Traveling near the speed of light

[PeterDonis]

Do you mean that if someone were to live on Earth 85 years, (s)he would also live 85 years on the spaceship (assuming the same life style on Earth and spaceship) according to the spaceship's clock

Yes.

 

[Stephanus]

Yes.
I'm not sure I understand. How is this different from boosting the ST diagram in any V we want?

Come on, you know better
.

To calculate simultaneity of E1 and E2, we (us) have to use the big picture. What the world really look like? We (us) use the right bottom picture. Here, we see that blue and red speed actually differ more than we see in the big picture.

 

[PeterDonis]

Come on, you know better

No, I don't. If I understood what you were trying to say, I wouldn't have asked the question I asked.

What the world really look like?

This is a meaningless question; no particular frame tells you what the world "really" looks like. "Really" is not a scientific word.

Here, we see that blue and red speed actually differ more than we see in the big picture.

No, that's not what we see. First of all, as above, no particular frame tells you what is "actually" the case. "Actually" is not a scientific word.

Second, the relative velocity of blue and red is an invariant; it doesn't depend on which frame you choose. If you are getting the result that the relative velocity of blue and red is different in different frames, you are doing something wrong.

 

[Stephanus]

This is a meaningless question; no particular frame tells you what the world "really" looks like. "Really" is not a scientific word.
No, that's not what we see. First of all, as above, no particular frame tells you what is "actually" the case. "Actually" is not a scientific word.

Good point. Now I know what scientific method is.

Second, the relative velocity of blue and red is an invariant; it doesn't depend on which frame you choose. If you are getting the result that the relative velocity of blue and red is different in different frames, you are doing something wrong.

Just the angle look different.
It's the $\frac{u+v}{1+uv}$

 

[HallsofIvy]

No. That is the whole point of relativity- all photons move at speed "c" relative to all reference frames. To a person "A" traveling toward another star at a large percentage of the speed of light, relative to person "B" on earth, the distance to that star is shorter that it is to "B". To person "B", "A" is traveling the greater distance but his time scale is dilated. So "distance divided by time" works out the same to each.

 

[PeterDonis]

Just the angle look different.

So what does that mean? I still don't understand what point you're trying to make.

 

[Stephanus]

So what does that mean? I still don't understand what point you're trying to make.

Perhaps I can't express myself clearly.
Supposed you are green in this diagram.

And you want to know if event E1 and E2 are simultaneous, so you boost the ST diagram so that the maroon world line are at rest. Then you'll find that E1 and E2 is simultaneous.
But to see the diagram with naked eye, it seems that red and blue WL is very close to green. Actually in the real world, the angle of red and blue is bigger if you put green at rest. See the yellow rectangle.
And IMHO, twins paradox is no more mistery than barn paradox and train/platform experiment. I'm new here. But in the past three months I think I can grasp basic SR. Still so much to learn tough.

 

[PeterDonis]

Actually in the real world, the angle of red and blue is bigger if you put green at rest.

What do you mean by "in the real world"? Calculate the relative velocity of red and blue in any frame; it will be the same. That means that, "in the real world", the relative velocity of red and blue is the same for all observers. The fact that the angle appears different on different spacetime diagrams is a fact about the diagrams, not about red and blue or anything "in the real world" (meaning, the objects and motions that the diagrams represent).

 

[Stephanus]

[..]That means that, "in the real world", the relative velocity of red and blue is the same for all observers.

GOOD POINT!. I'll never forget that.

The fact that the angle appears different on different spacetime diagrams is a fact about the diagrams, not about red and blue or anything "in the real world" (meaning, the objects and motions that the diagrams represent).

Yes, I do understand that. Like I said, I can't express myself clearly.
Consider this.
V_Blue wrt Red is 0.98c
V_Green wrt Blue is 0.6c
For Red, V_Green is 0.995c. Just slighty 0.015c than V_Blue. And if you boost the diagram where Blue is at rest, than you'll see that the different/angle between V_Green and V_Blue is 0.6c. I know, I know, we have to account for relative velocity addition.
It's like that we say.
"No, it's not Blue (660 THz) with V=0, it's Red (440 THz) with V = 0.2c"
Our eyes see it as Blue, our brain calculates it as Red (should compare it with Franhover lines, otherwise, you won't know if it's blue-shifted).
And in my opinion I think Twins Paradox is no more mystery than barn paradox or train experiment.
Perhaps the word "Paradox" came out when Relativiy was at its infancy, and the most natural phenomena such as time dilation for one of the twins was considered "amazing".
PeterDonis, I have a problem with Train Experiment, perhaps you might want to take a look at it in: https://www.physicsforums.com/threads/train-experiment-problem.825514/
Thanks

 

[DrGreg]

Perhaps the word "Paradox" came out when Relativiy was at its infancy, and the most natural phenomena such as time dilation for one of the twins was considered "amazing".

Paradoxically, the word "paradox" has (amongst others) two meanings that are almost opposites:

1. an argument that comes to a false conclusion (e.g.contradicts itself), via steps that appear, at first, to be valid
   
2. an argument whose conclusion may appear, at first, to be false, but is actually true

The "twins paradox", like some other paradoxes in maths and physics, is a paradox of the second type.

In this post I used "paradoxically" with a third meaning, "having apparently contradictory characteristics".