This is a summary of our account of special and general theories of relativity; the appropriate material in the book is quite a bit more detailed, and with a few exceptions covers everything we talked about. On this page, a brief summary of some most striking – and related – points of both theories is given. For more detailed overviews, see separate pages on special and general relativity.
Relativity theory deals with notions of space, time and gravity; it may be taken to consist of special and general theory. These theories appeared in the early 20th century, over the background of classical physics, completely altering its iron-clad perceptions of space and time. Some of the rather unintuitive aspects of space and time are revealed at very high speeds, and this is the domain of special relativity; general relativity deals with very strong gravitational fields – very large masses – and goes further, putting forth much deeper ideas. Special theory is contained in the General; both have Newtonian physics as their limits, as must be. (When applied to the typical speeds and masses that we experience, their equations readily recover Newton's laws, to within observed accuracy; this indeed must be if the theories are to be valid, since we know that Newton's laws do describe most of our macroscopic world rather well.)
Prior to relativity theory, space and time had always been assumed as simply given and absolute, certainly not changing in any sense. They are ‘there,’ always the same for everyone, quite regardless of other physical content, and are background for everything else; almost always they were mentioned, it was to assert that the concepts are ‘obvious and known to all’ [Newton]. Nowadays, our intuitive, everyday perceptions of them are the same.
Quite contrary to this, relativity establishes that space and time are not even independent of each other, and form a physical entity, called simply space-time, with the structure far from static and absolute. It is useful to look at examples of what happens when we disregard this, and treat time and space as separate entities. Consider systems moving relative to each other at very high speeds, comparable to the speed of light (an example is processes observed constantly in particle accelerators): distances and times are different when compared between observers in such systems. If we were to move at such a speed relative to someone, we would measure the width of an object they hold as shorter than they do; for the time it takes for snow around them to melt, our clock would time more than theirs. If they do two things at the same time, we will first see one, and then the other: simultaneity depends on who's watching, too. This is not a trick of any kind, the distance and time are different for observers moving relative to each other, simply because space and time each do not have an independent, physical meaning in the first place. (So, the strangeness comes from our attempt to consider space and time as separate and yet meaningful quantities: they are not, and measuring them on their own produces results that depend on the reference frame. But then, what had we been seeing all that time ... ? These effects are considerable only at speeds that are normally not present on earth. At our speeds, our usual perception of space and time, and rules for using them, are quite reasonable.) Further, by studying systems moving relative to each other at high speeds, it is found that mass differs too, for observers in these systems; if we were to measure the mass of someone we are passing by, we would get a number bigger than what they measure. (This does not refer to some physical ‘size,’ but to mass as a measure of inertia.) Pushing this finding further, one arrives at a profound conclusion: energy and mass are equivalent to each other. And fully, so matter can convert into energy and energy into matter: particles annihilate with each other, with some energy in the form of radiation leaving, and this happens all the time in particle accelerators. This completes our basic statement of special theory of relativity: distances and time separately do not have any definitive meaning, and so are even measured as different (by observers moving relative to each other); one has to consider them as bundled components of the space-time. Also, mass is different when measured in moving frames – and fully equivalent to energy, so that matter and energy can convert into each other. (How? For such an involved concept, the math turns out surprisingly simple: E=mc2.)
Much more complex behavior of the space-time can be observed in strong gravitational fields. (Like the ones studied in astrophysics.) But let us first state one striking property of gravity, seen even on earth: it is equivalent to acceleration. One example of this principle is the common fact that different masses fall with equal speed. But the meaning of it goes well beyond this example. In a system that is freely falling in a gravitational field, one cannot observe gravity at all; or, put differently, in a system that is accelerating one can in fact use the exact same laws of physics as in a system moving with a constant velocity – by adding a gravitational field (equal and opposite to the acceleration). In this way, the restriction of special relativity (that it works for unaccelerated frames only) is removed, and thus for the first time there is a theory that does not need concepts such as ‘absolute space and time,’ and that applies to any and all observers, and equally. But, general relativity goes much further than this. The space-time, in special relativity seen as unaffected by the present objects, in fact depends on the mass that is there; it is a physical quantity that is determined by the energy content of the surrounding. This is an extremely deep idea, that goes against every bit of our normal intuition about space and time. The first, most striking consequence is the fact that objects, having certain mass (or simply energy, like radiation), distort the space around them. A wrinkled cloth is not as smooth and flat as it is when ironed, and going over its wrinkled surface is a different journey; the path an ant traces is different than the one when the surface is smooth and flat. Our space-time is similarly “curved” by the mass, and the shortest path between two points is not the straight line anymore. That is, not as seen by an observer from afar, from a region where the distortion is small; but for a light beam traveling through strong gravity, the space simply is as it is, and the effect of gravity on its motion is that – it still follows the shortest path, in this space. (And now this is a line different from what would be the usual straight line when there is no mass present.) The light coming to us from distant stars, passing close to the Sun, is seen by us as bent, by the gravitational field of the Sun (this is one of the first confirmations of general relativity); for all that the light-beam knows, it simply follows the shortest path through the space, as it happens to be around the Sun. The gravity is thus understood as a changed geometry of space (due to mass present), and there is no need to discuss ‘forces.’ Clearly, since we must only speak of space-time (and not space separately), this distortion applies to time too, and the way each is distorted affects that of the other (and depends on it). In a simple example: the length of an object we hold is different as we move to different spots in a gravitational field, as well as is the rate at which our clock ticks. Finally, the actual equations of general relativity deal not with mass, but with energy-momentum; this rounds up the profoundity of the statement: the energy-momentum that is present determines properties of space-time. (“Energy-momentum” is a quantity composed of energy – as a fundamental concept, not kinetic energy or such – and momentum, in much the same way the space and time combine into space-time.)
In addition to being theories that describe many phenomena inaccessible by classical physics, the meaning of relativity theories is much more fundamental. They introduce a far deeper concept of space and time, as not being fundamental physical notions, but rather components intertwined into a structure of “spacetime;” this space-time is determined by mass, and more generally, energy – being completely equivalent to mass. The space-time properties vary from a point to a point in a field of such mass; it can be wrinkled and distorted, or barely slightly curved, depending on the strength of the gravitational field of the said mass. It changes around, in accordance with certain laws of physics, just like any other physical quantity; there are no absolute space and time. Given this, the force of gravity itself (of a certain mass) need not be considered as a separate ‘force’ – its effect on the motion of objects around is that this mass carries a distorted space-time, and the objects thus normally follow their shortest paths as they would, but in such, curved, space-time.
All theories in physics that improve on already existing ones – known to be good under certain conditions – must be able to show that under these same conditions, they reduce to the old ones. This requirement very much holds for relativity theory: we have been observing the world around us for a long time, and we know that Newtonian physics works, under conditions in which we have established it. Both special and general relativity can show that for these conditions they recover Newtonian physics; their full effects are seen mostly in extreme environments, present either in the distant Universe, or in events created in powerful accelerators. By now many phenomena have been observed, and experiments are being done regularly, that clearly confirm these theories. Until we find yet better ones.