If you wanted to simulate the universe in a computer, the information you would need
to enter is first all the laws of physics, the initial conditions of the universe, and
about 26 fundamental constants. These constants are needed In order to describe the universe
as best we know it. And if you did this, and let the program run, you would end up with
a universe, which would be pretty much identical to what you see all around you.
We are familiar with some of the laws of physics, but what are these 26 fundamental constants?
These are constants that have to be measured, and are what they are. There is no current
theoretical basis to predict what they should be.
The first 15 of these are the rest masses of the fundamental particles of the standard
model - 6 quarks, 6 leptons, and 3 bosons.
4 of these numbers are the quark mixing parameters.These are required to describe the weak nuclear
force and nuclear decay.
Another 4 numbers are the neutrino mixing parameters. These describe how neutrinos mix
with each other.
There is the cosmological constant which describes the amount of acceleration present in the
universe’s expansion.
The fine structure constant which represents the strength of the electromagnetic interaction.
And finally, the strong coupling constant which defines the strength of the strong
nuclear force involved in keeping neutrons and protons glued together in the nuclei of
atoms.
But you’ll notice that these constants all apply to some kind of object in the universe
and how these objects interact with each other. They do not apply to all things everywhere.
So, perhaps they are not so fundamental in that sense.
There are however, 4 special constants that apply to everything everywhere. So these may
be the most important numbers in the universe. And what these constants reveal about the
universe is rather astonishing. What are these special constants? And what
do they tell us about the universe in which we live? That's coming up right now...
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Consider the simplest atom, the hydrogen atom. It consists of one electron and one proton.
To describe its interactions, at a minimum you have to know a few of its properties,
these would be properties such as the fundamentalcharge of the electron, the charge of the
proton, the mass of the electron, the mass of the proton, and the strength of the electromagnetic
force. These can all be found from the fundamental constants.
Fundamental constants means that they are measured properties because we do not currently
have any mathematical model that predicts what exactly these numbers would be. So these
cannot be derived, they have to be measured.
This is not to say that some mathematical model does't exist which could predict these
same numbers. But it does say that we currently do not know what such a theoretical model
is. It is possible that a future theory of everything perhaps, something like string
theory would predict these values.
Now, if we go back to the same hydrogen atom model, in order to model its behavior even
more precisely, we would have to take a few other fundamental constants into account.
The electron and proton for example, have rest mass, therefore they would gravitationally
attract each other proportional to the gravitational constant G.
This gravitational constant appears in both Newtonian gravity and general relativity.
It can be thought of as the proportionality factor between the strength of gravity and
the masses creating that gravity.
Since gravity applies to everything everywhere, G is the first of 4 constants that is universal.
It has units of length cubed divided by mass times time squared.
The electron and proton would attract each other proportional to the permittivity of
free space epsilon naught because this permittivity is the electric constant based on James Clerk
Maxwell’s equations.
And since the electron is spinning, it would have a magnetic moment proportional to the
permeability of free space Mu naught, because it is the magnetic constant also according
to Maxwell’s equations.
Mu naught and epsilon naught are constants that have to be measured. There is no theory
that predicts their values. It turns out that mu naught and epsilon naught determine the
maximum speed of light in a vacuum. This was found by James Clerk Maxwell.
The speed of light is a very interesting constant. One way to think of it is as a conversion
factor between Mass and energy as found by Albert Einstein in in famous equation E=MC2.
But it can also be thought of as a conversion factor between the time dimension and the
three spatial dimensions of our 4 dimensional universe. C also applies to everything everywhere
and is the second of 4 universal constants. It has units of distance over time.
Another constant which applies to everything is h, Planck’s constant. It is the fundamental
constant that sets the minimum scale of quantum phenomena. It can be found in just about
any quantum mechanics equations, from Schrodinger’s equation, to the QED Lagrangian, to the Dirac
equation. It is associated with quantum states and transitions of quantum states. Planck’s
constant has units of mass times distance squared divided by time.
Finally, there is Boltzmann’s constant which also applies to everything. It plays a role
in determining the amount of vibrational energy contained in an atom related to temperature.
It is just the definition of the energy contained in one degree Kelvin. It is in units of energy
per degree.
And using just three of the 4 constants, G, c, and h we can get some extraordinary insights
into the nature of the universe. So for example, if we take these three constants and manipulate
them mathematically like this. We get a length. What is this length? Well, this is the Planck
length. It is the minimum length that would be meaningful in quantum mechanics. :
Similarly, by manipulating them mathematically, we get time. What is this time? It is the
Planck time. It is the minimum time that can exist that would be meaningful in quantum
physics.’
We can also get energy by rearranging some of these constants. This is the Planck energy.
This is the maximum energy that could be contained in a cube that had a size of one Planck length.
We can convert this Planck energy into mass by using Einstein’s famous equation. This
represents the maximum mass that a cube of one Planck length could have.
These are values for the Planck scale. This scale really applies to everything in the
universe. The units of these scales may be the most natural units for measuring things.
Since these numbers are ubiquitous in physics, physicists often just use what’s called
natural units, and set these 3 constants equal to one.
But what is the significance of the Planck scale? The Planck length is the shortest length
that means anything in the equations of quantum mechanics. This is not to say that something
smaller doesn’t exist.
For example the singularity at the center of a black hole is supposed to be an infinitely
small point with infinite mass density. But Planck length is the smallest unit that we
can measure.
it is the smallest scale that we can theoretically probe with particle accelerators. These scales
are the theoretical limit, but in fact, it is many orders of magnitude smaller than what
we can actually measure today with the most powerful accelerators like the large hadron
collider.
The Planck length is fundamental. So for example, if string theory is true, then the strings
would presumably be as small as the Planck length. Any smaller, and they could not be
defined in physics.
This would also be the smallest size of the loops in loops quantum gravity.
And these strings would vibrate at minimum time scales of the Planck time.
In loop quantum gravity, the movement of the spin network would occur like a digital clock
in increments of Planck time. Planck time is the time it takes for light to travel one
Planck length. It is the smallest measurement of time that has any meaning in quantum mechanics.
This is the closest time to the beginning of the universe, occurring right after the
big bang that we could theoretically model. This would be around the time that all four
fundamental forces were one, just shortly before gravity separated out and became a
distinct force from the other three.
We have no idea what occurred prior to this time, nor do we have a model for what could
have occurred.
Using the word before may in fact be meaningless because time itself started at this point.
This would be the true beginning of creation.
Even though we have no model for what occurred, or what may exist at scales smaller than the
Planck scale, many people including scientists speculate what that could be.
For example, it could be a kind of quantum foam where gravity could fluctuate or be in
superposition. Perhaps this is where gravity and quantum mechanics unite somehow. Or it
is possible that space-time itself is quantized at this level, and there is nothing smaller
than this.
Could space-time be in superposition like other quantum phenomena? Perhaps, but this
would violate some of the current understanding of gravity.
Quantization of space time at these scales is the kind of universe that the theory of
Loop quantum gravity implies.
What about Planck energy? If the Planck energy was confined to the volume of a cube the size
of one Planck length it would form a black hole.
The Planck mass is considered the smallest possible mass that a black hole could have.
If we could create a black hole like this in a particle accelerator, it would have gravitational
effects at the quantum scale. And we could perhaps crack the holy grail of physics by
understanding how gravity works at quantum scales, and finally come up with a theory
of quantum gravity.
If we actually built an accelerator that achieved the Planck energy for a particle like an electron,
a black hole would form. So it would
not help to go to higher energies than that since the black hole would just get bigger.
And there would be no information that we could attain. That is why the Planck length
is the smallest length scale that we could theoretically probe.
Note that Planck energy converted to Planck mass is really a lot of emass packed into
a very small space. This is why black holes form. The mass is equivalent to about 1% the
size of a mosquito. Although this sounds really small. It is really large in energy terms.
In fact, this mass converted to energy is equivalent to the energy contained in a tank
of gasoline or petrol in your car.
When you pack that much energy or equivalent mass to a size as small as a Planck cube,
you get a black hole.
This is a pretty large amount of mass for such a small volume. Why is this the case?
You have to remember how weak gravity is. It is the weakest force in the universe. It
is 10^39 times weaker than electromagnetism for example. And because it is so weak, we
have to pack a lot of mass for the gravity to be strong enough to form a black hole within
that volume.
Some people have used the precision of the various constants to argue for fine tuning.
This is the claim that the conditions which allow life in the universe lie within such
a narrow razor’s edge, that any slight variation would have resulted in conditions which would
either not have created matter, or large astronomical structures like solar systems, or complex
compounds, or life as we know it.
And some argue that the chances are so small that there we must live in a simulation where
these precise constants were entered into the program, or that a supernatural being,
God must have chosen the constants, just so life could exist.
Others counter this argument by saying that, the universe isn’t all that fine tuned for
life because by all accounts, almost all the volume of the universe supports no life. There
is only limited number of planets in limited solar systems, that are within limited distances
from their stars with a specific combination of compounds, namely carbon and water that
are conducive to life as we know it. But if you look at the vast number of planets available
in the universe that nature has to work with, there is bound to be life on some of them.
Or that the constants are but one variation in a vast multiverse
of universe, and life in a different form could exist with a different combination of
constants.
None of these claims is currently falsifiable. I think any way you look at it, we have won
the cosmic lottery. The big question is how many tickets did we buy? And how many simulations
did our overlords create?
I’d like to thank my generous supporters on Youtube and Patreon. If you like my videos,
then consider joining them. And if you have a question, post it in the comments, below and I will try to
answer it. I will see you in the next video my friend!