Measuring distance, speed and clock

[Mentz114]

Sorry, I hastily calculated.
About 4.8 or 4.9?
[Add:] And the close the angle to -45⁰ the knots will be separated farther and farther?
[Add:] Oh I see, with my spread sheet, it will be difficult to see the 4.8 and 4.9, I have to transform it manually according to Lorentz transformation boost in the x-direction.

The knots as you call them are the ticks of the green clock. If you count up it comes to about 4.9 and to get seconds we divide by 20 because we decided that 20 ticks is one second.
It is important to understand that every clock tells the proper length of its worldline. This is a big change from Gallilean relativity.

 

[Stephanus]

The knots as you call them are the ticks of the green clock. If you count up it comes to about 4.9 and to get seconds we divide by 20 because we decided that 20 ticks is one second.
It is important to understand that every clock tells the proper length of its worldline. This is a big change from Gallilean relativity.

Hmhhh, all this time every time I calculated time, I used the reverse of pythagoras. $t' = \sqrt{y^2-x^2)$ How can I didn't see the knots before?
Btw, this is my source numbers and the resulting text files. You might want to rename Source ST-03.txt to Source ST-03.rtf, because PF forum doesn't allowed uploading RTF files.

 

[Stephanus]

This is how I calculate ST diagram with the help of ST plotter and spread sheet.

Then, I calculate events that I already know the coordinates.

E6 (0,0), of course
E4 (1125,1875) -> 1500 * gamma = 1875, x = 0.6 * 1875 = 1125
E2 (1125,1275) -> E4 - 1200 = 1275
And I calculate all events by the help of algebra eliminations and the logical light rays.
Then, I connect the necessary events coordinate to draw light rays.
Wait, I'll a draw a Twins Paradox world lines

 

[Mentz114]

Hmhhh, all this time every time I calculated time, I used the reverse of pythagoras. $t' = \sqrt{y^2-x^2}$ How can I didn't see the knots before?
Btw, this is my source numbers and the resulting text files. You might want to rename Source ST-03.txt to Source ST-03.rtf, because PF forum doesn't allowed uploading RTF files.

I wondered why you didn't see the 'knots'.

You have made the connection with proper time, $\tau = \sqrt{t^2-x^2}$ which is good.

I'm not going to download any of the stuff you posted. I find your methods complicated and baroque but if it makes sense to you then that's fine.

 

[Stephanus]

Twins paradox

There is something very wrong here?
Those I area that I circle. Why there are so much lines? I've calculated my numbers twice (may be three times) But the lines at the red circle are crowded?? I'm afraid there's something in my text files that ST Plotter won't receive.

 

[jbriggs444]

Twins paradox
Those I area that I circle. Why there are so much lines?

If you looked at those south-east to north-west yellow lines as light signals sent from the green twin to the blue twin then that close spacing would be called a Doppler shift.

 

[Stephanus]

What about this? This looks right to me.

 

[Mentz114]

What about this? This looks right to me.
View attachment 86136

That looks OK. But, as usual, I'm wondering why you need all those light pulses ?

The time between parting and meeting on the blue clock is the number of blue knots between the events, and the time on the green clock is the total number of green knots.

You could also calculate the green clock times using $\tau=\sqrt{t^2-x^2}$ for the green triangles.

 

[Stephanus]

That looks OK. But, as usual, I'm wondering why you need all those light pulses ?

The time between parting and meeting on the blue clock is the number of blue knots between the events, and the time on the green clock is the total number of green knots.

You could also calculate the green clock times using $\tau=\sqrt{t^2-x^2}$ for the green triangles.

I don't know
I just try to draw ST diagram quickly. I saw an ST diagram for Twins Paradox, there were lights rays from every "knots". And I just copy paste the formula. Doesn't have to drag many lines. Okay, just don't explain to me about Twins Paradox now. Studying doppler first.

 

[Stephanus]

[..]Time dilation we cannot directly measure. This was discussed in another thread just a day or so ago: https://www.physicsforums.com/threa...ver-be-directly-observed.820770/#post-5152104

The link/thread you gave me is very useful. I just read it now. Thanks.