Antonio Padilla is a theoretical physicist and cosmologist at the University of Nottingham. He has been the Chair of British Cosmology for over a decade and is known for his frequent guest appearances on the popular YouTube channel, number phil.
Below Antonio shares 5 key takeaways from his new book, Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity. Listen to the audio version – read by Antonio himself – in the Next Big Idea app.
1. 0.0000000000000001
This is a small number, and small numbers reveal something unexpected. For example, I’m a really bad singer. I’m definitely not expected to win The x factor or american idol. You could say that the probability that I win is a really small number.
The Higgs boson is also unexpected, so it also has a small number. You may have heard of the Higgs boson. It made headlines after being discovered at the particle physics laboratory CERN in 2012. Back then, particle physicists ran around excitedly. The Higgs is said to have been the last piece of the particle puzzle that helped explain the origin of mass in our universe.
What nobody tells you is that we particle physicists were also a bit ashamed. Our best microscopic theories told us that the Higgs boson was able to shape the shift into other fundamental particles. All of this shapeshifting should weigh the Higgs down so much that it weighs just a few micrograms — about the weight of a fairy fly, a tiny wasp that just so happens to be the world’s smallest insect.
“The Higgs is said to have been the last piece of the particle puzzle that helped explain the origin of mass in our universe.”
The thing is, elementary particles don’t weigh as much as insects. Although the Higgs theoretically should weigh as much as a fairy does not. It’s 0.0000000000000001 times easier and nobody understands why. We’ve tried to explain what’s happening in a variety of ways: we’ve considered extra dimensions, fancy supersymmetries where we double the number of particles in nature, and we’ve even tried to break the Higgs down into tiny little parts. In vain, because the experiments at CERN have not yet found any proof for the explanation of the Higgs boson. The secret remains.
2nd 10th(-120)
The Higgs was unexpected, but it’s not as unexpected as our universe. Our universe is described by a really small number: 10(-120). That’s less than one part in a googol.
The universe is expanding, which means the space between galaxies is getting bigger, not because the galaxies are racing away from each other, but because space itself is expanding. This expansion is accelerating. Something is pressing on the universe, making it grow at an ever-increasing rate.
Most physicists believe it is powered by the energy of empty space. This is the so-called vacuum energy– the energy that is left when you empty the universe of all stars, planets, people and little green men, leaving only the vacuum. You might think that something so empty can’t carry energy, but that’s not true. Quantum mechanics tells us that the vacuum is a pulsing place, a bubbling broth of virtual particles ebbing and flowing into existence. These particles depress the vacuum in the same way they depressed the Higgs. They give the vacuum an energy that can propel the universe forward.
The problem is that it wants to push it too hard. If you do the calculation, you realize that the vacuum should have a heck of a lot of energy. In fact, the energy is so great that it was supposed to bring the universe to oblivion the moment it was born – but that didn’t happen. The universe grew big and old. That’s because the true energy of the vacuum is much less than we expected. To recreate the amount of cosmic acceleration we see through our telescopes, we need a vacuum energy of 10(-120) times smaller than our theoretical prediction.
It’s garbage, isn’t it? I’ve spent most of my career pondering this problem. The universe must have known from the start that it was going to grow big and old. There had to be some degree of foreboding.
3. A googolplex.
Maybe you’ve heard of a googol? It’s a 1 followed by a hundred zeros. Well, a googolplex is bigger: it’s a one followed by a googol zero! To really appreciate how big that is, consider a Googolplician universe. That’s a universe that’s a googolplex diameter in meters, inches, or some other Earth-like unit.
“In a Googolplician universe, your doppelganger is out there, probably reading Book Bites.”
In a Googolplician universe, you’ll find something remarkable: doppelgangers. Exact copies of me, you and everyone you know. I don’t just mean doubles, but replicas down to quantum DNA: same nose, same hair, even the same mind.
It all has to do with how many different ways there are to compose a human-sized volume of space. There’s far less than a Googolplex way to do this. The reason has something to do with the physics of black holes. Anyway, one of these assemblies corresponds to me, one to you, one to empty space, etc. As you move through the Googoplician universe, it’s inevitable to see repetitions. There just aren’t enough precautions to keep it different every time.
In a Googolplician universe, your doppelganger is out there, probably reading Book Bites.
4. Graham’s number.
Think of a really big number and try to visualize it. Are you there? If so, I’m pretty sure you didn’t think of Graham’s number because if you did you’d be dead.
Graham’s number is large. In fact, it has long been considered the largest number ever to appear in a mathematical proof. Graham’s number isn’t just as big as a trillion or even a googolplex. It’s a true leviathan. If you tried to picture its decimal representation written out in its entirety, digit by digit, your head would collapse into a black hole. It is a condition known as black hole head death and has no known cure.
It happens because Graham’s number contains an insane amount of information and information weighs. What if we got Justin Bieber to think about Graham’s number? As the digits of Graham’s number entered his brain, he took on mass. At some point there is so much of it that his brain gets hot and wants to explode. Assuming he can avoid this, what then? More digits, more information, more weight. Eventually he reaches a point where the only object that can store that much weight in a space the size of his head is a black hole.
“The hope is that one day we’ll be able to figure out what’s really going on at the center of a black hole, and maybe just may beat the moment of creation.”
Head-sized black holes are super dangerous. The problem is that the black hole’s surface is very close to the dreaded singularity that lurks within. Here space and time are infinitely torn and twisted and the gravitational field becomes infinitely strong. If a black hole beaver were approached by a fan, the tide of gravity on its black hole head would tear the fan to shreds. Graham’s number would be bad news for anyone obsessed with Justin Bieber.
5. Infinity.
Black Hole Biebers may sound fanciful, but black holes are unmistakably real, and within them all lies the singularity – the place where space-time touches infinity, where the gravitational field spirals completely out of control. Here the physical world seems to collapse and our equations no longer make sense. Singularities are not only found inside black holes. You can also find them at the Big Bang if you trace the universe back to the beginning of time.
To transcend these infinities, we need a quantum theory of gravity – a way to think about the strongest gravitational fields and how they interact with the entire material world on the smallest scale. We need a theory of everything.
What is meant by this is a theory in which the building blocks of nature are not particles but threads. Tiny little threads that twist and vibrate that make up each and every one of us and space-time itself. These threads are designed to eliminate the infinities of gravity, and we hope that one day we’ll be able to use them to find out what’s really going on at the center of a black hole, and maybe just may be, at the moment of creation. At genesis.
Through the symphony of strings we may one day know the mind of God.
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