RELATIVITY & SPECIAL RELATIVITY

RELATIVITY & SPECIAL RELATIVITY topics

In 1905, Einstein produced 3 seminal papers ( seminal means "pregnant with possibilities") one of which is his "Special Relativity".

Relative motion is the comparison of positions, velocities and accelerations as we move from one "frame of reference" to another.

Consider two cars approaching each other head on, one at 60 kmh^-1, the other at 40 kmh^-1. But these velocities are measured relative to the side of the road, the side of the road is the understood "frame of reference".

If we now move into one of the cars, say the 60 kmh^-1 one and make it our frame of reference; then the road goes backwards at 60 kmh^-1 and the other car comes towards us at 100 kmh^-1. We have changed our frame of reference, so the relative motions of ground and other cars to alter.

The relative motion statement in algebra of the above is

v_BrelA = v_BrelG - v_ArelG (1) ( "BrelA" means "B relative to A" , G is the ground )

To see this in 2D, go to the animation below of two ships, A and B passing relative to a lighthouse, the ground, G.

In two dimensions, we use vectors to add or subtract velocities to move from one frame to another. Our usual frame is considered "stationary". As a result, we see motion relative to that frame possibly moving "sideways" or "backwards". We see this when sitting in a car with other traffic around us. Our brain interprets the situation as normal - we don't think about it consciously.

The equation is assumed by us in everyday life and was by Newton. Indeed, the equation is a statement of "Newtonian relativity" (also called the Galilean velocity transformation).

Newtonian physics holds that the only things to stay the same when moving between inertial frames of reference are acceleration and Newton's Laws. ( Things that stay the same from frame to frame are called INVARIANTS. ) In Inertial Frames, no matter who you are or what you are doing, you will, when measuring a racing car's acceleration, get the same value as everyone else (providing you didn't stuff up the experiment)!

It is automatically assumed that momentum and energy laws are the same between inertial frames as they are apparently part of Newton's Laws. ( This turns out to be false.)

Non accelerating frames are "inertial" - Newton's Laws clearly apply, but accelerating frames are non-inertial and Newton's Laws seem to go wrong. When in a car is going around in a circle, it is accelerating, velocity is changing, a force SEEMS to push you outwards - the so called "centrifugal" force. The car is accelerating so non Newtonian Forces seem to exist. Step outside and look from the side of the road which isn't accelerating, and it is clear that an inward force exists on the car. Newton's Laws rule OK.

In Newtonian physics, all inertial frames - frames moving at a "constant velocity" - are the same and that an experiment carried out entirely in such a frame cannot tell the experimenter its absolute velocity, only its velocity compared to other inertial frames. Sit in a smoothly running carriage or plane and it seems motionless UNLESS you look outside. Is there a frame TRULY AT REST? Newtonian physics cannot find one. To Newtonian physicists, all inertial frames of reference are "relative".

THE TROUBLE WITH LIGHT

James Clerk Maxwell developed a set of equations in 1861 which actually PREDICTED the speed of light and modelled light in terms of electric and magnetic fields. This was a brilliant step forwards.

In the C19th, physicists only had mechanical models as their standard. They tended to think in terms of Newton's Laws, so to them, light should have a medium to flow through. As sound has air, light should have a "Luminiferous ether", and as air is to sound, the ether was to light. ( Note - "ethernet" is used today by computer nutters - how out of date is that! )

("Aethers" have a long history in physics - Descarte used vortices in an aether to describe - incorrectly- the planets' motions. The word means "an unearthly, delicate substance".)

Properties of the ether

1. It has to be inside any and every transparent material including glass and diamond - else why can light pass through?

2. It has to be very, very "stiff" - high rigidity - as otherwise waves will not move very fast in it!

3. It has to be so very, very thin that it causes no drag to motion, planetary or animal.

Good stuff isn't it.

The trouble is that it seems that this is an ABSOLUTE FRAME if we accept the equation (1) above. In otherwords, different people should see different speeds depending on what they are doing! The ether frame should be measurable by experiment by measuring the speed of light while travelling at different velocities.

So, physicists believed that electromagnetism had an Absolute Frame of Reference - the ether frame, but Newton's physics had NO absolute frame. A dilemma.

Attempts to detect the ether. Michelson.

Special Relativity