Re: Is it true that you cannot measure particles below a certain mass?

Date: Wed Mar 18 15:46:18 1998
Posted By: Dan Berger, Faculty Chemistry/Science, Bluffton College
Area of science: Physics
ID: 890130907.Ph
Message:

Is it true that you cannot measure particles below a certain mass?

I have heard that physicists cannot measure particles below a certain mass because the very act of measuring affects the properties of those particles. Is this true?

No, there is no lower limit on the mass of a particle which may be measured -- as long as you can get the particle to interact with something. There are particles called neutrinos which may or may not have mass; but since it is very hard indeed to get them to interact, they are quite difficult to measure. On the other hand, photons have zero mass, but since they interact quite strongly with matter it's very easy to measure them. You can do it with your eyes.

Actually, it's the really massive particles (other than stable particles like protons and neutrons) which are the mischief to measure, because to generate them one has to pump in literally astronomical quantities of energy. (Mass is a very concentrated form of energy, and sometimes the simplest way to generate a particle is to provide enough energy for it to be created.)

It is true that the very act of measuring affects the properties of ... particles. This was first realized by Werner Heisenberg. His famous gamma-ray microscope thought experiment gave a graphic illustration of his "uncertainty principle."

The Heisenberg Indeterminacy Relation says that, at the microscopic level, there are certain pairs of complementary properties. The more one knows about one of a pair, the less it is possible to know about the other.

One such pair of properties is position and momentum. Mathematically, the relationship is expressed as

(Dx)(Dp) >= h/2p
where Dx is the indeterminacy in position and Dp is the indeterminacy in momentum. h is Planck's constant, which is about 7x10-34 Joule-seconds, so you can see that the uncertainty in measuring either the position or momentum of a normal-sized object will be truly miniscule.

However, the Heisenberg Relation doesn't effect our ability to detect or measure a particle in general; it only limits what we can know about one particular particle. The limiting factor in our ability to measure particles is, rather, how strongly a particle interacts.

The Gamma-Ray Microscope

Heisenberg first recognized that, in order to detect something using electromagnetic radiation, the radiation must have a wavelength l smaller than the size of the object. Thus, optical microscopes cannot resolve objects smaller than about 10-6 meters in size because the wavelengths of visible light are 0.4-0.7x10-6 meters.

Since electrons are very tiny indeed, Heisenberg postulated a microscope which used gamma-rays (l < 10-10 meter). However, since a photon has a momentum inversely proportional to its wavelength

p = hc/l
a gamma-ray photon will have a large momentum relative to an electron. So if a gamma-ray photon hits an electron, said electron will zip off like a scared rabbit, in some unpredictable direction. So you know where it was, or what momentum it had...

A good account of the gamma-ray microscope can be found in Baggott's The Meaning of Quantum Theory, published by Oxford University Press.

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