On the Definition of an Inertial Frame of Reference

[prometheus]

And your stinking red herring is relevant to the discussion, how?

How is it a red herring that you're wrong?

 

[Tach]

How is it a red herring that you're wrong?

What does it have to do with the absence of covariance of Maxwell's laws in Shubert's crackpot formalism?

This is why is a stinking red herring. And you wonder why crackpots like Schubert flourish in this forum? They get encouragement from pretenders like you, Guest254, etc.

 

[Tach]

What are the Christoffel symbols for the following metric?

$$ds^2 = -dt^2 + dr^2 + r^2 \left(d\theta^2 + \sin^2 \theta d\phi^2 \right) $$

Transform back from polar into cartesian coordinates, the above metric becomes:

$$ds^2 = -dt^2 + dx^2 + dy^2+dz^2$$

All the Christoffel symbols are zero.
The spacetime is flat, there is always a system of coordinates that makes the Christoffel symbols zero.

 

[prometheus]

Transform back from polar into cartesian coordinates, the above metric becomes:

$$ds^2 = -dt^2 + dx^2 + dy^2+dz^2$$

All the Christoffel symbols are zero.
The spacetime is flat, there is always a system of coordinates that makes the Christoffel symbols zero.

Shall I take this as an apology? You stated previously that if the Riemann tensor (a coordinate invariant quantity) vanishes then the Christoffel symbols must also vanish. The Christoffel symbols are not coordinate invariant and as I have shown, do not vanish in polar coordinates.

It's my pleasure.

 

[Eugene Shubert]

If you tried to calculate the jacobian for Schubert's crackpot transforms

x'=x'(x,t)
t'=t'(x,t)

you would have found out that you cannot prove that it is non-degenerate.

Every Unapologetic Mathematician knows how to compute the Jacobian for my nonlinear transformation by the chain rule. And my factorization makes the computation extraordinarily easy to do. It easily follows that the determinant of the Jacobian is precisely 1 everywhere.

 

[Tach]

Shall I take this as an apology?

No, you should consider this as an indication that you keep munching on a red herring.

You stated previously that if the Riemann tensor (a coordinate invariant quantity) vanishes then the Christoffel symbols must also vanish.

Which they do, see the proof in Moller p.377. Why do you keep munching on rotten red herrings?

The Christoffel symbols are not coordinate invariant and as I have shown, do not vanish in polar coordinates.

Transform back into cartesian coordinates and you get null Christoffel symbols. A change of coordinates doesn't change the nature of spacetime. It doesn't make it curved if you go from cartesian to polar.

It's my pleasure.

Congratulations! What does this have with the subject of the OP? Hint: nothing.

 

[Tach]

Every Unapologetic Mathematician knows

Doesn't mean that you know. You don't.

how to compute the Jacobian for my nonlinear transformation by the chain rule.

When you do that with your crackpot transforms you find that , your jacobian (much like its author) is degenerate.

It easily follows that the determinant of the Jacobian is precisely 1 everywhere.

Yours isn't, you idiot. Calculate it starting from your demented transforms (54)(55).

 

[prometheus]

This is going from bad to worse.

 

[Tach]

This is going from bad to worse.

If you do not have anything to contribute to the subject of the thread maybe you should stay out.
Let's try a simple exercise , looking at Shubert's crackpot transforms (54)(55), calculate its jacobian (Shubert in not able to do it for himself).

 

[Green Destiny]

This is going from bad to worse.

Tach is the coal. You are the fire.

Go figure.

 

[prometheus]

If you do not have anything to contribute to the subject of the thread maybe you should stay out.

You're trout from physorg aren't you? I thought it was you by your posting style but I also thought that it couldn't possibly be trout because he at least know a bit about relativity. Guess I was wrong about something.

 

[Tach]

You're trout from physorg aren't you? I thought it was you by your posting style but I also thought that it couldn't possibly be trout because he at least know a bit about relativity. Guess I was wrong about something.

But you proved to be a pretender that doesn't have the least of clues of what is being discussed in this thread. Sad.

 

[Eugene Shubert]

Let's try a simple exercise , looking at Shubert's crackpot transforms (54)(55), calculate its jacobian (Shubert in not able to do it for himself).

Translation: Sir Knight would greatly appreciate it if someone checked his hunches because he is consumed by some irrational passion to find a significant conceptual or mathematical error in my paper. Would anyone here like to put Sir Knight out of his misery?

 

[Tach]

Translation: Sir Knight would greatly appreciate it if someone checked his hunches because he is consumed by some irrational passion to find a significant conceptual or mathematical error in my paper.

You mean the piece of crap you keep peddling in the absence of being able to submit it to a reputable journal?

Would anyone here like to put Sir Knight out of his misery?

Why don't you do it yourself? Start from the demented (54)(55) in your "masterpiece" and calculate the jacobian.

 

[prometheus]

But you proved to be a pretender that doesn't have the least of clues of what is being discussed in this thread. Sad.

You're the one who thought that Christoffel symbols must vanish if the Riemann tensor vanished. Pretty funny actually.

 

[Tach]

You're the one who thought that Christoffel symbols must vanish if the Riemann tensor vanished. Pretty funny actually.

They do, you dork. If you don't understand the proof, I can email you the page from Moller's book.

 

[prometheus]

the definition of the Christoffel symbols:

$$\Gamma^\rho_{\mu \nu} = \frac{g^{\rho \lambda}}{2} \left(\partial_\nu g_{\lambda \mu} +\partial_\mu g_{\lambda \nu}- \partial_\lambda g_{\mu \nu} \right)$$

take for example $$\Gamma^r_{\theta \theta}$$:

$$\Gamma^r_{\theta \theta} = \frac{g^{r \lambda}}{2} \left(\partial_\theta g_{\lambda \theta} +\partial_\theta g_{\lambda \theta}- \partial_\lambda g_{\theta \theta} \right)\\
= \frac{g^{r r}}{2} \left(\partial_\theta g_{r \theta} +\partial_\theta g_{r \theta}- \partial_r g_{\theta \theta} \right)\\
= -\frac{g^{r r}}{2} \partial_r g_{\theta\theta} \\
= - \frac{1}{2 r^2} \partial_r r^2\\
= -\frac{1}{r} $$

Calling me a dork. Wow, that makes you right.

 

[Tach]

Calling me a dork. Wow, that makes you right.

Transform back from polar into cartesian coordinates, the above metric becomes:

$$ds^2 = -dt^2 + dx^2 + dy^2+dz^2$$

All the Christoffel symbols are zero.
The spacetime is flat, there is always a system of coordinates that makes the Christoffel symbols zero.

 

[prometheus]

They do, you dork. If you don't understand the proof, I can email you the page from Moller's book.

Evidently you don't understand the proof, because it shows that there exists a coordinate system where the Christoffel symbols vanish, not that they vanish for all coordinate systems.

 

[Tach]

Evidently you don't understand the proof, because it shows that there exists a coordinate system where the Christoffel symbols vanish, not that they vanish for all coordinate systems.

Did I tell you that they vanish for all coordinate systems? Would you stop hijacking the thread with your rotten red herrings?