Discussion: Lorentz invariance of certain zero angles

[Tach]

I disagree. We've already started discussing the vector transformation issue, I think we should finish that issue first.
I'll message the mods for a ruling.

No, the first flagged issue was the fatal flaw in your derivation. See here, immediately after your posted solution, the very next post. So, as per rules, please address the issue.

In the meantime, I've twice asked you a direct question you haven't answered. I will ask it again in my next post to the debate thread. Please answer it.

I will (re)start answering AFTER you address the flaw I flagged first. As an aside, the document contains all the answers, I even spared you the effort to track down the references, I included the complete derivations in the document.

 

[Pete]

It's really not appropriate for you to edit that document after you've presented it to the debate. Please revert it back to it's original form, and post any corrections or additions to the debate thread.
This is why I didn't want calculations in an offsite document to begin with.

 

[Tach]

It's really not appropriate for you to edit that document after you've presented it to the debate. Please revert it back to it's original form, and post any corrections

There are no "corrections"

or additions to the debate thread.

The additions are simply in order to explain away your misunderstandings. I ended up posting every intermediate step of each derivation. Either way, you should address the issue I raised at post 119. Please do so.

 

[Pete]

Now, please could you stop the diversions and answer the question posed at post 119. That was the FIRST question, it should be addressed FIRST. If you need some time to track down the exact pages in Rindler, take your time (I have provided you with the exact derivation in my document, so you should be able to address the issue right away).

Tach, there is no question posed in post 119.
I'm also a little concerned over your impatience.
Don't you agree that it is important that we both understand how to transform vectors?
If we don't, then we can't constructively discuss something that relies on that understanding, right?

 

[Pete]

The additions are simply in order to explain away your misunderstandings. I ended up posting every intermediate step of each derivation.

Thanks, I'll check itout.

Either way, you should address the issue I raised at post 119. Please do so.

Yes, I will do so when we're both satisfied that we both understand how vectors transform. That understanding is fundamental to this part of the discussion, so I think it's important that we get it right before moving on.

 

[Tach]

Yes, I will do so when we're both satisfied that we both understand how vectors transform. That understanding is fundamental to this part of the discussion, so I think it's important that we get it right before moving on.

No, it isn't. The flaw in your derivation is fundamental.

 

[Tach]

Tach, there is no question posed in post 119.
I'm also a little concerned over your impatience.

I pointed out a fatal flaw and I gave you the reference to the condition your derivation fails. That is the question you need to address FIRST.

Don't you agree that it is important that we both understand how to transform vectors?

Sure, and I gave you references, I also explained the various approaches in great detail. Problem is, the flaw in your derivation transcends vector transformation.

 

[Pete]

With your permission, I will edit the tracking list in[post=2895831]post 121[/post] to mark:
3.1.1 Lorentz transformation of vectors as Complete
3.1.3 Angle between surface and velocity in the low velocity limit (Galilean spacetime) as Active

3.1.3.1 Rindler's proof of angle invariance as Active​

 

[Tach]

With your permission, I will edit the tracking list in[post=2895831]post 121[/post] to mark:
3.1.1 Lorentz transformation of vectors as Complete

With the caveat that the transformation for displacement vectors is clearly dependent on the condition of simultaneity. A different result is obtained for different conditions of simultaneity. Yet a different result is obtained when no condition is imposed.

3.1.3 Angle between surface and velocity in the low velocity limit (Galilean spacetime) as Active

3.1.3.1 Rindler's proof of angle invariance as Active​

ok.

 

[James R]

Pete:

Regarding adherence to the agreed rules, I'm not sure what it is exactly that you want arbitration about. Is there still an issue? If so, what is it? And what outcome are you seeking?

----

Comment on the debate:

I already explained to you how the answer depends on the simultaneity condition. It all depends in which frame you mark the endpoints simultaneously. I prefer the condition since it (re)produces the longitudinal length contraction. Moller's doesn't.

Since Tach was the first to bring Moller into the discussion, I can only wonder why Tach would want to rely on a source he considers flawed or substandard. :shrug:

 

[Pete]

With the caveat...

So, not complete. I'll mark it "Pending."

... that the transformation for displacement vectors is clearly dependent on the condition of simultaneity. A different result is obtained for different conditions of simultaneity. Yet a different result is obtained when no condition is imposed.

That can go in the debate thread if/when we return to that topic.

 

[Pete]

Pete:

Regarding adherence to the agreed rules, I'm not sure what it is exactly that you want arbitration about. Is there still an issue? If so, what is it? And what outcome are you seeking?

The issue has passed, thanks.

 

[Pete]

With your permission, I will edit the tracking list in[post=2895831]post 121[/post] to mark:
3.1.1 Lorentz transformation of vectors as Complete
3.1.3 Angle between surface and velocity in the low velocity limit (Galilean spacetime) as Active

3.1.3.1 Rindler's proof of angle invariance as Active​

I can't edit that post anyway. It can wait for the next page.

 

[Tach]

So, not complete. I'll mark it "Pending."

Excellent, I just posted an explanation.

 

[Pete]

I've replied.
I don't think we disagree on how to transform vectors.
I think the issue is specifically with how to transform the tangent $$\hat{P_t}(t)$$ transforms to the tangent $$\hat{P_t}'(t')$$, so I'd like to start that as a new subissue.

 

[Tach]

I've replied.
I don't think we disagree on how to transform vectors.
I think the issue is specifically with how to transform the tangent $$\hat{P_t}(t)$$ transforms to the tangent $$\hat{P_t}'(t')$$, so I'd like to start that as a new subissue.

I agree, it narrows down to this particular sub-issue. I have responded.

 

[Pete]

It seems we're now focused on the general Lorentz transform for displacement vectors.

 

[Tach]

It seems we're now focused on the general Lorentz transform for displacement vectors.

Yes. More exactly on the transformation of non-stationary vectors.

 

[Pete]

No, displacement vectors in general.

 

[James R]

In order to get the formula for a displacement vector you need to subtract two position vectors, which means that you need to differentiate.

This is nonsense. Essentially:

$$\Delta r = r_1 - r_2$$

And dr is just the limit of this as the difference between the two displacement vectors becomes infinitesimal.

There's no differentiation involved here.