A brief history of Hawking’s scientific legacy

The world is mourning the passing of iconic theoretical physicist Stephen Hawking, an inspiration for his scientific achievements as well as his tenacity in dealing with a debilitating illness. Much has been written about Hawking’s impish wit, his celebrity and his personal life. But what about his scientific legacy?

Professor Hawking’s work concerned Einstein’s general theory of relativity, our best theory of gravitation, that recently received further triumphant confirmation through the discovery of gravitational waves.

But going beyond pure gravitation, he also thought deeply about how the very different quantum world, usually thought of as applying solely to the microworld of atoms and elementary particles, might interact with the astrophysical and cosmological macroworld dominated by the force of gravity.

THE BIG BANG SINGULARITY

Professor Hawking’s earliest work uncovered a troubling aspect of Big Bang cosmology: the singularity.

Mathematically, a singularity denotes a time or a place where some quantity becomes infinitely large. In physics, singularities are generally considered pathologies that signal the breakdown of a theory - since we have never detected or observed systems of infinite density or forces of infinite strength.

Building on earlier work by British mathematician Roger Penrose and others, Stephen Hawking demonstrated that, if general relativity is exactly true, then the universe must have begun at a singularity where matter was squashed to infinite density and the gravitational force was infinitely strong.

This overturned a view held by some that a singularity could be avoided if the full complexity of the expanding universe and the stuff within it was accurately modelled. Professor Hawking’s result proved that our best theory of gravitation, that otherwise described the expansion of the universe beautifully, must break down at the Big Bang itself.

But what replaces it?

Imaginary time

Working with American theoretician James Hartle, Stephen Hawking proposed that quantum effects dramatically alter the nature of space and time near the Big Bang, and this avoids the most egregious of the singularity’s evils.

The term “imaginary time” seems like a perfect obfuscation, or a mystical incantation, but here is what it really means: The universe today has three dimensions of space, and one distinct dimension of time. We can move around in space, but we are constrained to experience time as unidirectional, always from the past to the future.

The Hartle-Hawking proposal is that quantum effects turn the time dimension into a fourth dimension of space at the Big Bang (the mathematics of this involves “imaginary” numbers, such as the square root of -1). Time’s “Brief History” ceases to exist, and the singularity is somewhat tamed.

Does the real universe behave in this fascinating way? That still remains unknown.

Black holes and Hawking radiation

General relativity predicts the existence of black holes, regions of space where matter and energy are so dense that nothing can escape from their gravitational pull, not even light.

Adding to a lot of very convincing earlier circumstantial evidence for their existence, the recent observation of gravitational waves from binary black hole mergers provides direct proof that these extreme astrophysical objects populate the universe.

Stephen Hawking, to the astonishment of both himself and the scientific community, proved that black holes are not the bottomless pits - devouring all matter and radiation that falls into them, never to return - that they were thought to be.

By applying the laws of quantum mechanics to the stuff falling into a black hole, he found that black holes actually have to emit radiation. Unless a black hole keeps being fed with matter and radiation, it will eventually evaporate due to the loss of mass and energy through what we now call “Hawking radiation”.

While this effect has not yet been observed in real life – that is a very challenging goal! – the results of the calculations are clear. It is hoped that the Large Hadron Collider might observe the evaporation of mini-black holes predicted by some speculative theories of particle physics that postulate extra dimensions of space, but so far there are no such signals.

Is our world a hologram?

Hawking radiation also has deeper consequences.

Building on independent work by Israeli physicist Jacob Bekenstein, Stephen Hawking showed that since black holes radiate, they also have a temperature and an entropy.

Entropy is a thermodynamic quantity that measures the disorder in a system composed of many constituent parts, such as the atoms of a gas.

But what “constituent parts” can a black hole have? Expressed another way, what happens to the information that is stored in an object that is swallowed by a black hole? Is the information destroyed, or does it get preserved in some subtle way?

Professor Bekenstein and Hawking showed that the entropy is proportional to the surface area of the black hole, not its volume. This suggests that if information is preserved, then it resides in fluctuations on the black hole surface.

Inspired by these big thoughts, Dutch Nobel Laureate Gerard `t Hooft proposed the “holographic principle”, which was further developed by American theorist Leonard Susskind and others.

A conjectured upshot is that the information content in the volume of the entire universe is encoded on its surface, just as a 3D optical hologram is an image produced from a 2D film.

The radical suggestion is that the 3D world we experience is a kind of illusion, with the underlying reality being 2D. Argentinian physicist Juan Maldacena, working in the US, showed that this idea has strong support from superstring theory, which is considered by many physicists to be the best candidate for the ultimate theory of everything.

It is not yet clear where these “strange realms of thought” will eventually take us. But we can thank Stephen Hawking for a legacy that will keep generations of theoretical physicists very busy indeed.

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