“The Grand Design” by Stephen Hawking and Leonard Mlodinow (1)

A few years ago my general interest in how things work led me to the quantum physics section in the local library. I have since read a few dozen books on the subject and developed a reasonable understanding of the issues involved. Some of my previous posts cover aspects of the mysterious world the physicists have been uncovering bit by bit in the last hundred or so years:

https://da-boss.com/2012/05/28/universe-2/
https://da-boss.com/2012/05/29/universe-3/
https://da-boss.com/2012/06/01/the-anthropic-principle/

First a confession: I am not a great fan of the writing style of Stephen Hawking. He comes through somewhat dry and his jokes are forced. But the presentation of the subject matter is first rate – clear, concise, logical. In the opening chapter of “The Grand Design” we are teased with an intriguing question:

“Why there is something rather than nothing?”

I will now, as best I can, summarise Stephen Hawking’s answer presented in the book. One of the problems with the Big Bang theory was the law of conservation of energy. It is generally accepted that this law applies to all closed systems, large and small, and so the energy budget of the Universe before and after the Big Bang had to be the same. No energy could have been either created of lost when a miniscule volume of space started expanding madly 13.7 billion years ago. So, one moment there was nothing and a split second later the early Universe was teeming with particles which later combined into nuclei, which then became atoms, which formed galaxies, stars, planets and, ultimately – us. As per the Einstein’s famous equation mass is equivalent to energy so the troubling question was where all the energy required to create the stuff occupying the Universe had come from.

Well, Hawking is kind enough to answer this question in the final chapter of his book and his explanation goes something like this. First let us re-affirm that the energy of an isolated body surrounded by empty space is positive (which means that one has to do work to assemble the body). Had the energy of a body been negative, the stuff could spontaneously pop out of empty space in a state of motion, with the negative energy of the body precisely balanced by the kinetic energy of its movement. Intuitively, this can not happen – we do not see fast-travelling chunks of stuff appearing out of nowhere in the everyday life. The physical argument is that if energy of a body were negative then the space would be locally unstable. This is not what we observe so, for space to be locally stable, the energy of a body has to be positive.

Ok – so at the moment of Big Band some stuff appeared and there is no obvious place from where the energy had come to allow its creation. But let us digress. An apple, hanging off a branch of an apple tree, has a certain amount of potential energy. It may fall, hit the ground and split. So now we have the same apple (only smashed) lying on the ground. What provided the energy to split the apple? Well, the potential energy of the apple in the gravitational field of the Earth converted into the kinetic energy which then converted into mechanical energy on collision with the ground. The bruised apple lying on the ground now has less potential energy in the gravitational field of the Earth. In the big picture the Earth has a certain potential energy with respect to the gravity of the Sun and the Milky Way as a whole has potential energy as it gravitationally interacts with other galaxies.  The matter in the Universe would have the least amount of combined potential energy if it were all clumped together (which it is not). As long as lumps of mass are separated they can converge under the pull of gravity, releasing their potential energy in the process.

So, there is an amount of potential energy in the Universe just because not all mass is clumped together. It is possible to assess how much potential energy was contained this way in the early Universe and the result is surprising – roughly as much as the energy required to create all the mass within it. How can that be? According to Stephen Hawking the answer is simple – the potential energy of the gravity field is NEGATIVE. What it implies is that mass can pop out of nothing as long as its positive energy is balanced by the negative energy of the gravity field it resides in. This is referred to as a Zero-energy Universe theory. Because the potential energy increases with the distance of the gravitationally interacting objects (they have a longer way to fall) the energy-neutral creation of mass can only happen on a cosmic scale. As in: an apple will not pop out of space but Universes may (and do).

The physical formulation of this idea is delightfully simple: the space is locally stable but cosmically unstable, meaning that it is perfectly possible for a Universe to be created out of nothing. Quantum physicists have a wicked sense of humour and have coined a quirky name for this: Free-lunch Universe. Alan Guth, the author of the cosmic inflation theory (which deserves a dedicated post), has put it thus:

Our Universe is just one of those things which happen from time to time

“The Grand Design” by Stephen Hawking and Leonard Mlodinow (2)

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