Einstein introduced a “postulate”, which he defined as “the purport of which will hereafter be called the ‘Principle of Relativity’”. He went on to add “Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by ‘time’. We have to take into account that all our judgments in which time plays a part are always judgments ofsimultaneous events. If, for instance, I say, ‘That train arrives here at 7 o’clock’, I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events’.” He went on further to say: “It might appear possible to overcome all the difficulties attending the definition of ‘time’ by substituting ‘the position of the small hand of my watch’ for ‘time’. And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch”.
From the above, it is clear that he introduced a “postulate”, which defined time as “time series of events occurring at different places”, and he evaluated (measured) “the times of events occurring at places remote from the watch”. Measurement requires a real and absolute unit – otherwise there cannot be any result of measurement. Thus, the watch must be real and absolute measure of time. The watch is a mechanical device, which has to real and subject to mechanical errors. Can such a unit be absolute?
He goes on to add: “If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ‘A time’ and a ‘B time’. We have not defined a common ‘time’ for A and B, for the latter cannot be defined at all unless we establish by definition that the ‘time’ required by light to travel from A to B equals the ‘time’ it requires to travel from B to A. Let a ray of light start at the ‘A time’ tA from A towards B, let it at the ‘B time’ tB be reflected at B in the direction of A, and arrive again at A at the ‘A time’ t’A. In accordance with definition the two clocks synchronize if: tB - tA = t’A - tB)”.
If we go by his postulate that the speed of light is constant, then tA should be equal to t’A if the distance between A and B is fixed. If the distance between A and B is variable, then they will be different. If the variance is random, the two cannot be correlated as each time we will have a set of different readings. If the variance follows a fixed patten, then the two times can be correlated and they would not be relative. Hence ths definition is not free from contradictions as Einstein assumes.
Einstein further says: “We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:
- If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
- If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other”.
What the above statement means is: if both the watches at A and B synchronize with the watch at C, then the watches at A and B synchronize. Thus, the watch at C is treated as a fixed reference frame. Then how can the watches at A and B be relative? If they give reading free of mechanical error and if the readings are different like seconds and nano-seconds, then the readings are not relative, but the units are different. If there is some mechanical error in one of these watches which shows a different reading, will time become different? Einstein actually uses a privileged frame of reference to define synchronization and then denies the existence of any privileged frame of reference. How do you explain this?
Further he adds: “The ‘time’ of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.
In agreement with experience we further assume the quantity:
2AB / t’A - tA = c to be a universal constant - the velocity of light in empty space”.
We have shown above that if the velocity of light in empty space is constant, then either t’A = tA or distance between A and B is variable, in which case they could not be related simply. If there is a pattern in this variance, we could come to t’A = tA after applying suitable corrections. If there is no pattern, then t’Acould not be related to tA. In otherwords, if 2AB = 2 x AB, then t’A - tA = 0 and c is infinite. If 2AB = AB + BA, where AB ≠ BA, then either c = 0 or indeterminate, according to whether there is a pattern or not. How do you explain this contradiction?
Assuming time is relative to motion of the observer, how could we measure it in another frame of reference that is accelerating with reference to us? Einstein says: “We now inquire as to the length of the moving rod, and imagine its length to be ascertained by the following two operations:
(a) The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest.
(b) By means of stationary clocks set up in the stationary system and synchronizing in accordance with § 1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated ‘the length of the rod’.”
The method described at (b) is misleading. We can do this only by setting up a measuring device to record the emissions from both ends of the rod at the designated time, (which is the same as taking a photograph of the moving rod) and then measure the distance between the two points on the recording device in units of velocity of light or any other unit. But the picture will not give a correct reading due to two reasons:
· If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.
· If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the recording device and the picture we get will be distorted due to different Doppler shift. Thus, there is only one way of measuring the length of the rod as in (a).
Here also we are reminded of an anecdote relating to a famous scientist, who once directed two of his students to precisely measure the wave-length of sodium light. Both students returned with different results – one resembling the normally accepted value and the other a different value. Upon enquiry, the other student replied that he had also come up with the same result as the accepted value, but since everything including the Earth and the scale on it is moving, for precision measurement he applied length contraction to the scale treating the star Betelgeuse as a reference point. This changed the result. The scientist told him to treat the scale and the object to be measured as moving with the same velocity and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of sodium light is infinite. To a surprised scientist, they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of sodium light!
Some scientists we have come across try to overcome this difficulty by pointing out that length contraction occurs only in the direction of motion. They claim that if we hold the rod in a transverse direction to the direction of motion, then there will be no length contraction. But we fail to understand how the length can be measured by holding the rod in a transverse direction. If the light path is also transverse to the direction of motion, then the terms c+v and c-v vanish from the equation making the entire theory redundant. If the observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod while moving with it, he will not find any difference because the length contraction, if real, will be in the same proportion for both.
The fallacy in the above description is that if one treats “as if all three were at rest”, one cannot measure velocity or momentum, as the object will be relatively as rest, which means zero relative velocity. Either Einstein missed this point or he was clever enough to camouflage this, when, in his 1905 paper, he said: “Now to the origin of one of the two systems (k) let a constant velocityv be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks”. But is this the velocity of k as measured from k, or is it the velocity as measured from K? This question is extremely crucial. K and k each have their own clocks and measuring rods, which are not treated as equivalent by Mr. Einstein. Therefore, according to his theory, the velocity will be measured by each differently. In fact, they will measure the velocity of k differently. But Mr. Einstein does not assign the velocity specifically to either system. Everyone missed it and all are misled. His spinning disk example in GR also falls for the same reason.
SPACE, TIME, DIMENSION: Both space and time arise from our sense of sequence (priority-posterity) and interval. When this perception is related to objects, the interval between them is called space. When it is related to changes in objects, i.e., events, the interval is called time. We use an easily intelligible and fairly repetitive interval and subdivide it to get the unit. For space, we use hand or foot measure or some other standardized interval and for time, we use the day or the year and then subdivide these to get feet, meter and second, etc. As you can see, the interval is empty - without a physical existence in the absence of objects and events. It is imagined through alternative symbolism. Thus, space and time are really the measurement of intervals, which keeps changing irrespective of our perception or measurement. Hence both these are fundamental in perceptual sense. Now we will justify your statement.
Physicists without exception talk about extra dimensions: 10, 11, 26 or 'n'th dimensions. Dimension is the interface between the internal structural space and external relational space of objects. Since we perceive form through electromagnetic interaction, where the electric field and the magnetic field move perpendicular to each other and both move perpendicular to their direction of motion, we have three mutually perpendicular dimensions. In solids, where the 'form' is fixed, these dimensions are invariant under mutual transformation. You can change length to breadth or height without disturbing the form. Since time does not fulfil this criteria, it is not a dimension, though every objects exists in time only. There is nothing like extra dimensions, which could not be discovered even after more than a century. Yet, almost all physical theories are based on extra dimensions.