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This is an excerpt from “The Best Mind since Einstein” by Christopher Sykes.

The original clip is part of the Cornell Lectures archive.

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Sagan briefly describes the course of evolution from the beginning of life to the present.

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SPECIAL RELATIVITY

Special relativity is a theory of the structure of spacetime. It was introduced in Albert Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:

1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:

• Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
• Time dilation: Moving clocks are measured to tick more slowly than an observer’s “stationary” clock.
• Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
• Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
• Maximum speed is finite: No physical object or message or field line can travel faster than light.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell’s equations of electromagnetism and introduction to special relativity).

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GENERAL RELATIVITY

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion; an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics.

This is incompatible with classical mechanics and special relativity because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and momentum within it.

Some of the consequences of general relativity are:

• Time goes slower in higher gravitational fields. This is called gravitational time dilation.
• Orbits precess in a way unexpected in Newton’s theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars).
• Rays of light bend in the presence of a gravitational field.
• Frame-dragging, in which a rotating mass “drags along” the space time around it.
• The Universe is expanding, and the far parts of it are moving away from us faster than the speed of light.

Technically, general relativity is a metric theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially.

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Measuring the electromagnetic spectrum

You actually know more about it than you may think! The electromagnetic (EM) spectrum is just a name that scientists give a bunch of types of radiation when they want to talk about them as a group. Radiation is energy that travels and spreads out as it goes– visible light that comes from a lamp in your house and radio waves that come from a radio station are two types of electromagnetic radiation. Other examples of EM radiation are microwaves, infrared and ultraviolet light, X-rays and gamma-rays. Hotter, more energetic objects and events create higher energy radiation than cool objects. Only extremely hot objects or particles moving at very high velocities can create high-energy radiation like X-rays and gamma-rays.

The different types of radiation in the EM spectrum, in order from lowest energy to highest:

Radio: Yes, this is the same kind of energy that radio stations emit into the air for your boom box to capture and turn into your favorite Mozart, Madonna, or Justin Timberlake tunes. But radio waves are also emitted by other things … such as stars and gases in space. You may not be able to dance to what these objects emit, but you can use it to learn what they are made of.

Microwaves: They will cook your popcorn in just a few minutes! Microwaves in space are used by astronomers to learn about the structure of nearby galaxies, and our own Milky Way!

Infrared: Our skin emits infrared light, which is why we can be seen in the dark by someone using night vision goggles. In space, IR light maps the dust between stars.

Visible: Yes, this is the part that our eyes see. Visible radiation is emitted by everything from fireflies to light bulbs to stars … also by fast-moving particles hitting other particles.

Ultraviolet: We know that the Sun is a source of ultraviolet (or UV) radiation, because it is the UV rays that cause our skin to burn! Stars and other “hot” objects in space emit UV radiation.

X-rays: Your doctor uses them to look at your bones and your dentist to look at your teeth. Hot gases in the Universe also emit X-rays .

Gamma-rays: Radioactive materials (some natural and others made by man in things like nuclear power plants) can emit gamma-rays. Big particle accelerators that scientists use to help them understand what matter is made of can sometimes generate gamma-rays. But the biggest gamma-ray generator of all is the Universe! It makes gamma radiation in all kinds of ways.

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At TEDGlobal 2010, author Matt Ridley shows how, throughout history, the engine of human progress has been the meeting and mating of ideas to make new ideas. It’s not important how clever individuals are, he says; what really matters is how smart the collective brain is.

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