Galileo and Einstein Home Page

**G****ALILEO
AND**** E****INSTEIN
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In the ancient port city of *irrational *numbers! The Greeks had some ideas
about elements and atoms. Hippocrates looked for non-supernatural causes of
disease. Plato formulated a rationale for higher education, and thought about
atoms.

A brief review for moderns of facts familiar to almost everybody in the ancient world: how the sun, moon and planets move through the sky over the course of time.

A brief look at the beginnings of science and
philosophy in

We look at some startlingly good measurements by the Greeks of the size of the earth and the distance to the moon, and a less successful (but correct in principle) attempt to find the distance to the sun.

Strato understood that falling bodies pick up speed
(contrary to Aristotle's assertions). Aristarchus gave a completely correct
view of the solar system, anticipating Copernicus by 2,000 years or so. Science
flourished for centuries in

Nailing down the square root of 2. Zeno's paradoxes: Achilles and the tortoise. Proving an arrow can never move - analyzing motion, the beginning of calculus. How Archimedes calculated Pi to impressive accuracy, squared the circle, and did an integral to find the area of a sphere.

The universe is like an onion of crystal spheres: Plato, Eudoxus, Aristotle. More earthly ideas: Eudoxus and Aristarchus. Understanding planetary motion in terms of cycles and epicycles: Hipparchus and Ptolemy. These methods were refined to the point where they gave accurate predictions of planetary positions for centuries (even though Ptolemy believed the earth was at rest at the center of the universe).

How Greek Science Reached Baghdad PDF

Some Later Islamic Science PDF

Copernicus challenged Ptolemy's worldview. Evolution of the telescope. Galileo saw mountains on the moon, and estimated their height - the first indication that the moon was earthlike, not a perfect ethereal sphere at all.

A few facts and anecdotes to try to give something of the flavor of Galileo's life and times, plus references to books for those who would like a more complete picture.

One of Galileo's most important contributions to science (and engineering): the realization that since areas and volumes scale differently when the size of an object is increased keeping all proportions the same, physical properties of large objects may be dramatically different from similar small objects, not just scaled up versions of the same thing. We explore some of the consequences.

Galileo argued against Aristotle's assertions that
falling bodies fall at steady speeds, with heavier objects falling
proportionately faster. Galileo argued that falling bodies* pick up speed at
a steady rate* (until they move so fast that air resistance becomes
important). He constructed an experiment to prove his point (and we reproduced
it).

This lecture presents the core of Galileo's
analysis of motion in free fall, which he referred to as "naturally
accelerated motion". This is challenging material if you're new to it, but
*crucial *in progressing from an Aristotelian or medieval worldview to
that of Galileo and

A simple introduction to the modern way of
describing motion using arrows - "vectors" - to indicate speed and
direction. Galileo (and, later,

These two colorful characters made crucial
contributions to our understanding of the universe: Tycho's observations were
accurate enough for Kepler to discover that the planets moved in *elliptic*
orbits, and find some simple rules about how fast they moved. These became
known as Kepler's Laws, and gave

This lecture links to more detailed lectures I gave previously.

A brief account of

Aristotle thought it was infinite, Galileo tried
unsuccessfully to measure it with lanterns on hilltops, a Danish astronomer
found it first by observing Jupiter's moons. Rival Frenchmen found it quite
accurately about 1850, but a far more precise experiment was carried out in
1879 in

By the late 1800's, it had been established that light was wavelike, and in fact consisted of waving electric and magnetic fields. These fields were thought somehow to be oscillations in a material aether, a transparent, light yet hard substance that filled the universe (since we see light from far away). Michelson devised an experiment to detect the earth's motion through this aether, and the result contributed to the development of special relativity.

Galileo had long ago observed that in a closed windowless room below decks in a smoothly moving ship, it was impossible to do an experiment to tell if the ship really was moving. Physicists call this "Galilean relativity" - the laws of motion are the same in a smoothly moving room (that is to say, one that isn't accelerating)as in a room "at rest". Einstein generalized the notion to include the more recently discovered laws concerning electric and magnetic fields, and hence light. He deduced some surprising consequences, recounted below.

The first amazing consequence of Einstein's seemingly innocuous generalization of Galileo's observation is that time must pass differently for observers moving relative to one another - moving clocks run slow. We show how this comes about, and review the experimental evidence that it really happens. We also show that if times pass differently for different observers, lengths must look different too.

Another essential ingredient in the relativistic
brew is that if I synchronize two clocks at opposite ends of a train I'm on,
say, they will *not *appear to be synchronized to someone on the ground
watching the train go by. (Of course, the discrepancy is tiny at ordinary
speeds, but becomes important for speeds comparable to that of light).

At first sight, it seems impossible that each of two observers can claim the other one's clock runs slow. Surely one of them must be wrong? We give a detailed analysis to demonstrate that this is a perfectly logically consistent situation, when one remembers also to include effects of length contraction and of lack of synchronization - special relativity makes perfect sense!

Some famous paradoxes raised in attempts to show that special relativity was self-contradictory. We show how they were resolved.

An elementary review of these basic concepts in physics, placed here for the convenience of nonscience majors who may be a little rusty on these things, and will need them to appreciate something of what relativity has to say about dynamics - the science of motion.

A straight forward application of the new relativistic concepts of time dilation, length contraction etc., reveals that if you walk at exactly 3 m.p.h. towards the front of a train that's going exactly 60 m.p.h., your speed relative to the ground is not 63 m.p.h. but a very tiny bit less! Again, this difference from common sense is only detectable if one of the speeds is comparable with that of light, but then it becomes very important.

How the very general physical principle of momentum
conservation in collisions, when put together with special relativity, predicts
that an object's mass increases with its speed, and how this startling
prediction has been verified experimentally many times over. The increase in
mass is related to the increase in kinetic energy by *E* = *mc*^{2}.
This formula turns out to be more general: any kind of energy, not just kinetic
energy, is associated with a mass increase in this way. In particular, the
tight binding energies of nuclei, corresponding to the energy released in
nuclear weapons, can be measured simply by weighing nuclei of the elements
involved.