/sci/ - Science & Math » Thread #13919669

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Anonymous Fri 03 Dec 18:29:37 2021 No.13919669 View Reply Original Report

Quoted By: >>13919798 >>13919837 >>13920014 >>13920704

Is it ok to cancel the r vectors like this?

The algebra works but it feels like cheating.

Anonymous

Anonymous Fri 03 Dec 2021 18:35:06 No.13919702 Report

Quoted By:

yes but actually no

Anonymous

Anonymous Fri 03 Dec 2021 18:44:19 No.13919748 Report

Quoted By:

Yes of you are a physicist. No if you are a mathematician.

OP Fri 03 Dec 2021 18:54:14 No.13919798 Report

Quoted By:

>>13919669
I would say yes

Anonymous

Anonymous Fri 03 Dec 2021 18:55:16 No.13919807 Report

Quoted By:

I would say yes

Anonymous

Anonymous Fri 03 Dec 2021 19:00:08 No.13919837 Report

Quoted By: >>13919887 >>13920024

>>13919669
Chain rule

Anonymous

Anonymous Fri 03 Dec 2021 19:10:17 No.13919887 Report

Quoted By: >>13919903 >>13920024

>>13919837
This. The operation is fully legal even for strict mathematicians, because it is not an algebraic cancellation, it is the reverse of the chain rule.

(there is an assumption, that r is a one-to-one function of the coordinates, etc)

Anonymous

Anonymous Fri 03 Dec 2021 19:13:14 No.13919903 Report

Quoted By: >>13919920 >>13920024

>>13919887

But it's a dot product, not a summation of terms.

Anonymous

Anonymous Fri 03 Dec 2021 19:17:00 No.13919920 Report

Quoted By: >>13919934 >>13920024

>>13919903
Anon...what is a dot product?

Anonymous

Anonymous Fri 03 Dec 2021 19:20:41 No.13919934 Report

Quoted By: >>13919994 >>13920024

>>13919920

the product of the length of two vectors and the cosine of the angle between them.

If you expand the equation in the pic into components to try and evaluate the dot product it doesn't get you anywhere. The algebraic cancellations get you back to where you started. Try it.

Anonymous

Anonymous Fri 03 Dec 2021 19:36:07 No.13919994 Report

Quoted By:

>>13919934
You get the Kronecker delta, try it again.

Anonymous

Anonymous Fri 03 Dec 2021 19:41:43 No.13920014 Report

Quoted By:

>>13919669
>he fell for the relativity meme
ngmi

Anonymous

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Anonymous Fri 03 Dec 2021 19:45:17 No.13920024 Report

Quoted By:

>>13919837
>>13919887
>>13919903
>>13919920
>>13919934
Is pic related true?

Anonymous

Anonymous Fri 03 Dec 2021 19:45:29 No.13920026 Report

Quoted By:

You cannot formally do that. You need to be careful, and naive cancellations like this in GR will make you get the wrong answers.

Anonymous

Anonymous Fri 03 Dec 2021 22:31:26 No.13920704 Report

Quoted By:

>>13919669
I have no idea but I use exact same arrows and notes in MS Paint.

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