1. Revision + Notation Flashcards
What is Einstein’s principle of SR?
The laws of physics are the same in all inertial frames of reference
What is always true when you take the product of a covariant and contravariant 4 vector?
It is always invariant
How can you form a covariant 4 vector from a contravariant 4 vector?
Using the metric lowering operator g_mu nu
How are the metric raising and lowering operator different and the same?
They have the same matrix elements
- They are operators, so they have different effects
Describe the space time cone
Events falling inside the cone are time like
Events on the cone are null/light like
Events outside the cone are space like
When can one event be causally related to another event
If and only if the separation squared is time like
Can space like events affect each other, and why?
No as the point x_1 will be outside the light cone of x_2, and information cannot propagate faster than the speed of light
Briefly describe wave-particle duality
Particles have associated de Broglie wavelengths
Briefly describe the wavefunction interpretation
The state of a system is described by a complex values wavefunction
- The square of the magnitude gives the probability density
Briefly describe HUP
The uncertainty princile implies a limit on how well pairs of observables can be known simulataneously
Briefly describe the PEP
No two particles can simultaneously occupy the same quantum state
- Applies to fermions (spin 1/2) but not bosons (spin integer)
Is the SE relativistically invariant, and why?
No it is not
- Use the non relativistic expression for KE in the derivation
- Equation contains second order derivatives wrt the space like coords, but first order derivative wrt time coords (s-t are not on the same footing)
What is the main problem with regular QM?
It fails when the particles become relativistic
When can we consider particles becoming relativistic?
When a particles kinetic energy approaches its rest mass
