This stage often ends with the person discovering something new that they would like to explore or developing new ideas to solve the problems they have found. ... Although a Copernican system was much simpler than the Aristotelian, it still had its own problems. ... He proposed, that instead of many systems of circles, the planets moved in an elliptical fashion. ... This allowed for many of the complications caused by the circular system to go away, and involved a much simpler system, which matched relatively well with actual observations. ... With his theory of Gravity, the equations that gov...

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• Has Bibliography

This part of the problem, therefore, will be left for our descendants to solve. ... Through the equations of general relativity, these properties alone determine how space-time is distorted by a region of false vacuum. ... Not so, however, say the equations of general relativity. ... A quantum system can make a discontinuous transition from one configuration to another, even when the system would not normally have enough energy to exist in the intermediate configurations. ...

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• Grade Level: Undergraduate

Applying the Einstein Field Equations to collapsing stars, Kurt Schwarzschild discovered the critical radius for a given mass at which matter would collapse into an infinitely dense state known as a singularity. ... Although many physicists doubted the existence of gravitational waves, physical evidence was presented when American researchers observed a binary pulsar system that was thought to consist of two neutron stars orbiting each other closely and rapidly. ... In other words, the stars were spiraling toward each other, and by the exact amount predicted if the system were losing energy by...

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