We've just started with this new notation in class and I'm just trying to get a little more insight into the basics so have a few very basic questions if someone here can help?(adsbygoogle = window.adsbygoogle || []).push({});

1)

dx^{μ}= (dt,dx,dy,dz) I understand thats it's just a four-vector with four componants but, what would

dx_{μ}be equal to? the same thing?

2) FREE INDICES what does this term mean? free to do what? i.e.

"A^{μ}A_{μ}is a scalar because you have no free indices"

Do the upper and lower indices pair?

similarly:

"g_{μv}g^{μv}is also a scalar as it has no free indices"

also

"A^{μ}B^{v}has two free indices"

Why because they are not paired, what does all this mean?

Thanks for any points in the right direction.

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# Quick question on "free indices" - four-vector notation

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