: Einstein proves x=ct=x’=xt’, which is possible only if time runs faster when length contracts; Einstein then goes on to prove that time runs slower when length contracts. We must select one of the two contradictory proposals of the special theory of relativity. Which of these two contradictory proposals is right?


Introduction


Einstein painstakingly establishes the compatibility of law of propagation of light with principle of relativity. A mere reading of the first line of the abstract is enough for any physicist to realize the contradictions in the two fundamental proposals of physics; but for us, it is more important to know, which of these two contradictory proposals is correct?

In this paper, which can turn the physics upside down, we will try to resolve this inherent contradiction but more importantly, we will try to establish the validity of Lorentz symmetry.


First, let us analyze the contradictory proposals of theory of relativity,


Discussions


As Einstein sets out to establish compatibility of the law of propagation of light with the principle of relativity, he asks,

“In other words: 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?”

And provides the answer too,

“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.”

However, Einstein’s analysis leads to two contradictory answers; to resolve this theoretical problem, let us now conduct a thought experiment but before that let us briefly examine another important observation of Einstein.

“The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case.”

This is where idea of perceived reality (including the reality of the perceived motion) being on par with the quasi reality originates. Einstein suggests that there is no difference in the perceived motion and real motion.

If three different physicists conduct same experiment in three different inertial frames then they must get same result even though their frames of reference may not exactly be identical.

Let us start our experiment now…

We remove all the air from the setup in reference body a, which is in the state of rest and start a stopwatch that has a trigger that shoots a laser beam as soon as the stopwatch starts ticking and stops as soon as stopwatch stops ticking. We run the stop watch for one second and freeze the laser beam. We cut an iron to the exact size of the laser beam; this becomes our unit-measuring rod (m) of one meter and gives us the distance traveled by the light in one second.

Now, we repeat the same experiment in the reference body b that is moving at a velocity of 0.5c. As per theory of relativity, the clock runs slower for a body in motion, therefore, the laser beam gets extra time (1.15t) to travel and hence distance between two ends of laser beam increases to 1.15x when measured with the same measuring rod. However, we also know that the measuring rod m contracts to 0.86 meters at velocity v = 0.5c, therefore, our measurement shows that speed of the light has increased to 1.33 meters per second. As per theory of relativity, speed of the light is independent of the speed of the medium it is propagating in; therefore, we can assume that length of the laser beam remains same if the interval between the two ticks of clocks remains constant irrespective of the conditions clock is operating in.

We now move to the reference body c, which is moving at a velocity of 0.75c and repeat the same experiment. To our surprise, speed of light now measures 1.5 meters per second.

Based on the experiments conducted by him, our observer concludes that an increase in the velocity of the train causes light to move faster. Obviously, we cannot conclude that speed of light in vacuum is constant because speed in itself is not a directly measurable quantity and depends on the measure of distance (rod) and measure of time (clock). If these two measures do not have absolute values then speed of light cannot be absolute in any medium including in vacuum unless we can show that all measurements change proportionally and therefore, measured speed of light must remain constant in all frames of reference.

The fact that we have not conducted the experiments in the same inertial frames does not make any difference because assumption of the theory of relativity is that speed of light in vacuum is constant in all frames-of-reference provided the experiment is conducted in inertial frame-of-reference.

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.”

Let us find out how Einstein establishes this relationship.

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, one meter of light beam must actually measure more than one meter.

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.

What is surprising is that Einstein himself has shown that the absolute value of the x and t in the equations x=ct and x’=ct’ is not same. We have to show that,

C = x/t and c = x’/t’ or x/t = x’/t’

Let us examine these equations,

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 be equal to 1.25t or else

X = ct cannot be equal to x’= ct’.

Let us analyze the equations through which Einstein establishes this relationship.

If we assume that a light signal travels at a velocity of 3,00,000 km/sec then in reference body k (that is in a state of rest), laser beam travels 3,00,000 km in one second.

x=ct = 300000*1= 300000.

Now, we move to the reference body k’ that is moving at a velocity of 1,50,000 km/sec.

The light signal will cover a distance x’,
x’= (c-v)t/√1-v2/c2

At v= 1,50,000 km/sec, we get, x’= 150000/0.86 = 173205

Similarly, t’ = (1-v/c)t/√1-v2/c2

At v= 1,50,000 km/sec t’ = 0.5/0.86 =0.57,

By replacing the values of x’ and t’ in the equation c=x’/t’, we get, c=173200/0.577 = 300000

and in the equation, x’=ct’, we get

173000 = 300000*0.57=173000

Therefore, x = ct and x’ = ct’, however, we also find that x ≠ x’ and t ≠ t’and x = ct ≠ x’= ct’.

Therefore, the suggestion that measuring rod must exactly be same in reference frames k and k’ is not correct.

Einstein assumes,

“The principle of relativity teaches us that, as judged from K, the length of a unit measuring-rod which is at rest with reference to K' must be exactly the same as the length, as judged from K', of a unit measuring-rod which is at rest relative to K.”

One can see that when x = 300000, x’ = 173205 and when t = 1, t’ = 0.57.

However, Einstein here puts the phrase, ‘as judged from K’ in his observation, therefore, we must look at these results a bit differently. As per theory of relativity a length measuring 3 meters must contract to 1.73 meters at 0.5c. For a person actually in motion, the rod remains 3 meters, whereas another rod actually in a state of rest but appearing to be moving at 0.5c to the person in motion must appear contracted. Therefore, even if judged from K, the two rods cannot be same.

However, this is not what principle of relativity teaches us. Principle of relativity only teaches us that all laws of physics must be same in all frames-of-reference and this condition is satisfied if length and time contract proportionally.

Einstein has shows us that they do!!!

When length contracts, time runs faster and when length expands, time runs slower.

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 the theory of relativity, the speed of light must remain constant in all conditions and 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’=1 second, therefore absolute interval between two ticks of the clock must reduce. This means light has less time to travel and we have to measure this unit 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!

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. Absoluteness is not achieved by showing that absolute values of the x and t do not change. A snapshot taken of the two rods will show a difference in the length of the rods and yet the results of all the measurements will be same.

Einstein’s interpretation does not leave any scope for relativity in the universe but this interpretation suggests that if we measure speed 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. In simple words, if we do not measure all the quantities in the same frame-of-reference then we have to encounter relativity.

Let us confirm these observations through a simple thought experiment.

We connect two mirrors to two ends of a meter rod so that if rod contracts then the distance between the mirrors 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.

If rod contracts then the distance between the two mirrors reduces making the clock run faster as the time interval between the two ticks reduces.

This experiment confirms our conclusion that when the length of the rod contracts, the interval between two ticks reduces and therefore, the clock run faster.

Einstein presents another elaborate analysis to show that when length contracts, time dilates. How does Einstein reach this conclusion?

Let us examine following analysis,

“Let us now consider a seconds-clock which is permanently situated at the origin (x' = o) of K'. If t’ = o and if t’= I are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = o and t = 1/√1-v2/c2.

As judged from K, the dock is moving with the velocity v; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but 1/√1-v2/c2. seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest.”

There is absolutely no issue with the mathematics but the logic leading to the mathematics is faulty. We can see the logical error in this argument without even questioning the highly unscientific definition of time given by Einstein.

An object spatially separated from the clock by any arbitrary distance apparently has an instantaneous effect on the rate of flow of time of the clock. Thus, as per theory of relativity, the object in motion and the clock are entangled entities experiencing spooky action at a distance.

How can motion of one body affect the physical properties of another body?

As per theory of relativity perceived motion cannot affect the flow of time of any entity that is spatially separated from it by an arbitrary distance and yet we have this contradictory proposal that perceived motion can causes an instantaneous change in the physical properties of another physical entity.

A sound theory must precede the mathematics but Einstein does not provide us causal explanation for Lorentz transformation. We do not know why and how motion makes the time run slower or faster for an entity and how does motion results in contraction of length?

Einstein just tells us that motion, whether it is real or perceived, causes a change in the physical properties of an entity but does not answer two related questions, ‘Why?’ and ‘How’.

Even as per proposals of theory of relativity, perceived motion cannot be equated with the real motion.

Even otherwise, it is difficult to understand what Einstein is proposing in the first three sentences of this quote and then connect it with the ticks?

t is supposed to be a tick, it is an event and therefore, t = 1/√1-v2/c2 does not make any sense at all as an event cannot have a value attached to it. t = 1/√1-v2/c2.

What we are actually looking at is the interval between light beam striking the first mirror and the light beam striking the second mirror. If this interval is x in reference body K then we must find the value of x in the reference body K’.
If we apply these arguments to our above clocks then the two events – light beam striking mirror A and light beam striking mirror B are represented in the above arguments of Einstein as : t = o and t = 1/√1-v2/c2. This does not make any sense at all because the event of light beam striking either of two mirrors cannot have a mathematical value. Two ticks are just two events and events cannot have mathematical values.

Einstein goes one step beyond and suggests that these two events can actually have ‘n’ number of mathematical values simultaneously provided there are ‘n’ number of observers moving at different velocities vis-à-vis the clock. This means that a clock must show different times to different observers. If different observers moving at different velocities watch the clock using a powerful telescope then each one of them see clock running at a speed that is different from the speed that other observer notice. Theory of relativity suggests that a clock can actually run at different speeds simultaneously.

This is exactly what the suggestion of failure of simultaneity also proposes. Even as per theory of relativity, the can be alive and dead simultaneously but we can even watch the cat and alive and dead simultaneously. In fact, we can watch the entire life of a cat from the moment she is born to the moment she is dead simultaneously. We just have to place a few thousand mirrors at different places. This is only a thought experiment but it shows the sort of illogical possibilities theory of relativity creates.

Theory of relativity opens the same possibilities, in fact, a lot more illogical possibilities than the quantum mechanics. All the proposals of quantum mechanics turn logical if it adds two words to its proposals, ‘for us’.

For us, it is not possible to know the physical state of a cat in the sealed box and therefore, for us, the cat is dead and alive simultaneously. However, our observational does not allow us to conclude that a cat can be in two different physical states simultaneously or something can be wave or the particle at the same time.

One can see special theory of relativity is self-contradictory and yet theory of relativity has enormous value for physics but definitely not in its present form. The biggest supporters of the theory of relativity are its biggest enemies because they just do not want to assess it and make changes in it. With few modifications, it can still be a very valuable theory for physics.

Conclusions


We have noted in this paper that special theory of relativity contains more than one contradictory proposal. If only Einstein had stopped at x=ct=x’=ct’, physics would have been a lot different and a lot logical than it is today.

This small correction has enormous implications but we cannot discuss the implications of these observations in one paper, therefore, readers are encouraged to visit my website www.norlabs.org for more information.

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