Guide to the Cosmos

 Making the Wonders of our Universe Accessible to Everyone

Happy Birthday to:

General Relativity & Feynman Simplified



I am greatly relieved to announce that Feynman Simplified has finally been delivered after 22 months of hard labor. I thank my tireless and ruthless editor, my beautiful bride (of 46 years), Joan Piccioni.


Feynman Simplified brings Feynman’s genius and comprehensive understanding of nature to a broader audience: those who don’t walk on water. This is Real Science for Real People. You can view the selection on our website. So far, over 5,000 Feynman Simplified eBooks have been purchased.



As 2015 draws to a close, we also celebrate the one hundredth anniversary of Einstein’s greatest achievement: the General Theory of Relativity.




General relativity is the most profound theory of physics, and is regarded by many as the greatest achievement of a single human mind. It precisely describes the motion of any object, with any velocity, and with any acceleration. General relativity is a comprehensive theory of gravity, energy, space and time. It enables us to understand the universe, and its most exotic denizens: neutrons stars, black holes, and quasars.


Ten years earlier, Einstein published his special theory of relativity. This theory is “special” in that it applies only to an especially simple situation: motion at a constant velocity.  Special relativity properly describes an enormous range of natural phenomena, and is the most extensively and precisely tested principle in science. But it cannot describe objects accelerated by forces, such as gravity.






Special relativity supersedes Newton’s laws of motion, whereas general relativity supersedes Newton’s theory of gravity — both gold standards of science for over two hundred years.






Einstein excelled in describing profound truths with simple equations, the most famous being E=mc2. For general relativity, the field equation is:


G = 8π T


Here, G represents the geometry of the universe, the curvature of spacetime, and T represents everything in the universe, matter and energy. This equation says:



Matter and energy tell spacetime how to curve;
spacetime tells matter and energy how to move.


Newton said space and time are absolute, autonomous, and eternally immutable. Einstein said space and time are dynamic, eternally changing, and definable only in relation to something else.


For Newton, space and time are like a Shakespearean stage upon which the actors, mass and energy, play their parts. For Einstein, spacetime is like a Cirque du Soleil stage that plays an active role in the drama of the cosmos.


With precise space-telescope measurements, general relativity yields this simple equation for the evolution of our universe:


3 H2 = 8π ε


Here, H is the Hubble expansion rate, and ε is the density of all forms of energy, including light, normal matter, dark matter, and dark energy. With measured values of H and ε, we can calculate how the universe has grown in the past, and what its future will be.


Since the universe is now expanding, we know that H is now greater than zero.  And since ε is never zero, H can never be zero — H can never pass through zero and change from positive to negative.


Looking to the future, this means our universe will always expand, and will never collapse into a Big Crunch.


Now let’s look back into the past to see where we came from. Imagine that we had a movie of our universe from long ago to today, and that we can play that movie backwards, so that the cosmic clock spins in reverse. We would see a universe that is always contracting — always, that is, until its size becomes zero.


This means our universe must have had a beginning, a Big Bang, an instant when everything and everywhere was contained within a tiny ball of almost zero size. From the latest satellite data, we know that instant was 13.82 billion years ago, with an uncertainty of ±0.05 billion years.


One last juicy morsel: general relativity says two massive stars orbiting one another must emit energy in the form of gravity waves, ripples in the fabric of spacetime. That continuous energy loss causes the stars to orbit ever closer, and eventually merge.


Sixty years after Einstein published general relativity, Russell Hulse and Joseph Taylor observed two neutron stars orbiting one another once every 8 hours. Over the next 30 years, astronomers have observed this 8-hour orbital period slowly decreasing as the neutron stars move closer together. The measured rate of change of the orbital period is 76.5±0.8 seconds per million years.


For these neutron stars, general relativity predicts an orbital period change of 75.8 seconds per million years.


This graph illustrates the excellent agreement between measurements (black dots with uncertainty bars), and general relativity (parabolic curve).



Seventeen years before the discovery of the neutron, and 52 years before the first observation of a neutron star, Einstein sat at his desk, with only paper and pen, and conceived the theory that precisely predicts a completely unexpected phenomenon occurring 120,000 trillion miles from Earth.


This is a stunning demonstration of the power of the human mind.




Best Regards,



Dec 15, 2015


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