The Relativity of Time
The essence of the disagreement between Newton and Einstein concerns the nature of time and space. Under the Newtonian view both space and time are absolute. This means that they underlie our basic perceptions of objects, their duration, and their movements. Distances and durations can be measured without taking into account the relative movement of observers or the nature of light. Time flows at the same rate independent of the speed at which a body moves in relationship to the observer. The universe is stable, not because of any lack of change in its size or character, but because the underlying character of space and time are enduring, constant, and reliable.
Special Relativity concern motion in the absence of all forces, such as gravity. It is an abstraction from the real world. We can imagine it as taking place in outer space where neither gravity nor atmospheric phenomena play a significant role. Where Newton’s Principle of Inertia, and the ideal of uniform linear motion may be approximately realized. Where the speed of light is not influenced by gravity, or by atoms that can bend, slow, or rob it of energy. In this ideal situation any body that is in uniform linear motion can be used as reference, and is referred to as an inertial system. We can pretend that such a situation can be approximated here on earth using a train, a gun, or a man walking as representing such an inertial system.
The essence of Special Relativity (SRT) consists of two assertions:
(1) The laws of physics are identical in all inertial frames, or equivalently, the result of any experiment is the same in any such frame assuming the conditions under which it is performed are the same.
(2) Light travels at constant speed, c, in all directions independent of the motion of the source.
The first principle is natural, intuitive and clear. So it is tempting to leave it at that. But we must look at it more carefully. It applies to all laws, and does not exempt light. It says among other things, that the motion of a walker, or a bullet, or even a photon is the same whether the motion takes place on a speeding train or on the ground. The motion is relative to the coordinate system with respect to which the motion is defined, regardless of the motion of that system with respect to another inertial system.
The second fundamental principle applies only to light and, in essence exempts it from the first principle. According to the first principle if we fire a gun on a train the speed of the bullet with respect to the ground will not be the same as if the gun had been fired while stationary on the ground, and the same is true for light. But according to the second principle it doesn't matter whether the source is in motion, on the train, or stationary on the ground. The velocity of a photon is the same with respect to the ground. This obvious inconsistency between the two principles can only be resolved if we abandon traditional concepts of space and time.
Furthermore, we need an independent argument for the relativity of time, as opposed to the relativity of the speed of light. In his book of l917, his attempt to justify the relativity of time independently from the above two principles rests on the analysis of the concept of simultaneity.
Einstein begins this book by questioning the traditional concepts of time and space, and asserting that these traditional ideas are in conflict with the idea that light propagates at a constant speed. He maintains that it is the relativity of 'simultaneity' which 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.
(This book, written ten years after his original paper, is both more clear, and more clearly wrong than his original work. The earlier work dove into mathematics very quickly and so obscured the reasoning, which led him to his equations.)
But he forgets 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 door bell and a siren at the same time. The other type occurs when two observers become aware of one event at the same time, such as an explosion or an earthquake.
'Relativity' applies only to the first type of simultaneity, and means that different observers, due to their different location, may not agree that two events or signals are simultaneous (e-simultaneity). This type of simultaneity does not depend on the use of a clock - we simply need to notice when two events are concurrent. 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). It is not 'relative'. The two observers either concur that the event happened at the same clock time, or they concur that it happened for them at different clock times.
Einstein confuses these two, and so comes up with the bold assertion that simultaneity is relative. What he needs is for o-simultaneity to be relative but borrowing the idea from e-simultaneity is not legitimate.
In addition, Einstein is unclear in that he sometimes refers to the simultaneity of events when he talks about the origin of the signals from which they emanate, and sometimes about the signals as received by an observer, or by two observers.
We can use a bolt of lightning and an exploding dirigible as an illustration. This example has the advantage of showing the independence of e- and o-simultaneity. In the limiting case, which we could call true-simultaneity, the bolt of lightning strikes the dirigible and it 'simultaneously' explodes. Now all observers, wherever they are, or however fast they are moving, will see these two events 'at essentially the same time' - they originate at about the same time from the same place, and therefore take the same time to reach any given observer.
However, observers may be at different distances from this double event, so they will not experience it 'at the same time'. We are using the phrase 'at the same time' in two different ways. It can mean 'concurrently', if it relates to the two events, but it also can refer to the clock time when we compare the time that the signal reaches different observers.
By not keeping track of the different meanings we can easily draw false conclusions. E-simultaneity does not imply o-simultaneity - and the relativity of one does not imply the relativity of the other.
For Einstein's theory it is o-simultaneity that is the real issue - whether two observers in relative motion can compare experiences in a time frame common to both. But he also needs the property of e-simultaneity, that is, relative simultaneity. It is only by combining these two distinct concepts together into one, that he can have both.
Einstein's fundamental idea is that what is constant and non-relative is the speed or 'velocity' of light - not space, and not time.
The paradox is that the very notion of 'velocity' involves time and space. 'Velocity' tells us the time it takes to travel a given distance - the less the time, the greater the 'velocity'. So time and space take precedence over velocity. But if the velocity of light is to be primary, as well as constant, then we can ask in what space and with what clocks are we to measure this constant?
When we say that the top speed of a plane is, say, 600 miles per hour, we are referring its speed either to the ground or to the air stream through which it is flying. The speed is always relative to some body or coordinate system.
If we are watching the speed of a car from a moving train, the velocity of the car with respect to the train is different from its 'normal' value. Its 'true' velocity is constant, only its apparent velocity with respect to the train is different.
There is a profound difference between a pulse or photon of light and any material moving object. The difference is that we can't see the light. What this paradoxical statement means is that we can take a time exposure on a train of a walker, a car, or a bullet in transit next to the train, and can infer the apparent velocity from the blurring. Or we can measure it with a stopwatch. We can't do this with light. We must destroy or stop the light in order to detect it.
For material objects we can have an observer either in the coordinate system in which the object is moving, or in a system in relative motion, since he can observe the object in transit. But for light, we need to know the point and time of origin, the distance, and the time of detection, and can then infer the velocity in the system in which the light is moving - it can never be measured in transit from a system in relative motion. The idea of 'apparent velocity' which is appropriate when we watch a walker next to the train from the train is not appropriate, or measurable, when applied to the velocity of light.
If we could see the light in transit, we could reason as follows. Suppose we are on a train and are observing a photon, or a walker, traveling alongside. If the train is moving more slowly than the walker, but at nearly his speed, we can count his steps, say 40 per minute. These will be independent of the train's velocity, but his motion with respect to the train will be very much slower than with respect to the ground (in the limit as the train approaches his speed his forward motion will be zero).
So each step doesn't get him very far as seen from the train - his frequency is constant but his wavelength goes to zero, along with his apparent velocity, to use the terminology of light waves. According to this metaphor we would expect the apparent velocity of light (which remains a metaphor, not a reality) to be less as we approach the speed of light, and in the limit it is zero.
Einstein sees the observer, in this case, as stationary on one crest of the wave, (by assuming him to be in the same system as the light). But, seen from the train, the oscillations continue, the frequency remains constant, the wavelength decreases, similar to the walker on the embankment, moving at close to the same speed as the observer on the train!
Einstein's 'Aarau Vision', an idea he had at the age of sixteen about travelling on a light beam, makes the mistake of letting the observer exit the train and, in essence, climb on top of the walker walking on the embankment next to the train. The consequences, which flow from this logical error, are not to be underestimated. This unconscious jumping between coordinate systems is also what is behind Einstein's second principle of Special Relativity.
There are many ambiguous terms and statements sprinkled throughout his books and papers. Some of the more glaring and significant ones are discussed below:
"The 'source' of the light, (or the wave)" can mean:
(1) The object from which the light pulse, (or the wave) emanates, or,
(2) The place of origin of the light pulse, (or the wave).
In his exposition Einstein speaks about the body from which the light originates. But in fact he is not concerned with whether this is a star, a laser or a candle. What matters in the mathematics is the location and time of the point of origin of the light. His theory deals with geometry, time and motion.
"The movement of a walker (or light) relative to the train":
There are two interpretations, based on the ambiguity of the term 'relative':
(1) The movement of a man who walks on the ground in the same direction as the train, as it would appear to an observer on the train. (If the man is moving slower than the train he will be seen to move towards the rear of the train. If the train is moving slower than the walker he will move in the forward direction but the speed relative to the train will be less than on the ground.)
(2) The movement of a man walking ON the train as it appears to an observer on the train (he is seen walking forward with his own natural speed).
Einstein confuses these two interpretations and therefore concludes, in his critique of Newton, that a light pulse, originating on the ground, and having a velocity c there, will have a speed less than c ON the train.
Another ambiguity that plays an important role is the following:
"The round trip from the origin to a distant place and back to the beginning":
This can mean:
(1) Beginning at the rear of the train and ending up at the rear of the train. (The round trip from the point of origin as defined in the system in which the velocity is measured).
(2) Beginning at the rear of the train and ending at the point on the embankment where the rear of the train was when the trip began. (The round trip terminates at the place where the origin was located at the time the motion was initiated).
This ambiguity leads to a mistaken interpretation of the Michelson-Morley Experiment.
"The velocity of light is constant", can be interpreted to mean:
(1) All wavelengths travel at the same speed.
(2) The velocity has the same value for all photons independent of the speed of the coordinate system in which they are generated.
(3) The velocity is constant relative to the coordinate system in which the light originates.
(4) The speed of the photon in vacuum cannot be increased.
(5) The velocity of a photon is the same whatever coordinate system is chosen.
(6) The velocity has the same value measured by an observer at rest with respect to the origin as for an observer moving towards or away from it.
1 through 4 are compatible with "the velocity of light is constant when measured in the coordinate system in which the origin of the light is at rest.", or, more simply but less accurately, "the velocity of light is relative". 5 and 6 are incompatible with these statements. 5 because its meaning is ambiguous (there is a difference whether the choice is made before the experiment is conducted or afterwards). 6 because it implies a new, and unclear meaning of 'velocity' that is incompatible with the traditional definition of velocity.
There are logical flaws in Einstein's reasoning, which I can summarize from his book.
Einstein presents his argument (see his l917 book, Relativity, chapter 9) using, implicitly, the relativity of e-simultaneity to infer that observers cannot perceive an event at the same time, and that clock time itself is relative.
Here is this amazing leap, based on his frequently used example of an observer on a train and one on the embankment.
"Events which are simultaneous with respect to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (coordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event". [My own translation]
The first sentence essentially asserts that e-simultaneity is relative, which is true, and, as was explained above, this has nothing to do with clocks. The signals reach the observer on the embankment 'at the same time', but because the train is in motion the two signals don't reach the observer on the train 'at the same time'. 'At the same time' in this context means 'concurrently'.
The second sentence comes out of the blue. It does not follow from the first unless you identify e- with o- simultaneity, and that is simply not right.
For Einstein's theory it is o-simultaneity that is the real issue - whether two observers in relative motion can compare experiences in a time frame common to both. But he also needs the property of e-simultaneity, that is, relative simultaneity. It is only by combining these two distinct concepts together into one, that he can have both.
To further reinforce the need for his Special Relativity Theory, Einstein criticizes the Newtonian Point of View.
His critique of the Newtonian View, in his book of 1917, is based on an example of a walker and his motion relative to a train.
In section 7, Einstein explains why he sees a problem with the Newtonian View. In that discussion, dealing with two systems in relative motion, the embankment and the train, he does not carefully differentiate what is seen from a train, and what takes place on the train, but simply uses the expression "...movement relative to the train". He can reject the Newtonian View only because, at the critical point in his argument, he picks the wrong meaning. (Einstein's book is intended for the general, intelligent reader. It deserves to be read critically, especially since it is the only place where he lets us see beneath the mathematics into the underlying thought processes and their problems.)
The difficulties are seen clearly in section 7, which is quoted and analyzed below:
".... let us assume that the simple law of the constancy of the velocity of light c (in vacuum) is justifiably believed by the child at school. Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties? Let us consider how these difficulties arise."
"Of course we must refer the process of the propagation of light (and indeed every other process) to a rigid reference body (coordinate system). As such a system let us again choose our embankment. We shall imagine the air above it to have been removed. If a ray of light be sent ALONG THE EMBANKMENT, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment. {Notice that the coordinate system for the ray of light is the embankment, not the train.}
"Now let us suppose that our railway carriage is again traveling along the railway lines with velocity v, and that its direction is the same as that of the light ray, but its velocity of course much less. Let us inquire about the propagation of the light RELATIVE TO THE CARRIAGE. "
He means to say, the propagation if the coordinate system is the train.
"It is obvious that we can here apply the consideration of the previous section, since THE LIGHT PLAYS THE PART OF THE MAN WALKING ALONG RELATIVE TO THE CARRIAGE." In German: "Der relativ zum Eisenbahnwagen laufende Mann spielt die Rolle des Lichtstrahles".
This does not make clear whether the man is on, or next to the train, but from section 6 (the previous section) we see that he is in fact walking on the train- so he has shifted the light to the coordinate system of the train.
"The velocity W of the man RELATIVE TO THE EMBANKMENT, is here replaced by the VELOCITY OF LIGHT RELATIVE TO THE EMBANKMENT"
Here is where he loses it- because the man is supposed to be on the train, but the original intent was to propagate the light along the embankment.
" w is the required velocity of light WITH RESPECT TO THE CARRIAGE, and we have w = c - v. The velocity of light RELATIVE TO THE CARRIAGE thus comes out smaller than c. "
This would be true if he meant to say the velocity as seen from the carriage' but he wants to believe that is the velocity if the coordinate system is the carriage. By mixing the two meanings of 'relative to' he generates nonsense.
(Note: capitalization of phrases is intended to call attention to the ambiguities.)
So the contradiction between the two fundamental principles cannot be lifted by appealing to an attempt to discredit the Newtonian view, or by establishing the relativity of time apart from the contradiction which forces this view.
The Bottom Line: Special Relativity embodies ambiguous concepts, contradictory assumptions, and faulty arguments. But most serious of all is the fact that it builds on the Lorentz Transformation (LT) which in turn depends on the existence of relative, rather than universal time. Since there are no independent, valid arguments for relative time, the LT cannot be used as foundation for SRT, and in consequence all that follows from Special Relativity is irrelevant to the physical universe. It has the same status as other mathematical structures that may provide fodder for the imagination, but should not be confused with physics.
A THOUGHT EXPERIMENT
Consider two inertial systems - one, a speeding train, the other, the embankment. For simplicity we let the train be 300,000km long. On the embankment we have a source of light and 300,000 km down the track a detector. We also have a source at the rear of the train. By Einstein’s first principle, we can say that it will take one second for the light pulse on the train to reach the front, and it will take one second for the pulse on the embankment to reach the detector - both systems are equal for expressing the laws of physics.
As the rear of the train reaches the point where the source of light on the embankment is located, we let both sources emit a pulse of light. The pulse from the train has velocity c with respect to the embankment, as asserted by the second fundamental principle of SRT. (The motion of the source on the train, with respect to the embankment, does not affect the speed of light emitted by it. The speed will be c with respect to the embankment as well as the train.)
Consequently both pulses should reach the detector at the same time, since both travel a distance of 300,000km from the time and point of emission to the detector.
During the time of transit of the light pulses, the front of the train, which initially was even with the target, is moving past the detector. If the train happens to move at one-half the speed of light, the front will be 450,000 km from the point of emission after one second. Since it takes the pulse on the train one second, at any speed, to reach the front of the train, it will have passed the detector on the ground long before the second is up. So it is much faster with respect to the ground than the other pulse! Both principles can't be true simultaneously.
This conclusion is based on the Newtonian View. There is no distortion of space or time to force the two principles to consistency. Einstein used the Lorentz transformation, the underlying device of Special Relativity Theory (SRT), in an attempt to circumvent this contradiction.
HOME PAGE
INTRODUCTION
THE PRINCIPLE OF RELATIVITY
SPECIAL RELATIVITY - 1905
SPECIAL RELATIVITY - 1917
THE MICHELSON-MORLEY EXPERIMENT
THE LORENTZ TRANSFORMATION
MICHELSON-MORLEY PLUS LORENTZ, CONDENSED
THE DOPPLER EFFECT
A COUNTER EXAMPLE TO SRT
A COUNTER EXAMPLE TO GRT
THE AGE OF THE UNIVERSE
THE SPEED OF LIGHT
CONCLUSIONS
APPENDIX I: TYPE 1A SUPERNOVAE
APPENDIX II: A EUCLIDEAN MODEL OF THE UNIVERSE
APPENDIX III: MASS AND ENERGY
All contents copyright 1997, 2006