure fantasy, with no connection to reality — it ignores the physics of two way travel. There can be no physical significance to the square root, i.e. the gamma factor, or to any concepts or quantities containing this factor.?
If we don't have a continuous film of the event, we only capture a given moment in the expansion. If radiation travels at different rates, then depending on the frequency range we use in our 'camera', we in effect get at this point in time, here on earth, different snapshots in time, from there, millions, or billions, of years ago, where the expansion is occurring. The ring effect is not real there, where the event is happening; it is due to seeing, here and now, only one moment, at that frequency, in the distant past.
There is a NASA web site containing an image showing "a supernova remnant - the remains of a star that exploded in a nearby galaxy known as the Small Magellanic Cloud",, (see the next to the last image). The image shows, in false colors, what the supernova remnant looks like, at this point in time, here on earth, in the x-ray, visible, and radio regions of the spectrum. The outer circle is the radio region. Just a little smaller circle represents the x-ray region. Inside both of these circles is the visible region. Presumably the supernova was expanding from a very tight core over a period of hours, days, or weeks. The outer region corresponds to a later time than the inner region in the evolution of this supernova remnant. Thus we can conclude that the energy arriving now comes from different periods in the development of the supernova.
ATCA radio image by Shaun Amy; X-ray:NASA/CXC/SAO; Optical: NASA/HST
Fortunately for our ability to collect data, visible light seems to travel faster than either radio or X-ray ‘light”, and that apparently goes for gamma radiation as well. The image shows the visible region near the end of luminosity, not at the peak. The visible light from the central area, representing the initial time of creation of the supernova, has faded or passed. (Once we see the visible burst from a supernova, we can point to that location to pick up X-ray and Gamma Ray bursts that arrive later.)
The fact that the speed of light is not constant allows us to look more carefully at the question whether radiation has mass. As discussed in appendix 3, we can find good reasons that radiation has mass — visible light photons about one millionths the mass of an electron, X rays a thousand times more than visible light, gamma rays a million times more mass than visible photons. That I think will eventually be confirmed experimentally. For high-energy radiation the fact of a speed slower than c, can be conceived as connected to a greater mass than that of visible photons. On the other hand, with radio waves, the slowing down mechanism, in that case, is probably due to the imperfect vacuum through which the radio waves pass, and like radio waves generated here on earth, they bend and change 'frequency' and 'arrival time' at the slightest provocation.
Another indication that the speed of ‘light' is not constant can be found in even earlier empirical results. In looking at the time that light reaches us from a distant supernova, it was found that ultra violet energy peaks months before the X ray region shows a peak. [See Herbert Friedman, "The Astronomer's Universe", 1990, p.175.] This is a further indication that most probably the limit c is reached only for relatively low frequencies (i.e. visible light) and that high frequency radiation has a lower speed limit. The velocity difference, between UV and X-rays, may only be found in the fifth decimal of c, or even in the sixths or seventh, but that would be enough for some radiation to reach us tens or hundreds of years later than visual radiation, in the case that the origin of the light is millions or billions of light years away.
We can therefore question the meaning and interpretation of the formula E = mc², as derived from SRT. In a nuclear explosion, matter that supposedly disappears is obtained by adding up the neutrons, protons, and electrons, before and after — and the mass is less after. As an analogy, if we burn a wooden log and weigh only the ashes, we might conclude that mass has been lost. Einstein assumed that radiation has no mass, so nobody counts gamma rays X rays, etc. It is the fact that nuclear fragments reach immense speeds, speeds close to the velocity of light that most probably gives atomic explosions such immense power — it is not because matter is converted to energy.
Wikipedia has this to say about Theoretical Physics:
"Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics in an attempt to explain natural phenomena. Its central core is mathematical physics 1, though other conceptual techniques are also used. The goal is to rationalize, explain and predict physical phenomena."
I believe this tells us little about physics and nothing as to how theory relates to whatever physics is about.
Let me try a different approach: physics, at its most primitive, is about matter in motion – it could be an automobile on a street, a bullet fired from a gun, a stone rolling down a hill, a head of steam, a plane flying through the air, a rocket ship, a planet in motion around a star, or a burst of light from the explosion of a star. But physics is not concerned with a runner in a race, or an insect crawling up a wall, or a bee in flight. If the motion is associated with other than inanimate objects it is not physics — unless perhaps they are dead and lifeless entities that are not self propelled.
If we now look at typical observations, for example rocks, or other objects thrown down from the tower of Pisa, we can discover, empirically, some facts about motion: that all objects accelerate on the way down, with constant force or acceleration producing constant changes in velocity, not dependent on the size, weight, or type of material (ignoring of course friction or other second order effects). Theory enters when we generalize and quantify the character of the motion. For example, we could assert that if the height from which objects are dropped increases, the rate of change of velocity, the acceleration, will continue to be constant, without limit. That implies a Newtonian and open universe.
On the other hand, in the universe of Einstein there is a brick wall, the speed of light, c, that no particle of matter can penetrate or reach.
From Einstein’s view it follows that light, i.e., radiation, cannot be material (since, according to this view, radiation, in a vacuum, travels at exactly the velocity c regardless of its frequency or wavelength). It follows that Einstein must develop a rationale for preventing matter from ever reaching the velocity c. This leads Einstein to such results as the slowing of time, the distortion of space and the increasing of the mass of particles of matter as they reach for greater speed (the mass must necessarily approach infinity at the speed of light), all of which are required to support the existence of this ‘brick wall’. But such a brick wall is also pure and unjustified speculation.
The ultimate truth is still hidden from us but is somewhere between these extremes. We can play with the idea of instantaneous connections that may exist between events remote from each other in space — Bell’s Theorem, for example, is incompatible with SRT because SRT implies ‘locality’ – meaning that all connections are subject to the limit imposed by c, the finite speed of light.