Time paradox (?)


by tomatoking
Tags: general, light, observer, relativity, time
tomatoking
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#1
Jul23-10, 10:47 AM
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First of all, hello forum. I'm new.

Alright, so I was recently informed of two things. I'm no physics student, but nonetheless I was still interested in these things.

1. The speed of light is always constant for all observers.
2. To compensate for the paradox of a light particle having two different velocities to two different observers, time slows down in any region that the speed of light should be "increasing", and speeds up in any region that should be "decreasing".

So let's say I have observers A and B. A is stationary, while B is traveling in a straight line at a constant velocity. By the last two points, B's velocity doesn't mean that B's light is traveling slower than the speed of light relative to B, but rather, the light still travels at the speed of light relative to B. For A, this doesn't mean that B's light travels faster relative to A, but instead, B's light still travels at the speed of light relative to A by slowing down B's passage through time.

Well, here's a paradox I can't understand.

Since motion is relative, won't A be saying that B is slowed down in time, and vice versa? They both can't be slowed down in time... or am I just not thinking physics-like? Well, forgive my 14 year-old brain for not grasping it if that's the case. As far as I'm concerned, they both can't be seeing one another slowed down in time.

So what happens when B observes A back?

And I'm sorry if this is in the wrong forum section. I'm pretty sure that this fits under general relativity, but then again, I'm no student of physics.
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GRDixon
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#2
Jul23-10, 10:55 AM
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Quote Quote by tomatoking View Post
First of all, hello forum. I'm new.


1. The speed of light is always constant for all observers.
2. To compensate for the paradox of a light particle having two different velocities to two different observers, time slows down in any region that the speed of light should be "increasing", and speeds up in any region that should be "decreasing".

.
To appreciate how 2 observers can each measure the same value for the speed of light in his inertial frame of reference, you really need to mentally juggle 3 ideas: (1) time dilation, (2) length contraction, and (3) the way the distributed clocks in each frame are synchronized (relativity of simultaneity). These are the 3 core ideas that form the basis for the Lorentz transformations. It takes practice, but once you "see the light" you'll be amazed that such a counter-intuitive notion can actually be demonstrated. In general, each observer agrees that light is MEASURED
GRDixon
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#3
Jul23-10, 11:01 AM
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Quote Quote by GRDixon View Post
To appreciate how 2 observers can each measure the same value for the speed of light in his inertial frame of reference, you really need to mentally juggle 3 ideas: (1) time dilation, (2) length contraction, and (3) the way the distributed clocks in each frame are synchronized (relativity of simultaneity). These are the 3 core ideas that form the basis for the Lorentz transformations. It takes practice, but once you "see the light" you'll be amazed that such a counter-intuitive notion can actually be demonstrated. In general, each observer agrees that light is MEASURED
Whoops! For some reason I was prohibited from completing the thought. Each observer agrees that is MEASURED to be c by the other observer, when he uses his own grid and clocks. But each observer contends that the other guy's clocks are not synchronized, etc. On the other hand, each observer contends that the measurement in his OWN frame (using his own set of distributed clocks, etc.) is CORRECT. The lesson of Special Relativity is that there's no way of proving that one observer is REALLY correct, and the other is misled. Or for that matter, there's no way of proving that EITHER observer is correct; from the point of view of a 3rd observer, they're both measuring c for the speed of light, relative to their own frames, but they're both mistaken because their grids are length contracted, etc.

tomatoking
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#4
Jul23-10, 11:10 AM
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Time paradox (?)


Quote Quote by GRDixon View Post
Whoops! For some reason I was prohibited from completing the thought. Each observer agrees that is MEASURED to be c by the other observer, when he uses his own grid and clocks. But each observer contends that the other guy's clocks are not synchronized, etc. On the other hand, each observer contends that the measurement in his OWN frame (using his own set of distributed clocks, etc.) is CORRECT. The lesson of Special Relativity is that there's no way of proving that one observer is REALLY correct, and the other is misled. Or for that matter, there's no way of proving that EITHER observer is correct; from the point of view of a 3rd observer, they're both measuring c for the speed of light, relative to their own frames, but they're both mistaken because their grids are length contracted, etc.
Well, you just lost me. Heh. I feel like it's a stupid question, but why do lengths also contract, not just time? I know, I know, space ~ time and all that, but thinking from ground-up, why would length contract to an outside observer when moving at a constant velocity?
Fredrik
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Jul23-10, 11:11 AM
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Quote Quote by tomatoking View Post
First of all, hello forum. I'm new.
Hello, and welcome.

Quote Quote by tomatoking View Post
1. The speed of light is always constant for all observers.
2. To compensate for the paradox of a light particle having two different velocities to two different observers, time slows down in any region that the speed of light should be "increasing", and speeds up in any region that should be "decreasing".
If you replace "region" with "coordinate system", your statements are accurate enough for most purposes. I would describe things differently, and say things like: Time doesn't really "speed up" or "slow down"; a clock simply measures the proper time of the curve in spacetime that represents its motion. Unfortunately, a high school student isn't going to understand my preferred explanations of these things. You have a lot of work in front of you if you really want to understand relativity.

Quote Quote by tomatoking View Post
Since motion is relative, won't A be saying that B is slowed down in time, and vice versa?
Yes!

Quote Quote by tomatoking View Post
They both can't be slowed down in time... or am I just not thinking physics-like? Well, forgive my 14 year-old brain for not grasping it if that's the case.
I forgive you. They are both correct to say to each other that "right now, you are aging at a slower rate than me". This is possible because statements about their "experiences" are really statements about how they would assign coordinates to events.

Quote Quote by tomatoking View Post
And I'm sorry if this is in the wrong forum section. I'm pretty sure that this fits under general relativity, but then again, I'm no student of physics.
It's the right section. This is special relativity. All that stuff about the speed of light, time dilation, etc., is special relativity. General relativity is about gravity (and contains special relativity as a special case).
GRDixon
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#6
Jul23-10, 11:45 AM
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Quote Quote by tomatoking View Post
why do lengths also contract, not just time?
I once modeled (on a computer) a "macroscopic Bohr Hydrogen atom," with a massive, positively charged "nucleus," and a very light, equal but oppositely charged orbiting electron. In the rest frame of the central particle, I arranged the electron's orbital radius and speed to be such that it went in a circle around the central particle.

I then viewed things from a second inertial frame of reference, relative to which the central body moved with constant velocity. In that frame the electron experiences both an electric and magnetic field. But the Lorentz force law tells what the force on the electron is in that second frame. When I computed the electron's quasi-cycloidal motion, it cut above and below the central body at the usual radius. But it cut in front and in back of the central body at a length-contracted distance. Furthermore, it took LONGER in the second frame to make one complete cycle "around" the central body.

This little thought experiment/computer modeling project of course doesn't explain why length contraction is generally true. But it provides food for thought, since it is all based on Maxwell's equations (to derive the central body's electromagnetic field) and the Lorentz force law (for the force experienced in every case by the orbiting electron).
FawkesCa
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#7
Jul23-10, 05:42 PM
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[QUOTE=tomatoking;2811468]

Well, here's a paradox I can't understand.

Since motion is relative, won't A be saying that B is slowed down in time, and vice versa? They both can't be slowed down in time... or am I just not thinking physics-like? Well, forgive my 14 year-old brain for not grasping it if that's the case. As far as I'm concerned, they both can't be seeing one another slowed down in time.
QUOTE]

nope... you are completely correct. Relativity is a special kind of craziness. thats why i like to stick with the pretty pictures of Astronomy... that being said, we cant get to those pretty pictures without learning to make sense of said craziness. I suggest you read Michio kaku's Hyperspace and Brian Greenes The Elegant Universe. both explain the this as best as can be... unless you have 3 PhDs in physics and 2 in engineering

welcome to the club
Fredrik
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Jul26-10, 12:53 PM
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Quote Quote by FawkesCa View Post
I suggest you read Michio kaku's Hyperspace and Brian Greenes The Elegant Universe. both explain the this as best as can be... unless you have 3 PhDs in physics and 2 in engineering
I don't think Brian Greene explains SR very well. Taylor & Wheeler is often recommended to people without a strong mathematical background, so maybe that's an option. (I don't know anything about Kaku's book).


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