PhilDBasket wrote:
Duffy wrote:
So, in conclusion, you are unwilling or unable to explain the added benefit one would get from Carbo Pro. Thanks.
I'm not interested in electrodynamics, however...
Einstein's General Relativity
Einstein's general theory of relativity expanded on the special theory, explained gravity, and predicted phenomena such as black holes and the expanding universe.
The Special and General Theories of Relativity
Einstein published his special theory in 1905 and his general theory in 1916. The
special theory applies when no accelerations are involved and its effects become noticeable near the speed of light. The general theory applies when accelerations are involved and in the presence of strong gravitational fields. It explains gravity in terms of the curvature of four dimensional space-time.
Principle of Equivalence
General relativity is based on the principle of equivalence. The two statements of this principle are logically equivalent; either statement can be used to prove the other.
One statement relates to the concept of mass. Mass enters into Newton's second law, which states that the force needed to accelerate an object is proportional to its mass. This mass, the object's resistance to changing its velocity, is the inertial mass. Mass also enters into Newton's law of gravity. The gravitational force acting between two objects is proportional to their masses. This mass is the gravitational mass.
Is the inertial mass the same as the gravitational mass? Newton assumed that they were. Considering the question before concluding that they were, led Einstein to the general theory. The principle of equivalence states that the inertial mass equals the gravitational mass.
From this statement, it is possible to prove the other statement of this principle: Inertial forces are indistinguishable from gravitational forces. An inertial force is the apparent force felt when in an accelerating reference frame. When a car accelerates, the occupants feel pushed back into their seats. No real force is pushing them, but the car they are sitting in, their reference frame, is accelerating. So they feel an apparent inertial force pushing them back into their seats. The principle of equivalence states that it is not possible to distinguish between inertial forces and gravitational forces.
Light Affected by Gravity
Using the principle of equivalence, Einstein was able to show that light is affected by gravitational forces. To understand Einstein's reasoning, consider two enclosed rooms. One is at rest on the Earth's surface; the other is in space far from any gravitational forces but accelerating at exactly the same rate objects fall near Earth's surface. On Earth, the Earth's gravity causes objects to fall and have weight. In the accelerating room, objects will also fall and apparently have weight because the room is accelerating. It is an accelerating reference frame, so objects in the room experience an inertial force. From the principle of equivalence, it is impossible to distinguish between the gravitational force acting on objects in the room on Earth and the inertial force acting on objects in the accelerating room in space.
Consider a light beam shining across the accelerating room. Because the room is accelerating the light beam will strike the opposite wall slightly lower than its starting level. Inertial forces acts on the light beam. Because they are not distinguishable from gravitational forces the light beam should experience exactly the same effect in the room near Earth's surface. A gravitational force affects a light beam just as an inertial force does.
Geometric Nature of Gravity
Light has no mass, so Newtonian gravity predicts light is not affected by gravity. However Einstein concluded that light is affected by gravity and derived a new theory of gravity.
Einstein visualized gravity as a manifestation of the curvature of space-time - the three space dimensions and a fourth time dimension. Most of us cannot visualize a curvature of four dimensional space-time, so visualize a curved two dimensional rubber sheet. Placing a mass on the rubber sheet curves it downward like space-time curves in the presence of a mass. On such a rubber sheet a small mass can circle around the curvature produced by a large mass, just as planets orbit the Sun. Or a mass can roll straight downward just as an object falls to the Earth.
Einstein explained gravity as a result of the curvature of space-time near the presence of a mass. The differences between general relativity and Newton's law of gravity only become noticeable when the gravitational force is very strong.
So what's in Carbo Pro that's worth 3x the money?
Civilize the mind, but make savage the body.
- Chinese proverb