Time dilation with 3 bodies

[Dcallagh]

Okay, there is a similar question but not precisely mine. Imagine a stationary observer a and two objects x & y going away in opposite directions at .25 c.

A sees time slowed on x and y. X sees time slowed on a and y. Y sees time slowed on a and x. ???

How can they all see time slowed on the other?

[pzkpfw]

Why not?

 

X sees themselves as stationary, and A and Y moving away (Y faster than A).

Y sees themselves as stationary, and A and X moving away (X faster than A).

Each of them, looking at their own clocks, will consider time to be passing at one second per second. But the others clocks will be slower (by varying amounts).

 

Using these three bodies is no more "amazing" than two.

 

If C and D are moving (constant speed) relative to each other, each can consider themselves as at rest, and the other to be moving.

So for C, their clocks are "normal" and D's clocks are slow. Vice versa, for D their clock's are "normal", and C's are slow.

 

What's constant is the speed of light. That time and distance are squishy naturally falls out of that.

[mistermack]

Okay, there is a similar question but not precisely mine. Imagine a stationary observer a and two objects x & y going away in opposite directions at .25 c.

A sees time slowed on x and y. X sees time slowed on a and y. Y sees time slowed on a and x. ???

How can they all see time slowed on the other?

The way I look at it, because you are seeing events via light travelling from the event to you, what you are seeing is a RECORDING of the events, because of the finite speed of light. You aren't watching live.

When you are moving fast, relative to me, the recording I see of you is running slow, and so is the recording that you see of me.

So it's not that the two events are running slower than each other, it's the recordings that you each receive that run slower.

So if we each clap our hands three times, one per second, I can clap three times, and only see you clap twice, and you will see me do exactly the same.

It's because you can't experience things "live".

 

We get an illusion that events are live, in everyday life, because we move slowly compared to the speed of light, so things appear to happen instantly, and time dilation is so tiny day to day, that we can't notice it, and it feels like time can't vary.

[Janus]

Okay, there is a similar question but not precisely mine. Imagine a stationary observer a and two objects x & y going away in opposite directions at .25 c.

A sees time slowed on x and y. X sees time slowed on a and y. Y sees time slowed on a and x. ???

How can they all see time slowed on the other?

To use an analogy: You start with three men all walking abreast at the same pace. Two of them split off walking at an angle to the third man without changing their pace. From this point on, if you were to ask any of the men where the other two were with respect to the direction he was facing, he would say that they were behind him. In this example, "forward" is defined by each man's perspective. In Relativity we are moving through space-time, and somewhat like the way each man in the example has his own sense of the forward direction, we all have our own sense of the "direction of time" in space-time. If we are at rest with respect to each other we share the same direction of time. If we are in motion with respect to each other, we do not. (Even though this is true for any relative motion, at the speeds we are used to in everyday life, this difference is so small it is all but immeasurable. This is why seems like time should be a universal constant to us when it really isn't.)

[JohnLesser]

Okay, there is a similar question but not precisely mine. Imagine a stationary observer a and two objects x & y going away in opposite directions at .25 c.

A sees time slowed on x and y. X sees time slowed on a and y. Y sees time slowed on a and x. ???

How can they all see time slowed on the other?

Like in experiment they compare the measured time elapsed on their return to (A).

[KipIngram]

Dcallagh, all of our intuitions about things like this are based on our life experiences on Earth, where the relative velocities involved are never significant compared to the speed of light. The rules don't "change" when velocity is significant compared to c - it's just that when v is negligible the rules can be simplified, and it's those simplified rules that we've built our intuitions around. When you "visit a new environment" for the first time you have to build new intuitions; we do that all the time and this is no different.

 

When Einstein formulated special relativity, he dealt with experimental observations that showed c to be a constant no matter what by building that into his theory at ground zero - he assumed it from the outset. He then worked through the math to discover what that assumption implied for all of the usual kinematic relationships that we deal with every day, and time dilation was one of the results (along with Lorentz contraction).

 

You can spin up a similar "paradox" using distance. If I'm standing here holding a yardstick, and you travel by in the direction the yardstick is pointing at half the speed of light, and you are also holding a yardstick parallel to mine, I will see that your yardstick is shorter, and you will see that my yardstick is shorter. So that seems confusing too. But all of these things have to do with the fact that simultaneous events for me are not simultaneous for you.

 

What turns out to be the same for everyone, regardless of relative velocities, is length^2 - c*(time interval)^2.