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We are thankful to the readers for their response to this page. One of our visitors says,
"Your analysis is a physicist's delight. The beauty, the simplicity, and the subtlety of the arguments is never seen before in physics. I know every physicist will admire it but I can assure you that even a philosopher will enjoy it as much."
We are presenting even a more comprehensive analysis and therefore have reduced the discussion on the specific proposals of theory of relativity.
Principle of Absoluteness: "All measurements change proportionally when we move from one frame-of-reference to another frame-of-reference."
Therefore, all our experiments must produce same result provided we make all measurements in same frame-of-reference.
The Principle of relativity is one of the most important laws of physics; it states that laws of physics are same in all frames of reference.
The relativity principle does not explain relativity but is more about absolute nature of laws of physics and hence it will be more appropriate to describe this law as the principle of absoluteness.
Einstein took it upon himself to validate this law and through a meticulous analysis he showed us that x=ct in one frame of reference is equal to x'=ct' in another frame of reference.
Before we move forward, let us discuss the validity of one of the most important proposals of theory of relativity.
This basic premise of the theory of relativity is invalidated by its own proposals.
As we know, using the same Lorentz transformation, Einstein derives the space-time relationship and concludes, “We thus see that the velocity of transmission relative to the reference-body K' is also equal to c. The same result is obtained for rays of light advancing in any other direction whatsoever.”
Why is there a inherent contradiction in the theory of relativity?
Einstein suggests that due to velocity v, time runs slower. In accordance with this proposal, our stopwatch takes longer to record one second, which means light gets extra time to travel. Einstein also suggests that length of our measuring rod contracts, therefore, the same length of the light beam must actually measure more when measured with contracted measuring rod.
Obviously, there is no problem in our application of the proposal of Einstein. There is absolutely no problem in the derivation of the equations or the logic of Lorentz transformations either. Einstein suggests, c=x/t and c =x’/t’ or x/t=x’/t’
Let us examine these equations,
Value of ‘c’ is constant in both the equations and is same in both frames of reference and therefore x=ct can be equal to x’=ct’ only if x’ and t’ expand and contract in the same proportion, which once again confirms that length and time must contract proportionally.
Suppose x’=1.25x then, t’ must also be equal to 1.25t or else, x=ct ≠ x’=ct’.
Let us analyze the equations through which Einstein derives the conclusion, x=ct =x’=ct’.
Now, we move to the reference body k’ that is moving at a velocity of 0.5m/sec.
The light signal will cover the same distance (x’),
x’= (c-v)t/√1-v2/c2
At v= 0.5c, we get,
x’= 150000/0.86 = 173205
similarly, t’ = (1-v/c)t/√1-v2/c2
At v= 0.5c, we get, 0.5/0.86 =0.57,
and hence, ct’ = 173205
c=173200/0.577
and, x’=ct’.
However, we also find that x≠x’ and t≠t’; therefore, the suggestion that measuring rod must exactly be same in reference frames k and k’ is not correct.
One can see that when x = 300000, x’=173205 and when t=1, t’ =0.57, which means length and time contract proportionally.
Therefore, (x=ct)=(x'=ct')
If we assume that an entity like light covers same distance in one second in all conditions without being affected by the speed of the medium it is propagating in then according to above analysis, the speed of light must remain constant in all conditions and in all mediums, not just in vacuum.
In this case, light has less time to travel as t’=0.57t but for us, t=1 second and even t’=1second. This means light must cover less distance even if clock shows 1 second in both the cases. We have to measure the distance between two ends of the light beam through our measuring rod that also has contracted proportionally, therefore, measured speed of energy in all frames of reference, not just in vacuum must be same!
Let us confirm our observations through a thought experiment.
We connect two mirrors to two ends of a meter rod so that if rod contracts then the distance between the mirror reduces and if rod expands then the distance between the two mirrors increases.
We now shoot a laser beam that bounces between the two mirrors and every time it hits one of the two mirrors, the clock ticks once. Let us assume that the interval between the two ticks is one second as per our clock.
If rod contracts then distance between the two mirrors reduces making the clock run faster as the time interval between the two ticks reduces.
This experiment shows that when the length of the rod contracts, the interval between two ticks of the clock reduces and therefore, the clock runs faster.
In his examination of the effect of motion on the behavior of measuring rod and clock, Einstein suggests that length contracts and time runs slower at velocity v but his analysis of Lorentz transformation shows that time runs faster when length contracts. We have to select one of the two contradictory proposals of theory of relativity but even in appendix – I of the theory of relativity the same result is obtained as in the analysis of the Lorentz transformations and in our thought experiment.
Therefore, of the two contradictory proposals of Einstein, we have to select the proposal wherein he suggests that contraction of time is proportional to the contraction of length.
The significance of this analysis extends far beyond the measuring rods and the clocks. We will explore the full implications of this analysis later when we discuss space-time.
Einstein’s interpretation does not leave any scope of relativity in the universe but this interpretation suggests that if we measure length in one frame of reference and time in another frame of reference or even if we keep our clocks immune from any change in the conditions then we are bound to notice relativity of space and time.
This establishes the equivalence of all frames of reference. The equivalence is not achieved by showing that the absolute length of the unit measuring rods remains same in both the frames of reference.
Suppose, a person covers length x in one second in reference body k then the speed of the runner when measured with a unit-measuring rod (m) measuring one meter comes to 100 meters/t (x=100m). If we take this track to the reference body k’, its length reduces to 86 meters but the person has only 0.86t, therefore, he covers the same distance in time t. Since, measuring rod (m) too has contracted to 0.86m, therefore, the track still measures 100m and speed of the person remains 100 meters/t. Relativity enters the scene only if any of three values i.e. the length of the track, length of the measuring rod, or the time interval is measured in a different frame than the other two quantities.
We cannot have a universal equation for length contraction and time dilation for the simple reason that rods made of different material is bound to behave differently at the same velocity. In fact, different rods of the same material must behave differently at the same velocity. Self-generated motion must cause length contraction and therefore must make time run faster for a system whereas derived motion must cause length to expand and time to run slower for the system.
This relationship is applicable for all the factors that affect the length and the time.
The Principle of absoluteness (Principle of Relativity) suggests that laws of physics are same in all frames of reference not just in inertial frames of reference. However, to be able to establish the validity of Principle of absoluteness, we have to show that speed of light in all frames of reference and not just in vacuum is constant. You may immediately suggest that we know that speed of light changes with the change in the medium therefore the Principle of absoluteness is invalidated instantly. I request the visitors to be patient for a while as we join Einstein in asking, "Can we conceive of a relation between place and time of the individual events relative to both reference-bodies, such that every ray of light possesses the velocity of transmission c relative to the embankment and relative to the train? This question leads to a quite definite positive answer, and to a perfectly definite transformation law for the space-time magnitudes of an event when changing over from one body of reference to another."
The relativity appears only if we measure space in one frame of reference and time in another frame of reference. If we keep our clocks immune from the change in most conditions like change in the temperature then we find that speed of light changes with a change in the medium.
Since length of a standard meter rod is dependent on the duration of time therefore in any case, space interval and time interval will be directly proportional.
If we measure the speed and the distance in the same frame of reference then we find that speed of light is same in all frames of reference and not just in the inertial frames.
In fact, all measurements change proportionally when we move from one frame-of-reference to another frame-of-reference and hence all experiments must produce same result in all frames-of-reference provided all measurements are made in the same frame-of-reference.
Therefore, we have now established the the validity of the Principle of Absoluteness.
Another important proposal of theory of relativity is failure of simultaneity.
Let us first simplify Einstein's arguments and see what he has to say,
A light flashes at two different locations A and B simultaneously. An observer is so placed that his distance from location A is less than his distance from location B. The observer has with him a mirror in which he can see the light from both the locations. Einstein's argument is that since the observer is closer to the location A therefore he will notice the light flash first at location A and then at location B for the simple reason that light will take less time to reach him from point A.
Let us put two clocks at both the locations in such a manner that our friend can see both the clocks in the mirror. If we conduct the experiment in the night then our friend can see the clocks only when the light flashes. We assume that clocks show same time in all conditions. Since light flashes simultaneously, both the clocks will show same time irrespective of the distance of the observer from the two locations. Therefore, observer will know that events occurred simultaneously and yet he will see light from the two locations at different times. Is there a failure of simultaneity?
This paradox emerges from the assumption that light is the carrier of the information and not from any inherent contradiction in the theory of relativity. In my analysis of the total solar eclipse, I have shown that there is no failure of simultaneity because we can perceive the light at the place it is generated and at the time it is generated. Both the lights will flash in the mirror simultaneously and both the clocks will also show the same time.
If all the fundamental proposals of theory of relativity result in at least one paradox (some of which have been discussed in the different sections of this website) then is theory of relativity invalid?
I am sure all physicists know the answer but my contention is that in its present form, it is not a valid theory but with slight modifications in its proposals we can establish the validity of the Principle of absoluteness and not the restricted principle of relativity through Lorentz transformation.
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