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  • In our universe, when you change from a non-moving perspective to a moving one, or vice versa,

  • that change of perspective is represented by a what's called Lorentz transformation,

  • which is a kind of squeeze-stretch rotation of spacetime that I've mechanically implemented

  • with this spacetime globe.

  • A quick reminder - spacetime diagrams plot position on the horizontal axis and time on

  • the vertical axis, and something moving as time passes traces out a path through spacetime

  • called a worldline.

  • One of the first things you might notice about Lorentz transformations is that events that

  • were at different places at the same time before the transformation aren't at the same

  • time after the transformation.

  • This means that from the perspectives of people going different speeds, simultaneous events

  • for one person won't be simultaneous for the other, and vice versa.

  • For example, if from my perspective these two boxes spontaneously combust at the same

  • time, and you're moving at a third the speed of light to my right, then from your perspective,

  • that is, the perpective from which you're not moving so your worldline is purely vertical,

  • from your perspective the box on the right will combust first, and the box on the left

  • will combust second.

  • The takeaway here is that our universe has neither an absolute notion of time nor an

  • absolute sense of simultaneous events, and that simultaneity breaks down more the farther

  • away from each other two things are – a box even farther to the left that from my

  • perspective simultaneously spontaneously combusts with the others will, from your moving perspective,

  • be even farther out of sync with the box on the right.

  • This is described by the time part of the Lorentz Transformation equations, the part

  • that says t new = gamma times t minus v times x over c squared).

  • Because of the x in there, the farther away an event is from you, the more its time from

  • the new perspective will be out of sync with events closer to you.

  • Though because of the factor of c squared in the denominator, which is huge, it's hard

  • to notice anything being out of sync until either your speed or distance to the object

  • in question are really really really biglike, you'd have to be going half the speed of light

  • and be comparing things farther apart than the earth and moon before things would become

  • more than 1 second out of sync.

  • But in that case, events that were simultaneous from my perspective really would be out of

  • sync for you!

  • As surprising as this may seem, it might feel more familiar and comfortable when you remember

  • that thisgetting out of alignmentphenomenon happens to points at the same place in space,

  • too, which is literally what we think of as defining motionfrom my perspective, this

  • box is at the same position at different timesthat is, it's not moving; maybe, “simulspacious”–

  • but from your moving perspective it's at different positions at different timesit is moving.

  • Relativity of simultaneity is just the other side of the cointhe fact that events

  • that happen at the same time at different spatial positions happen at different times

  • when viewed from a moving perspective.

  • All together, in our universe, the takeaway is this: events that were previously either

  • all at the same place or all at the same time get out of alignment with each other when

  • you change to a moving perspective.

  • A big thanks again to Mark Rober for making the spacetime globe a reality, and to dive

  • more into the details of relativity of simultaneity, I highly recommend heading over to's

  • course on special relativity that they've been developing simultaneously with this video

  • series (well, at least, simultaneous from my perspective).

  • There, you can explore custom scenarios and do actual puzzles and problems that help you

  • build on what you learned in this video, like figuring out how laser tag would work at relativistic

  • speeds!

  • The special relativity questions on are specifically designed to help you go deeper

  • on the topics I'm including in this series, and you can get 20% off of a Brilliant subscription

  • by going to

  • Again, that’s which gets you 20% off premium access to all

  • of Brilliant's courses and puzzles, and lets Brilliant know you came from here.

In our universe, when you change from a non-moving perspective to a moving one, or vice versa,


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B1 中級

同時性の相対性|特殊相対性理論 第4章 (Relativity of Simultaneity | Special Relativity Ch. 4)

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    林宜悉 に公開 2021 年 01 月 14 日