# Relativity matters (!)

But my friends wouldn’t expect me to stop there!

John Wheeler had a great way of explaining both special and general relativity, and any of his books is worth the time spent to read them. Find this quote in his “Geons, Black Holes, and Quantum Foam”. He also came up with the terms “Black Hole” and “Wormhole”.

Depending on your grasp of the mathematics, a good book to start with might be his book written with Edwin Taylor, first edition in 1965, Spacetime Physics.

A much more demanding book from 1973 is “Gravitation”, a classic written with Charles Misner and Kip Thorne, which as its title implies covers General Relativity (i.e. relativity WITH gravity).

Of course, we hardly see space-time curvature in our day-to-day lives, just as we hardly see the direct effects of special relativity (although our lives depend on it in many ways at the subatomic level). Newtonian mechanics is a very good approximation for our everyday purposes.

But in high field strength gravitational fields, light will follow a curved path because in effect mass and space-time curvature go hand in hand. And at the special relativistic level (no gravity), at speeds near to the speed of light, physical effects are measurable such as time dilatation and length contraction.

These effects sound very odd, but given that a major axiom of relativity theory is that light always passes us at the same speed, no matter the velocity of the light source, any consequences are bound to be counter-intuitive. Our everyday experience is that, for example, a cricket ball bowled or thrown at us by someone running towards us is endowed with their running speed plus the speed of their arm. A ball thrown from a standing position with the same throwing or bowling action will be slower.

At speeds near to the speed of light (“relativistic” speeds), however, this additive “cricket ball” effect breaks down, and for light itself there is NO added speed if the source is moving towards us, even if the source is travelling at nearly the speed of light. (On a related point, light from distant sources in the Universe, travelling away from us very quickly, passes us at that same light speed, but is red-shifted. An interesting debate is to read Fred Hoyle on why there is so little blue-shifting, but that is a whole other discussion!)

Similarly for gravitation fields – it is only when the field strength is very high can we detect the predicted effects. The “lensing” or convergence of light from behind a massive star (like the sun) or the recent ground-breaking detection of gravitational waves thought to be issued by a pair of rotating black holes (the LIGO experiment) depend on very high gravitation fields we simply don’t encounter here on Earth.

General Relativity was used to calculated a predicted precession of the orbit of Mercury distinct from the Newtonian calculated precession – and it was found to agree with observation. But even that closely to the sun, the effect is tiny and would hardly have been noticed but for the intense scrutiny that was made as a test of Einstein’s theories.

Einstein’s creativity in postulating the constancy of the speed of light, and then his doggedness, using the mathematical tools then at his disposal (i.e. not our modern more evocative nomenclature and terminology that is more revealing of patterns in the required algebraic geometry) in solving the general Relativistic field equations show both his abundant inspiration, and lots of perspiration.

After all, to return to Wheeler’s duality of mass and spacetime geometry (curvature), for Einstein to solve equations that are reflexive in that the “independent” variables are also “dependent” is much harder than when you can assume that one set of variables is fixed and the others’ movement or variation doesn’t affect the first.

(Physics and mathematics are rich with examples of simplifying assumptions to help solve problems (often “linearizing” non-linear differential equations). For example, the general “three body problem” in Newtonian gravity is intractable, but the “reduced” three body problem (RTBP) IS tractable, the simplifying assumption being that one of the three bodies is postulated to be so small (e.g. a satellite in the presence of the earth and moon) that although it is affected by the gravitational field of the earth and moon, it has no effect itself on the sun and moon. In this way the problem is sufficiently decoupled (or linearized”) to be solvable).

100 years later Einstein’s theory still stands up. Probably quantum theory, and the union of it with General Relativity to create a GUT – a Grand Universal Theory – whether through string theory (maybe not) or loop quantum gravity (maybe) or some other yet to be fully formulated process will turn General Relativity into a “good approximation” just as Newtonian theory is a good approximation to relativity. Again Wheeler’s “Geons, Black Holes, and Quantum Foam” provides some food for thought.

But just as Newton loses none of his reputation as a giant of physics of his time, following Einstein’s work, neither will Einstein lose his as a result of any new all-embracing theory. They both had broad enough shoulders for others to use to develop our scientific understanding.

Is space-time real?

Einstein’s space-time is a mathematical construct to allow him (and us) to understand how space and time have to be inter-dependent. Look up the definition of “simultaneity” in the special relativity context, and you will see that simply modelling space and time separately with no interaction between them fails to allow for the fact that different observers moving at different speeds will disagree about whether events that happen that are spatially separated are simultaneous, or whether one event happens before the other. All three outcomes are possible depending on the speed and direction of motion of the observer, and this can only be postulated and resolved with a space-time model, NOT in a model with a fixed time axis. All this tells us that space-time IS physically real, in that the effects we would see if velocities were high enough are genuinely predicted and correctly calculated in the space-time model. Our lives are played out in such a definition of the interdependency of space and time, not in a fixed three dimensions with a fixed and separate time dimension shared by everyone. In the language of the theory, we all have our own “world-line” that is a combination of where AND WHEN we “are”, and these world lines have their own individual pace of time (not one shared by all), and at high speed differentials mean that we, and others, might observe events, as discussed above, happening in a different order from each other. There are limitations on how much and if these differences occur, depending whether the separation of space-time location of the events we are observing are “space-like” or “time-like” but Quora isn’t a great medium for illustrating that. But I can elsewhere is needed!