A Question on Relativity

[Superboy]

So I've recently started reading up on physics. Having absolutely no education on the subject prior, it's all pretty new and interesting, particularly since I decided to jump right ahead to Einstein.

I was reading up a website that describs relativity in laymens terms, and while it was explaining how time itself can appear relative, it says this:

We have Bert and Dana. Take a bus, and put Bert on the bus. The bus goes down the road. Dana, she sits here, on the side of the road. He's in the bus and she's on her ass. And now take a rock off of the moon, and let it fall at them. It hits the air and cuts in two. The two bits burn, and then land just as Bert and Dana are side by side. One hits the dirt up the road a ways, and one hits down the road a ways. Dana sees each rock at the same time, but Bert sees one rock and then sees the next rock. Now: if Bert and Dana both see Dana as the one who is "at rest", they both will say that the two bits came down at the same time. Dana will say, "I am 'at rest', and I saw them both land at the same time, so they both did, in fact, land at the same time." And Bert will say, "I move away from the rock down the road, so when I add that fact in, I can see that if I were 'at rest', I'd have seen both land at the same time. So it must be the case that they did land at the same time." Okay, but what if Bert and Dana now see Bert as the one who is "at rest"? Eh? You get to pick who is "at rest" and who isn't, no? So make Bert be "at rest". Now Bert will say, "I am 'at rest', so the one up the road beat the one down the road, on the way to the dirt, just the way I saw it." And Dana will say, "I saw them land at the same time, but I move away from the rock up the road, so when I add that fact in, I can see that the rock up the road must have beat the one down the road."

This comes from a website that's almost a joke (it tries to explain relativity without using any words bigger then 4 letters), but I can't seem to find this explained any better elsewhere, so I was wondering if someone here could clarify.

Why would Bert see one rock land, then the other, instead of at the same time? How does the fact that he's moving effect this?

[Surlethe]

So I've recently started reading up on physics. Having absolutely no education on the subject prior, it's all pretty new and interesting, particularly since I decided to jump right ahead to Einstein.

Don't do that. To understand where Einstein's reasoning comes from, you need to first understand classical mechanics and its failings. You should start with Newton and work your way up to Einstein.

I was reading up a website that describs relativity in laymens terms, and while it was explaining how time itself can appear relative, it says this:

<snip>

Why would Bert see one rock land, then the other, instead of at the same time? How does the fact that he's moving effect this?

Okay, let's take a classical example: you are sitting in outer space, and someone speeds by at .8c or something like that. The guy on the ship has a flashlight and a mirror, and he proceeds to shoot a pulse of light from the flashlight onto the mirror, which then bounces back from the mirror to the flashlight. There are a couple of key differences between what you see and what he sees:



Note how the person sitting outside the ship sees the light beam traveling a further distance than the person sitting inside the ship. Since c has to remain constant, the time in the ship must be slower than the time in the rest frame.

I'm simplifying somewhat, but this gets the basic idea across.

[Kuroneko]

Dana is stationary, so that as the light reaches her (Bert's original position), Bert has already traveled some distance already, which the light beam will have to traverse as well in order to catch up to Bert. Thus, the light behind Bert must travel more distance to reach him. Similarly, the light in front of Bert travels less to reach him as compared to Dana, for reasons of symmetry.

Don't do that. To understand where Einstein's reasoning comes from, you need to first understand classical mechanics and its failings. You should start with Newton and work your way up to Einstein.

That's certainly advisable, but a familiarity with calculus and differential equation is much more important.

[Surlethe]

Don't do that. To understand where Einstein's reasoning comes from, you need to first understand classical mechanics and its failings. You should start with Newton and work your way up to Einstein.

That's certainly advisable, but a familiarity with calculus and differential equation is much more important.

I was thinking in terms of the intellectual context rather than the formal tools required for a deep and subtle grasp of the theory; I agree calculus and diffeq are quite important in terms of actually utilizng the theory, and even following some of the reasoning, but a person with only a passing knowledge of calculus can, with not too much difficulty, follow most of the basic logic Einstein employs to derive the special theory.

[Kuroneko]

If the goal is that limited, then the requirement of knowing Newtonian mechanics becomes very dubious. On the other hand, learning Newtonian mechanics is a boon precisely because it provides a working knowledge of such mathematical tools. I fully agree that your advice is a good way to learn relativity; what I disagree with is the implicit notion that relativistic mechanics is best understood as an extention or 'fixing' of Newtonian mechanics. In most relativistic cases, Newtonian mentality hinders rather than illuminates.

[Wyrm]

What I'm about to give is the Ghetto Introduction to Special Relativity, so bear with me. The root of all the wierdness in SR boils stems from one fact: Bert and Dana can't agree on how to synchronize remote clocks.

The following diagram summarizes the problem:



The vertical arrow represents Dana's worldline, the series of events she passes through as her watch advances. The almost-vertical arrow is Bert's worldline, who is riding a bus. Dana and Bert have arranged for their watches to be synchronized as they pass at t_0.

Dana has set up ahead of time a bunch of clocks with reflective faces. How can she verify, sitting where she is, that the clocks on her x-axis are synchronized? Well, since for her, the speed of light (c) is a constant, she defines her line of simultaneity this way: suppose the clocks at A and B are both a distance d away from her. She shoots pulses of light at A and B from the event labeled 1 on the diagram, where t_1 = t_0 - d/c, where they reflect off the faces and she sees the pulses of light returning at event 2, where t_2 = t_0 + d/c. Since light travels at c, the pulses must have reflected at her t_0, and since the faces of her clocks flashed when they too read t_0, her clocks must be synchronized. Dana's x-axis is her line of simultaneity, which is the locus of all events where if she sent out a pulse of light at t_a = t_0 - a, she receives a reflected pulse at t_a' = t_0 + a.

But what if Bert were to perform the same analysis on Dana's clocks? In order to bounce a pulse of light off an event at A, Bert has to emit a pulse of light at event 1' with his t_1' = t_0 - b and receive the reflection at event 4, at his t_4 = t_0 + d and b ≠ d; A is not simultaneous with his t_0! Similarly with event B, where he must send out a pulse at event 3 (with his time t_3) to receive the pulse at event 2' at his time t_2'. If the meteors were to strike at events A and B, then both Bert and Dana agree that Dana's clocks nearby both read t_0, but Dana says that the clocks are synchronized to her watch, while Bert says that the clocks are NOT synchronized to his watch.

Both are right, because by the way we've defined simultaneity. What we have demonstrated is the failure of simultaneity; events considered simultaneous in one frame of motion are not necessarily simultaneous in another.

What events does Bert regard as simultaneous to his own t_0? A' and B', since if he sents out a pulse at t_3 = t_0 - e to bounce off his own clocks at A' and B', then he will receive the pulses at t_4 = t_0 + e, and is able to verify that his clocks at A' and B' are synchronized with his watch, and defines his own x-axis, his own line of simultaneity. Dana disagrees with him, and sees Bert's line of simultaneity as tilted (as he does her own), and both are right.

Everything follows from here: length contraction, time dialation, mass dialation, the whole works.

[Surlethe]

I fully agree that your advice is a good way to learn relativity; what I disagree with is the implicit notion that relativistic mechanics is best understood as an extention or 'fixing' of Newtonian mechanics. In most relativistic cases, Newtonian mentality hinders rather than illuminates.

I didn't mean to imply that; rather, I was attempting to put relativity in the context of revolutionizing Newtonian physics. I agree a Newtonian mentality hinders relativistic understanding.