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Hey Crazies.
We’ve been doing a lot with space-time diagrams lately.
Figuring out how different observers measure the passage of time.
But that got several of you asking:
Does that mean the future is predetermined and we don’t have freewill?
Well, maybe, maybe not.
Deep questions like this require careful scrutiny.
All we know for sure from diagrams like this is that time exists.
That doesn’t necessarily mean that the future or even the past exist.
Hmm.
Maybe we should define these words first.
The past is the time, or period of time, before the present.
The future is the time, or period of time, following the present.
So both of these are defined in terms of the current moment.
That kind of makes sense.
The present, the “now” is what we’re experiencing.
But it feels like the past exists.
We remember the past happening.
Well, none of us remember that.
Or that.
But I certainly remember all of these moments, whether I want to or not.
But does that exist? or is that just a memory we're experiencing now?
The future also feels like it’s going to happen
even if we don’t know what it’ll be.
Does that exist? or is it just a prediction we're making now?
Hmm.
Let’s see what this looks like on a space-time diagram.
You are here.
This event represents your present. Your now.
Whether you’re stationary, moving at a steady speed, constantly accelerating,
or doing something completely random, you can’t go any faster than light.
Light travels along these diagonal paths, so your path is stuck inside those lines.
This half happened before your present.
It’s your past.
All the events that might have influenced you.
This half will happen after your present.
It’s your future.
All the events you might influence.
Your entire life is contained inside these regions,
no matter what you might have done or what you might decide to do.
Those two regions are called your past and future light-cones.
Cones? How are those cones?
Oh, right right right. Let me explain.
Only having a single space axis makes these look like triangles,
but if you include a second space axis, you can see they’re really cones.
You just have to consider light traveling in any direction.
Actually, there are three space axes.
Yeah yeah, but our axis limit is three and one of them has to be time.
Besides, most motion happens in two dimensions anyway.
Let’s not over-complicate this.
Anyway, this still leaves some things open.
I said the word "might" a lot during that space-time diagram.
So are we predetermined to travel our space-time paths or not?
This comes down to an idea called causality or "cause and effect."
And relativity rule number 6 says it must be maintained, no matter what.
That means, if one event causes another, then everyone agrees they happen in that order.
Cause before effect.
Let’s say you are the cause and you want to affect me at particular time.
I must be somewhere in your future light-cone.
Maybe I’m directly on the path you’re taking, so you’ll be able to touch me.
Maybe I’m not on your path, but I’m close enough to throw a rock at.
Maybe I’m so far away from you, the only way you can affect me is with light.
In all cases, from all points of view, the cause comes before the effect.
So is all of time just a string of cause and effect?
Eh, not so fast.
If an event happens outside your influence, the distinction between past and future kind
of melts away.
Say there’s an event outside your future light-cone, outside your influence.
You might still think it happens in the future because, on your timeline, it happens at a
later time.
But someone else might say it happened in the past
because, on their timeline, it happened at an earlier time.
Wait wait, something can happen in one person’s future, but another person’s past?
Yep.
So the future and the past are very personal concepts.
They belong to an observer.
But an observer is only in the present, which reminds of something.
There’s one property of the universe we haven’t considered: Locality.
or in local-ity.
We’ve discussed this in previous videos, but it could bear some repeating.
Whether we’re talking basic mechanics, electromagnetism, space-time curvature,
or even quantum fields; the universe is inherently local.
The idea is that a physical thing can only be influenced by its immediate surroundings.
In other words, in order for a thing over there to affect
me here, it has to either come here or send something here.
Which brings us to another relevant question:
How big is here?
It’s really small.
Local for a person might look like this.
This is pretty small for me.
OK, I have to admit, this is a little uncomfortable.
Anyway, this is my space, my here.
And it works for anything the size of me.
If that local box is too small, like it would be for my space station,
then it’s a little overkill, but it’s fine.
If it’s way too big, like it would be for particles,
then it simply won’t work.
So smaller is better.
Ideally, it would have exactly zero size, but that poses a few problems.
The main problem being that we can’t divide by zero.
It just doesn’t work.
Luckily, we’ve got a trick that gets us around this problem.
Let’s start with two points separated by this much space.
Say this point is at 5 and this point is at 6, or 5 plus 1,
because they’re separated by one unit.
Maybe it’s inches, maybe it’s centimeters.
Whatever. It doesn’t matter.
If we make the space a little smaller, maybe the second point might be at 5 plus one half,
or 5 plus one tenth, or 5 plus one hundredth, or 5 plus one thousandth.
The points keep getting closer together.
They’re almost the same point, but not quite.
We can keep this up, we can get closer and closer
and closer.
Until the points are at 5 and 5 plus an unimaginably tiny number.
So tiny, it’s not even useful to label it as a number anymore.
We call it an infinitesimal and label it dx.
Welcome to calculus!
I know my calculus.
You plus me equals us.
Anyway, an infinitesimal is an amount of space that is as close to zero as we can get
without actually being zero.
It’s as local as our math can get.
Of course, dx is just one dimension.
dx and dy make two dimensions.
Include a dz and you’ve got three dimensions, also known as space.
Include a dt and you’ve got a four-dimensional space-time.
The volume dx dy dz is the local here and the dt is the local now.
That’s all that really exists.
There is no universal reference frame because there is no universe
at least in the way that people usually understand it.
This space-time diagram is only a map of predictions about a non-existent future.
and predictions about a non-existent past.
It’s attached to you as you move through space-time.
Space-time doesn’t deny you freewill because the future doesn’t exist.
All that exists for anyone is their local here and their local now.
You might not have control over much in your life.
But you always have a choice about what kind of person you are here and now.
Make that choice a good one.
Please share your thoughts 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.
Why is the speed of light that specific number?
Well, we know it can’t go at infinite speed, because that would violate causality.
It has to be finite.
But the exact value is kind of an accident, as far as we can tell.
It could just as easily be a different value in a different universe.
That universe just might not have humans in it.
Anyway, thanks for watching!
Fast Fast!