Topics: Special relativity, Spacetime, Lorentz transformation Pages: 12 (2321 words) Published: April 3, 2014
Modern Physics

Fall/Winter 1900, Max Planck’s paper “Ueber das Gesetz der Energieverteilung im Normalspectrum”, Annalen der Physik IV, 553 (1901) – peak in 1920s/30s

Two major parts: modern relativity, first 4 - 6 lectures

Quantum mechanics and its applications, rest of the course –also main content of Phys 312 to follow next quarter ----------------------------------------------------------

What is Physics all about?

concepts and their connection, i.e. mathematically formulated equations/laws,

concepts and laws are derived from interplay between theory and experiment, this makes sure only good theories survive and theories get better over time

some “fundamental” concepts such as space and time are much older than Physics and are sort of common sense knowledge (Kant’s “a priori” concepts) and may even be inherited genetically

but: Werner Heisenberg (in Physics and Philosophy)

“Any concepts or words which we have formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning; that is to say, we do not know exactly how far they will help us in finding our way in the world. ... This is true even of the simplest and most general concepts like “existence” and “space and time”…

The concepts may, however, be sharply defined with regard to their connections. This is actually the fact when the concepts become a part of a system of axioms and definition which can be expressed consistently by a mathematical scheme. Such a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. …

So modern physics will be in large parts contrary to our intuition because it deals with the very fast, i.e. speeds comparable to the speed of light and the very small, atoms, molecules, elemental particles.

Our (possibly inherited) lack of appreciation that the world of the very fast and the world of the very small may well be very different from the world we are used to makes modern physics difficult to comprehend, but Heisenberg showed the way, see above, we have to stick to the mathematical schemes that connect concepts and have to redefine well known concepts, such as space, time, causality, … to fit these schemes Relativistic Mechanics - Special Relativity

Galileo, Newton: Inertial reference frame:
Newton’s (first) law: a body continues to be at rest or continues moving with constant velocity if there is no net force acting on it

v = 0 or constant if


m = inertia, that is where the reference frame gets its name from

Galileo, Newton: all laws of mechanics are the same in inertial reference frames, all reference frames are equally valid, there is no preferred inertial reference frame – classical concept of relativity

Classic relations between an event as observed in two different (v = 0, v’ > 0) inertial reference frames are related by Galilean transformation

Galilean transformations

two different sets of coordinates: space coordinates (x,y,z), time coordinate t at rest; (x’,y’,z’;t’) in motion

x = x’ + v tx’ = x – v t

y = y’y’ = y

z = z’z’ = z

t = t’t’ = t ,

event has one set of coordinates in one system and another set of coordinates in another system

(back transformation are the same except for sign of v)

leads to vector addition law of velocities, if event moves in unprimed frame with velocity u, v and u add up

ux = = = =

ux = ux‘ + v

uy = uy’

uz = uz’

Nota Bene: space and time coordinates do not mix,
importance of these equation is that they ensure the physical laws that are invariant with respect to these equations are valid everywhere and at all times (if we use our common sense ideas of space and time)

Result of Galileian relativity: there is no mechanical experiment that can detect absolute motion, you can eat your dinner in an air plane (when it is not...
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