Hey there Crazies.
In our video about the universe being a big simulation, we said this.
What about Planck time?
and John...
John
He was wondering what the heck Planck units were.
First things first.
What are units?!
Units are really important!
We can sit and theorize all day but, eventually, we’re going to have to take
some measurements in the real world.
and that demands a unit!
Which could really be anything as we saw in the faking gravity video:
It's about 5 football fields,
or 3 and a half Giza pyramids,
or 110 Volkswagen Jettas,
or 733 tube socks!
It doesn’t matter what the unit is, just that we all agree and understand
what it is.
Otherwise, you end up with a Mars Polar Lander crashing into Mars
because someone didn’t do a unit conversion.
Seriously, links in the doobly-doo.
Actually, it matters a little.
The metric system is based on 10’s which is
significantly easier to use than the imperial system used in the United States.
[Groaning Noises]
So here’s the problem.
What if you wanted to communicate the average height of a human being to an alien race?
[Alien Noises] Yes, Milton, like you.
They’re not going to understand football fields or tube socks
or any abstract units like miles or meters.
You need something you know that they are familiar with.
We call these types of units "natural units" because they’re based on nature.
They’re supposed to be independent of our subjectivity.
You know, that stuff we impose on almost everything.
For example, I could measure my height in ground-state hydrogen atoms.
All of which are identically about 1/10 of a nano-meter tall.
We sometimes call that an Angstrom after the Swedish physicist.
That would make me about 18 billion hydrogen atoms tall.
That's pretty average for a human.
This is kind of what Planck Units are, but instead of being based on ideas like atoms,
they’re based on the fundamental constants of nature.
The gravitational constant, which dictates the influence of gravity.
Planck’s constant, which determines how lumpy and uncertain the quantum world is.
The Speed of Light, which is how quickly different parts of space-time can communicate.
Coulomb’s constant, which governs electricity.
And Boltzmann’s constant, which controls the statistical behavior of large systems
of particles.
We’re pretty sure they’re the same everyone in the universe.
But, again, aliens are going to have their own units
and, if they have a different number of these, they’re not going to use base-10 math either.
To make these more universal, we need to do something crazy.
Just for the sake of argument, let’s set all of these equal to one.
The number one exists in all base-systems and there are no more units.
Wait ,how can you just do that?
Well, you can’t, unless you change everything else too.
Changing those constants to one, changes what units we use for:
Length, Time, Mass, Charge, Temperature, and, frankly, any other units based on those.
Area, Volume, Force, Energy, Power, Momentum, Frequency
The list goes on!
Every single one of those is now measured in what we call a “Planck Unit”
named for the German physicist Max Karl Ernst Ludwig Planck,
or just Max Planck for short, who invented most of them back in 1900 CE.
Historically, understanding physical quantities starts with length,
so it was very natural for Planck to do the same with his units.
Plank Length is about 10 to the negative 35th meters.
To understand how small this is, we need to turn back the clock a little.
To the time machine!
Playing the expanding universe in reverse, we can look way back in time.
At one point, the universe was the size of a basketball,
and then a human egg cell, and then an atom, and then a proton.
At 10 to the negative 18 meters, we reach the smallest distance we’ve ever measured.
Planck length is 17 more decimal places!
It’s insane!
When the universe was this small, we call that the Planck Era.
It was one Planck length across, one Planck time old,
and one Planck temperature hot, which is really hot!
OK, let’s get back to the lab!
What’s so special about Planck length?
Nothing really.
At least, not yet.
Some models of quantum gravity say that Planck length is the smallest possible distance.
Because quantum mechanics loves it when things are quantized like that.
But remember, we’ve only been able to measure down to 10 to the negative 18 meters,
so we’re not really sure about anything smaller.
And no model of quantum gravity has experimental evidence anyway.
Even if space has a smallest amount of chunk or whatever.
It could just as easily be a 10th of the Planck length or 1000 times the Plank length,
as long as it’s less than 10 to the negative 18 meters.
What I find interesting is how ordinary some of the other Planck units are.
Planck Mass is about the mass of a flea egg.
Planck Energy is about what we could get out of a 16 gallon tank of gasoline.
Planck Resistance is about 30 ohms, which is resistor I use all the time.
That’s kinda cool.
So, do you think the Planck units have any physical significance?
Let’s continue this conversation in the comments.
Thanks for liking and sharing this video.
Please subscribe if you’d like to see more science like this.
And until next time, remember, it’s OK to be a little crazy.
In the last video a clone fell into a black hole.
Comment response time!
Amit Patel was wondering why larger black holes don’t spaghettify you like smaller
ones do.
An event horizon is an event horizon, right?!
Yes, an event horizon is always a place of infinite time dilation
and yes, bigger black holes have stronger gravity,
but that’s okay because the strength of gravity isn’t what rips you apart.
It’s the difference in strength between, say, your head and your feet.
Those differences are bigger around smaller black holes even though,
overall, those holes are weaker.
Kamikaze Katorin and DavidCH12345 asked what the rest of the universe would look like to
the expendable clone as he fell into the black hole.
At first, I thought maybe the entire future of the universe would pass before his eyes,
but that’s not actually the case.
Even though the rest of the universe does speed up from his point of view,
it doesn’t speed up enough for him to see the end of the universe.
The last light he sees is not the last light that arrives at the horizon.
Infinity is so weird!
Johan was thinking maybe the event horizon and the singularity are equivalent.
Mathematically, that’s not that far off.
A singularity is just a place where an equation blows up to infinity.
The black hole singularity is what you’d call a physical singularity.
It’s there no matter what your point of view is.
The event horizon is what you’d call a coordinate singularity.
It’s there in one set of coordinates, like the ones I'd use on my space station watching at
a safe distance, but not another set of coordinates,
like the ones my clone would use as he's falling into the black hole.
So they're very similar mathematically, but physically they are very different things.
If you’re looking for a more thorough conversation about how Hawking Radiation might affect the
fall into the black hole, the comment thread started by david21686 is
a good place to start.
Otherwise, you’ll have to wait until I’m ready to do a video on the Black Hole Information
Paradox.
It’s tough stuff, so it’s taking a while.
And, finally, Your Master seems to want to start a clone
union to protect all my clones from all the science we do here.
That’s no fun!
I’m not entirely sure how I feel about this, but good luck getting them to organize.
I have a hard enough time and they’re my clones.
Anyway, as usual, links to all the comments in the doobly-doo
and thanks for watching!