Newtonian Physics What Is Physics?

⚫ The main proposition of science is that the universe can be understood in terms of natural laws. The origin of these laws is not a subject of modern science, but may become a subject of science some day in the future.

⚫ Scientists call “physical” anything that can be objectively observed or measured (at least in principle). Coordinates

⚫ Both space and time are physical, we can measure them using “clocks” and “rulers”.

⚫ Any spatial position can be characterized by three numbers - coordinates. They are usually denoted by letters x, y, and z. Time is represented by the letter t.

⚫ Thus, any point in space at every instant in time - an event - can be fully described by four numbers: (x,y,z,t). World Lines

Time Me goingto the right(anduptime) in Me goingto the(and left in up time) Space goinginup time) Me standing(still World Lines

time World line: moving forward in time moving anywhere in space

space Frame of Reference

⚫ Different observers may have different sets of coordinates (x,y,z,t). A set of coordinates specific to a particular observer is called a frame of reference. ⚫ Not all frames of reference are equal. There is a special subset of all possible frames of reference called inertial reference frames. They are associated with observers that move freely, with no external force acting on them. Inertial Forces

⚫ In the non-inertial frame of reference there appear ”fictitious” forces such as centrifugal and Coriolis forces. These forces are called inertial forces.

⚫ These forces are fictitious in a sense that there is no physical interaction responsible for these forces. However, a person in a non-inertial frame of reference will feel them quite real! Coriolis Force Centrifugal Force

⚫ The Second Law of Newton looks very different in inertial and non-inertial reference frames!

⚫ In the inertial frame of reference:

⚫ In the non-inertial frame of reference: Kepler’s Laws of Planetary Motion

⚫ Kepler figured out how planets move: 1. Planets orbit the Sun in an ellipse, with the Sun at one focus. 2. The line from the Sun to the planet sweeps out an equal area in an equal time. Thus, planets move faster when they are nearer the Sun. 3. The square of the period of the orbit is equal to the cube of the semimajor axis of the ellipse: P2 = R3. Kepler’s First and Second Laws Kepler’s Laws Made Easy

⚫ First Law:

Solution of this equation is the ellipse. There is no deep physics there, just math. ⚫ Second Law:

When R is smaller, V is larger – planets move faster when they are closer to the Sun. Kepler’s Third Law

Period for a circular orbit:

Plug this into the last equation from the previous slide, and we get:

If we measure P in years and R in AU, then 2 GM = 4 Galilean Relativity

⚫ A physical quality is said to be: invariant, if different inertial observers would obtain the same result from a measurement of this quantity. Example: the mass of an object. relative, if different inertial observers would obtain different result from a measurement of this quantity. Example: the speed of an object.

⚫ Question: is color relative or absolute? Galilean Relativity Galilean Relativity

⚫ The principle of Galilean relativity states that Newton's laws of motion are the same in all inertial frames of reference.

⚫ Until about 1860s, the Newtonian physics was considered complete, giving the ultimate and final description of the universe. (Recall, what Aristotle thought about his teaching?) James Maxwell (1831 – 1879)

⚫ Finalized the work of others on electricity and magnetism. ⚫ He formulated Maxwell Equations for the electromagnetic field. ⚫ His equations predicted the existence of electromagnetic waves that propagated with the speed of light. “The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.” Maxwell Equations Electromagnetic waves

⚫ They propagate in vacuum. ⚫ Waves of different frequencies move with the same speed, the speed of light c.

c = 299,792,458 m/s = 1,079,252,849 km/h Electromagnetic spectrum Speed of Light

⚫ In Maxwell's theory the speed of light is the same in all reference frames, i.e. it is invariant, rather than relative. However, the principle of Galilean invariance states that the speed of anything, including light, is a relative quantity. ⚫ The notion of waves propagating all by themselves, rather than in some medium (like sound waves in the air, ocean waves on the surface of the ocean etc) was also unusual to scientists, and thus disturbing. Ether is Back

⚫ A resolution was quickly discovered: light was propagating not by itself, but in a special medium called luminiferous ether. So, the ether came back. ⚫ The luminiferous ether had no other reason for its existence than to provide the expected medium for the propagation of light. ⚫ Ether was massless and invisible. It could not be directly detected in the lab. Ether is Back

⚫ It was generally assumed that the Maxwell equations were valid only in the frame of reference of this ether. Thus, the speed of light was equal to c = 299,792,458 m/s only in the ether frame of reference. ⚫ In other inertial frames it would be different according to the principle of Galilean invariance. In particular, it should be different on the Earth which moves through the ether. ⚫ There was also a problem with magnetic field lines – check Thorne’s book. Michelson-Morley experiment

In 1887, two American physicists, Albert Michelson and Edward Morley set out to measure the motion of the Earth with respect to the ether. Michelson-Morley experiment

(remember this design, we will meet it again!) Michelson-Morley experiment

⚫ The result of their experiment was negative. They found that the speed of light along the Earth orbital direction was the same as the speed of light perpendicular to the Earth orbital direction to within 5 km/s (the accuracy of their measurement). ⚫ Since the Earth orbital speed is about 30 km/s, the experiment clearly demonstrated that the speed of light was the same in all reference frames, in a clear contradiction to the principle of Galilean invariance. The ether was gone! ⚫ Michelson still got his Nobel prize, though – he also was the first chair of the Physics Dept. at UChicago. The End of Classical Physics

⚫ Another problem with the standard physics was explaining the radiation of a parcel of highly heated gas, the so called blackbody radiation.

⚫ From these two small “clouds” on a clean horizon of XIX century physics two hurricanes came: Einstein's theory of relativity and quantum mechanics.