Scaling - Inverse relationship between uncertainty and mass

[bhobba]

The Kindle version of this book is only $10.44 so I bought it for my library.

That reminded me - I have been meaning to get a copy as well and just got the Kindle edition.

I read a lot of more advanced texts on QM but enjoy those at a more elementary level.

Thanks
Bill

 

[Dave1939]

Broadly yes. But its not from 'scaling' - which I don't understand your meaning of. It's because objects in the everyday world are constantly observed and decohered by the environment.

Bill, I think you are owed an explanation of what I mean by scaling. What follows is a few quotes and a paraphrasing of Brian Greene’s comments on page 97 of The Fabric of the Cosmos.

The uncertainty as to momentum and location of an electron and that of a car are vastly different. The Heisenberg principle not only declares the uncertainty of knowing anything about an electron’s momentum when its position is known, “it also specifies - with complete certainty - the minimum amount of uncertainty in any situation”. I take this to mean that at the macroscopic scale we can know both momentum and location with negligible uncertainty. Hence, uncertainty is a function of scale or as you say environment; things like the electron are clearly subject to the uncertainty principle and things like a car, not so much - scaling.

As to the scaling connection to the inverse relationship between mass and uncertainty, the mass of an electron is magnitudes of difference from that of a car. To illustrate this, Green says: “In day-to-day life we routinely speak about things like a car passing a particular stop sign (position) while traveling at 90 miles per hour (velocity).” He goes on to say, I paraphrase, such talk has no precise meaning in QM as we cannot simultaneously measure a definite speed and a definite position. Yet, we get away with this technically incorrect statement because on macroscopic scales the amount of uncertainty is tiny and generally unnoticed or unfelt. He says the position of the speeding car as it passes the stop sign is known within a centimeter and the uncertainty in speed is just shy of a billionth of a billionth of a billionth of a billionth of a mile per hour.

To consider what happens on microscopic scales, replace the massive car with an almost massless electron having a known position within a billionth of a meter (almost certain), then the uncertainty in its speed would be a whopping 100,000 miles per hour. Scaling changes the amount of uncertainty we get when measuring things; on microscopic scales it is very apparent but this is not the case on macroscopic scales. In Greene's own words: "Uncertainty is always present, but it becomes significant only on microscopic scales.

This is probably another example of a physicist writing for a popular audience who sacrifices exactness for simplicity but surely not, I hope, to the extent of saying something that is wrong. Probably, like Prof Wolfson, it is a reasonable approximation of uncertainty that is good enough for philosophers but not physics students.