Equation 78 · Part 1 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol m_rm op

m_{\rm op}

m_{\rm op}

What this part means

$m_r$ m op is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

$m_r$ m op is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol m_rm opArticle meaning

The passage around this formula

Two degenerate limits of the proper-time form confirm the derivative is doing the right job rather than hiding a division problem. As m $\to$ 0 , $\Delta$ $\phi$ $\to$ 0 at every fixed $\Delta$ $\tau$ , so the slope — and therefore $m_{\rm op}$ — vanishes identically: a massless worldline is exactly the case with no proper time to speak of in the first place, and the formula correctly returns nothing to divide. And if the two branches are held at equal proper time, $\Delta$ $\tau$ =0 , then $\Delta$ $\phi$ =0 regardless of m ; a single…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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