Godel’s
incompleteness theorems

It is not strictly science, but rather a very
interesting set of mathematical theorems about logic and the philosophy that is
definitely relevant to science as a whole. Proven in 1931 by Kurt Gödel, these
theories say that with any given set of logical rules, except for the most
simple, there will always be statements that are undecidable, meaning that they
cannot be proven or disproven due to the inevitable self-referential nature of
any logical systems that is even remotely complicated. This is thought to
indicate that there is no grand mathematical system capable of proving or
disproving all statements. An undecidable statement can be thought of as a
mathematical form of a statement like “I always lie.” Because the statement
makes reference to the language being used to describe it, it cannot be known
whether the statement is true or not. However, an undecidable statement does
not need to be explicitly self-referential to be undecidable. The main
conclusion of Gödel’s incompleteness theorems is that all logical systems will
have statements that cannot be proven or disproven; therefore, all logical
systems must be “incomplete.”

The philosophical implications of these theorems
are widespread. The set suggests that in physics, a “theory of everything” may
be impossible, as no set of rules can explain every possible event or outcome.
It also indicates that logically, “proof” is a weaker concept than “true”; such
a concept is unsettling for scientists because it means there will always be
things that, despite being true, cannot be proven to be true. Since this set of
theorems also applies to computers, it also means that our own minds are
incomplete and that there are some ideas we can never know, including whether
our own minds are consistent (i.e. our reasoning contains no incorrect
contradictions). This is because the second of Gödel’s incompleteness theorems
states that no consistent system can prove its own consistency, meaning that no
sane mind can prove its own sanity. Also, since that same law states that any
system able to prove its consistency to itself must be inconsistent, any mind
that believes it can prove its own sanity is, therefore, insane.

Antimatter
Retrocausality

Antimatter is the opposite of matter. It has the
same mass but with an opposing electrical charge. One theory about why
antimatter exists was developed by John Wheeler and Nobel laureate Richard
Feynman based on the idea that physical systems should be time-reversible. For
example, the orbits of our solar system, if played backwards, should still obey
all the same rules as when they are played forwards. This led to the idea that
antimatter is just ordinary matter going backwards in time, which would explain
why antiparticles have an opposite charge, since if an electron is repelled
while going forwards in time, then backwards in time this becomes attraction.
This also explains why matter and antimatter annihilate. This isn’t a
circumstance of two particles crashing into and destroying each other; it is
the same particle suddenly stopping and going back in time. In a vacuum, where
a pair of virtual particles are produced and then annihilated, this is actually
just one particle going in an endless loop, forwards in time, then backwards,
then forwards, and so on.

While the accuracy of this theory is still up for
debate, treating antimatter as matter going backwards in time mathematically
comes up with identical solutions to other, more conventional theories. When it
was first theorized, John Wheeler said that perhaps it answered the question of
why all electrons in the universe have identical properties, a question so
obvious that it is generally ignored. He suggested that it was just one
electron, constantly darting all over the universe, from the Big Bang to the
end of time and back again, continuing an uncountable number of times. Even
though this idea involves backwards time travel, it can’t be used to send any
information back in time, since the mathematics of the model simply doesn’t
allow it. You cannot move a piece of antimatter to affect the past, since in
moving it you only affect the past of the antimatter itself, that is, your
future.

Cosmic
Strings

Shorty after the Big Bang, the universe was in a
highly disordered and chaotic state. This means that small changes and defects
didn’t change the overall structure of the universe. However, as the universe
expanded, cooled, and went from a disorderly state to an orderly one, it
reached a point where very small fluctuations created very large changes.

This is similar to arranging tiles evenly on a
floor. When one tile is placed unevenly, this means that the subsequent tiles
placed will follow its pattern. Therefore, you have a whole line of tiles out
of place. This is similar to the objects called cosmic strings, which are
extremely thin and extremely long defects in the shape of space-time. These
cosmic strings are predicted by most models of the universe, such as the string
theory wherein two kinds of “strings” are unrelated. If they exist, each
string would be as thin as a proton, but incredibly dense. Thus, a cosmic
string a mile long can weigh as much as the Earth. However, it would not
actually have any gravity and the only effect it will have on matter
surrounding it would be the way it changes the form and shape of space-time.
Therefore, a cosmic string is, in essence, just a “wrinkle” in the shape of
space-time.

Cosmic strings are thought to be incredibly long,
up to the order of the sizes of thousands of galaxies. In fact, recent
observations and simulations have suggested that a network of cosmic strings
stretches across the entire universe. This was once thought to be what caused
galaxies to form in supercluster complexes, although this idea has since been
abandoned. Supercluster complexes consist of connected “filaments” of galaxies
up to a billion light-years in length. Because of the unique effects of cosmic
strings on space-time as you bring two strings close together, it has been
shown that they could possibly be used for time travel, like with most of the
things on this list. Cosmic strings would also create incredible gravitational
waves, stronger than any other known source. These waves are what those current
and planned gravitational wave detectors are designed to look for.

Quantum
Tunneling

Quantum tunneling is an effect where a particle
can pass through a barrier it would not normally have the energy to overcome.
It can allow a particle to pass through a physical barrier that should be
impenetrable, or can allow an electron to escape from the pull of the nucleus
without having the kinetic energy to do so. According to quantum mechanics, there
is a finite probability that any particle can be found anywhere in the
universe, although that probability is astronomically small for any real
distance from the particles expected path.

However, when the particle is faced with a
small-enough barrier (around 1-3 nm wide), one which conventional calculations
would indicate is impenetrable by the particle, the probability that the
particle will simply pass through that barrier becomes fairly noticeable. This
can be explained by the Heisenberg uncertainty principle, which limits how much
information can be known about a particle. A particle can “borrow” energy from
the system it is acting in, use it to pass through the barrier, and then lose
it again.

Quantum tunneling is involved in many physical
processes, such as radioactive decay and the nuclear fusion that takes place in
the Sun. It is also used in certain electrical components, and it has even been
shown to occur in enzymes in biological systems. For example, the enzyme
glucose oxidase, which catalyses the reaction of glucose into hydrogen
peroxide, involves the quantum tunneling of an entire oxygen atom. Quantum
tunneling is also a key feature of the scanning tunneling microscope, the first
machine to enable the imaging and manipulation of individual atoms. It works by
measuring the voltage in a very fine tip, which changes when it gets close to a
surface due to the effect of electrons tunneling through the vacuum (known as
the “forbidden zone”) between them. This gives the device the sensitivity necessary
to make extremely high resolution images. It also enables the device to move
atoms by deliberately putting a current through the conducting tip.

## No comments:

## Post a Comment