Werner Heisenberg developed the uncertainty principle, which states that the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa. This stems from the quantum nature of matter, where measuring devices disturb the system being measured. A thought experiment is described where observing an electron's position with a photon impacts the electron's momentum in an unpredictable way. The uncertainty principle is expressed as ΔxΔp≥h/2π, meaning the product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 2π.

1. THE UNCERTAINTY
PRINCIPLE
Cruz. Dy. Espiritu
Physics Reporting
4th Quarter

2. THE UNCERTAINTY PRINCIPLE
Name: Werner Heisenberg (1901-
1976)
+Made many significant contributions
to physics, like the Uncertainty
Principle (this won the Nobel Prize in
1932).
+Developed an abstract model of
quantum mechanics called matrix
mechanics.
+Predicted two forms of molecular
hydrogen, and theoretical models of
the nucleus.

3. THE UNCERTAINTY PRINCIPLE
• If you were to measure the position and speed of a particle at
any instant, you would always be faced with experimental
uncertainties in your experiments.
• Based on classical mechanics, no fundamental barrier to an
ultimate refinement of the apparatus or experimental
procedure exists. This means that it is possible, in principle, to
make such measurements with arbitrarily small uncertainty.
Quantum theory however, predicts that such a barrier exists.
This is best explained by the Heisenberg uncertainty principle.

4. THE UNCERTAINTY PRINCIPLE
• If a measurement of position is made with precision dx and a
simultaneous measurement of linear momentum is made with
precision dpx, then the product of the two uncertainties can never be
smaller than h/2
where h=h/2pi.
Thus, it is physically impossible to measure simultaneously the exact
position and exact linear momentum of a particle, due to the inverse
relationship between dx and dpx.

5. THE UNCERTAINTY PRINCIPLE
• This stems not from imperfections in
measuring instruments, but rather from
the quantum structure of matter---
From effects such as the unpredictable
recoil of an electron when struck by a
photon or the diffraction of light or
electrons through a slit.

6. THE UNCERTAINTY PRINCIPLE
• Here's a thought experiment:
Suppose you wanted to measure the position and linear momentum of an
electron as accurately as possible. You might be able to do this by viewing
the electron with a powerful light microscope. For you to be able to see the
electron and thus determine its location, at least one photon of light must
bounce off the electron, and pass through the microscope into your eye.
But when it strikes the electron, the photon imparts some unknown amount of
its momentum to the electron. Thus, in the process of your locating the
electron very accurately, that is, making dxvery small by using a light with
short wavelength (which has high momentum)---the very light that allows you
to succeed changes the electron's momentum to some undeterminable
extent (making dpxvery great).

7. THE UNCERTAINTY PRINCIPLE
• In analyzing the collision, note that the incoming photon has momentum h/pi. As a
result of the collision, the photon transfers part of all of its momentum along the
x-axis to the electron. Thus, the uncertainty in the electron's momentum after the
collision is as great as the momentum of the incoming photon: dpx = h/pi.
• Furthermore, since the photon also has wave properties, we expect to be able to
determine its position to within one wavelength of the light being used to view it,
so dx = lambda.
• Multiplying these two uncertainties gives: dx * dpx = lambda (h/lambda) = h. The
value h represents the minimum in the products of the uncertainties. Because the
uncertainty can always be greater than this minimum, we have:dx * dpx>= h. Apart
from the numerical factor 1/4pi introduced by Heisenberg's more precise analysis,
this agrees with

8. THE UNCERTAINTY PRINCIPLE
• In summary, the Heisenberg Uncertainty Principle is applied such that the better
you know that position of a particle, the less you know about its momentum. This
goes vice versa. To put it into a equation,
• Dx is the measurement uncertainty in the particle's x position. Dpxis its measurement
uncertainty in its momentum (recall: mass*velocity or kg*m/s) in thex direction and
• This relation holds true for all three dimensions. Therefore:

9. References
• John Wiley &Sons Inc. (2012). Quantum Physics and
the Heisenberg Uncertainty Principle. Retrieved from
http://www.dummies.com/how-
to/content/quantum-physics-and-the-heisenberg-
uncertainty-pri.html
• Serway, R.A. &Beichner, R.J. (1982). Physics For
Scientists and Engineers with Modern Physics 5th
Edition. Saunders College Publishing: Florida,
Orlando.