A unified theory of everything has a monumental
task on its hands. It must bring together the strangest elements
of quantum mechanics and relativity – the rules on the macro scale and the micro. Which is really hard to do because there are
some very weird things going on in the quantum world. Uncertainty. Quanta. Superpositions. So let’s begin there. After my last video on this topic, I got loads
of different comments from you all, eager to hear my take on the answer to everything. I claimed last time that I believed some form
of string theory offered the best chance at a unified theory of everything. It’s time to show you how much heavy lifting
strings can do on the quantum scale. I’m Alex McColgan, and you’re watching
Astrum. While I don’t claim to have solved the theory’s
mathematics, I believe that I’ve come up with a model that pieces all the phenomena
together. Quantum physics’ mathematics has rapidly
overtaken its understanding of why the things we observe are going on. Let’s try to help conceptual understanding
catch up. As I said in my last video, it all starts
with strings. Let’s discuss a few properties of a vibrating
string. This will help us to see why they lend themselves
to quantum principles. We need to start with that first word; quantum. Simply put, quantum is derived from the same
root as the word quantity. It’s the strange principle that on a small
enough scale, the universe seems to work in discrete quantities rather than operating
on one continuous scale. This is a little unintuitive, much like many
things in quantum mechanics, so let’s illustrate what we mean with an example. If you are running, I could ask you to half
the speed you are running at. You could half your speed again, and again,
and again. Is there a limit to how many times you can
half that speed? While you might struggle with the precision
necessary to do it, in classical physics there’s no reason you couldn’t keep halving and
halving your speed infinitely, as there’s no limit to the number of times you can divide
a number by 2. There’s always a smaller number. In the quantum world, this is not so. When it comes to energy levels, momentum,
and other attributes, when you reach a small enough number, you discover that the universe
does not work on a continuous scale, but rather in discrete quantities. An electron in a hydrogen atom can have exactly
-13.6 eV of energy, or it can have -3.4 eV, but under no circumstance can it have an energy
level between those values. This has been proven experimentally. A theory of everything must make use of an
underlying universe geometry that is fundamentally quantised. The concept of some kind of web of strings
fits that bill well, particularly when you bring in transverse standing waves and harmonics. When plucking a guitar string, a standing
wave can form that has one peak, or two, but not a value in between those. This is because harmonics are formed by the
combination of waves travelling along the string in one direction perfectly resonating
with waves travelling in the other. If the speed or frequency of the waves don’t
line up perfectly, the two waves will ultimately disrupt each other, leading to the collapse
of the standing wave. Only waves with just the right amount of speed
and energy can create standing waves on a given string. So, immediately, we have an interesting mirror
to our observation that subatomic particles have quantised momenta and energy levels. So do standing waves on strings. The next interesting point to note about waves
is that by combining the correct sequence of sine waves, you can create any wave pattern
of wave you might desire – handy for creating the rich complexity of a universe. This mathematical principle was first discovered
by Jean-Baptiste Joseph Fourier, a French mathematician, and is very useful in the study
of heat transfer and vibrations as it works the other way too – any wave can be broken
down into a number of constituent sine waves. When two waves try to occupy the same place,
they will amplify each other if they’re both rising or both falling, but will cancel
each other out if they are in opposition. This can lead to all sorts of waves being
formed: square waves, intermittent waves, and even waves that only have a single peak
and are flat at all other locations. This becomes easier to do the more waves you
have to overlap. This is an interesting observation, as it
helps answer an important question that any theory of everything must be able to answer:
where do particles come from? When I say particles, I am not specifically
talking about molecules or atoms, but the components that make these objects up. Atoms split into protons, neutrons and electrons. Protons and neutrons split into quarks, and
there are also leptons and bosons. Without needing to go into exactly what all
of these things are, or why they have some of the weird names that they do (who decided
to call a quark “strange”, “charm,” or “bottom”?) it’s enough to say that
they come in many different flavours. These are the smallest building blocks of
reality that we know of so far. Why do they exist? Well, in a model using strings, they are the
rising and falling of a wave. This matches Einstein’s observation that
mass and energy were essentially just the same thing in different forms, as laid out
in his e=mc2 equation. A wave is the motion of energy. Mass can be that too. The narrower the peak of the wave, the more
defined a particle is in terms of its location on that string. You might take issue with the idea that both
of these waves represent the location of a single particle. However, curiously, this matches another important
facet of particles – they sometimes are a little vague about where exactly they are
in space. If you know much about quantum mechanics you
have likely heard of Heisenberg’s Uncertainty principle. This is the idea that we cannot know a particle’s
momentum and position at the same time. We can get a decent approximation at large
scales – it’s easy to see where you are, and where you’re going – but at small
enough levels this becomes impossible to do. The more precisely we know where a photon
is, the less information we have about its momentum. And vice versa. This isn’t just because we have bad techniques for observing them, this
is apparently a fundamental truth. If we think about particles being the sum
of many overlapping waves, however, this suddenly makes a lot more sense. Take a look at this wave. It is perfectly defined in terms of where
it is going, but if we consider the peaks of this wave to represent the location of
the subatomic particle – or at least, the possibility that the particle is at this location
– there are a lot of places it can be. So for this given string, we have perfect
knowledge as to its speed and direction, but are uncertain about its position in a given
space of string. Perfectly in line with Heisenberg’s uncertainty
principle. If we converge several different waves onto
a single point, we can take advantage of Fourier’s mathematical trick to cancel out some of the
peaks of our wave. The more waves we add coming in from different
directions, the more our particle becomes defined in space… but look at our particle
now. How many strings are running through it? Each of these is a separate
vector line, representing momentum in a different direction. It is no longer quite so possible to pin down
where this particle is going next, as there are several options that could be true. Perfectly pinning down a particle in terms
of its location would require vector lines that could lead anywhere. This is starting to get into territory where
you need information from the entire universe before a single particle can be truly “solved”
in terms of its location in space and time, which is a little headache-inducing. Perhaps the universe makes
do with close approximations most of the time, until someone looks closely. For this model, we must discard our concept
of a particle as a localised object, but instead we define them as the convergence of different
waves, coming together at a single point and then diverging again. This divergence doesn’t feel right to us. We are uncomfortable with the idea of our
particles only being really there at a given moment, and dissipating afterwards. However, those of you familiar with the double
slit experiment (which I’ve covered in an earlier video) will recognise that this is
an uncanny match to another odd experimental result: a single photon released from an emitter
and passing through two slits will somehow pass through both slits, interfering with
itself on its journey. The photon reaches the far detector as a single
particle again, indicating a new convergence at that point, but by sending many photons
along this path it becomes clear that interference is taking place in the intervening space. The photon seems to leave as a particle and
arrive as a particle, but in the intervening space it takes on the properties of a propagating,
rippling wave. Already, we begin to see how some of the strangest
aspects of the quantum world fit with the idea of strings carrying waves of energy. But this is only the first part of my model. To really see how such a theory matches the
universe around us, we need to explore the motion of particles across time and space. To better understand
entanglement and superpositions. And to do that, we need to explore how strings
lead to gravity, time dilation, and other principles of relativity on larger scales. We need to have a clear concept of how time
works. My model accommodates that. But it will have to wait until my third video
in this series to fully explain. In the meantime, do you agree with what I’ve
said so far? Are there other aspects of quantum mechanics
that you feel suit or do not suit the concept of strings? Leave a comment in the description below to
let me know. Thanks for watching and thanks
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