Neither mechanics norregardless of the constant in Maxwell's equations electromagnetics had revealed an absolute frame of reference. All experiments seemed to indicate that any inertial frame was as good as another. What this suggested to Einstein was that some kind of relativity principle was in evidence that applied across the whole of science, according to which physics should be the same for all observers. Or putting it another way, the equations expressing all physical laws should be covariant between inertial frames. Following Lorentz, but with an aim that was general and not restricted to a subset of physics, Einstein set out to discover a system of transforms that would make this true. Two postulates formed his starting point. (1) The relativity principle applies for all of physics across all inertial frames, which was what the intuitively satisfying solution he was searching for required. (2) The velocity of light, c, is the same for observers in all inertial frames regardless of their state of motion relative to each other. For that's what Maxwell's equations said, and being a physical law, it had to apply in all frames for (1) to be true.
And what he did in his paper on special relativity, published in 1905, was rediscover the Lorentz Transforms. This was hardly surprising, since they gave the right answers for electromagnetismhence anything saying otherwise would have been wrong. But there was a crucial difference. Whereas Lorentz's application of them had been restricted to the special area of electromagnetism, Einstein maintained that they applied to everythingmechanics as well.
But, wait a minute. If the relativity principle was to be observed, and the new transforms applied, how could they still be compatible with Newton's long-established mechanics, which was enthroned as being consistent with the classical Galilean transforms, not with the new Lorentzian ones?
The only answer could be that Newtonian mechanics wasn't as invincibly established as everyone thought it was. Recall the two assumptions we mentioned earlier that the Galilean transforms imply: that space and time intervals are invariant. What Einstein proposed was that the velocity-dependencies deduced by Lorentz were not part of some fudge-factor needed for electromagnetism, but that they expressed fundamental properties of the nature of space and time that were true universally, and hence called for a revision of mechanics. However, the new mechanics could hardly render invalid the classical results that centuries of experimenting had so strongly supported. And indeed, this turned out to be so; at the low velocities that classical science had been confined to, and which shape the common sense of everyday experience, the equations of the new mechanics merged into and became indistinguishable for all practical purposes from the Newtonian ones.
Where the two systems began departing significantly was when very high velocities were involvedof the order of those encountered in electromagnetism and late-nineteenth-century experiments on fast-moving particles, where it had already become clear that classical mechanics couldn't be correct. Space and time were no longer fixed and unchanging but behaved weirdly at extremes of velocity that everyday experience provided no schooling for, with consequences that Newtonian mechanics hadn't anticipated. These are well-enough known now to require no more than that they be listed. All have been verified by experiment.
Addition of velocities. In classical mechanics, a bullet fired from an airplane will hit a target on the ground ahead with a velocity equal to that of the plane relative to the ground plus that of the bullet relative to the plane. But according to relativity (henceforth the "special relativity theory," or "SRT"), what appears to be obvious isn't exactly so. The velocity in the target's frame doesn't equal the sum of the two componentsalthough at the speeds of planes and bullets you'd never notice the difference. The higher the velocities, the greater the discrepancy, the relationship being such that the bullet's velocity in the target's frame never manages to exceed c, the speed of light. Thus even if the plane is coming in at 90% c and fires a bullet that leaves the plane at 90% c, the bullet's velocity measured by the target will be 90% c plus something, but not greater than c itself. (In fact it will be 99.45% c.) In the limit, when the bullet leaves the plane at c, the resultant, bizarre as it sounds, is still c. It has become a photon of light. Its speed is the same in both the frame of the airplane (source) and that of the target (receiver). Add two velocitiesor as many as you likeeach equal to c, and the result still comes out at c. And that's what all the Michelson-Morley-type experiments confirm.
Relativity of simultaneity. The upper limit on velocity makes it impossible to devise a method for synchronizing clocks in a way that enables different frames to agree on whether two events happen simultaneously. Some arbitrary frame could be chosen as a reference, of coursesuch as the Sun-centered frameand a correction applied to decide if two events were simultaneous as far as that frame was concerned, but it wouldn't mean much. One person's idea of simultaneity would still be no better or worse than any other's, and the term loses any real significance. Establishing absolute simultaneity without a privileged frame would require an infinitely fast synchronizing signal, which SRT says we don't have.
Mass increase. Mass measures the amount of resistance that an object exhibits to being acceleratedthat is, having its state of motion (speed and/or direction) changed. A cannon ball has a large mass compared to a soccer ball of the same size, as kicking or trying to stop one of each will verify. Though unobservable at everyday levels, this resistance to being accelerated increases as an object moves with higher speed. In particle accelerators, far more energy is required to nudge the velocity of a particle an additional tenth of a percent c faster when it is already moving at, say, 90% c than to accelerate it the first tenth of a percent from rest.
Mass-energy equivalence. As the velocity of a body increases, it stores more kinetic energy. From the preceding paragraph, it also exhibits an increase in mass. This turns out to be more than just coincidence, for according to relativity mass and energy become equivalent and can be converted one into the other. This is true even of the residual mass of an object not moving at all, which still has the energy equivalent given by the famous equation E = m0 c2, where E is the energy and m0 the object's mass when at rest. All energy transitions thus involve changes in mass, but the effect is usually noticeable only in nuclear processes such as the mass deficit of particles bound into a nucleus or the yield of fission and fusion bombs; also the mass-energy balances observed in particle creation and annihilation events.
Time dilation. Time, and hence processes that are time-dependent, runs slower in a moving frame than in one at relative rest. An example is the extended lifetimes shown by muons created by bombardment of the upper atmosphere by protons from the Sun. The muons reach the Earth's surface in numbers about nine times greater than their natural decay time (half-life 2.2 microseconds) says they should. This is explained by time in the muon's moving frame being dilated as measured from the surface, giving a longer decay period than would be experienced by a muon at rest. High-accuracy clocks on rocket sleds run slower than stationary clocks.
The mathematician Hermann Minkowski developed the Einstein theory further by showing that it entailed a reality consisting not of the three-dimensional space and separate time that are ordinarily perceived, but of a strange, non-Euclidian, four-dimensional merging of the two known since as spacetime. Only from the local standpoint of a particular Galilean frame do they separate out into the space and time of everyday life. But the space and time that they resolve into is different in different frameswhich is what the transforms of SRT are saying.
Although many might remain unconvinced, this kind of thing is what scientists regard as a simplification. When phenomena that were previously thought to be distinct and independentsuch as space and time in the foregoingturn out to be just different aspects of some more fundamental entity, understanding of what's going on is deepened even if the techniques for unraveling that understanding take some work in getting used to. In the same kind of way, momentum and energy become unified in the new four-dimensional world, as do the classical concepts of force and work, and electric current and charge.
This also throws light (pun unintended, but not bad so I'll let it stand) on the interdependence of the electric and magnetic field quantities in Maxwell's equations. In Maxwell's classical three-dimensional space the electromagnetic field is formed from the superposition of an electric field, which is a vector field, and a magnetic field, which is a tensor field. In Minkowski's spacetime these merge into a single four-dimensional tensor called the electromagnetic tensor, and the four three-dimensional equations that Maxwell needed to describe the relationships reduce to two four-dimensional ones. Hence the interdependence of electric and magnetic fields, which in the classical view had to be simply accepted as a fact of experience, becomes an immediate consequence of their being partial aspects of the same underlying electromagnetic entity.
In SRT, Minkowski's four-dimensional spacetime is considered to be "flat"uncurved, like the classical Euclidian space of Newton. An object's "world-line"the path showing its history in spacetimewill be a straight line when the object is in a state of rest or uniform motion. What differentiates accelerating frames is that their world-lines become curved. In developing his general theory of relativity (GRT), Einstein sought to remove the restriction of inertial frames and extend the principle to frames in general. In doing so he proposed that a region of space subject to gravitation is really no different from a reference frame undergoing acceleration. Inside an elevator, for example, there's no way of telling if a pen falling to the floor does so because the elevator is accelerating upward or because the floor is attracting it downward. 67
If a gravitational field is equivalent to acceleration, motions associated with it will also be represented by curved world-lines in spacetime. Hence, in GRT gravitation is interpreted geometrically. Instead of somehow attracting bodies like planets to move in curved paths through flat space, the presence of the Sun's mass itself warps the geometry of spacetime such that the paths they naturally follow become curved. An analogy often used to illustrate this is a stretched rubber sheet, representing undeformed space. Placing a heavy object like a bowling ball on the sheet creates a "well," with sides steepening toward the center, that the ball sits in, but which would be indiscernible to a viewer vertically above who had no knowledge of a dimension extending in that direction. If a marble is now rolled across the sheet, its trajectory will be deflected exactly as if the sheet were flat and the ball exerted an attraction. In the absence of any friction, the marble could be trapped in a closed path where the tendencies to fall down the well and to be lifted out of it by centrifugal force balance, causing it to orbit the bowling ball endlessly.
If spacetime itself is curved in the vicinity of masses, then not just massive objects but anything that moves through space will also follow paths determined by the nonflat geometry. So stars, for instance, should "attract" light, not just material bodies. That this is so is verified by the observed deflection of starlight passing close to the Sun. So once again, all forms of energy exhibit the equivalence to a property of mass.
Finally we're back to a situation where we have the principle of relativity, a universal statement of the laws of physics (the new mechanics, which subsumes electrodynamics), and a system of transformations that are mutually consistent. Science has been integrated into a common understanding that's found to be intellectually satisfying and complete. Its successes are celebrated practically universally as the crowning achievement of twentieth-century science. So what are some people saying is wrong with it?