So I went to my bookshelf and started looking in Harold McGee's wonderful On Food and Cooking (a book that should be on every serious cook's shelf) to find out what was going on with the cloudy egg white.
A cloudy white, it turns out, is actually a sign of freshness. Take it away Harold McGee:
...the moment the egg leaves the hen, it begins to deteriorate in important ways. There is a fundamental chemical change: both the yolk and the white get more alkaline (less acidic) with time. This is because the egg contains carbon dioxide, which takes the form of carbonic acid when it's dissolved in the white and yolk, but is slowly lost in the gaseous form through the pores in the shell....
The alkalinzation of the white has highly visible consequences. Because albumen proteins at the pH of a fresh egg tend to cluster in masses large enough to deflect light rays, the white of a fresh egg is indeed cloudily white. In more alkaline conditions these proteins repel each other rather than cluster, so the white of an older egg tends to be clear, not cloudy. And the white gets progressively more runny with time: the proportion of thick albumen to thin, initially about 60% to 40%, falls below 50-50.
Random link from the archive: April 18, 1906
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