Tachyons can travel faster than light,
which means they should travel backward in time.
Could they be used to make some kind of telephone
that would allow us to talk to our past selves?
No. No, they can't.
[Intro Music]
Hey Crazies.
Aside from the fact that tachyons are purely hypothetical particles,
they could not be used this way, even if they did exist.
The order of cause and effect must be maintained.
Causality shall not be violated!
[Phone Ringing]
Hello?
(Phone): Look, I know you’re excited, but don’t get ahead of yourself.
(Phone): Start at the beginning.
Oh yeah. I guess I should probably explain what a tachyon is first.
Most particles travel slower than light.
We call them bradyons because “brady-” is Greek for “slow.”
Some particles, like photons and gluons, travel at exactly the speed of light.
We call them luxons because “lux” is Greek for “light.”
You're probably noticing a pattern here. Scientists love Greek.
That means any particle traveling faster than light should be called a tachyon.
“Tachy-” being Greek for “swift.”
Unsurprisingly, none of these particles can do that.
None of them are tachyons.
We've never detected a tachyon. We're not even sure if we could.
But math doesn't say they can't exist, so what if they did?
Let's begin with what we know and then maybe we can extrapolate.
Consider an electron inside a very long particle accelerator.
The longer it travels, the faster it goes.
The faster it goes, the slower its clock ticks.
To be clear, this isn't an actual clock. Electrons don't wear watches.
In physics, a “clock” is just shorthand for the passage of local physical time.
Basically, if we were to take a measurement of time in a reliable way, what would that tell us?
In this case, whatever processes this electron experiences,
it experiences them slower than normal
As the electron approaches the speed of light,
time slows to an almost standstill for it.
If this pattern were to continue,
time would completely stop at exactly the speed of light
and reverse when the speed of light is exceeded...
...like we'd see with the tachyon.
So let's say this is a tachyon phone, also known as an anti-telephone,
and I want to call my past self at the beginning of this video.
What would that take?
You're going to do a spacetime diagram, aren't you?
Yep, you called it.
As a refresher, location is measured along the horizontal and time along the vertical.
Why?
Tradition!
Since I haven't changed location, my path looks something like this.
As time passes, I simply move up, which is forward in time.
This is me now and this is me from a few minutes ago.
If I were to use an ordinary phone,
my signal would go forward in time along these diagonals.
Radio is a type of light ...and all light travels along those diagonals.
They form my future light cone.
Inside it are all the slower than light particles I can send.
Outside it are the faster than light paths.
This is where tachyons travel.
The bigger the angle is from my path,
the faster the particle is going relative to me.
Though, to get a signal to my past self,
the tachyons would have to go straight down.
Fast fast!
That's an angle of 180 degrees though. How fast is that exactly?
We can convert to speed using this simple equation.
The tangent of 180 degrees is... zero?
Hold on a second!
If we graph the tangent function across all angles, we get something like this.
The speed of light is right here, which is 45 degrees along the diagonal...
exactly as expected.
All slower than light particles are below that.
Tachyons are above that.
But look at this. It's broken at 90 degrees.
As the tachyon speeds up, it approaches 90 degrees in the spacetime diagram.
At 90 degrees, the tachyon would be traveling at infinite speed.
What does anything above that even mean?
I guess we should be more careful with extrapolation.
Yeah, exactly.
Math is a tool and, like any tool, you have to know how to use it.
Saying a clock goes in reverse is not the same as saying something travels back in time.
In the spacetime diagram, these paths go back in time, but these go forward.
So, clearly, not all tachyons go backward in time.
Maybe some, but not all.
The boundary between them is infinite speed.
That would put those tachyons at every point in space at that moment.
What Star Trek Voyager would call “Warp 10.”
(Emily off camera) Only Voyager?
It was mentioned in one episode of Voyager and then never brought up again.
(Emily off camera) Gotcha. (Nick) We’re not going to talk about that episode anymore.
That's an infinite discontinuity between the two types of tachyons.
For the slowest tachyons that do go back in time, you’d get a negative speed.
Not a negative velocity. A negative speed.
And that's true all the way up to the 180 degrees we needed to go straight backward.
That's not all that weird if it goes back in time, though, right?
Okay. Okay.
Let's keep going and assume that backward tachyons are possible.
They're not, but let's assume they are for a couple more minutes.
How do we get paths like this, if this path is infinite speed?
How do we get over that discontinuity?
Your first thought might be to send it from another location.
Unfortunately, we'd run into the same problem.
I might not need 180 degrees from here to get to the past,
but I'd still need an angle larger than 90.
I would need to somehow make tachyons go faster than infinite speed,
which I can't do.
Or maybe I can.
What if we give them a boost?
A Lorentz boost.
What if we bounce the tachyon signal off something that's already moving?
Like this probe zipping away at 80% the speed of light?
For this to work, the probe must have started its journey
before the time in the past I'm trying to reach.
Creating an anti-telephone takes preparation.
Let's say my tachyon signal travels at five times the speed of light.
That corresponds to an angle of almost 79 degrees in a spacetime diagram,
which is less than infinite speed and still toward the future.
That signal is received by the probe at just the right moment
and then retransmit it back toward me,
again at five times the speed of light.
But here's the thing. That signal wasn't sent by me.
It was sent by the probe.
And that probe is traveling at 80% the speed of light
or about 38 degrees,
which means its coordinates are not the same as mine.
The probe might think it's sending a signal at 79 degrees.
but this is what that looks like in our coordinates.
The signal gets a boost of 38 degrees, putting the total angle at 117.
That doesn’t look like 117 degrees!
Okay. Okay. I'll admit there's some distortion in this picture.
It's important to understand that, in relativity,
it's the coordinates that change, not the paths.
But, if you insist, we can undistort the axes.
Now it actually looks like 117 degrees.
Since that angle is greater than 90, we've successfully sent a signal into the past.
(Phone): Hello?
Look, I know you're excited, but don't get ahead of yourself.
Start at the beginning.
What about causality, though?
Didn't you say it can't be broken?
Yes, I did.
Now, let me explain why Past Me will never receive that message.
That rebound signal might be traveling at five times the speed of light for the probe,
but, in Past Me’s coordinates, it's much slower and away from him...
...like in the opposite direction.
According to Past Me, the signal never arrives, which means he isn't affected by it.
Causality shall not be violated!
So, wait, how did I receive that message earlier?
Whatever.
Causality always wins.
But this isn't the only weird thing about tachyons.
Just like ordinary particles can't accelerate to the speed of light,
tachyons can't decelerate to it.
They're trapped in FTL.
To make matters worse, the faster they go, the lower their total energy.
If a tachyon goes fast enough, its total energy can be less than its rest energy.
Absolutely absurd!
And, if we look a little deeper, we can see where the problem is.
This is the equation for relativistic momentum.
For slower than light particles, we get fairly ordinary values.
You plug in the mass and the speed and you get an answer.
For speed of light particles, we get a zero in the denominator.
The only way that's allowed is if you also have a zero in the numerator.
In other words, photons can't go that fast unless they have zero mass.
For tachyons, the denominator is imaginary,
which means the mass must also be imaginary.
What I'm trying to say here is “tachyons are imaginary.”
Just because something is mathematically possible, that doesn't make it real.
Math always gives us an answer to our question,
even when our question isn't about reality.
And until next time, remember, it's okay to be a little crazy.
I just want to take a moment to thank everyone who supports the channel.
Your generosity really makes a difference.
A special thanks goes out to our new asylum counselor, Richard Senegor;
our new asylum orderlies, Chloe Joan Lopez, James Smith, Joel Wolhendler, and Peter Engrav;
and our new Einsteinium crazies, Sheila Owen and Matias Cveczilberg.
Thank you so much for all of your support.
You should have used a hyperbola instead of a circle. Spacetime is hyperbolic.
Actually, you can use either one depending on your choice of axes.
The circle might be unconventional,
but it's mathematically valid if you move some terms around.
Anyway, thanks for watching.
I want more feeling!
How do you say “causality” with feeling?