Is frozen milk heavier than liquid milk?

Dear Cecil:

Yesterday one of the men who works in my company's cafeteria was looking in the milk dispenser (one of those things that has milk in plastic bags inside a cardboard container). He told another worker that the milk was frozen. She replied that she wasn't surprised, because it seemed awfully heavy when she put it in there. My question is, does milk really get heavier when it freezes?

Cecil replies:

Well, relativistically speaking, there is less molecular motion in frozen milk (or frozen anything) than there is in liquid milk. Less molecular motion (in ordinary terms, less heat) means less energy, and less heat means less mass according to Einstein’s famous equation E = mc^2 (energy equals mass times the speed of light squared). But to answer your question, there is no humanly detectable difference in the weight of frozen versus liquid milk.

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