Relativity - Oh dear, here we go again!

[Ziggurat]

Their clocks were started from a flash of light emitted from a point exactly mid-distance between them.

In other words, you're choosing the unique reference frame in which they're both moving in opposite directions at the same speed. Which is fine, but that still is choosing a unique reference frame.

Or perhaps they are both travelling in opposite directions around a common circular path.

A circular path (as opposed to a spiraling but drifting path) can only be defined in relation to one reference frame (the frame which defines the stationary center of the orbit). Which is fine, but you've selected a unique frame. And you're also no longer studying the twin problem, since now their situation really is symmetric.

They synchronise their watches when they pass.

That's fine for starting the experiment, but unless they come back together, how do you tell them when to end? What counts as simultaneous when they're not in the same place depends on your choice of reference frame.

Look at post 195. I drew the traveling twin trajectories as viewed in three different reference frames. Do those diagrams make sense to you?

 

[BillyJoe]

OK, I just assumed that it was a space-time diagram. In that case, I haven't seen that exact scenario before. I think it's better to use one spatial dimension instead of two because that makes it much easier to draw a space-time diagram. The scenario I've seen before is basically your scenario projected onto the x axis.

I used only one space dimension.
(at four successive time intervals)

It wasn't my choice to start discussing the twin paradox into this thread. It's certainly not necessary to discuss problems that are that difficult to learn the basics of SR.

It also seems ynot regrets doing so.

However, the resolution of the paradox can't be made much simpler than I've made it. The problem would have been more complicated if I had chosen to make the acceleration finite.

Agreed.
That's why I tried to eliminate acceleration and to show that time dilation still occurs when you do.
Seems I failed.

 

[Fredrik]

I used only one space dimension.

So it is a space-time diagram. When you said that there's no time coordinate at all in it, I thought you meant that there's no time axis in it, and that would have meant that the vertical axis is another spatial dimension. That's why I concluded that I must have been wrong to think it was a space-time diagram in the first place.

If the time axis is the one drawn vertically, then time is increasing in the down direction. This can be seen from the "<" and ">" symbols that indicate if the velocities are negative or positive in the O frame.

You said that there are no units or speeds in your diagram, but the slope of the lines clearly indicate the speeds of A,B and C in the O frame, in some units, and although the diagram doesn't reveal what those units are, we can at least see that they are such that the speed of light isn't anywhere near the usual 1. It seems to be >2.

That's why I tried to eliminate acceleration and to show that time dilation still occurs when you do.

What you did was to show that acceleration can be removed from the twin paradox problem without changing anything relevant. That might be enough to get a person to think about the twin paradox in a different way, but it doesn't make it any easier to solve the problem.

 

[Paulhoff]

Humans just like to make everything complicated.

Paul

 

[Fredrik]

Ynot, if you are serious about understanding the basics of relativity, I have some "homework" for you:

(Some of these exercises are so easy they might seem to be trick questions. Some of the others require some thought).

1. Draw a space-time diagram describing the following scenario (from your own point of view): You're not accelerating. At (t,x)=(-T,0) you send out light both to the right and to the left. The light is reflected by mirrors that have been placed at locations such that the reflected light reaches you at (t,x)=(T,0).

2. What are the (t,x) coordinates of the events where the light rays bounce off the mirrors?

3. Which events in space-time are simultaneous with (0,0) in your frame?

4. Draw the world line of an observer who is moving with velocity v (0<v<1) relative to you, and passes you at (0,0).

5. What set of events in space-time have x'=0?

Suppose that he resets his clock (i.e. sets his time coordinate t'=0) when he meets you at (0,0), and that he uses a position coordinate x' such that in his frame, he's stationary at x'=0 and your velocity is -v.

6. Imagine that he does the same thing you did in in 1: He sends out light at time (t',x')=(0,-T') and the reflected light reaches him at (t',x')=(0,-T') (where T' doesn't have to be equal to the T we used in 1). Draw the world lines of the light rays in the same space-time diagram where you drew his world line.

7. What are the (t',x') coordinates of the events where these light rays bounce off the mirrors?

8. Draw a line in the same diagram that goes through all events that are simultaneous with (0,0) in the other observer's frame.

When you can do these exercises you should have pretty good understanding of simultaneity, and we'll be able to move on to time dilation.

 

[BillyJoe]

So it is a space-time diagram.

Let's just say there are 4 single-dimension space-diagrams separated by a time interval.

You said that there are no units or speeds in your diagram, but the slope of the lines clearly indicate the speeds of A,B and C in the O frame, in some units, and although the diagram doesn't reveal what those units are, we can at least see that they are such that the speed of light isn't anywhere near the usual 1. It seems to be >2.

The speed of light doesn't even figure in my diagrams!!!

What you did was to show that acceleration can be removed from the twin paradox problem without changing anything relevant. That might be enough to get a person to think about the twin paradox in a different way, but it doesn't make it any easier to solve the problem.

At the time I posted this, ynot was thinking that time dilation is caused by acceleration, not velocity. What I was trying to say to ynot is "Look in this scenario there is time dilation but there is no acceleration, so time dilation is not caused by acceleration."

 

[ynot]

The twins have left the thread! At least for me they have. From now on I will only talk about clocks. I will try to explain what I mean again using clocks . . .

A, B, and C are clocks that are in the same frame. A and C then travel in opposite directions away from, and then back to, B. They travel at the same speed and distance. During the period of travel all clocks have different frames. When the clocks get back together they are back in the same frame again. They then compare their times.

B will observe that A and C have time dilated (same amount), and A and C will see that B has time dilated (same amount), and that they have also time dilated compared to each other.

It seems to me that the different views of the clocks are contradictory when they are all back in the same frame.

Relativity seems to only consider one view from one frame. I am considering three views from one frame.

Sorry I don't have time to answer posts. I’m taking off shortly to spend a week on the lovely Gold Coast of Australia. Don’t think I will have much time to contribute to the thread but will look in whenever I can.

 

[Fredrik]

Let's just say there are 4 single-dimension space-diagrams separated by a time interval.

I don't understand what you're saying here.

The speed of light doesn't even figure in my diagrams!!!

Then it isn't a space-time diagram. I don't get it, does the vertical direction represent time or space?

 

[BillyJoe]

There is no vertical axis. I have drawn four diagrams in one spacial dimension. Each successive diagram considers the change that has occurred in the one before after an unspecified time interval.

It wasn't meant to be a space-time diagram.

 

[BillyJoe]

B will observe that A and C have time dilated (same amount), and A and C will see that B has time dilated (same amount), and that they have also time dilated compared to each other.

ynot, we have failed you miserably.

 

[Fredrik]

Relativity seems to only consider one view from one frame. I am considering three views from one frame.

This doesn't make any sense. A "view" is a frame, so you're saying that you're considering three frames from one frame. That's probably why things seem contradictory to you.

I told you everything else about this scenario in #256.

 

[Fredrik]

There is no vertical axis. I have drawn four diagrams in one spacial dimension. Each successive diagram considers the change that has occurred in the one before after an unspecified time interval.

It wasn't meant to be a space-time diagram.

That doesn't make it any clearer to me. The diagram is two dimensional. If the vertical direction isn't time, then I can't see any explanation for it unless it represents a second dimension of space. I also don't understand why you talk about four diagrams. I only see one diagram with four lines in it.

 

[BillyJoe]

And then there were four:

time = t

[B]o[/B]                      [B]a[/B]                        [B]b[/B]        
                       >                        <

time = t + 1

[B]o[/B]                               [B]ab[/B]                                            [B]c[/B]
                                ><                                            <

time = t + 2

[B]o[/B]                  [B]b[/B]                    [B]ac[/B]
                   <                    ><

time = t + 3

[B]o[/B]     [B]bc[/B]                                         [B]a[/B]
      <<                                         >

o is the rest frame.
a, b, and c are spaceships travelling at constant speed in a straight line.
> and < indicate the direction of travel.

When a meets b, they synchronise their clocks.
When a meets c, c matches his clock to a's.
When b and c meet, they compare times.

The time on c's clock will be less than that on b's clock
There has been relative time dilation because of the greater speed of c relative to b.
Acceleration cannot be the cause because no one has accelerated.
In other words, relative time dilation is a function of relative speed, not acceleration.

 

[Atlas]

Billy, your diagram is as elegantly comprehensible as it is mundane. Fredrick gave us colors and curvey lines and stuff that fire the imagination into the realm of weirdthought.

I loved the depiction of the nonsimultaneous aging where both twins age faster than their sibling in the first few years of flight.

As if Johnny has a birthday aboard the rocket Puttputt traveling at .2c. After his birthday dinner he retires to cargo bay 2 and fills the space with 12 massive burrito farts which he then evacuates into deep space.

Meanwhile Janey, his sister, has launched from Earth on the rocket Whamzing traveling at .823c on an intercept course and collides with the malignant gas cloud.

The funny thing is, Janey thinks to herself, "That smells like my brother but his birthday isn't til tomorrow."

Your diagram inspires no such humor... sorry.

 

[BillyJoe]

Atlas,

Well, Freddy has trouble comprehending it.
But I also like his diagram.
(Though I fail to see humour in it. )

But that's not the point.

We have ynot, who is having trouble understanding this thing, and I'm pretty sure this diagram has no chance in hell of helping him.
He is struggling with the basics.

I was actually aiming for something really simple and, therefore, necessarily mundane, in an attempt to explain as simply as possible that time dilation is real and is not caused by acceleration.
So your criticism is a kind of forehand compliment.

But, what the hell, we both failed.
(Maybe not entirely our faults though)

regards,
BillyJoe

 

[Atlas]

You've only failed with ynot. I've been lurking and learning a lot during this review of Relativity.

I've been confused about the nature of speed versus acceleration in observing time dilation. Perhaps because gravity produces similar time distortion and the math is so similar to acceleration. Or perhaps because I tend to stupidly add a 1g acceleration component when contemplating relativistic rocket problems even where the problem does not include it. I wasn't aware I was doing that but somehow some early problem description has polluted my thinking, I guess.

Anyway, your diagram stripped that away. I grasped what you were saying from your first presentation. Even where it missed your intended target, be sure, it penetrated innocent bystanders like me.

 

[Paulhoff]

When I was taking a home study electronics course, one of the writers had written, and I paraphrase

“You can read many books on the same subject and you just don’t understand it until you finally read that one that little sentence that talks to you like you think and it all becomes clear”.

Paul



And remember KISS

 

[Fredrik]

OK, now I see four ASCII pictures and the description makes sense. This confirms what I concluded earlier. The original diagram is a space-time diagram (even though it wasn't intended to be) with time increasing in the down direction and units such that c > 2.

It is equivalent to the simple space-time diagram I posted in #246 (possibly with a different slope of line C). My diagram is from B's point of view. Yours is taking a fourth point of view.

Your scenario is equivalent to the twin paradox, with B as the Earth and A and C as the twins.

This is what I said in #246. I just got confused when you said that I was wrong.

 

[BillyJoe]

You've only failed with ynot. I've been lurking and learning a lot during this review of Relativity.

I've been confused about the nature of speed versus acceleration in observing time dilation. Perhaps because gravity produces similar time distortion and the math is so similar to acceleration. Or perhaps because I tend to stupidly add a 1g acceleration component when contemplating relativistic rocket problems even where the problem does not include it. I wasn't aware I was doing that but somehow some early problem description has polluted my thinking, I guess.

Anyway, your diagram stripped that away. I grasped what you were saying from your first presentation. Even where it missed your intended target, be sure, it penetrated innocent bystanders like me.

 

[BillyJoe]

When I was taking a home study electronics course, one of the writers had written, and I paraphrase

“You can read many books on the same subject and you just don’t understand it until you finally read that one that little sentence that talks to you like you think and it all becomes clear”.

Paul



And remember KISS

(Yeah, KISS: Keep It Short and Simple. )