- [Voiceover] I am about to do something
that most of you will probably find disconcerting,
in fact, the first time that I saw someone do this,
I too found it disconcerting.
So, just as a little bit of background,
so far, when we've been thinking about
our space axis, and we've really just been
focusing on one dimension of space,
we've been focusing on the x dimension,
or the x prime dimension, depending on
whose frame of reference we are talking about.
We measured that in terms of meters.
We measured that in terms of meters,
and then when we thought about time,
well, we said, initially, we said, "Well, time is
"fundamentally something different than space,"
so we had a different set of units called seconds,
in fact, you know, this goes well before we,
well before the 20th century when we got
special relativity, this goes all the way back to well
before even that, where we said time is something different.
We measure it in units of time, in seconds,
or minutes, or hours, or days.
While distance, which is different than time,
we measured in meters, or feet, or miles,
or kilometers, or whatever else.
But as we started to get into this world of
special relativity and we started to see that
space and time are not each absolute.
And, in fact, we can actually think of all events
as happening in this continuum called spacetime.
And I say it fast, "spacetime".
Because it's not saying "space-time".
Two different things.
It's saying that they're really just different directions
in this continuum spacetime.
And so, if they are all the same thing why do we
use different units for space and time?
Why do we use seconds for time and meters for space?
Or at least in the examples that I've been doing so far.
And so to fix that, instead of calling this
the "t-prime axis" or the "t axis," instead of labeling
it in terms of seconds, what we can do
and this is the part that many of you
will find disconcerting, let's call this
the "c times t-prime axis."
And let's call this the "c times t axis."
And the "c times t-prime axis."
Well, what's that going to do?
Well, we know that the speed of light is an absolute.
It is, if we are measuring it in,
and I'll do approximately because it's actually
two point nine something.
But, approximately three times 10 to the 8th
meters per second.
For the sake of all of these videos I'm just assuming
it's three times ten to the 8th meters per second.
For simplicity it's roughly that.
So if we were to take c times time
instead of this being one second, in terms of seconds,
well, we multiply it times
three times ten to the 8th meters per second.
Well, the seconds cancel out and we're left...
If we want to measure time in terms of meters,
would be three times ten to the 8th meters.
So this is three times ten to the 8th meters,
instead of calling it one second.
This over here is negative.
So that over there is negative
three times ten to the 8th meters.
Along the "c t-prime axis."
Likewise, this what we called one second,
right over here, instead we can call this as
three times ten to the 8th meters.
This we could call negative
three times ten to the 8th meters.
Now this will be counterintuitive to you
because you've always viewed time as fundamentally
something different than meters.
You haven't been thinking in terms of spacetime.
In fact, in our normal human experience we don't experience
the world in terms of space time.
Time is something that we are just falling forward into
and space is something that we feel like we have more
agency and we can move in the different dimensions
of space more easily, while time just feels like we're
plummeting forward in that dimension.
But now we're thinking in terms of spacetime
and this makes our units the same.
Now if it helps you, you could view this as
three times ten to the 8th light meters.
So you could think of this as the time it would take
for light to go three times ten to the 8th meters.
Likewise, if we wanted everything in terms of what
we traditionally conceive of as our time dimensions,
we could have kept this as one second,
instead of calling this three times ten to the 8th meters
we could have called this one light second,
which would be the distance that light travels
in what we measure, or what we consider to be one second.
But the benefit of this is now we're consistent.
We're measuring different directions in spacetime,
which is kind of a continuum,
there is no separate time and space.
We're measuring them all in the same units,
which we will find is very, very convenient.
So, I know this is going to take a little bit of time
to get your head around, and I'll maybe do a few
more videos to make you feel comfortable with
this type of idea, but this will be a
convenient thing for us.
Especially as we start to have a metric in our,
what we would call, our Minkowski spacetime.
Because we are going to be operating in the different
dimensions as if they have the same units.
So, hopefully, I encouraged you to kind of sit and ponder
and think about this a little bit,
and hopefully it doesn't bother you too much.