This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American
More than any other scientific idea, Einstein's relativity has cemented the notion that space and time are inseparable qualities of the universe.
It began with Einstein's reworking of the classical transformation of moving coordinate systems in special relativity, and culminated a mere - but painful - decade later as he generalized and expanded these ideas to describe accelerating and gravitating systems. Space and time became space-time, or just spacetime - the cosmic fabric into which we are all woven.
But what does general relativity actually tell us about the specific properties of space-time? In simple terms the theory proposes that matter and energy influence space-time's shape, or geometry. For example, what Newton's more approximate physics calls 'the force of gravity' is really a consequence of the distortion or warping of space-time by mass - altering what the shortest paths are through a region.
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The mathematical construct that guides us from mass to warped space-time is Einstein's field equation, a hairy monster that can nonetheless be tamed into a moderately non-threatening form:
On the right hand side of this equation the 'T' symbol contains information that we might insert about the distribution of matter and energy within a particular piece of space-time - like a planet, or a star, or a galaxy. This 'T' is also known as the stress-energy tensor. The left hand side 'G' symbol represents the resulting details of how space-time responds to this stuff, how it is warped or curved (also known as the Einstein tensor).
The phrase 'stress-energy tensor' is a clue to how this equation works. Mass and energy, and their behavior (rotating, moving, static), place stress on space-time, which responds according to its intrinsic properties.
So just how resilient is space-time? The bunch of physical constants on the right hand side of the field equation give us an answer. The ordinary G here is just Newton's gravitational constant, and c is the speed of light. If we plug in the measured values for these, the field equation suddenly looks rather different:
What does this mean? It means that from our perspective it takes a HUGE amount of stress on space-time to produce an appreciable amount of warp or curvature ('G'). In fact it takes objects like the Earth (all 6 trillion trillion kilograms of it) to warp space-time to a level that we're intimately familiar with.
To produce enough warp to create an object like a black hole - with an extreme, maximal amount of space-time curvature - the universe has to concentrate mass and energy to an extraordinary degree. In other words, an immense amount of stress has to be created. For example, producing an Earth-mass black hole would involve squishing all those kilograms into a region roughly the size of a US penny to generate enough local stress. It's analogous to how the fine point of a nail concentrates enough force to break wood fibers.
It turns out that space-time is very stiff, very resilient. But it can, and does, yield to stress. That's fortunate, because without a little bit of warping there'd be no stars or planets, and we'd not be here to celebrate Einstein's wonderful insights.
(In my book 'Gravity's Engines' I provide more detail on Einstein's discoveries, and the scientific story of black holes and their very real presence in the universe.)
