tag:blogger.com,1999:blog-8883034.post110805079360539768..comments2024-03-23T23:26:40.813+01:00Comments on atdotde: Things and NumbersRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-8883034.post-1108145325192997542005-02-11T19:08:00.000+01:002005-02-11T19:08:00.000+01:00I've always enjoyed that Feynman story too.
The r...I've always enjoyed that Feynman story too.<br /><br />The reason it was completely idiotic to add the temperatures of those stars is that (I bet) they were measured in Celsius or Fahrenheit. In these systems, the "zero" of temperature is a highly arbitrary thing: the melting point of water in Celsius, and the coldest possible liquid salt-water mixture in the case of Fahrenheit. <br /><br />So, addition of temperatures in these systems has the curious property of depending on complicated facts of chemistry.<br /><br />It makes more sense to add temperatures in Kelvin, because the zero is not such an arbitrary thing. <br /><br />As you note, temperature starts out being a mere ordered set, defined by the property that T < T' iff a body<br />of temperature T' will transfer heat energy to a body of temperature T.<br /><br />However, more sophisticated laws of physics make it sensible to subtract<br />temperatures, and ultimately to make <br />temperatures into an affine space.<br /><br />The laws of physics concerning absolute zero give this torsor a preferred origin, making it into a 1-dimensional vector space. <br /><br />It takes even more work to make this 1-dimensional vector space into a copy of the real numbers: for that we need a preferred "1" of temperature, e.g. the Planck temperature.<br /><br />It would be fun to work out all the details. Some philosopher of physics should have done it. I don't know if any has, but there has been a lot of careful work on the foundations of thermodynamics.John Baezhttps://www.blogger.com/profile/11573268162105600948noreply@blogger.com