Quick question, index notation, alternating tensor.

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SUMMARY

The discussion centers on the use of index notation in tensor calculus, specifically demonstrating that ε^{0123} equals -1 given ε_{0123} equals 1. The solution involves the metric tensor g_{\alpha\beta}, where ε^{0123} is expressed as the product of the metric components g^{00}, g^{11}, g^{22}, and g^{33} multiplied by ε_{0123}. The participant seeks clarification on the equality ε^{0123} = -ε_{0123}, confirming that g_{00} is indeed -1, aligning with the Minkowski metric η_{00} = -1.

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Q) I am using index notation to show that ε[itex]^{0123}[/itex]=-1 given that ε[itex]_{0123}[/itex]=1.

The soluton is:

ε[itex]^{0123}[/itex]=g[itex]^{00}[/itex]g[itex]^{11}[/itex]g[itex]^{22}[/itex]g[itex]^{33}[/itex]ε[itex]_{0123}[/itex]=-ε[itex]_{0123}[/itex]

where g[itex]_{\alpha\beta}[/itex] is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.
 
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g00=-1, correct? Really, η00=-1.
 

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