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The lifts experiment and equivalence principle
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The lifts experiment and equivalence principle
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The lifts experiment and equivalence principle
«
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14/05/2008 09:16:32 »
The lifts experiment and equivalence principle
Background and actual explanation
The equivalence principle was exemplified by Einstein with a thought experiment. Imagine two elevators, one at rest of the Earth's surface, one accelerating in space. To an observer inside the elevator, without possibility to observe the external world, there is no physical experiment that it could be performed to differentiate between the two scenarios.
Consider an elevator moving with constant acceleration like in fig 1. Suppose that a source of light emitting a fascicle perpendicular to the elevator's direction of motion enters the elevator through a hole on the left wall and strikes the right wall. Let’s compare what’s happened for an internal observer from elevator in comparison with an external observer.
Suppose now that at a moment t1 a light beam hit the wall in a point A1. It leaves the lift at t2 from a point A2. In between t1 and t2, the elevator has moved, so that A2 is lower than A1 (elevator is going up). For an elevator observer the light passed through left wall, will follow a curved path and will hit the right wall of elevator in a lower point.
Now, in a rested elevator, the trajectory of light observed by the observer in the lift is a straight line, off course (dotted line).
The equivalence principle tells us that we cannot distinguish between an elevator accelerated and an elevator experiencing a constant gravitational force. A very surprising corollary of equivalence principia regards light comportment in a gravitational field. It follows that the same effect should be observed if we place the elevator in the presence of a gravitational force: light paths are curved by gravity.
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Figure 1
Proposed explanation
This is a nice thought experiment, but incomplete and also with a faulty explanation in frame of general theory of relativity.
Let’s reconsider the lift movement in a little bit more possible movements.
For a simpler interpretation, the external observer S is considered stationary relative to the light source O, and case of three lifts like in fig 2 is considered.
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Figure 2
One lift is stationary relative to S observer and implicit to source O, the second lift is accelerated upward with acceleration a, and the third lift is moving with constant speed v in the same direction like previous accelerated lift. Besides external observer S in every lift there is still one observer able to see only the trajectory of light fascicle inside lift.
For the S observer light fascicle follow a line trajectory like in fig .
In a) case, the observer inside lift will observe a straight line trajectory of light fascicle similar to external S observer.
In b) case the lift observer will see a curved trajectory for the light fascicle, case already presented by Einstein so it’s not the moment to insist.
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Figure 3
Novelty is represented by c case; what will see an inertial observer, which is not accelerated, but it moves with constant speed, in this case.
From this point of view, if the light pass the left wall at time t1 and arrive at right wall at time t2, in this interval of time, the lift is moving upward with a certain amount so the observer will observe that fascicle of light is curved. Experimentally the speed v can be arranged in such manner, to have the same deviation in case c like in case b.
But if for accelerated observer the trajectory of light beam is an arc of parabola, for an inertial observer the trajectory of fascicle beam is a line tilted with a certain angle relative to initial direction of motion. In both all cases the form of trajectory seen by lift observer is due to the composition of light speed with lift speed.
Following the logic of two cents, already formulated by equivalence principle, we must invent a special property of inertial frame and due to this property the light is curved for this observer. If we continue with this simple logic, it is possible to demonstrate the absolute motion of a referential.
The conclusion of general relativity, regarding the impossibility of a closed observer to determine his state of motion (relative to an external reference) or his relative acceleration is a stupidity. And this stupidity forms the basis on the highest theory of physics, which can be understood only by a elite of ,,certain physicists”.
In proposed theory there is a clear difference between a cinematic effect and a real effect.
Of course photon like a mass particle is acted by force of gravity and its trajectory is modified as consequence of this action. But in case of a lift moving with constant speed or accelerated, simple cinematic effects appear and the form of trajectory will depend also on the position and motion state of observer. In case of a gravitational field the trajectory of the photon is modified, and after escaping from this gravitational field, photon will move with modified energy and modified trajectory. In case of moving observer, the modification of trajectory is apparent to the observer, and is due to the proper motion of the observer. For any other observer or for any other direction of motion the trajectory will have another form.
It is impossible to make equivalence between an accelerated field and a gravitational field, even both are consequences of real forces and even for some special observers the final effect over the photon is the same. Even in a case when for all observers, independent on their state of motion or direction of motion there is a fully equivalence between action of an accelerated field and a gravitational field it will be difficult to make such assumption.
The experiment up presented can be used in order to establish a movement of a body (relative or accelerate) to another body (source of light), even the actual theory of relativity does not permit this. In principle the difference of height due to the trajectory of photons can be measured by internal observer and the direction of motion can be easily obtained. Admitting the fact that lift observer, can in principle, observe the form of the trajectory of photons inside lift (see cloud chamber principle), the closed observer can determine also if the lift has an accelerated motion or an inertial motion.
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