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# General Relativity Theory of Gravitation

by Ron Kurtus (revised 21 February 2011)

In 1915, Albert Einstein formulated the *Theory of General Relativity* as an extension to his *Theory of Special Relativity* and as a new way to explain gravitation.

Newton's *Law of Universal Gravitation* had defined gravitation as a property of matter that is force of attraction acting at a distance. The theory works well for ordinary gravitational fields but is inaccurate when the gravitational intensity is high. Discrepancies were seen when measuring the orbit of the planet Mercury and the effect of gravitation on light.

Einstein's theory states that matter curves space and distorts time, causing objects to move toward each other. The Theory of General Relativity became accepted after it predicted the orientation of Mercury's orbit. However, some scientists see flaws in the Theory of General Relativity, due to phenomena that the theory does not explain, especially at the quantum level.

Questions you may have include:

- What is the relativity theory of gravitation?
- What are predictions proving the concept?
- What are some problems with the relativity explanation?

This lesson will answer those questions. Useful tool: Units Conversion

## Einstein's theory of gravitation

In 1905, Albert Einstein published the *Theory of Special Relativity, *a theory about space and time. In the following years, Einstein had noticed that acceleration produced the same effect as gravitation. For example, if you were in an accelerating spaceship—or even an elevator—you could not tell if the force on you was from inertia or gravitation. This led him to look at the mathematics of relative motion and gravitation.

(

See Artificial Gravity for more on gravitation from acceleration.)

Then in 1915, he unified the Theory of Special Relativity with Newton's Law of Universal Gravitation to establish the *Theory of General Relativity*, which is a geometric explanation of gravitation.

### Curvature of spacetime

While the classical explanation of gravitation is that it is some sort of force-at-a-distance, Einstein took a different approach, stating that matter curves space and distorts time, causing objects to move toward each other. His theory states that time is a fourth dimension, adding to the three dimensions of space. He called this four-dimensional geometry *spacetime*.

Straight lines curve toward mass

In ordinary situations, particles travel along straight lines in this geometry of space, following Newton's laws of motion. However, according to Einstein's theory, matter affects the geometry of spacetime causing it to be curved toward the matter. A particle that is freely moving at a constant velocity will follow such a line toward the object, as if it was attracted by some force.

### Speed of gravitation

Newton's *Law of Universal Gravitation* considered the effects of gravitation to act instantaneously—even over great separations. This meant that the speed of gravitational changes (or *speed of gravitation*) is infinite.

Einstein's equations state that gravitational changes are transmitted at the speed of light, which is the maximum speed for transmitting energy or information. These equations also imply that gravitation can be transmitted as a waveform.

(

See Gravitational Speed for more information.)

### Mathematics complex

Mathematical expression describing the properties of a gravitational field surrounding a given mass is stated in a set of formulas called the *Einstein Field Equations*. They are highly complex a system of partial differential equations, which are beyond the scope of our material. However, the equations reduce to Newton's Universal Gravitation Equation under simple conditions.

## Tests verifying Relativity explanation

The Theory of General Relativity gained acceptance in the scientific community after a several predictions and tests proved correct, including an accurate prediction of the orbit of Mercury and of the deflection of light by a strong gravitational field. However, verification of the theory still remains difficult.

### Orbit of planet Mercury

The orbit of the Mercury—the closest planet to the Sun—exhibits perturbations and a precession that could not be fully explained by the Law of Universal Gravitation.

Application of the General Relativity equations predicted the motion of Mercury to a high degree. This proof caused most scientists to accept the General Relativity's explanation of gravitation.

### Deflection of light

Both Universal Gravitation and General Relativity predict that light can be deflected by gravitation. However, the calculation of the amount of deflection from Newton's theory was only half of what Einstein predicted.

Several years after the General Theory of Relativity was proposed, scientists measured the deflection of light from a star as it passed by the Sun during a solar eclipse. Measurements agreed with Einstein's predictions.

### Other predictions

The General Theory of Relativity also predicted light coming from a strong gravitational field would have its wavelength shifted toward longer wavelengths, called a *red-shift*. The theory also predicted the existence of Black Holes.

(

See Gravitational Escape Velocity from a Black Hole for more information.)

Both gravitational red-shift and Black Holes were also considered possible in the Universal Gravitation theory, but measurements corresponded better with Einstein's theory.

## Problems with General Relativity Theory

Although General Relativity does a good job of explaining gravitation at very high levels, it does run into some problems indicating it may not be a complete theory.

### Gravitation and other forces

Gravitation, nuclear, magnetism and electrical forces are fundamental entities in the classical, as well as Quantum Mechanics theories. However, General Relativity does not look at gravitation as a force but instead a property of spacetime. This discrepancy between gravitation and the various forces is a concern to some scientists that the relativity theory is not complete.

(

See Gravitation as a Fundamental Force for more information.)

### Dark matter

Measurements on the rate of expansion of the Universe indicate there is some force slowing it down. Some scientists proposed there exist what they called *dark matter*, which seemed to have the property of *anti-gravitation*. The possibility of an anti-gravitation force is not explained in the Theory of General Relativity.

(

See Effect of Dark Matter and Dark Energy on Gravitation for more information.)

### Hofava theory gives different view

A very recent theory called *Hofava gravitation* discounts the spacetime connection and states the space and time are separate entities. The Hofava concept looks at gravitation during the Big Bang and works well with Quantum Gravitation.

This theory has had good results in predicting gravitational phenomenon, but it is new and does not yet have universal acceptance from the scientific community.

## Summary

Albert Einstein formulated the *Theory of General Relativity* as a new way to explain gravitation. The theory states that matter curves space and distorts time, causing objects to move toward each other.

While Newton's *Law of Universal Gravitation* works well for ordinary gravitational fields, it is inaccurate when the gravitational intensity is high. The Theory of General Relativity became accepted by scientists after it correctly predicted the planet Mercury's orbit. However, the theory has areas it does not explain, such as at the quantum level.

Try something new

## Resources and references

### Websites

**Understanding General Relativity** - Rafi Moor, Israel

**Einstein's Theory of General Relativity** - Andrew Zimmerman Jones, About.com

**General Relativity** - Wikipedia

**The Meaning of Einstein's Equation** - John C. Baez, University of California-Riverside and Emory F. Bunn, University of Richmond (Virginia)

** The Einstein Field Equations** - Larry Smarr, University of Illinois

### Books

**Top-rated books on Gravitation**

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## General Relativity Theory of Gravitation