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Measuring time in meters in Minkowski spacetime

As counterintuitive as it might sound, it will become extremely convenient to use the same units for space and time. Happily, we can do that just by multiplying the time axis by c, the speed of light. Here's how.

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• This to me looks like a trick that works only because we made the speed of light absolute. Now, I don't know on what observations that is based... So ok... But if the speed of light was not absolute in vacuum, we couldn't do it... Right?
• Every measurement we have done for the speed of light gives the same value. The idea of a universal speed limit is part of the core that theories of Relativity were built off of and it is one of the most accurately verified theory we have.

Here is a post by Sean Carroll about the speed limit of the speed of light: http://www.preposterousuniverse.com/blog/2016/11/24/thanksgiving-11/
• I still can't understand how can we measure time in meters and what does measuring time in meters actually mean,does it mean that the unit for measuring time is meter (because it's going to seem strange if we tried to measure speed in meters per meters(m/m))or does it mean that the 1 second of time is equivalent to 300000000m on the space time diagram (the distance between (t=1 & t=2) on the graph is equal to the distance between (x=300000000 & x=600000000)on that same graph)?
• I still don't understand the essence of using ct axis i.e. just blindly multiplying c with the time on y axis and calling it 'spacetime'? How is it useful and what if we didn't do that?
• I'm lost as to how it follows from time differing between frames of reference that it's continuous/synonymous (?) with space?
• at which point is that said? can you identify it for me please? See if I can clarify it for you
(1 vote)
• If it is possible to measure time in meters then it is possuble to measure space in seconds either since space and time merge into spacetime?
• I understand that distance and location are not independent of time and vice-versa, but it seems that they are not equivalent; special relativity still indicates some restrictions on how one can move in time, in ways that do not similarly restrict left vs right or up-down,does it not? One can not travel into the past or to a time before an event that has taken place, correct?
• some studies are being done into this field. Before you go saying that, you might want to consider this: 200 years ago, man had never even dreamed of flying, and now, here we are, with an office room floating in space and a flag on the moon. So don't say it isn't possible. Just say it may not work.
(1 vote)
• Are we plotting DISTANCE against DISTANCE?
• If we can use the same units for both distance and time,
does that make speed, which is distance divided by time,
a dimensionless unit? What then, does speed even mean?
(1 vote)
• We don't use the same units for distance and time. In this video Sal has to multiply t by c to get things in the same units. ct is a unit of distance.
(1 vote)
• can i have a ruler that measures in seconds and minutes?
(1 vote)
• For one second you would need a ruler that was 299,792,458 meters long. Or about 3 nanoseconds would be a ruler a meter long.
(1 vote)
• can the transformation of axes move into quadrants II and IV?
(1 vote)

Video transcript

- [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.