The Equivalence Principle, True or False ?

Why such a question ?

Galileo Galilei At the end of the 16th century, Galileo Galilei (according to Vincenzo Viviani) demonstrated that the speed of falling bodies is not proportional to their weight, throwing two spheres from the leaning tower of Pisa : the surprised audience had to admit that in spite of their different weights, the two objects reached the ground at the same time. Four centuries later, this experiment would still disconcert people.

This fact is the consequence of what physicists call the Equivalence Principle (EP) (Albert Einstein's Postulate) or Universality of Free Fall (UFF). It says that an acceleration effect (inertia) and a gravitational one (attraction between two gravitational masses) are equivalent. For example, let's imagine a motionless elevator around our planet, and someone in it. Then, because of this Equivalence Principle, no experiment could tell that person if her weight is caused by the attraction of the Earth, or by someone accelerating the elevator, pulling it.

Albert Einstein Until now, no violation of the EP has been discovered. But for how long ? In fact, the Superstrings Theory implies such a mismatch between gravitational and inertial mass, no matter how small … (and why should Nature necessarily be bound to the rules scientists wrote ? even physicists …). That's why our goal is an experimental one : to test a new way to find this hypothetical violation. By the way, note that the Superstrings Theory hasn't been confirmed yet (and neither rejected) by no experiment.

Today, despite the spectacular technical progresses and the increasing complexity of the scientific experiments, Galileo's spheres are still the leading principle to test the Universality of Free Fall. Our idea is to take the advantage of a “zero-g” situation to compare, in a very simple way, the angular acceleration of two masses, instead of a translation one, which should give us the opportunity to “blow up” the results precision. And that's where our principle would totally innovate. As for the measure of this system's acceleration, it can be done with the interference figure of a laser ring, using an interference effect, known as the Sagnac Effect. In a simple way, we can say that this effect makes an acceleration detectable as the presence of an acceleration shifts the interference figure (the "shadow and light lines" alternation).

La tour de Pise What about the “zero-g” situation ? It allows us a fall of approximately 22 seconds. In other words our Pisa tower will be 2 km high and the laser, during those, will have covered 6 600 000 km ! Compare it with the few meters of the actual systems using laser interferometry and you see where the precision comes from ... (all the more as this distance has a role of lever arm in our “rotational” system).

This experiment would then be a good opportunity to focus on this main physics principle, either on a theoretical and a pragmatic point of view : what it means in our every-day life and to the latest physics theories, and hence what his violation would imply.



And now, how can we know ?

General Principles :
Since Galileo, we know that two objects fall on Earth with the same acceleration.
If we drop a « dumbbell » (two masses rigidly connected), its angular velocity will stay constant while falling. This means that if we drop it with a certain angle, without giving it any impulsion (no angular velocity), the dumbbell will keep that initial angle.

Les deux masses, avec une accélération angulaire nulle
Einstein extended that idea to the Equivalence Principle : «A body's inertial mass equals its gravitational mass». In other words, distinguishing an acceleration and a gravitational force is impossible.

Equivalence Principle :

Acceleration on Earth is the same for any body (in free fall), whatever its mass.

Yet, a few modern theories predict the violation of that principle :

In that case, acceleration would be proportional to the ratio between gravitational mass and inertial mass :

Hence, two bodies in free fall wouldn't fall with the same acceleration. In the case of our dumbbell, this means that the angle is going to be modified ! There will be an angular acceleration !
Les deux masses avec une accélération angulaire
This experiment can be realised in a very simple way. However, the effects, if they do exist, would be so slight that we need drastic manipulation conditions and accurate measurements too :

A sufficient drop time.
Negligible air friction.
High precision measurements (cf. next paragraph).

Such conditions are unreachable on Earth. In fact, velocity is proportional to the square of the drop time and air friction has always to be considered.
And that's where the advantages of a parabolic flight appear : during the parabolic flight, the airplane falls for 22 seconds ! About 2 kilometers ! Moreover, the air surrounding our experiment falls as fast and thus the effects of air friction can be avoided.
A third main point to consider is the development of a high-precision measuring device. This is the subject of our next paragraph.


Measurements and Sagnac Effect :

1) General Points
The aim of our experiment is to measure an angular acceleration. To do so we will use a Sagnac interferometer. This is an experimental device allowing to analyse the fringe pattern coming from a laser light. The light is split in two parts by a semi reflecting mirror and then sent into a ring interferometer, made of optical fibre. One beam propagates clockwise and the other counter-clockwise. This is not the same as in Michelson 's interferometer, where light follows a straight path. Depending on the rotation state of the system, a change in the phase will sense the angular acceleration of the whole system. Michelson 's interferometer allows to measure linear acceleration ; a ring interferometer based on the Sagnac effect allows to measure angular acceleration. This effect can be compared to a Doppler effect caused by the rotation. It was first understood by a French scientist, Georges Sagnac, in 1913.
This is summarised by two equations :

where delta-t is time difference between the beams and delta-phi the phase difference, omega the angular velocity and A the interferometer's surface.

2) Measurements :
To be able to observe the possible angular acceleration of the whole system, the interference pattern has to be observed continuously. A camcorder will record the interference pattern constantly. Whether the camcorder is a digital or a numeric one, we will have to convert the data into numeric form or not, after the actual flight. Once we will have numeric data, we will be able to detect with a software any significant change and continuous displacement of the interference pattern. Such a change would follow from an angular acceleration due to a difference between inertial and gravitational masses. Sudden changes would be induced by external hits or discontinuous wavelength shifts from laser light but the interesting phenomena is only a slow and continuous shift of all interference fringes.

So we will build the following device :

Dispositif schématisé


Two masses with different densities will lay on both sides of a platform where the whole interferometer is tied. The interferometer consists of a laser, a semi reflecting mirror, an optical fibre and a camcorder. The laser will be a vertically oriented laser diode, powered by batteries, fixed onto the platform. The angle between the laser beam and the mirror will be 45°. So, the mirror will split the beam in two sub beams. The optical (multi-mode) fibre is vertically wound. The more turns, the greater the sensitivity to an effect because it virtually increases the interferometer surface. Both fibre ends are placed so that they will catch one of the sub laser beams. In consequence, each sub beam will follow the same path but in opposite directions. Going out from the fibre, each beam will be once again split into a transmitted and a reflected part. The space around the mirror is divided into four parts : the laser side, two sides with the optical fibre and the last side where the fringe pattern occurs. So, one part from each sub beam comes and superposes in the fourth side of the mirror to build up the fringe pattern, which is recorded by the camcorder. Thus, we have to fix the camcorder on the fourth side, horizontally, on the platform. It will be powered by his own batteries.

For explanations about interferences : this way ! it's about sound but it's exactly the same for light (which is an electromagnetic wave)

It may look somewhat surprising that the interferometer is laying on the lever arm. However, if the mass equivalence principle is correct, the interferometer won't have any effect on the lever during the free fall. If this principle is violated, by placing all the devices (laser, camcorder and so on) on the side of the denser mass, and away from the center of mass of the lever arm we will increase the sensitivity to an effect. The whole system is closed inside a box which protects it from outside mechanical, atmospheric and electromagnetic disturbances. Moreover, protecting foam will cover the inside box wall. Another small platform on the inside bottom side of the box will be put down on a “spring carpet” whose aim is to give a small upward impulsion to the free falling system at the beginning of the parabola. As the phase just before the parabola is a high downward acceleration phase, the subsequent stretching of all springs will give the impulsion allowing the system to loose any contact with the box during the parabola. To control the total spring impulsion, stop screws will enable us to limit the maximum spring contraction. Consequently the impulsion can be adapted to avoid the system to hit the upper side of the box. The top cover of the box will include a trellis to allow eye watching and intervention on the system.The two masses, on both sides of the platform, will have different densities and will be made from nonmagnetic material so that we can avoid any external electromagnetic field influence.

We don't aim at measuring an accurate value but rather look for a upper limit to such an effect. We are aware of the small magnitude of the expected effect. We don't expect to measure a significant angular acceleration, but our experiment is an original way to reach a very good precision and involves some rather nice though basic physics concepts.