In the prior video, I explained how General Relativity works, and what the math of Einstein’s
field equations are trying to say. These are some of the most proven equations in science.
But we found that quantum mechanics, which is at least as proven, ruins them.
For example, if you consider the simplest atom, the hydrogen atom, consisting of one proton and
one electron, quantum theory says that the electron is in a superposition. This means
that it is in multiple locations at various distances from the nucleus at the SAME time.
We only know the probability of finding it at a particular radius, if we were to measure it.
This is a problem because since the electron has mass, according to general relativity,
it must curve space-time. But if it is in multiple locations at the same time,
then where is the curvature? Is it also at multiple locations at the same time?
There is no such thing as superposition in General Relativity. Another problem occurs in the case of black holes.
There is a region of space inside called the singularity where, matter and energy is
supposedly compressed to an infinitely small point with infinite curvature of space-time.
But the equations of general relativity treat space-time mathematically
as being flat at infinitesimally small distances, and then calculate
the overall curvature based on this presumption. This does not work at the singularity because
infinite curvature at an infinitely small point results in nonsense
results in the math of general relativity. So the question is, is there any way we can
reconcile these two highly proven theories so that we can have a true picture of how reality works?
There are two theories that attempt to tackle this reconciliation, loop quantum
gravity and string theory. The explanation of how these two theories work is coming up right now...
Before I get into Loop quantum gravity and String theory,
let me tell you what inspired me to do this video.
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I highly recommend Magellan TV! But be sure the use the link in the description.
The best and most accurate theory of the nature of reality is represented by the
standard model of particle physics. This is like the periodic table of chemistry,
except it is for fundamental particles. Although this looks fairly simple,
it is really a visual representation of many equations that are behind it. Here’s
a glimpse of what those equations look like. I want to draw your attention to the red gauge
boson on the chart. These represent the fundamental particles responsible for 3 of
the 4 known forces in the universe. The gluon is responsible for the
strong nuclear force. The photon is responsible for electro-magnetism. And the W and Z bosons
are responsible for the Weak nuclear force. The way a force is conferred is through the
exchange of virtual bosons. So for example in electromagnetism, an exchange of virtual photons
results in an exchange of momentum which results in two like charges
repelling each other. Attraction happens through the exchange of negative momentum
similar to this boomerang analogy. I made a video recently on how these
forces work at the subatomic level if you are interested in viewing it.
You will notice that one force is conspicuously missing from this picture. And that is gravity.
This is because according to our best model for gravity, Einstein’s General relativity, gravity
is not a force, but is a result of the curvature of the background – the curvature of space-time.
But the equations of General relativity treat space-time as a bending of the continuous
background of space-time, not as a result of discrete particles that confer a force.
This is a problem. Stars and planets are made of molecules, atoms and radiation.
These are ultimately made up of the elementary particles of the standard model. And we know
that these are made of discrete units of energy. And the forces that hold the atoms together are
also due to discrete units of virtual particles represented by the gauge bosons. It is the
exchange or swapping of these virtual bosons that holds or breaks up atoms and molecules.
The universe is bumpy. There is no such thing as continuous matter and energy. This is why
Einstein’s general relativity is a problem. Why should reality have two sets of rules,
quantum mechanics for the very small, and general relativity for the very large?
Even if they appear to follow two separate rules, they should unite at some fundamental level.
One set of laws should emerge from the other, because we live in one reality,
not two different realities. This is partly the reason that
Most physicists believe General relativity is incomplete. You could ask, well, why can’t
quantum mechanics be the one that is incomplete? Here’s part of the reason. Of the 4 fundamental
forces, 3 have very robust theories rooted in quantum mechanics. Only gravity lacks a
quantum description. Not only the forces, but also the vast majority of particles,
including atoms and molecules have very robust quantum theories explaining them.
Quantum mechanics also has almost all of classical physics within in its limits. On the other hand,
classical physics like that of general relativity, does not include any quantum effects. We came
up with quantum theories because classical physics did not work under all circumstances,
and it could explain more observations. What we have learned in the past 90 years
is that Quantum physics is the fundamental language of reality.
This is why it is thought that gravity needs to be brought into the fold and not
the other way around. One way to do this is to hypothesize that perhaps the background,
space-time is itself quantized. This is what loop quantum gravity or LQG attempts to do.
It attempts to show that the fabric of space-time is not continuous as Einstein presumed,
but is itself made up of discrete quanta. Think of a TV screen, even an HDTV is, at its
smallest level made up of discreet pixels which cannot be further reduced.
This is different than every other theory including string theory. Because even in
string theory, space is the background or the canvas, on which strings vibrate.
In LQG this space-time background is itself quantized, like your television.
So this means that distance has a minimum quantity about equivalent to the plank length
or 10 to the -35 m. Similarly, area has a minimum value of 10 to the -70 m squared,
and volume has a minimum value of 10 to the -105 m cubed - below which it cannot go.
This is super tiny. To give you an idea of the smallness of the scales we are talking about.
LQG says that there are about 10^99 quanta of volume in
every cubic centimeter of space. This quantum of volume is so tiny
that there are more such quanta in a cubic centimeter than there are cubic centimeters
in the entire visible universe -- 10^86 cubic centimeters. And Time itself has a minimum quantity as
well which is about 10^ -43 seconds or close to plank time.
And what do these space-time quanta look like? Well, space time is basically made up
for finite loops with nodes connecting them. The nodes that intersect is where the quanta
volumes of space reside. It has a volume that is a multiple of the plank volume 10 to the -99
cubic centimeters. The loops in between the nodes represent 2 dimensional areas.
and large quantities of these loops and nodes are called
“spin networks.” -- because their properties are related to a particle quality called spin.
Space is defined by the geometry of this spin network. And time is defined by the
moves that rearrange this spin network. The spin network, when combined with these
quantum movements of time, is called a spin foam. Time does not flow like a river in the spin foam,
it ticks like a digital clock. And each quantum tick or movement of
the spin network is about 10^ -43 seconds. Every location in the spin network where a quantum
move takes place, time has ticked once. How do particles traverse this quantized
space? When mass and energy are added to this spin foam, the shape
of the volumes of the spin network is distorted. This distorts space and time, because any movement
of these quanta also affects the time quanta. Time is essentially movement of these volume quanta.
And this distortion of space and time is what we perceive as gravity.
The exciting thing about LQG is that makes some predictions that could be tested. For example,
it predicts that the speed of light has a small dependence on energy. Photons of higher energy
travel slightly slower than low-energy photons. The effect is very small, but it amplifies over
time. So two photons, produced by a gamma-ray burst for example billions of years ago,
if they are of different frequency, should arrive on Earth at slightly
different times. And this time delay should be large enough to be detected by our instruments.
But sadly, this has not been observed. It is possible that either the theory is wrong,
or our instruments are not sensitive enough.
A second way to quantize gravity is to theorize a completely new framework of reality based on a
new understanding of fundamental particles. This is what string theory attempts to do.
In string theory the fundamental particles of the standard model are replaced by something even more
fundamental, one dimensional fiber-like strings. The simple change of treating point like particles
as one dimensional string-like particles makes a huge difference in the mathematics.
Now if you take those strings and show that they can vibrate, it turns out that different types of
strings with different vibrations behave just like the elementary particles of the standard model.
So, the various particles of the standard model can now be simplified by replacing then
with fundamental strings. This sounds great, but one of the
biggest problems is that these strings would need to vibrate not just in the 3 spatial dimensions
we are used to, but in at least 6 more spatial dimensions in order to mathematically account
for the various particles that that we know of. So the question is where are these other extra
dimensions? It does not appear that additional large dimensions in our universe exist, so
physicists speculate that these dimensions could be very small and hidden from our perceptions.
This is analogous to the way that a rug appears smooth from a distance,
but if you look closely, you will see small loops and fibers in its structure.
Strings vibrating in these different dimensions is analogous to the way that a wind instrument
can make different sounds depending on the way the air flows through its various surfaces.
This is similar to the way that the same string can take on different properties when vibrating
in different combinations of dimensions. Strings can be open strings or closed strings.
The interesting thing is that if you treat the universe as strings vibrating in 9 dimensions,
a particular closed string vibration results in a unique graviton particle. This appears
naturally in the mathematics of string theory. So this would allow for the existence of
a force-carrying particle just like the force carrying particles of the other 3 three forces.
However, it is not clear how the idea of a discrete quantum graviton could be reconciled
with the smooth background of general relativity. Similarly, particular sets of strings and
vibrations could account for the quarks. And particular vibrations in specific dimensions
could account for the different color charges of the quarks, red, blue and green. So for example,
we could have two up quarks of different colors, and one down quark of a third color.
This would be a proton, since they are made up of two up quarks and one down quark.
Note that the 6 dimensional Calabi-Yau manifold depicted here as a 3D-like structure is for
illustration purposes only. The 6 small spatial dimensions are not something that we can imagine
with our 3 dimensional minds. The actual structure of this manifold and the vibrations within it is
not something that can be visuallized, particulary if you add the dimension of time to this picture.
The promise of string theory is that most if not all the fundamental constants could come out of
it. In addition all the charges, and properties of fundamental particles could also emerge.
This would be huge. It would be a true theory of everything.
It is ambitious. But it also has some problems, the most obvious of which
is the idea of 9 spatial dimensions. Some scientists have attempted to detect this,
for example by creating microscopic black holes at the LHC. The idea being that if gravity is
being diluted due to 9 spatial dimensions, then creating black holes on very tiny scales in only
the smaller 6 dimensions may require a lot less energy, than in the same 6 plus our 3
larger dimensions. But so far no small dimensions have been detected in this or other experiments.
The other problem is that Super string theory requires the existence of super symmetry.
This is the idea that each particle of the standard model has a shadow partner particle
with different masses. The problem is that in a decade of searching for them
at the Large Hadron Collider, no trace of supersymmetric particles has been found.
String theory probably won’t work without it. The reason that quantum gravity is such a
difficult problem to solve is partly because Gravity is so incredibly weak. For example,
it is 10^39 times weaker than electromagnetism. This is why a magnet can easily pick up another
magnet against the pull of the entire earth. We may never be able to detect the effect of
gravity for example between an electron and a proton inside a hydrogen atom.
It will be completely overwhelmed with the electromagnetic force between them.
Quantum gravity predictions may be impossible to test. We may likely have to
verify it through other predictions that such a theory makes. Any theoretical formulation is
almost certainly going to be driven by thought experiments, rather than real experiments.
Loop quantum gravity is inspired by Einstein’s idea of treating gravity not as a force, but as
the curvature of the background. It just quantizes this background. But it largely ignores the other
forces. This is why it is not currently a theory of everything, but a theory of quantum gravity.
It is not clear that it can incorporate the other forces or particles of the standard model.
On the other hand, String theory is inspired by the standard model,
but introduces a completely new mathematical formulation which attempts to bring gravity
along with everything else into the fold. But, it assumes that space and time already exists,
and does not attempt to create them. So in that sense, the nature of the background space and time
is not something that string theory can answer. So neither theory at this point is well-developed
enough to be a satisfying theory of quantum gravity, let alone an
all-encompassing theory of everything. Now, what if these two theories could be
combined together? That could be exciting, and some researchers are working on this very idea.
So that could be the next big thing. Or of course, all this could be wrong. But we won’t know that
until the next Einstein comes along, and shows us mortals how the universe actually works.
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