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I’d like to describe the length of the question text. I’m fairly certain that is not outside the realm of physics, however if I measure it in “bytes” it’s not clear to me how to convert that to SI units.

My best guess would be to find the temperature $T$ of the hard drives where copies of this string are (it gets sent from the Stack Exchange server over EM waves to the antenna on my phone, then stored locally on the hard drive, then transmitted via light in the visual range from my screen to the cameras in my head [my eyes!], then stored locally in my brain), and get a bound using Landauer’s limit $kT\ln(2)$ for the minimum energy it takes to erase one of those bits.

If the length of this string can’t be measured in SI units, is it outside the realm of physics? Another way to phrase this question is why, exactly, isn’t “bit” an SI unit directly, and does that imply that physicists are not yet ready to admit that information is part of the physical world?

Qmechanic
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Jackson Walters
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1 Answers1

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SI units are specified for physical measurement, and are 'international' partly because of trade practicalities.

Bytes, and bits, measure information; the "length of this question" might be a count of symbols, which would be an integer. Or, could be an information measure (bits) after compression with a language-aware compression algorithm. Both are meaningful length measures, and other than mathematical precision, do not have to respond to any authority (such as Systeme Internationale).

The "length of this question" could also be the pixel count of a 7x9 array for each of the characters in that text. As I sit here reading the question, that's the minimum info required to render it on a screen; the actual info for a color screen is higher by a factor of 24, 30, or 36 depending on the DVI system version.

SI offers no guidance on which of these measures is correct.

Whit3rd
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