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Welcome to Arts and Ideas in the Air, under the tent around Baltimore, Wondrous Wednesday.
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Today I'm going to try to describe the ideas behind the relativity of simultaneity.
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That's a bit of a mouthful, but the basic idea is the stuff that's happening right now from my perspective
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may not be the same stuff that's happening right now from your perspective.
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I mean, in actuality, we're probably going to agree upon it because we're not really traveling very much relative to each other,
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but if you were going half the speed of light away from me, we would definitely disagree on what was happening right now.
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So, last week we talked about the idea of speed of light being constant, and what that means.
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And I didn't really get into it, but one of the kind of principles of relativity is, well, being relative.
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And the idea is that if you are in sort of a constant speed motion from the perspective of someone else,
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then from your perspective you're stationary and they're going in the opposite direction at that speed, basically.
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You know, both of you are perfectly valid frames of reference for physics.
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That is to say, neither of you can say, "I am in the right frame."
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And, you know, this really comes from the fact that the speed of light is constant,
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because before that, you know, speed of light, having a certain speed, one could measure it,
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and the idea was there was an absolute space and an absolute time.
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It was kind of a right kind of frame of reference, and, you know, you could be going at this other speed,
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and you could, you know, you could figure out what that is, and you could deduce your laws of physics,
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but, you know, that speed, you know, the speed of light would change along with that speed.
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And so the idea of the speed of light being constant broke all that and said, "Huh, regardless of your constant velocity,
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the two of you, you know, have equally valid frames of reference. Okay, great."
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So that means that, you know, everything that I see from my perspective happening should follow from the laws of physics,
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as if I'm sitting still, and everything you see from your perspective should also follow from physics
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with the idea that you're just sitting still. It should all just kind of work out. Sounds great.
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Now, there are some things that go on. Now, last time we deduced that when a person is moving with respect to you,
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when you look at what's going on, it looks like time has slowed for them, and also that distance has contracted.
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The time slowing came from the idea of you have a clock, kind of a light clock, where a pulse of light bounces up and then down.
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And so from a stationary perspective, it just goes up and down.
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But from someone who's watching it as it travels by, it's going on a diagonal path, and that's going to take longer.
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Since the speed of light is constant, the distance is longer because of that diagonal thing,
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and the speed of light being constant means that time has to be going slower in order to allow that particle to travel that longer distance,
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you know, at the same speed and happening everything at the same time.
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And then by rotating the clock so it's in the direction of motion, we had just deduced the time being delayed.
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And so, you know, now it's going slower, and so, I mean, it's taking, well, the length contraction comes from that, too,
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just because of the time having been changed and the light speed being, again, constant.
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So the distance traveled has to be shorter in order to compensate for that.
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All right. So that was kind of before. Now we have a new thought experiment also involving trains.
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We love trains around here. Trains are cool.
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The idea here is you've got a train moving along, and there's a person on the train and a person right next to the train,
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and at the moment that they're aligned, the person who's not moving with the train thinks that a lightning bolt struck both ends of the train at the same time.
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So in a normal world, you'd think the person on the train would also see the lightning bolt striking the ends of the train at the same time.
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But I shouldn't say normal world. I should say in our naive world, the real world is different.
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So, anyway, lightning bolts strike both ends of the car. Great. Now, the stationary person is, and again, this is, what should I say, the non-train person.
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Remember, both can kind of view themselves as stationary. The non-train person, what do they see?
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They see the lightning bolt light coming at them. Let's say this was in the middle of the train, so that the two rays meet at the same time at the non-train observer.
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That's why they would say it happened simultaneously, because equal distance apart from where they are, and they see the lightning flashes at the same time.
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I don't know what else you'd want to call that, but being simultaneous seems to me to make sense. It happened at the same time.
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Now, of course, one thing to keep in mind is that they don't see the lightning bolt when it strikes, right? They see it delayed.
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The speed of light is not infinite. It takes some time. We don't usually observe it because it's incredibly fast.
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But, you know, as you get in longer distances, like say between the Earth and the Sun, you know, that takes some time.
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I didn't look it up, but I think it was about eight minutes for light to travel from the Sun to the Earth.
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In any event, one can deduce when you see two things happening, you see the same thing happening with you, like the light strikes you,
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and they're happening from places equal distance from you that they happen at the same time.
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That's sort of what we mean by simultaneous.
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Good. So, now, the person on the train is, of course, moving forward and goes towards the front lightning bolt.
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And so, that light will strike them first. That will happen. And then the light from the back of the train will hit them later, right?
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Because they're moving, right? They're going to encounter that thing first.
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And so, the person on the train sees this and says that's what will happen. Okay, good.
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Now, from the perspective of the person on the train, they are stationary and the speed of light is constant.
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And they see the light hitting them first from the front of the train.
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Now, from their perspective, the train is still, like, they're still in the middle of the train.
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So, the light has traveled and hit them first over the same distance, you know, that the light from the back of the train is going to hit them.
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So, and the speed of light is constant. It's the same speed, you know, for both light rays.
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And so, that to them says, well, I see this first, you know, it had to travel the same distance at the same speed, so that had to happen first.
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So, for them, the lightning bolt striking the front of the train happened before the one on the back of the train.
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And in fact, it happened before they even aligned with the person in the middle.
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And the lightning strike at the back of the train happened after they had passed that person, that non-train person.
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All right, so that's a really kind of important idea to kind of really grasp.
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If you look on Wikipedia for relativity of simultaneity, they have a nice little diagram of these two things.
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I believe they call them Mr. Green and Mr. Blue, but whatever. Just the basic idea that, you know, this is from their perspective, which should be taken seriously, is a perfectly good frame of reference.
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You know, what happened first was the lightning train got struck by the lightning.
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Then they passed this non-train person, and then the lightning struck the back of the train.
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That's what they see happening.
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Based again on how they could measure equal distances between the middle and the front and back of the train.
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And, you know, basically that's the speed of light.
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You just compute what the time is from that, because if you've got distance and you've got speed, then you can get your time.
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And the time for them to see that to make sense is that it had to happen earlier.
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From the perspective of the non-train person, the lightning bolt struck both the front and the back at the same time as they passed the person on the train.
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That was kind of the setup of the problem, but that's their perspective.
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So what happens right now depends on your motion in time.
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I mean, depends on your motion.
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So time is not fixed.
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It is, I mean, now is not fixed.
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Very much varies based on the particulars, and you can't say which one's right.
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Either should be acceptable.
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So this is one of my major bones of contention with sci-fi stuff.
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And I realize why they have to do it, because they've got to tell a story.
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But, you know, like, say in Star Trek, you've got ships flying faster than light, warping around, fine, whatever.
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It's not true, but whatever.
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But then they make a call home, they call Earth, and they're talking at the same time.
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And the question is, what is that time?
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What is now for them?
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You know, like, it's not defined, so it's not clear what they're, you know, what's going on.
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And I realize, like, if you really try to deal with this, it's a whole different kind of show, and it's not fun anymore.
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But that's really kind of the thing that really annoys me.
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Like, now is not now.
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There is no now. What is now?
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I don't know.
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Another example of this is called the twin paradox.
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Or, I mean, it's not problematic in actuality, but it's a little bit of something.
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So, maybe the easiest way to think about it first is, again, with trains.
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You have a set of clocks on the train and on the tracks.
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And, you know, they're all in sync with one another.
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And the non-train person will look at the train that's moving and will see the clocks running slow.
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So, you know, even if they agreed at this one instant later on, they won't.
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But the same is true for the person on the train looking at the stationary clocks.
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They run slow.
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That's just how it goes.
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That was the time slowness.
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Okay, now, so they're both seeing time slowing for the other person.
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Great.
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But it's not just mechanical clocks.
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It's everything.
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So, the twin paradox is you've got a person on Earth, your twin, and you're traveling away from Earth at, you know, three-fourths the speed of light.
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Now, the person on Earth looking out at the person traveling away will be like, "Whoa, that's going slower."
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And so they're, you know, you know, so the ages no longer sync.
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And the person going away on a rocket ship sees also the Earth going slower.
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And so they also say the time, you know, isn't in sync.
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But remember that they're kind of the reverse.
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So time is slowing down, I guess, on Earth from that perspective of the person moving away because the Earth is moving away from them.
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And so, you know, they're aging more slowly.
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But the person on the rocket is also aging more slowly than the person on Earth, right?
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So they're both seeing it differently.
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Now, the rocket ship turns around and comes back.
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And the paradox is, well, the question is so what happens?
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Do they come back to be the same age because it's all relative, right?
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Or do they come back and one's older than the other?
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Well, it turns out the one on Earth is older.
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And the thing that was different was basically the person on the rocket ship turned their direction and came back.
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And that turning breaks the framework of special relativity.
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Special relativity is all about uniform motion.
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So nothing changes its direction.
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Now, when you change your direction, you have acceleration.
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And so that's where the anti-symmetry comes in.
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And during that brief turnaround, decades elapse on Earth.
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And so that's why the person on Earth actually gets older than the person on the rocket ship.
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It's just that one turnaround.
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So there you go.
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Okay.
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So that's the relativity of simultaneity.
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It was a little bit long day, but it's kind of a long topic and it's very interesting.
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It's really important to understand that there is no kind of now.
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That's defined upon by everybody.
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It all depends on your relative motions.
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Good.
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And you can say more about like, okay, how do I define now for me?
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And it's basically the idea, I mean, you can define a now in various ways.
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But the simplest one is saying, like, how long does the light take to get to me from this place?
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You know, the minimum, like the first time light can strike from this place is kind of like the immediate, is the now.
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So it's the idea that, you know, just like with the lightning strikes at the end of the train,
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I say it's now because I can compute that after traveling the distance that it did, the light reaches me at the same time.
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And so they're the same.
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And you just kind of extrapolate that kind of idea.
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Anything, you know, using the speed of light to kind of like create this framework of, well, okay, this would say that if, you know,
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like let's say it takes eight minutes for light to get from the sun to the earth and might, you know,
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I have a clock that says 1043 and I just look at the light coming from the sun.
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I'm going to say that light happened at 1035 because it took eight minutes to kind of get to me.
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That's the basic idea of what now would mean in a sensible way.
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Now next week I intend to revisit the quantum mechanics dilemma of needing a now when relativity says there is no now.
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This is really the heart of the biggest conceptual problem facing physics that we have when we have no resolution to it.
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But I just want to kind of go over both things and make sure that, you know, you can at least understand what the question is.
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So sorry for the length of time, but so it goes.
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I was measuring time in a thing that was moving away from me and just got out of control.
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So have a good one and talk to you later.