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Equation 31 · Part 6 · The Clock That Comes Back Wrong by Exactly Its Mass

multiplication

X=−ib⋅P/ℏX=-i\mathbf b\cdot\mathbf P/\hbar
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

That triviality is what makes the loop phase exact rather than approximate. Write X=-ib\mathbf b⋅\cdotP\mathbf P/ℏ\hbar and Y=-iv\mathbf v⋅\cdotK\mathbf K/ℏ\hbar . Their commutator is

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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