Today our focus is on Tachyons, a hypothetical
particle that travels faster than light and has an imaginary mass, and even more so on
time travel, which we need to talk about before we get to some of the other subjects like
wormholes. Last time we talked about the basics of Special
Relativity when it came to making time slow down and we cleared up some confusion people
often have with that subject before talking about Quantum Entanglement.
Today we’ll be expanding on those notions a bit so if you haven’t already watched
the first episode you should do that now unless you have a pretty solid grasp of Special Relativity
already. Which is to say if you’ve seen these two
equations before and used it several times you’re good, otherwise not. Now these equations
didn’t show up last time but ought to look fairly familiar. Last time we talked about
distance and time contracting, today we are more interested in mass.
So we’ve three new quick concepts to look at. Rest mass, the Lorentz Factor, symbolized
by the lowercase Greek Gamma, and the Capital Greek Beta. That last one is the easiest,
when we are dealing with truly relativistic velocities we always talk in terms of the
speed of light. Something is going .9 c, or .5 c, and we just use Beta for that, if Beta
equals .5 then you are going at half the speed of light. Saves time and makes for a smaller
equation. The Lorentz Factor, Gamma is much the same
thing, if you calculate gamma for any given speed you can just multiply or divide it by
your proper length or time to find out how much time is dilated or length is contracted.
You can also multiply it by rest mass to figure out what the relativistic mass is.
Now rest mass is a simple concept but has some tricky aspects. It is literally how much
mass something has when measured when it isn’t moving, when it is at rest. But we usually
don’t use non-rest mass, relativistic mass, in favor of just keeping that invariant and
thinking in terms of the objects total energy. So we use energy, momentum, and rest mass
energy together a lot. This makes gamma way more convenient but also
means we often like to talk in terms of gamma, not Beta, since its effects are more intuitively
obvious. I mentioned last time that an object moving at 87% of light speed, or Beta=.87,
would appear to be scrunched up in the direction of motion by half and have its clock running
at half speed, and that one doing 97% would be condensed down to a quarter and have time
running at a quarter speed. That’s the case for gamma equal 2 and for respectively, and
that’s easier to think with. Here on this table I have selected gammas by their beta
value. And as gamma rises time slows down more and more and the energy you need to get
to that speed rises sharply. As you can see you never quite reach Beta
=1, or light speed, until gamma is infinite, meaning anything with rest mass needs infinite
energy to get to light speed. And you’d need more than infinity, something of a nonsensical
concept, to accelerate anything with rest mass over light speed. Of course if anything
started off with that speed to begin with, like our tachyons, they wouldn’t need infinite
energy to get there, same as photons don’t need infinite energy to be at the speed of
light since they have no rest mass. This is where imaginary mass comes into play.
If you pump in a value for Beta of more than 1, say 1.41, then Beta Squared equals 2 and
1-2=-1. Now we have a problem again because there’s no real solutions to the square
root of a negative number. That’s why Rene Descartes, best known for
“I think therefore I am”, created what we call an imaginary number, i, which when
multiplied by itself equals -1. Hopefully you’re already familiar with that because
I don’t want to spend time discussing it, but odds are good you don’t know that the
reciprocal of i is –i, so when we get 1 over i here we can just replace it with –i,
giving us a negative imaginary gamma and a negative imaginary mass.
We don’t really care about that negative and don’t usually mention it to avoid confusing
with negative mass, which we’ll be talking about a lot when we get to the Alcubierre
Warp Drive and stable Wormholes, so we usually just say imaginary mass.
Now imaginary numbers bug people, especially in terms of physics which unlike math is only
supposed to deal with reality, but imaginary numbers come up a lot in physics, and even
trigonometry features them though we usually hide it. And imaginary mass isn’t limited
to tachyons, this hypothetical particle now in disfavor, we use it for tachyonic fields
for the Higgs Boson too. We also use imaginary time in Cosmology.
Conceptually the easiest way to explain the tachyon running back in time is just to think
how as time slows down as you approach the speed of light, freezing at the speed of light,
that it just starts running backwards above the speed of light.
Now Tachyons are a whole class of particles, anything which might move faster than light.
We don’t assume it to be a single particle like an electron. In this context we also
have the luxon, any massless particle like the photon or gluon that travels at the speed
of light and experiences no internal time, and the Bradyon or Tardyon. Tachyon comes
from the Greek word for rapid, and Tardy is Latin for slow, whereas Brady is Greek for
slow so Bradyon is probably more consistent but neither gets used much. But a Bradyon,
or Tardyon, would be any normal matter with a rest mass.
The application of the Tachyon is obvious. If you can generate them then you can send
them back to a given place and time to be received. Time travel telephone or radio,
and presumably something you could use to send people back in time too, or homicidal
androids. The tachyon was first proposed in the early
sixties, though it was known as a metaparticle at the time and soon renamed. It made a couple
appearances in science fiction novels in the seventies but its first use I know of in TV
or film was in Doctor Who, during the episode the Leisure Hive whose last installment amusingly
was on the day I was born. That combined with the obvious time travel application of a particle
that moves back in time is why the intro for this series has the doctor who theme. It’s
going to come up a lot in the series because there are not many situations where you can
travel faster than light without traveling back in time.
I wanted to discuss these issue of Temporal Paradoxes back in episode 1 but I didn’t
want to run overly long and Time Travel, pardon the pun, is a time consuming subject. Time
travel and its paradoxes tend to give people headaches, probably because its use in fiction
necessitates it not quite making sense, but today we’ll be trying to explain how it
works minus the headache. That pretty much ends our interest in the Tachyons though,
they are simply a vehicle to time travel and their hypothetical status means we have no
proof they exist, they might not exist, and we have no idea how we’d ever detect them
if they did. So let’s move on to time travel. Fortunately it’s also a topic you are probably
already acquainted with. The two classic examples, in terms of paradox, are known as the Grandfather
Paradox and the Casual Loop. There are some other ones, but they usually represent the
same thing under a different name or minor thematic rather than functional variation.
The Grandfather Paradox is when you go back in time and keep your grandparents from every
meeting, this causing you to never be born, thus preventing you from ever traveling back
in time to prevent that meeting, erasing the problem. In terms of alternate timelines or
Many Worlds theory this can have different effects we’ll come back to in a bit.
The Casual Loop is the other angle on the paradox. Casual Loops, as the name implies,
are where effect precedes the cause, or has a sort of chicken and egg thing going on.
An event causes another event which in turn causes the original one. A loop of cause and
effect, or a causal loop. The evil computer intelligence finds itself
losing a war with the human resistance and notes that the leader of the resistance seems
to be an abnormally larger factor in the loss and deduces that if he had never existed the
resistance would never have existed either or been far weaker. So he sends a murderous
robot back in time to prevent the birth of said resistance leader by killing his mom.
The resistance leader sends his own guy back in time to protect his mom who then ends up
being his father and forewarns the mother of a lot of the problems, so she ends up raising
a kid who really is an abnormally skilled resistance leader, leading the machine overlord
to correctly deduce that removing him from play before the game even got started would
be a smart move. In the grandfather paradox you never travel
back in time to kill Hitler because having killed him you erase your motivation to travel
back in time and do it again. In the casual loop paradox, you get this chicken and egg
aspect, your time travel ends up causing your reason for time travel.
Skynet decides he has to eliminate John Connor in the past, not now, because he made the
resistance so much more dangerous, but the reason for that was because the attempted
assassination resulted in him having the foreknowledge and training to be dangerous. This is why
casual loops are also called Retrocausality, pulling yourself up by your own bootstraps,
or Self-Fulfilling Prophecies. Now we need to talk about Quantum. In Quantum
Physics there are numerous interpretations of seeming Quantum Randomness. The two you’re
most familiar with are Copenhagen and Many Worlds. We don’t really have a way to test
which is true, if any, because they are all designed to match what evidence we do have.
Copenhagen looks at Schrodinger’s Cat and says the critter is simultaneously alive and
dead until you look. I prefer to think of it as coin that’s spinning,
simultaneously heads and tails, until you grab it, since I like cats. Plus I think a
spinning coin better represents the concept of an undetermined state.
In Many Worlds you don’t know the result until you observe it but it assumes the event
actually spawned two different realities, one alive, one dead, or one heads, one tails.
The result is already determined, you can’t predict which universe you’re in but the
contents of the box or the coin flip are already resolved you just need to check them.
Time Travel is mostly not a problem in Many Worlds. If you jump back in time you just
spawn a new timeline. In fact there ought to be a version of reality right now where
by sheer quantum randomness various atoms in your front lawn have coalesced into a blue
police box some gentleman just stepped out of, complete with detailed but fake memories
of time travel. That’s the irritating thing about quantum,
since any given atom has a finite chance to change into another atom, there is a much
smaller chance of two of them doing it at about the same time and place, and a far smaller
but still finite chance of that happening in many atoms to produce some macroscopic
and weird thing out of nowhere like and individually wrapped candy bar or a person possessing an
entirely randomly created memory. So in many worlds there’s already a reality in which
someone has appeared genuinely thinking they’re a time traveler even though they didn’t
even exist till five seconds ago. This concept is merely an extension of the
notion of a Boltzmann Brain, in a truly random system any state that can exist will eventually
exist, and that would include a brain, complete with everything it needs to keep surviving,
like a body, assembling itself randomly, and that can also include a fake memory, leading
that entity and other people to assume they existed before, a concept we’ll look at
from a different angle when we discuss the Simulation Hypothesis.
But real time travel is nominally viable in Many Worlds anyway, since you wouldn’t even
risk a paradox so long as you were jumping to a time, ahead or behind, in a reality that
was not your own. And it need differ by nothing more than that a single random uranium atom
in the core of the planet that did decay into thorium and Helium five seconds ago in our
reality did not do so in the one you want to jump ahead in time into.
Or a version of the past where an atom of uranium still around now had previously decayed
as Julies Caesar was born, and events are otherwise effectively identical. It’s not
your past or future you are messing with so no paradox is created by your actions.
You need not even necessarily be moving in time anyway, as a parallel reality might simply
have time running there a bit slower or faster so you are simply stepping into a place that
is otherwise identical but a bit further ahead or behind your own time. In many worlds it’s
kind of debatable if going to those other worlds is really the same as time travel or
not, but from a practical standpoint it is. Of course you could still setup a casual loop
in this setup too, though it might be better to think of it as a wave. You get your hands
on a time machine, or reality jumping machine, and wait till the next news report of some
big gold strike on relatively cheap land or some other event less random than the lottery,
like a new tech patent, and jump a bit back in time into a reality where a copy of you
exists waiting for such data too, hand it off to him and he takes off, leaving you there
to assimilate into a near-identical circumstance but now very rich due to your knowledge.
He arrives in the next carbon copy and cuts the same deal with your other quantum clone
and rinse and repeat until eventually some difference exists that breaks the chain and
the wave crashes to an end. This isn’t a casual loop in that chicken and egg sense
since you had a definite starting and stopping point.
Now the Copenhagen Interpretation, that our cat or coin is in two states at once until
observed, doesn’t actually prohibit alternate timelines or other realities, it simply has
no need for them. There’s tons of different ways you can have places besides our own Universe
after all, and some of our other FTL concepts for instance would involve popping into a
parallel Universe, meaning one that has bits and pieces corresponding to our own, that
was smaller than our own or had a higher speed of light and just zipping through there until
you reached that point of congruity and popping back into our own Universe.
But again in Copenhagen there’s no need for these alternate realities, and we often
assume there is just a single timeline. After all an issue with Many Worlds, an incorrect
one but a common concern, is that these branching new realities are all new universes forming
from nothing and breaking energy conservation, or getting you something from nothing.
Which considering our own universe is assumed to have violated that in the first place shouldn’t
be a big concern but normally in many worlds, or in some variations of it, the assumption
is these alternate universes already existed and always have. Think of it as alternate
pasts, not just alternate futures. More than one state of affairs can lead to
an identical final result, a concept that relates to our next concept, and would still
apply even though it assumes there are no alternate timelines.
In the context of Copenhagen Interpretation, with no alternate timelines or realities,
or at least where if they do exist they are inaccessible, we have something called the
Novikov Self-Consistency Principle. Igor Novikov, who came up with the Novikov self-consistency
principle of time travel, argued temporal paradoxes weren’t possible. He closes out
paradoxes in time travel, which are permitted in some solutions of the Einstein Field Equation
for General Relativity, by asserting any event that would give rise to a paradox or change
the past in anyway must have a probability of zero.
This doesn’t ban time travel in and of itself though. It simply is arguing that any time
travel has to result in no paradox or it would be infinitely improbable to occur. Novikov
is arguing that regardless of whether or not time travel is possible, you will not be able
to do anything that causes a paradox. In a conceptual sense, don’t think of this
as some sort of Time guardian who pops out and stops you, but rather that the moment
you take a paradoxical route things would reset to a scenario where you hadn’t taken
it yet and keep doing it until you picked a path that didn’t cause that.
Since in Copenhagen there is always a chance one of the random quantum events will spiral
itself up to the macroscopic level one will eventually occur that results in a non-paradoxical
action. There’s no deletion, our coin that can normally
be heads or tails will simply never land on heads if it doing so would cause a paradox.
You would not remember these resets of course, they will have never happened for the same
reason that once you open Schrodinger’s box or catch the coin, the observed reality
erases the alternate possibility, and as we discussed with Quantum Entanglement, that
erasure is not constrained by the speed of light nor does it even seem to care if it
has to reach back in time to fix it. Again this isn’t implying anything is selecting
that solution that counters the possible paradox, there would be many that did, and many that
didn’t, and one would happen same as a drop of water falling from the sky will eventually
take a path leading to the ocean, whether it does so by falling right into the ocean,
or on your roof and following drainage ditches and waterways to the ocean, or even falling
on a desert and evaporating. The Self-Consistency Principle tends to bug
people a bit as confusing since it sort of seems like a tautology. Paradoxes are impossible
because paradoxes are impossible, but the difference is that it’s asserting the laws
of physics can’t be chucked out the window by time travel. There’s a comment on this
that this principle seems to permit any type of action can be done through time travel
except killing yourself, since you obviously can’t travel back in time if you’re dead.
I’d say even that doesn’t work though, and something will happen to resurrect you,
like one of those freak quantum events I mentioned earlier where a blue police box and guy with
fake memories of time travel is spontaneously spewed out by quantum randomness. Or someone
discovers cloning and mind uploading, something we’ll be talking about in the future.
Again it’s not that something is stopping specific actions, it’s just that all your
possible state and actions will only be non-zero probabilities when they won’t cause a paradox.
Now Novikov’s views are hardly considered canon, however it comes up a lot in time travel
talk so I wanted to discuss it. Same reasoning as the Tachyon, although in the tachyon’s
case, while it has fallen a bit out of favor in science fiction it has seen a recent in
resurgence in all sorts of pseudoscience especially for methods of immortality, and again we’ll
be looking at that subject ourselves soon, though we will be mostly focusing on plausible
science. Next time in this series we’ll be looking
at the Alcubierre Warp Drive, taking our first dip into how general relativity allows us
to warp spacetime, and another type of exotic matter, particles and fields possessing negative
mass or energy. From there we will move on to wormholes, which rely on many of those
same general relativity concepts and negative mass as well.
I haven’t decided on an exact order to the next few videos since I want to redo the old
Dyson Dilemma video without having to interrupt our regular schedule, but subjects we’ll
be looking at in the near future in no particular order will be a return to the Habitable Planets
Series for a look at Double Planets, a return to Megastructures series for a quick look
at Hoopworlds, neither of which are going to require very long videos so will probably
be sooner than later. We’ll also be taking a deep look at the
Simulation Hypothesis, the concept that we might all be living in a giant simulated Universe,
and some of the implications that would have in regard to the Fermi Paradox. As well as
an introduction to the concept of transhumanism and biological immortality and especially
the latter’s implications to the Fermi Paradox. If we get a chance we’ll look into the Carter
Doomsday Argument and its own implication for the Fermi Paradox, and as you might guess
this jump back into the Fermi Paradox is a major motivation for finally redoing the Dyson
Dilemma, and if I get a chance the Fermi Paradox Solutions video as well. So a busy next couple
months, assuming I can hold to the current weekly schedule.
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