Stephen Hawking: a brilliant mind.

Exactly one week ago the science genius Stephen Hawking passed away, today I want to write a little about him in this post. You can really say very little, that it has not been said about this incredible scientist. One of the most difficult things is to define it, given its great contributions to science.

However it can be said that he was an imminent theoretical physicist. But above this, his contributions to cosmology, astrophysics and dissemination have perhaps been as important as what has been achieved within his specialty.

A curiosity is that Hawking never won a Nobel ... nor could he have won it.

The Nobel in physics is awarded to empirically confirmed findings that can be verified by observable data, but Stephen's contributions to theoretical physics and astrophysics are so overwhelmingly difficult to detect that we may not have the technology to do so for centuries.

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His contributions with Roger Penrose were cornerstones for the advancement of knowledge and understanding of the strangest objects in the universe, predicted from Einstein's equations: Black holes.
His works laid the foundations for the understanding of singularities, whether black holes, or the Big Bang itself.

In the company of James Bardeen and Brandon Carter he proved that the evolution of a black hole only depends on its mass, its electric charge, and how it is rotating.
This implies that no matter how the black hole was formed, once it is born as such there is no way to differentiate it from another with the same mass, charge and spin, even though they have been formed from totally different objects.

Another achievement of Hawking was to solve a formidable paradox:

• Black holes can not emit anything.
• Every body that emits some radiation has temperature.
• If a black hole can not emit anything then its temperature is absolute zero.

But another way of understanding temperature is through the concept of entropy that relates the internal state of a system with its temperature.

• If a hole has no temperature its entropy must be zero.

On the other hand, the area (horizon of events) of a black hole can only remain stable (if it is "asleep", inactive), or grow (if the black hole absorbs more mass of the objects that fall into it). Entropy, (degree of disorder of a system) can also only remain stable or grow.

• This subtle analogy allowed us to infer that the entropy of a black hole was proportional to its area.
  But that did not make sense!
• If a black hole has an area that grows, it has entropy ...
• and if it has entropy, it has temperature ...
• and if it has a temperature it emits something ...
• but can not emit anything.

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The answer to that paradox: Hawking radiation

Quantum physics teaches us that in the most absolute vacuum there are particles and virtual antiparticles that are constantly created and annihilated spontaneously.

To understand the radiation of Hawking it is necessary to understand that the vacuum does not exist: quantum mechanics tells us that the vacuum is full of virtual particles, identical to the real ones, with the only difference that appear and disappear in very short periods of time. For example, a virtual proton and antiproton can only exist for 10 ^ -24 seconds before disappearing again in a vacuum.

If that happens in the region surrounding the event horizon of a black hole, it is possible that some of them will fall into the black hole while their companions manage to escape ...
Those that escape become real particles (typically photons), and would be observed from the outside as a radiation that leaves the black hole.

A black hole emits thermalized Hawking radiation, according to a distribution identical to that of the black body corresponding to a given temperature.

That is the Hawking Radiation ... and paradoxically, its existence implies that, when leaving energy of the black hole, this must necessarily reduce its mass ... with the running of the eons, every black hole that is not feeding, it will go away evaporating slowly until disappearing in a burst of Hawking Radiation.
This work solidified his reputation as one of the key thinkers of his generation and he was elected as a member of the Royal Society of London, at the age of 32, becoming one of the youngest people to have that honor.

But if you pay attention, in these considerations we have "joined" two separate universes: Relativity, with its majesty over everything macroscopic, and the virtual particles that reign in quantum physics, mistress of everything tiny.
Right on the "surface" of the event horizon (there is no such thing as a physical surface, but only a region of empty spacetime) both universes touch.
Those two irreconcilable antagonists, quantum and relativity, for a moment greet each other.

What is the message of that greeting? What is the language they speak?

Again Hawking along with Bekenstein, they were there to elucidate it:
The message is entropy.
Language is mathematics.

Thus, an extraordinary formula emerges, capable of competing with the famous E = mC ^ 2 of Einstein:

The entropy of Bekenstein-Hawking:

source FB News Post

It seems strange?
Do not be scared ... it's simple:

SBH: Bekenstein-Hawking entropy
A: Area of the event horizon.

• Entropy is proportional to the area of the event horizon.
  The constant of proportionality includes several known old ones:

• h is the reduced Planck constant.

• c is the speed of light.

• k is the Boltzmann constant.

• G is the gravitational constant.

Do you realize the wonder?

Quantum mechanics, relativity and thermodynamics, are united in a constant whose value is nothing less than the ratio of proportionality between entropy (temperature, in some way) and the "size" of a black hole.
This opens unsuspected doors for current and future theoretical physicists:

There is a possibility that a viable quantum gravitation theory could offer an interpretation of the entropy associated with black holes in terms of microstates.
Although the theory of the strings allows an interpretation for some classes of extreme black holes, for the rest its complexity does not allow to be described by this same theory at a quantum level. Likewise, loop quantum gravity proposes an interpretation of entropy but only for a certain type of black hole.

Do you understand why your contribution is beyond any Nobel?
It would be impossible to prove it today ... but perhaps, in the distant future, someone will win a Nobel in his honor.