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Physics: The Relativity of Simultaneity


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About this Lesson

  • Type: Video Tutorial
  • Length: 11:13
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 120 MB
  • Posted: 07/01/2009

This lesson is part of the following series:

Physics (147 lessons, $198.00)
Physics: Relativity (9 lessons, $18.81)
Physics: Einstein's Special Theory of Relativity (4 lessons, $7.92)

This lesson was selected from a broader, comprehensive course, Physics I. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers kinematics, dynamics, energy, momentum, the physics of extended objects, gravity, fluids, relativity, oscillatory motion, waves, and more. The course features two renowned professors: Steven Pollock, an associate professor of Physics at he University of Colorado at Boulder and Ephraim Fischbach, a professor of physics at Purdue University.

Steven Pollock earned a Bachelor of Science in physics from the Massachusetts Institute of Technology and a Ph.D. from Stanford University. Prof. Pollock wears two research hats: he studies theoretical nuclear physics, and does physics education research. Currently, his research activities focus on questions of replication and sustainability of reformed teaching techniques in (very) large introductory courses. He received an Alfred P. Sloan Research Fellowship in 1994 and a Boulder Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998. He is the author of two Teaching Company video courses: “Particle Physics for Non-Physicists: a Tour of the Microcosmos” and “The Great Ideas of Classical Physics”. Prof. Pollock regularly gives public presentations in which he brings physics alive at conferences, seminars, colloquia, and for community audiences.

Ephraim Fischbach earned a B.A. in physics from Columbia University and a Ph.D. from the University of Pennsylvania. In Thinkwell Physics I, he delivers the "Physics in Action" video lectures and demonstrates numerous laboratory techniques and real-world applications. As part of his mission to encourage an interest in physics wherever he goes, Prof. Fischbach coordinates Physics on the Road, an Outreach/Funfest program. He is the author or coauthor of more than 180 publications including a recent book, “The Search for Non-Newtonian Gravity”, and was made a Fellow of the American Physical Society in 2001. He also serves as a referee for a number of journals including “Physical Review” and “Physical Review Letters”.

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Albert Einstein's special theory of relativity is based on two premises. Premise number one: the laws of physics are the same in any inertial reference frame. It's a perfectly reasonable idea that says that you can't tell whether your reference frame is at rest in some absolute sense. You can talk about relative velocities between reference frames, but nobody's reference frame is special.
Postulate number 2 is the weird one. It says the speed of light is a law of physics - the speed of light in vacuums (3 x 10^8 m/sec) is the same in all reference frames, no matter whether the source is moving or you're moving. If you measure the speed of light, you always get the same number. Very counter-intuitive - it disagrees with our sense that if something's running towards me and I'm running towards it, I should measure something going faster. That's what I think should happen. It's not what happens with light or with anything when the speeds involved are close to the speed of light.
This fact has many consequences. And one of the consequences I want to talk about right now is that it really calls into question your deep-seated ideas about what time is and how time works. Let's think about events. Events are really the way physicists describe what's going on in the world. You talk about an event, which means you've got a position x, y and z that describe where the event occurred and then you have to tell when the event occurred. And this describes something that happened, like the snapping of a finger happened at a place and a time.
If I'm in a different reference frame, I'm going to have different coordinates - x', y', z', t' - different numbers to describe the same event. Now let's think about two events which occur at different places. So I'm going to snap my fingers in two different places, but at the same time, these two events are simultaneous. That seems meaningful and I can get good at it and really make them very accurately simultaneous. And how do I know they were simultaneous? You should think about how you measure where an event takes place and when. For me, it's easy. I'm in the middle of my two hands. As I snap my fingers, a sound wave and a light wave of the event, telling me about it, travels towards me. Those two things happen at different speeds. The sound gets to me after the light. But I'm equidistant and the sound and light arrive at my ears or my brain. The two sound waves arrive simultaneously later. So I conclude that the two events were simultaneous. It all seems perfectly intuitive. But now, let me ask you, what would it look like if you watched those same two events from a train that was moving by in this direction at some high speed. You have to think about it very carefully, because your immediate gut reaction is, those two events, if they were simultaneous for me, they'll be simultaneous for the person who is moving by. And let me convince you that that's not correct.
Let me, first of all, think of a different pair of events and here's the way I'm going to set up the events. Here's a train car, and I'm going to live in the frame of the train. So I'm sitting inside this train car. I'm at rest. I see the world going by me at speed z, but never mind. I don't care. I'm in a perfectly valid inertial reference frame. And I flash a light bulb. So the light flashes. Light waves start propagating out towards the outside of the train. I'm going to use light because light is traveling at a very high speed, and so relativity - Einstein's special relativity - effects will become important.
As this light travels outward, if the flash was right at the center of the train, then, remember Einstein says the speed of light is the same in all directions for everybody. So it's going to be traveling away from me, symmetrically - same speeds to the right and to the left. So if I flashed in the middle, the light will strike the two edges of the train simultaneously in my reference frame. This is an event. The light strikes the edge of the train. Perhaps there's a detector there that goes, "ping!" And the two pings are simultaneous. These are space-time events. You have to describe them by x, y, z and t.
So I have just set up a scenario where I've got two events and they are absolutely, without question, simultaneous. Now, let me watch this exact same procedure, but from the ground. So let me flip to the new reference frame. Here's the Earth's frame. And I see I will have a flash of light - it's the same event - and the light begins to travel outwards. But remember two things. The train is now moving, with velocity v as far as I'm concerned. So the back of the train is moving to the right and the front of the train is moving to the right. And here's the weird thing. In any reference frame, the speed of light is always the same. So this beam that's heading to the right and this beam, which is heading to the left, as far as I'm concerned, they're both traveling at the speed of light (c), one to the left and one to the right.
So what happens as time goes by? The train catches up to this beam, and the train is running away from this beam, so at a later time, I see this scenario. The train has caught up to this beam, on the backside, where the front side is still trying to run away. It's closer, but it hasn't yet made it. So the event of light striking the back of the train happens first. And later on, the next event will happen. So these two events - light striking the back of the train, light striking the front of the train - one person thinks they're simultaneous events. Another perfectly valid physics observer says, "No, this event happened and the other event happened later." This is really weird.
What I'm telling you is it's meaningless to ask whether those two clicks were simultaneous. It's meaningful to say were they simultaneous in my reference frame. But it doesn't make any sense to ask in some absolute way, did they happen at the same time? This really throws into question our intuition about what time means. Galileo would have said, "Of course, time is absolute. All observers agree that time is passing, like some cosmic clock, ticking away. And if I think they were simultaneous, everybody should think they're simultaneous." Einstein says, "No, not if the speed of light is the same for all observers."
Let me show you another similar story just to try to get this idea about how events can be simultaneous in one frame and not in another. I've got two train cars, 1 and 2. Train number 1 is moving with velocity v with respect to the tracks. Train number 2 is sitting at rest with respect to the tracks. And all of my pictures - I have to show you a picture from some reference frame. My reference frame is the frame of the tracks.
Supposing that there are two lightning strikes - one at the two ends. So instead of having an event that started in the middle and working its way out, now I'm going to have two events that started at the outside and work their way towards the middle. These are two events. They have a place and a time, and the question is, were they simultaneous? Let me first ask that question in the reference frame of number 2. So let me focus my attention on observer number 2.
First of all, at this moment in time, for observer number 2, observer number 2 doesn't know anything's happened yet. It takes a finite amount of time for light to travel. It's fast, but it's a finite amount of time. So 2 is just sitting there, oblivious of the lightning strike. A brief instant later, however, the light will have traveled and 2 is sitting in the middle of the train. The speed of light is the same in all directions. So these two waves are traveling towards observer number 2 at the same speed, c. And so observer number two will see the two waves striking together and concludes that the two original strikes must have been simultaneous at some earlier time. When this happens, that's when 2 knows that lightning had struck, and by working backwards - calculating backwards - the distances were the same. The speed was the same. Velocity x Time = Distance, so the times must been the same. So these two lightning strikes are simultaneous as far as observer number 2 is concerned.
Now let's just watch what happens to observer number 1. Let me add an intermediate step. So remember, observer number 1 is traveling to the right. So a little brief moment later, the waves haven't quite reached number 2 yet, but number 1 has been shifting over. And so the wave from the right has reached observer number 1. So observer number 1 is sitting there, thinks that she's sitting still - right, everybody thinks they're sitting still - and she sees a light wave coming from the right and nothing else. So she concludes that there was a lightning strike on the front of the train. And then what happens? She's still moving to the right. This wave is catching up. And at some later time, the wave has finally caught up.
So what did she observe? She's sitting there. A wave comes from the right. And then, she waits a while, and then a wave comes from the left. So, she scratches her head and walks around. She thinks she's at rest. And she sees a lightning scar over on this side and a lightning scar over on that side. And she says, "I was in the middle the whole time. I was symmetrically in the middle and the pulse from one side came first, so it must have occurred earlier." Observer number correctly concludes that the lightning strikes were not simultaneous. The lightning strike at the front of the train happened at an earlier time.
It's weird. And you ask yourself, "Well, who's right? Did the lightning strike occur simultaneously or was one earlier than the other?" And that's as much of a nonsense question as it is to ask, "Who was really at rest?" It depends on the observer and all observers are equally valid. One observer says two events are simultaneous, another says they're not. They're both correct in their reference frame.
So this is this crazy result of Albert Einstein's special theory of relativity. We abandoned our deep-seated intuition that it makes sense to talks about simultaneity and some absolute time that's ticking away independent of us. Time is relative. Time depends on the observer.
Understanding Einstein's Special Theory of Relativity
The Relativity of Simultaneity Page [2 of 2]

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