- On one of the first pages of Stephen Hawking's PhD thesis,
there is a handwritten note saying,
"No copying without the author's consent."
But just before he passed away,
Stephen Hawking actually allowed for his PhD thesis,
which was titled "Properties of Expanding Universes,"
to be released publicly online.
That decision crashed the University of Cambridge website,
because so many people wanted to take a look at it.
So today I thought I would try and see
what all the fuss is about.
This 120 page document was written in 1965
when Hawking was 23 years old, and it represents
all of the work he did as a graduate student at Cambridge.
He was officially awarded the PhD in 1966, when he was 24,
and this was before he was famous,
and even before he was in a wheelchair.
In fact, Hawking was able to hand write
on the acknowledgements page,
"This dissertation is my original work, S.W. Hawking."
It had been a couple of years earlier when he was 21,
that he was diagnosed with motor neuron disease.
Finishing this thesis was something that after the diagnosis
looked like it might not happen at all.
Hawking was initially given only two years to live
and he became understandably quite depressed.
He spent very little time on his research
and a lot of time in his room,
apparently listening to classical music,
reading science fiction and drinking.
Hawking's family and his supervisor, Dennis Sciama,
encouraged him to return to his research.
And after a while, when his condition stabilized
and Hawking realized that death wasn't imminent,
he did return to finish his thesis.
Hawking is quite well known for some of his work
in science communication, including his book,
"A Brief History of Time."
That book was written for a general audience,
but is still jokingly referred to as
the most unread book of all time.
Now this thesis was not written for a general audience,
but instead for experts in cosmology.
So it is not easy to understand,
and there are a lot of calculations,
but I'll do my best to share the main ideas with you.
I myself am not an expert in this topic,
so it's just what I've been able to pick up.
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So looking at the thesis, it is all about the expansion
of the universe.
And the first line of the introduction is that,
"The idea that the universe is expanding
is of recent origin."
He talks about how all of the early cosmologies
were essentially stationary, including Einstein's.
But he says there are grave difficulties associated
with this, including the fact that, if the stars
had been radiating energy at their present rates
for an infinite time, they would need an infinite supply
of energy.
And there's a mention of the fact that not long before
this thesis was written, that the discovery of the recession
of the nebulae by Hubble, had led to the abandonment
of static models, in favor of ones which were expanding.
So this expansion is a relatively new idea
and Hawking goes on to say, there are a few possibilities.
One is that the universe may have expanded
from a highly dense state of finite time ago,
which is the big bang model or there's the bouncing
or oscillating model, where the universe is going
through periods of expansion and contraction.
Finally, Hawking says, "It is possible that the expansion
may have been proceeding at much the same rate
for an infinite time.
For this, it would be necessary to postulate
some form of continual creation of matter,
in order to prevent the expansion from reducing
the density to zero.
This is what is called the steady state model."
Now, Hawking will go on to talk a lot more about that.
It's also important to establish that a lot of this thesis,
relates to Einstein's general theory of relativity,
the idea that space and time are related
in this kind of fabric called space time,
where massive objects can warp space time,
explaining things like planetary orbits
or a gravitational pull.
Einstein himself had been so sure that the universe
was static and not expanding that he had added
the cosmological constant to his equations,
in order to keep it that way, which he would famously go on
to call his greatest blunder.
Chapter one is about "The Hoyle-Narlikar Theory
of Gravitation," and basically why it is wrong.
Fred Hoyle was an astronomer at Cambridge
and is most famous for his theory
of stellar nuclear synthesis, showing that elements
up to iron can be formed inside stars, in nuclear reactions.
He also came up with the term big bang,
which he used to mock the theory, because he rejected it.
He was instead a proponent of the steady state model
of the universe, that the universe didn't come
from anything, but is infinitely old
and the same in all directions.
And at all times in the past and future,
a steady state universe doesn't evolve over time.
Jayant Narlikar was Fred Hoyle's PhD student
and is still working in astronomy,
he's currently based in India.
Together, they came up with this theory to explain
how the universe could be expanding and still
in a steady state.
As Hawking said, in his introduction,
this would require some continual creation of matter.
So we have here the big bang model.
If all of these dots represent galaxies,
then with the expansion of the universe,
the distance between everything in between
all the galaxies increases.
Then for the steady state model,
the distance between individual galaxies marked here,
does increase by the same amount when the universe expands,
but this time there is extra matter created in between.
So the average distance between galaxies, remains the same.
Hoyle and Narlikar called this new matter, the 'C'-field.
And interestingly, it is based off work
from Richard Fineman's thesis.
Fineman had this theory of fields that were half backwards
and half forwards, which was derived
from an action principle that involved interactions
between pairs of particles.
In Fineman's thesis, he was able to show that
these fields could combine to give an observed field.
And Hoyle and Narlikar used the same theory for space time.
You can even see that they start their theory here,
by deriving it from something they call the action,
an integration over the world lines of particles.
Funily enough, when Hawking came to Cambridge as a student,
he had actually wanted Hoyle as his own supervisor.
And he was a bit upset when he was placed with Sciama.
But then in this thesis, he's really going
after Hoyle's theory, so maybe it worked out for the best.
All of this math goes on to show that
the steady state theory doesn't match observation.
He says that it excludes models that seem to correspond
to the actual universe.
Hawking points out lots of problems with the theory,
but interestingly, one of them is that it would require
some particles to have the property
of negative gravitational mass.
And he says, "There does not seem to be any matter
having these properties in our region of space.
And that the introduction of negative masses
would probably raise more difficulties than it would solve."
And this was actually before we had the idea of dark energy,
which kind of does have anti gravitational,
or a negative mass properties.
Chapter two is about perturbations.
These small variations in space time.
To describe this, Hawking uses the metric tensor
and works with the Einstein field equations.
I've got a link down in the description to some videos
that cover this math of general relativity,
in a much better way than I can here,
but all this math is done to show the conclusion
that galaxies cannot form as the result of the growth
of small perturbations.
But maybe, this is where Hawking got it wrong,
because these days we actually believe that
that is exactly how galaxies form.
However, now we have the additional component
of dark matter, providing enough invisible mass
to hold the galaxies together.
But it wasn't until 1980 that we had the idea of dark matter
when Vera Rubin published her work on galaxy masses.
And it was around that same year,
that dark energy was also proposed,
but this thesis was written 15 years earlier.
But I suppose statements like this one from Hawking,
do add to the weight of reason as to why we needed
something like dark matter, because without it,
there are a few things that just don't add up.
You can see how differently a thesis was written,
without modern tools like LayTec and word processors,
to type out the equations.
In fact, Hawking's thesis was tied up by his wife, Jane,
while she was also completing her own graduate studies.
No thesis would be complete without some spelling mistakes
that went unnoticed, but I only noticed them now
because of a lack of ability to understand what's going on
with the rest of the page.
Chapter three is "Gravitational Radiation
In An Expanding Universe."
This actually relates to what we now call,
gravitational waves.
They were first predicted by Einstein in 1915,
and we observed them for the first time in 2015.
LIGO picked up a signal from a merger of two black holes
that sent gravitational ripples all the way to earth.
Hawking mentions them a bit in chapter two,
but calls them slightly academic,
since gravitational radiation has not yet been detected,
let alone investigated.
And the treatment in chapter three
is much more mathematical, if you can believe it.
We've got the field equations, tensors, metrics.
This is the math of general relativity.
It's about describing how space moves
and if anything, it's really all about geometry.
Not much of this thesis is Hawking just pondering
about ideas for the universe, you can see that really,
most of it is about proving those ideas with mathematics.
It's why topics like cosmology and general relativity
are almost less of a physics discipline
and more about learning the math.
Often these researchers work within math departments.
Of course, everything looks strange
when I'm just throwing it in front of you on a page,
and it would make a bit more sense if you're following it
through line by line.
Like even with just more basic algebra,
if someone just showed you a random page of their working,
it'd be hard to make sense of it.
This math is hard because not a lot of us
are very fluent with tensors in this kind of way,
but that doesn't mean it's impossible to learn.
Now, I'm glad you're still around, because chapter four
is the last chapter and it's probably the most important.
It's about singularities.
He talks about open and closed models for the universe.
In an open universe, space has negative curvature
and the universe has no bounds and will expand forever.
For a closed universe, space has positive curvature
and is more like the surface of the sphere.
There's one other option which is, if space has no curvature
at all, which is a flat universe.
The evidence we have now makes us believe
that we live in a flat universe
and Hawking investigates this using a mathematical tool
called a Cauchy surface.
Hawking says that "A Cauchy surface will be taken
to mean a complete connected space like surface
that intersects every time-like and null line,
once and once only."
So I think it's some kind of slice through space time,
and it represents an instant in time.
For a closed universe with positive curvature,
the Cauchy surface is said to be compact,
whereas the non-compact surface represents
an open universe or one with negative curvature.
At this time, the mathematician, Roger Penrose
had a theory of a space time singularity
in the center of black holes.
And Hawking in his thesis, is applying this idea,
to not just black holes, but the entire universe.
His bold claims about singularities includes saying that,
"Penrose's methods are applicable
to non-compact Cauchy surfaces.
That is universes which had negative or zero curvature."
That is open or flat.
It means Hawking is really proving that singularities
can exist and are in fact essential for our universe.
That there is some infinitely small and dense point
at the beginning of space time.
And he's not just saying it, he can actually prove it.
And here's his proof right here, in fact,
it is a proof by contradiction.
He starts with saying, "Assume space time
is singularity free."
Doing this, he encounters contradictions.
His contradictions are that the universe would be both open
and closed at the same time.
He says, "This is a contradiction, thus the assumption
that space time is non-singular, must be false."
Later, Hawking would go on to work quite closely
with Roger Penrose and extend these theories
of singularities.
They published a 1970 proof that the universe
must have begun as a singularity, if it is to obey
the general theory of relativity,
it was these mathematical proofs of singularities
and of the big bang, that Hawking first became
quite well known for.
He then moved on to working with black holes
and showed that they can emit what is now called,
Hawking radiation.
And later he became involved with quantum mechanics
and thinking about ways to unite it with general relativity.
When Hawking released his thesis to the public,
he said that "By making my PhD thesis open-access,
I hope that I inspire people to look up at the stars
and not down at their feet.
To wonder about our place in the universe,
and to try to make sense of the cosmos."
When he later heard that so many people had tried
to download it, he said that he hoped
they were not disappointed by it.
I also hope that you gained some value
in what I was able to share with you.
Thanks for watching.
Thanks also to my Patreon supporters,
including today's Patreon cat of the day, Halloween.
(calm instrumental music)