Download lesson 6: Heisenberg Uncertainty Principle

Updated: May 2009
Course: SPH4U1
Unit: QUANTUM
LESSON 6: HEISENBERG UNCERTAINTY PRINCIPLE
1. Imagine that you are measuring the temperature of a small quantity (a thimble-full) of hot water with
a thermometer that is very cold. What happens? You will not be able to get an accurate reading
because your measurement changes the object you are measuring.
2. Imagine that you are in a dark room trying to locate a ping pong ball using a metre stick. What
happens? Again, your measurement changes the object you are measuring. You can find the ping
pong ball’s position at a specific time, but not its velocity.
When one measures really small things (on the level of atoms and electrons), the very act of measuring a
quantity (even one photon reflecting off something) disturbs the system and changes that quantity. Thus,
there is a limit to how accurately one can measure something.
(Aside: there seems to be a similar limit in large scale distances – e.g. trying to measure a 1 km distance
to the nearest mm. – temperature changes, … Now, laser range finders seem to work really well …)
Shorter wavelengths can measure the position of object more accurately. But shorter wavelengths mean
more energy, therefore the recoil of the object you are measuring is greater.

Electron microscopes can see smaller objects than light microscopes.

Why is Blu-ray called Blu-ray? Because it uses a blue laser … “to read and write to the disc. In part
because of the shorter wavelength (405 nanometres), substantially more data can be stored on a Bluray Disc than on a standard DVD, which uses a red (650 nm) laser. A dual-layer Blu-ray Disc can
store 50 gigabytes, almost six times the capacity of a dual-layer standard DVD.”1

One of the reasons why computer chips have been able to get smaller is that they are using shorter
wavelengths to draw the pattern on the chips. “Current state-of-the-art photolithography tools use
deep ultraviolet (DUV) light with wavelengths of 248 and 193 nm, which allow minimum feature
sizes down to 50 nm.” 2
Position can be measured to about x  
Now, when an electron or photon hits something, it has momentum of p = h /  .: p = h/
or p = h
h
This is changed to px 
(the two Pi comes from unit corrections between energy and freq.)
2
This is one of the formulas which is used to express Heisenberg’s Uncertainty Principle (1927): The
more precisely one measures the position, the less precisely one can measure the momentum (mass or
velocity), and vice versa.
1
2
From http://en.wikipedia.org/wiki/Blu-ray_Disc
http://en.wikipedia.org/wiki/Photolithography
Alternative formulation:
For a time t, energy may NOT be conserved by and amount E, where Et 
h
2
The delta reflects the error in measuring, but the whole equation is not a statement about the
inaccuracy of measurement instruments. The uncertainty is inherent in the nature of things.
RANGE OF FORCES
If a force involves the exchange of a particle, that particle has to "get back home before it is missed" in
the sense that it must fit within the constraints of the uncertainty principle. A particle of mass m and rest
energy E=mc2 can be exchanged if it does not go outside the bounds of the uncertainty principle in the
form
A particle which can exist only within the constraints of the uncertainty principle is called a "virtual
particle", and the time in the expression above represents the maximum lifetime of the virtual exchange
particle. Since this exchange particle cannot exceed the speed limit of the universe, it cannot travel
further than c times that lifetime. The maximum range of the force would then be on the order of