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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