Is there such a thing as the smallest unit of length or the shortest increment of time? That is the question I want to discuss in this thread. It may
seem like a stupid question at first glance, a bit like asking if there is such a thing as the largest possible number. Our natural intuition would
seem to tell us that space and time can be divided into infinitely smaller units. From our point of view time seems to be a smooth and unbroken
phenomena. Likewise, it's natural to think that we can zoom in infinitely on an object to get finer and finer detail.
After all, it's not like we live in a computer game right? Why should space be cut up into little discrete units of length and why should time be
split into discrete intervals? Could it really be possible that small particles are restricted to certain units of space and that they move between
those units in periodic intervals of time? While it may seem quite hard to grasp, I will now present several arguments which will make you strongly
question the possibility of quantized space and time, and hopefully convince you that it is more rational overall.
The first problem that crops up when you try to describe space as an infinitely divisible variable is that you open the door for a fractal universe...
if you are able to zoom in infinitely on any given patch of space you must accept the possibility that eventually you'll zoom in on a whole new
universe. You cannot argue that particles wont form at such small scaled because there is no such thing as "small scales" in infinitely divisible
space. The conclusion is that there is an infinite number of unimaginably small universes surrounding us and filling every part of space.
The next, and equally as concerning problem, is the concept of the big bang when interpreted through the lense of infinitely divisible time. If any
length of time is infinitely divisible, every passing moment is an eternity in some sense. When we calculate the age of the universe, we do so by
calculating how fast the universe is expanding and we work backwards, until all the energy of all the galaxies is condensed into a singularity. The
standard model breaks down however once you get too close to the singularity and the energy densities become too extreme.
The problem is essentially that if time is infinitely divisible, then our calculations will allow us to see closer and closer to the moments just
after the big bang, but it's always possible to get closer, so we need more and more computing power to look closer and closer, but the mathematics
breaks down before you can reach a meaningful conclusion. The only conclusion you can reach is a point of energy so dense where the curvature of space
is so high that it forms a singularity where all energy is condensed into one single point with no volume.
Another problem which arises when one is dealing with infinitely divisible space and time is a problem related to velocity. If space and time is
infinitely divisible, it means that a particle can occupy an infinite amount of different points in space. This is problematic because if a particle
isn't restricted to certain positions in space, it can be made to travel through space at infinitely slower and slower velocities. When we measure the
velocity of anything, we're talking about velocity relative to our own frame of reference, which is typically the Earth.
So when we measure the speed of a spacecraft exiting the Earth's atmosphere we say it's travelling at a certain speed, relative to our position on
Earth. But we also know the Earth moving. The true velocity of the craft is not what we measure it to be from our frame of reference, it's only true
from our frame of reference. But what is the velocity of Earth relative to? It can't be relative to the speed of light, because light behaves
according to the theory of special
relativity. If we can't even detect the end of the universe how can we even define what "truly stationary"
It's all relative unless we have some sort of fundamentally stable reference point, but there is no such point. There is no sign post out in the
universe which reads "this sign is absolutely stationary and can be used as a reference point for determining the true velocity of any object". But if
there is no such reference point then how can the speed of light be the universal speed limit? If everything is relative it makes no sense what so
ever to say that the speed of light is the universal speed limit, we don't even know how fast we are really travelling through the universe or
This is a huge problem for the standard model in my mind. However, if we accept the idea that space and time may be quantized, then we can calculate
what is the smallest possible length (planck length
), the shortest period of time
), and thus the limits on velocity, and how those variables relate to our own frame
of reference. It gives us some fundamentally stable reference point to base our observations upon. Having quantized time also allows us to step back
towards the moment of the big bang in discrete units of time instead of continuous time.
One theory which takes this approach is loop quantum gravity
. In this theory space and
time are broken up into discrete units and we can say with absolute precision exactly how much energy can fit into any given unit of space. Believe it
or not, this is achieved with very solid mathematics and theoretical models. When matter is sucked into a black hole the bits of information which
made up that matter are stored on the 2-dimensional surface of the event horizon around the black hole in a sort of holographic format.
One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive
quantity that scales linearly with the volume of the system. This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic
principle, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.
Black Hole - Event Horizon
The Planck length is the square root of the Planck area, which is the area by which a spherical black hole increases when the black hole swallows
one bit of information. The proof is relatively simple and was first set out by Jacob Bekenstein.
Planck Length - Physical Significance
Now if you're not a physicist, it may seem strange to measure matter in terms of informational "bits", but trust me it's very possible to do,
especially since all particles are quantum mechanical in nature. Loop quantum gravity takes the idea that any given Planck unit of space has a very
specific maximum energy density, so it's impossible to create a singularity or single point of energy which contains all the energy of the universe.
Instead, if you work back towards the big bang you find that at some point space becomes "full" and it causes a
Most loop quantum gravity theorists do not like to make presumptions about what led up the big bounce event. Loop quantum gravity does not predict
that the universe is cyclic or that it will re-collapse. It says that if the universe were to re-collapse then it would not end in a singularity like
general relativity would predict. Current observations indicate that the universe will in fact expand forever, which only makes the mystery of what
happened before the big bang much deeper and mysterious. But what reason is there to believe that loop quantum gravity is correct?
Well for a start it solves all of the paradoxes I just mentioned. Secondly, quantum mechanics already demonstrates the fact that everything we can
measure is quantized. There are no truly continuous or fractal energy states in nature. For example the energy states that an electron can possess
around the nuclei of an atom is broken into discrete energy states. Light comes in discrete little packets of quanta which we call photons. There is
no such thing as 1.5 quantas, one quantum is the smallest possible unit of energy, it cannot be broken into smaller units.
In physics, a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the
fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can
take on only certain discrete values.
Nature does not like infinite fractions when it comes to the behavior of particles and energy. For most quantum physicists it isn't a big leap for
them to accept that idea that space and time could also be quantized. In fact it becomes hard to see how space and time couldn't be quantized when you
look closely enough at the problem and realize that everything else is quantized. Particle physics is now becoming dominated by
quantum field theory
, which describes particles as quantized ripples in an underlying
For example the Higgs boson is commonly described as the result of a ripple in the Higgs field. The universe is telling us something, and that
something is that reality must be built on discrete units and not infinite fractions. That is why there does in fact appear to be such as thing as the
"smallest particle", that is why all particles look exactly the same. If you could divide energy up into infinitely small units, then nearly all
particles would look different, but in fact all fundamental particles in existence have the exact same structure (eg electrons).
I believe that the same rules apply for space and time because if they didn't apply it would result in a whole range of paradoxes. I don't think
everything is quantized because we live in a computer simulation, I think everything is quantized because that's just the natural state of reality,
it's impossible for anything to be defined with infinite precision and so the universe doesn't attempt to define anything with infinite precision. We
live in something which resembles a digital universe not because it's a simulation, but because information likes to be in a digital
edit on 16/9/2013 by ChaoticOrder because: (no reason given)