I get email, Part 2

I awoke this morning to one of the more charming pieces of email that I’ve gotten in some time.  I won’t quote it in its entirety, as it was incredibly long, but it was also packed with goodness.  A reader named Meir had just finished the “User’s Guide” and he had some questions: ten of them, actually.   And these were some damn good ones.  Although not necessarily appropriate for the “Ask a Physicist” column (several of them have either short answers or are too philosophical for my “just the facts” style column), I thought it might be fun to address some of Meir’s questions here.   Let’s begin at the beginning:

1. (p. 53) I am trying to understand if the Uncertainty Principle is an observational phenomenon, or a law of nature derived from some deeper principles. If I came up with a new type of detector, perhaps not using photons to query particles, and I claim that my detector can do better than the Uncertainty Principle, would you look at it, or would you just shrug and say “we don’t know where your error lies, but we do know that it contradict the Uncertainty Principle, so we know there is some error”, much the way you would respond to a perpetual motion machine suggestion.

First, can I say how much I love that he puts page references in his questions?  That is just awesome.  But secondly, he gets at a big issue that I’m dealing with in researching my upcoming “Crackpot” book: how much effort is it appropriate to put into deciding someone’s a crackpot?  As a theorist, if I read such a claim by an amateur, I would probably dismiss it out of hand.  I don’t have the particular expertise to figure out what’s wrong with his experiment.

But suppose I got a more theoretical paper, one that, say, purported to derive a theory to replace or overthrow special relativity.  Would I believe it?  I don’t have to guess.  I get emails like that all the time.  And I’ll be honest with you.  I skim through them, notice that the notation bears almost no resemblance to anything a physicist would recognize, remind myself that special relativity has passed every observational test ever thrown at it, and throw the manuscript into my “crackpots” file.

Is that fair?  Maybe not, but the reality is that I don’t have the time to debunk theory after theory, especially when these particular theories (SR and QM) are so successful at predicting observations and experiments that there is no obvious need to overthrow them.

But let me try to answer Meir’s question at a more fundamental level and ask why we believe in the uncertainty principle in the first place.  As a reminder, one of the most basic statements of the uncertainty principle is:

$Delta x Delta p ge frac{hbar}{2}$

Or in words, “the product of the uncertainty of a particle’s position and its momentum must be greater than a certain number.”  Or even simpler,”You can’t measure either the position or momentum of a particle with perfect certainty, let alone both.”

Practically speaking, there will always be some uncertainty in measurement, simply because a device has to truncate decimal places at some point, but Meir is right that it’s not immediately obvious that that is the only limiting factor.  However, there are numerous reasons (I’ll content myself to list just three here), why $hbar$ (the reduced Planck Constant) seems to play the magic role that it does:

• Einstein found that the energy and wavelength of light are related by Planck’s constant.  The uncertainty of light is related to its momentum.
• The double slit experiment shows that both photons and electrons have an uncertainty in their position (e.g. which slit they pass through) that is inversely related to their momentum.
• Observed systems, like hydrogen atoms (and even white dwarves and neutron stars), only work if there is an uncertainty principle at work.  You’d simply get the wrong spectrum otherwise (or if the constant that you plugged in was something other than Planck’s constant).

My point is that it isn’t just a matter of building a contraption that ostensibly measures momentum and position with higher accuracy than predicted by the uncertainty principle; the uncertainty principle (or really the Schroedinger wave equation which predicts the uncertainty principle among much else) is fundamental to so much of what we observe.

But let’s suppose you built such a device, would anyone listen?  Even if they should, they probably wouldn’t.  For the exact same reason that theorists tend not to put too much credence in randomly submitted manuscripts, an experimentalist would be highly suspect of a result sent in from an unknown researcher.

But suppose you were working at NIST and somehow found you could measure a set of complementary variables simultaneously?  That would cause an enormous interest.  Everyone would be reporting it, even if it wasn’t confirmed by other groups.  There would be an enormous motivation for others to repeat your results because essentially, if it were ultimately reproduced, all of quantum mechanics would be overturned.

Look forward to more of Meir’s questions (and you — other readers if you wish to send them) in the near future.

-Dave

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