Superluminal Motion: Fact or Fiction?
By
Ryan Frewin Renee George,Deborah Paulson
ABSTRACT
With the mathematical formulations around the turn of the century for the behavior of particles at velocities near that of light, the race was on to find a way to break Einstein's ultimate speed barrier. As early as the 1930's scientists began developing theories and experiments to search for particles traveling faster than light. New theories suggested the existence of such particles, known as tachyons, just as Dirac's theories predicted the existence of the first known anti-particles. Until recently, experimental methods have not been adequate to test the myriad of theories. In the last decade, however, instances of superluminal travel have been positively and verifiably identified, mostly in the field of quantum mechanics and quantum barrier penetration, or tunneling. Consideration of the many paradoxes of relativity leads to questions of time reversal and problems with causality, but a careful examination of the experimental evidence leads to the conclusion that superluminal transmission of particles is possible without interfering with Einstein's causality problem. In the following paper, the evidence for superluminal motion will be presented, along with an analysis of the implications of such a discovery.
INTRODUCTION
With the publication of his general theory of relativity in 1905, Einstein showed Newtonian physics to be inadequate. He introduced the idea of an ultimate speed limit known as c,the speed of light.Aswith any limit human nature brings a desire to exceed it. With this goal scientists have devised theories and experiments to test the validity of Einstein's theory. In fact a closer mathematical look shows thatcis not a limit at all, but a barrier. It is not possible to accelerate an object to a velocity faster than light, but it is possible for the object to have a velocity greater thanc.Within recent years, new scientific evidence in the fields of electricity and magnetism and quantum mechanics has supported this claim.
WHERE DOES THE SPEED OF LI6HT COME FROM?
One of the exciting and broadly applicable areas of physics is electricity and magnetism. This field was unified in the 1860's when a brilliant man, named James Clerk Maxwell, derived four equations which summarized all of the effects which had been observed. One of the more hidden consequences of these equations was a constant speed of light: The equations said that electromagnetic waves should travel with the speed c equal to 1/sqrt(e0*m0) where e0 is permitivity of free space and m0 is the permeability of free space. This was odd because m0 and e0 ore both physical constants easily determinable through experimentation. How could light always be going one speed?
AN ABSOLUTE CONSTANT?
To soy that the speed of light is a constant is one thing. To say that it is the same absoluteconstant everywhere is quite another thing. Imagine for instance, that there is a man on a platform watching a train travel with speed v1 to the left and a car by the train travel with speed v2 to the right. Now switch the frame of reference to see the situation from the point of view of a woman in the car. Note that a frame of reference is a scientific word which is easily explained by calling it a point of view. In the man's frame of reference the train is going v1 m/s, but in the woman's frame of reference, it is going v2 + v1 m/s. If the speed of the train is an absolute constant, everybody sees the train going v1, and velocity addition does not work.
However, velocity addition seems so logical to scientists that it should be applicable to the velocity of light. This means that light could not have a constant velocity in all frames. In order to resolve this apparent conflict, they asserted that the speed of light was only constant in one absolute frame of reference, an ether frame. In any other frame, the speed of light varied according to its motion relative to this ether frame. This is like saying that the man on the platform has something special about him so that he always sees light goingc m/s and all others must measure the speed of light using their motion relative to him. This theory was so accepted that two men, Michelson and Morley, set out to prove that the ether frame existed. They did this by setting up an experiment to accurately measure the speed of light at different times. At one point the earth would have to be going the same direction as the ether frame and the speed of light would equal the speed of the earth plus the speed of the ether frame. At another point the earth would be going perpendicular to the ether frame and the speed of light would simply be equal to the speed of the ether frame. The only problem was that Michelson and Morley did not prove what they set out to prove. Instead they proved that the speed of light did not vary at all. Light really did hove an absolute constant speed.
CONSEQUENCES
What did this mean? The ability to just add velocities in order to switch between frames of references disappeared. If the train in the case scenario above is replaced by a beam of light, both the man and the woman see the light moving with speed vl equal to c.
This is where Einstein and his famous theory of relativity appeared on the scene. He took the results of the Michelson and Morley experiments and made two statements, called postulates, on which he based all of the rest of his theory. In order to understand the postulates, it is necessary to know the definition of an inertial frame:
Aninertial frame is any reference frame (that is, system of coordinates x, y, z and time t) where all the laws of physics hold in their simplest form.
The postulates of Special Relativity are:
FIRST POSTULATE OF RELATIVITY: If S is an inertial frame and if a second frame S' moves with constant velocity relative to S, then S' is also an inertial frame.
SECOND POSTULATE OF RELATIVITY: In all inertial frames, light travels through the vacuum with the same speed, c = 299,792,458 m/s, in any direction.
Many equations have been produced from these two postulates. One of the most illuminating ones is that describing the momentum, p.Momentum is the property of a moving body that determines the length of time required to bring it to rest when under the action of a constant force. According to Einstein,pis mathematically defined as: P = mu/sqr+(l - (u/c)2) whereuis the velocity or speed of any object. When this equation is solved foru,insite may be gained about limiting properties that Relativity had on the velocity of objects. u = 1/sqrt((m/p)2 - (1/c)2) ,the mass set equal to one. This is red line in the graph. Compare this with the blue line which represents the old Newtonian equation p=m*u. The Newtonian equation is a good approximation until u is greater than 0.6c. There are a few things which are left out by this graph. What if the object had on imaginary mass? This means that if one squares the moss, the result is negative. If the mass is held constant, equal to the square root of negative one, the graph is now the green line. Objects with imaginary mass are known as tachyons and will be discussed later. Notice that any such object has a superluminal velocity.
PROBLEMS WITH CAUSALITY
What are the problems associated with going faster than light? One thing scientists are concerned about is that superluminal motion would upset our whole cause and effect related system. One easy explanation is called the "Treaty of Shalimar".
Assume for instance that the Klingons and the Federation sign a treaty in which the Klingons promise peace in exchange for access to the Federation's Technical Information Database (TID). The Federation leaves to take the treaty back to their home world at a speed of .6c. This gives the Klingons time to access the TID and develop a faster-than-light ship called the "slaughtering Super". They then send the Super in pursuit of the Federation ship of negotiators. As it travels toward the ship, it destroys two bases along the way. These bases try to warn the ship, but of course any signal that they have can only travel at the speed of light which the Super easily outruns. The Super then gets to the negotiator's ship and destroys it, destroying all evidence of any treaty and throwing the Klingon nation and the Federation back into war. The problem comes in when one looks at this sequence of events from the Federation's point of view. If one uses the correct equations to switch all of these events into their frame of reference, then the negotiators sign the treaty at Shalimar, and take off. The next event that they see is their own destruction. If they had remained alive after this, they would have next seen event 2, then event 1, and then watched the Super be disassembled. They would have seen the pieces of base number 2 gather together and form back into a base as the Super traveled backwards through space to its creation where it would have been taken apart and destroyed by the Klingons.
Scientists concluded from arguments like this that there is a basic Law of Causality which states that if A and B are two events which are causally related (A causes B) there will be no frame of reference in which B happens before A. There can not be a slaughtering Super, or from the Federation's point of view, it would destroy the Federation ship before it was even created.