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## Minkowski spacetime

Aktuel tid:0:00Samlet varighed:4:58

# Measuring time in meters in Minkowski spacetime

## Video udskrift

- [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.