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Hey Crazies.
There still seems to be some confusion about how relativity works.
Before we do any more videos, let’s straighten a few things out.
Here are the fundamental rules of relativity.
Rules-ativity?
Nah.
Here are the rules you should know:
Rule #1: No point of view has preference over any other point of view.
Ever Ever?
Ever Ever.
That’s what it means for things to be relative.
Does the Moon orbit the Earth or does it orbit the Sun?
Depends on your point of view.
Both are correct.
Do the planets orbit the Sun in circles or do they orbit the Sun in spirals?
Depends on your point of view.
Both are correct.
Does this squirrel accelerate down toward the ground?
Or does the ground accelerate up toward the squirrel?
It depends on your point of view!
Both are correct!
Even though two observers can and often do disagree, neither one of them is wrong.
Well, as long as they’re taking measurements properly.
Which brings me to:
Rule #2: Every observer carries their own set of coordinates and their own clock.
The real world has dimensions and it’s filled with paths and shapes.
The things that we see around us look geometric.
But geometry isn’t a very versatile form of math on its own, so we invented something
called a Coordinate System.
A device that turns geometry into algebra.
It’s a way for us to label positions with numbers and label directions with signs.
We’ve already established that no one’s point of view gets preference.
So everyone has their own set of coordinates relative to themselves.
And, because this isn’t just about space, it’s also about time,
those coordinates include a clock that measures their personal time.
Some people call that proper time, but there’s nothing proper about it.
Don’t forget Rule #1: No one is proper!
Everyone’s time is on equal footing.
It’s a terrible name, so I’m not going to use it.
I do what I want.
The point is, as long as everyone is taking measurements using their own coordinates and
clock, it doesn’t matter if they disagree.
It’s fine.
Rule #3: If one observer wants to take measurements for a different observer,
then they need a coordinate transformation.
As the name suggests, it transforms one set of coordinates into another.
For special relativity, those are called Lorentz Transformations,
named after Hendrik Lorentz because he came up with the ones we use today.
Wow, Einstein gets a lot of credit for other people’s work.
Huh.
For general relativity, the transformation depends on what the geometry looks like.
Around the Earth, the transformation for time looks something like this:
Time passes slower on the surface than it does farther away in space.
That looks like math.
Is that math?!
I didn’t sign up for math.
Yes, yes, it’s math, but we going to try to work around it.
Consider two observers: Me and You.
Let’s assume I’m in a space station in the middle of empty space
Because that happens to be exactly where I am.
Let’s also assume you are in a spaceship traveling at, say, 55% the speed of light.
Fast Fast!
Now let’s remember the rules.
One!
No point-of-view has preference.
So neither one of us is special in any way at least as far as space-time is concerned.
Two!
Every observer carries their own set of coordinates and their own clock.
That looks like this for the two of us, at least from my point of view.
If I want to get an idea of what’s happening from your point of view, I need Rule #3.
I need a coordinate transformation.
Physically, that transformation would look like this.
Now you’re stationary and I’m the one that’s moving.
And, according to Rule #1, both points of view are correct.
Both of these are equally correct.
Whenever you work with relativity, you’ve got two options:
You can do the hideous math in all its glory, which works, but isn’t very interesting
or insightful.
Or!
You can use a space-time diagram to make the math easier,
which is more profound, but you have to accept a couple weird visual things.
If you haven’t guessed yet, I’m a fan of the second option.
To draw one of these space-time diagrams properly, we need another rule.
Rule #4: It will always look to an observer as though they are stationary in space.
Just to clarify, it doesn’t matter what you think you’re doing.
All that matters is what it looks like you’re doing.
If you’re in a car that’s driving, you certainly have a concept that you're moving
because your experience tells you that things like buildings can’t move.
But!
It doesn’t look very different from when you’re sitting on a couch watching TV.
It’s the things around you that are moving in both cases.
So what’s that have to do with space-time diagrams?
Right. Right.
That’s where I was going with this.
Let’s go back to you and me in space.
Here’s your spaceship again traveling at a steady 55% the speed of light.
If we focus on that for a minute and give it some coordinates, that looks like this.
But that’s just a space diagram.
We want a space-time diagram, so we add a time axis and show the spaceship
moving through time as well.
This is your ship’s space-time path.
My space station’s path is here.
Notice that my path lines up with the time axis.
That means these coordinates are mine.
Your time axis lines up with your path.
In a space-time diagram, a coordinate transformation is just a rotation,
but there's something a little weird happening here.
We’ve observed that space and time share similar but opposite behavior.
When the time axis rotates, the space axis rotates,
but in the opposite direction.
These are my coordinates and these are yours.
Each time axis is perpendicular to each space axis
including this one.
Yes, these are perpendicular.
Like I said, things look weird in space-time diagrams, but we can get powerful insights.
Did you notice what happened with the paths?
They didn’t change.
The coordinates changed, but the paths stayed the same.
Rule #5: Space-time paths are invariant under coordinate transformations.
Observers like you and me might measure different amounts of space or different amounts of time,
but we all agree on the space-time path.
For example, let’s say you started your stopwatch here and stopped it here.
You would say this much time had passed on your clock.
Using my own stopwatch, I would say this much time had passed
and I would say you went this far through space.
We might disagree on the coordinates and the time,
but we both agree you took this path.
We just need a coordinate transformation to properly compare the measurements
and if we strictly obey these rules, we see some even weirder things.
Let’s say this is the back of your spaceship and this is the front.
Now let’s say you have a light at each end that blink at the same time, like this.
But I will not see them blink at the same time.
For me, those events happen at different times.
I see the lights blink like this.
So we can disagree on how much time passes, how far your ship has traveled,
or even how much space your ship takes up.
For one observer, distance or time could even be zero, but not both.
If one observer says things happened at the same place and time,
then that’s just one event and everyone agrees on that.
Alright, so we may or may not disagree about things depending on the situation,
but there’s always one final rule that we can count on:
Rule #6: Causality must be maintained, no matter what.
Causality, also known as Cause and Effect, must hold for all observers.
If one event causes another, then we’ll all agree they happened in a particular order.
The cause will always happen before the effect.
Different amounts of time before, but always before.
This is the rule that limits the speed of light and, frankly,
the speed of anything that could cause an event.
Even if you think you’ve come up with some clever scenario, Conway79.
Let’s say I’m on my space station observing two ships.
I see these ships moving at 55% the speed of light in opposite directions.
Fast Fast!
If we shift to one of their points of view, you might think they observe
the other ship moving away at 110% the speed of light,
but that would be incorrect.
Remember Rule #3: We need the coordinate transformation.
The transformation between those two points of view
is not what you would expect from your personal experience.
The transformations for velocity actually look like this.
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So one ship would actually measure the other ship’s speed to be:
84.5% the speed of light, which is still less than the speed of light.
You have to remember all the rules if you want to work with relativity properly.
Rule #1: No point of view has preference over any other point of view.
Rule #2: Every observer carries their own set of coordinates and their own clock.
Rule #3: If one observer wants to take measurements for a different observer,
then they need a coordinate transformation.
Rule #4: It will always look to an observer as though they are stationary in space.
Rule #5: Space-time paths are invariant under coordinate transformations.
And Rule #6: Causality must be maintained, no matter what.
Those are the rules that space-time lives by and we have to live with the consequences.
Even if they’re weird.
So, got any questions about relativity?
Please ask in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s OK to be a little crazy.
The featured comment comes from Jack Beavington who asked:
Can light be affected by gravity?
Absolutely!
Gravity is curvature in space-time, so anything traveling through space-time
will be affected by it.
Even light!
Thanks for watching!