Revisiting the Flaws of the Light Clock in Special and General Relativity

[starthaus]

Hmm, out of curiosity I checked it, when we have:

\alpha = 329,356,000 m/s^2

\tau = 1 sIt is rather high but on the other hand if we consider the maximum acceleration from QT perspective then we should get to somewhere in the 5.56 x 10⁵¹ m/s² region.

Plenty of playroom it seems

You mean, for a rocket carrying atomic clocks ?
That has to turn around from +0.8c to -0.8c?
Do you think anything would be left out of the rocket and the clocks? :-)

I get a coordinate velocity of 0.8 and a coordinate acceleration of 7488461 m/s[sup2[/sup] about 2.3% or the proper acceleration.

This is incorrect since a=\frac{\alpha}{\gamma^3} where \gamma=1/0.6. Your result is off by one order of magnitude.

 

[Passionflower]

This is incorrect since a=\frac{\alpha}{\gamma^3} where \gamma=1.33. Your result is off by one order of magnitude.

Oh? I get a gamma of 1 2/3 not 1 1/3

How did you get 1 1/3?
The proper velocity is 1 1/3

 

[starthaus]

Oh? I get a gamma of 1 2/3 not 1 1/3

How did you get 1 1/3?
The proper velocity is 1 1/3

\beta=0.8
\gamma=1/0.6

 

[Passionflower]

\gamma=1/0.6

Wait, hold on...

Yes that is 1 2/3 not 1 1/3 right?

 

[starthaus]

0.6? You mean 0.8 right?

No, I mean exactly what I wrote above.

 

[Passionflower]

No, I mean exactly what I wrote above.

No ignore that.

1/0.6 = 1 2/3 right?

 

[starthaus]

No ignore that.

1/0.6 = 1 2/3 right?

Yes, whatever 1/0.6 comes out to be. Your coordinate acceleration is off by a factor of 10.

 

[Passionflower]

Yes, whatever 1/0.6 comes out to be. Your coordinate acceleration is off by a factor of 10.

Hold on, so now we agree that gamma is 1 2/3

Ok, you are right, I see what happened the coordinate acceleration is in ly/y^2 and alpha is in m/s^2.

In ly/y^2:

Alpha is: 34,668,889 ly/y^2
A is: 7488460.769 ly/y^2

With a ratio of 21,6%

Good spotting!

 

[starthaus]

Hold on, so now we agree that gamma is 1 2/3

Ok, you are right, I see what happened the coordinate acceleration is in ly/y^2 and alpha is in m/s^2.

In ly/y^2:

Alpha is: 34,668,889 ly/y^2
A is: 7488460.769 ly/y^2

With a ratio of 21,6%

Good spotting!

I knew we'll agree.

 

[Passionflower]

I knew we'll agree.

Yes in math there is no middle between true and false!