Course:

Interesting topics

Mathematics

Particle theory

Standard model

Freedom to address topics of interest

Impossible to address everything

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Syllabus (grading)

Text

Expectations:

  • Hard work (interesting physics! Need time on topic)
  •  

 

This is a good time to review what are the basic ingredients in a theory.  We search for the fundamental rules and properties that govern our world but what do we mean by this statement or at least how do we identify “fundamental”.

 

Your first assignment due on Thursday will be to review physics as you know it and list what you consider to be the fundamental formulation.

 

Not fundamental

  1. Maxwell’s equation can be formulated as integral equations or differential equations.

The formulations above are equivalent and one is no more fundamental than the other to me. Of course an argument could be made perhaps for either case.

 

  1. There is probably no fundamental reference frame. Perhaps what is fundamental is this lack of an absolute reference. This notion is one of the fundamental tenets of relativity.  We will discuss the nature of systems that have this property.

 

SYMMETRY:

When an object possesses the property that you can change something without any detectable change in the object then that object possesses symmetry.  If you can choose a new origin and there are no changes in the laws of physics then you theory is symmetric with respect to translations.

 

Are waves a fundamental aspect of classical physics?

 

NO!

 

In classical physics you build a medium from the basic elements of your theory and then consider the behavior of the medium.  If the medium is bound together or governed by spring forces (restoring forces that grow linearly as one moves away from equilibrium, spring forces) then the medium will exhibit wave behavior.  Disturbances will propagate in the medium as waves.

 

 

Vector calculus, Einstein summation conventions, partial derivatives … ? [Be sure you ask questions about notation and mathematics.]

 

 represents the disturbance as the point at time.

 

 

 

.  One typically derives the wave equation for a disturbance on a string by examining infinitesimal mass elements and the forces between them. 

 

see  http://hyperphysics.phy-astr.gsu.edu/hbase/waves/waveq.html

Assume conditions such that there is no motion along the string only up and down movement

then:

is the equilibrium tension for the rope at rest.

 and  are the tensions resulting from the disturbance.

The difference between the vertical forces results in an acceleration.

 

Divide by

 

is the equilibrium tension for the rope at rest.

Assume

Total force is the sum (where tangent approximates sine for small angles)

This derivation makes the small angle approximation more obvious

 

 

What is remarkable is that the medium transmits force in such a way that each element in this case a rope segment is lifted by the forces on each side then returned to its initial location is such a manner that the segment has zero velocity exactly at the moment it reaches its initial position.

 

Even though the wave equation was derived considering non fundamental aspects of a systems behavior, one can ask what are the fundamental features of waves and as stated these do appear to be characteristics that describe the most basic behaviors if quantum mechanics is correct.