Can you explain how gravity is explained as curvature of space-time?

Question

Can you explain how gravity is explained as curvature of space-time?

Answer 1

I always use this down to earth representation that I “created” for myself to understand it this problem better. I never asked anybody if it's right, but still it may help. I'm not a scientist, but in my humble opinion it's all about "reverse engeneering" the universe from what we see to what it actually is. We (humans) want to see travelling light (advancing light=time) as a straight line in 3D space, and 3D space is defined by three axes confined by three directions, represented by 3 straight lines (X, Y, Z-axes). But this is without the interaction between the resulting gravitational fields of matter in space and light in the universe. Gravity bends the track of light, making it follow a curved track.

To be able to make a representation of space where light travels in a straight line, you "straighten" this curved line of light, and then space will be curved around it.

To explain this: Imagine only the top of a circle. The base is a straight line in space, the curve is the path of light travelling through space. Now straighten the line of light, and the line of space will curve (the partial circle seems to flip horizontally). Because light travels the same distance in both pictures, this representation also virtually stretches space-time. Space can't actually stretch of course, but it looks like that because light that was bent and twisted on it's way (more actual distance at the same speed) then light travelling in a straight line, would reach it's destination later, and consequently virtually creating a "stretch" and"curve" in space-time. This stretched and curved space is what we actually see from earth with our eyes, because light is curved by gravity.

Another simple every day example I use to imagine this has nothing to do with gravity, but the representation is about the same. The light from stars that reach earth, are being curved in the atmosphere like it's going through a lens (re- and diffraction). If you'd straighten the curved line of light (correct for re- and diffraction), the origin of the celestial object seems to change position in space, and space curves.

The rubber sheet presentation is the following: There are various objects of various masses laying on a sheet of rubber that is hanging horizontally in the air. The bigger the mass of the object, the bigger the impression (or dent) it makes in the rubber sheet. Now you throw a small ball on the sheet like it's a roulette game. Everywhere the ball is entering a dent of an object, the ball will be changed in it’s course in direction of the object creating the dent. The bigger the object, the bigger the dent (in diameter and steeper slopes), the bigger the influence on the course of the ball towards the object.

There's a comprehensive video about curved space-time on this site:

http://www.pbs.org/wgbh/nova/elegant/program.html

If someone likes to comment on my examples, please do so.

Answer 2

like a gravity well in a garment. Throw a ball on a rubber blanket. Small objects will spin in to the larger objects. Gravity is like a big garment.

Answer 3

Have you seen Fritos corn chips? They're made for dipping. It's the same with the universe-the Big Dipper.

Answer 4

Einstein envisioned gravity as a curvature of space-time caused by the matter in it, as opposed to Newton’s idea of a force acting at a distance. Although objects try to move through space-time in straight lines, this warpage makes their paths appear bent.



The force that keeps us all glued to the surface of Earth, gravity dominates any discussion of the evolution and fate of the universe. Surprisingly, for all of its impact, it ranks as the weakest of the four fundamental forces in nature (the others being the electromagnetic and strong and weak nuclear forces). But the others pale when you talk about the universe as a whole because the two nuclear forces act only over very short distances, while most large objects are electrically neutral and therefore unaffected by the electromagnetic force.



Isaac Newton first described gravity and had the insight to realize that the force that holds us to Earth (and makes apples fall) is the same one that keeps the planets in their orbits around the Sun. He deduced the mathematical nature of the mutual force and correctly hypothesized that gravity acts across the entire universe. Albert Einstein modified this view of gravity by arguing that the gravitational force is a manifestation of the curvature of space-time. Although Einstein’s idea is necessary for describing the evolution of the universe as a whole, Newton’s theory works well enough when gravitational forces are not extremely strong.

Answer 5

no

Answer 6

Its just a way for physicist to say "we don't have a clue". The rubber sheet explanation is stupid because it doesn't expain what gravity is it just explains what gravity does. It like saying "gravity is caused by gravity".

Answer 7

Read this, and contact me if still in doubt.

THE GENERAL THEORY

The general theory of relativity is much more complex and difficult to understand than the special theory. It proves the force of Gravitation, as proved by Sir Isaac Newton, wrong. According to Newton, gravity was a force between two bodies, which depends on their respective mass and the distance between them.

The basic idea of general relativity can be illustrated with the help of an imaginary experiment as performed by Einstein. Suppose a lift is at rest in space. If a ball is released within the lift, it will float in space and not fall. If the lift accelerates upward, an observer within the lift will see the ball fall to the floor exactly as it would under the pull of gravity. The ball appears to fall because the floor of the lift, as seen from outside the lift, it accelerates upward toward the ball. All the effects we associate with gravity would be seen by the observer in the lift. Einstein called the phenomenon shown in this experiment the Principle of Equivalence. This principle states that it makes no difference whether an object is acted on by a gravitational force or is in an accelerated frame of reference. The result in both cases will be the same. From this principle, Einstein reasoned that matter in space distorts or "curves" the frame of reference of space. The result of this curvature is what we experience as gravity. The Euclidian or flat geometry was unable to explain the curve, so Einstein used geometries called Riemannian geometry to explain the effect.

According to Newton's theory, a planet moves around the sun because of the gravitational force exerted by the sun. According to the theory of general relativity, the planet chooses the shortest possible path throughout the four-dimensional space- time, which is deformed by the presence of the sun. This shortest possible path is called a geodesic. This may be compared to the fact that a ship or an aeroplane crossing the ocean follows the section of a circle, rather than a straight line, in order to travel the shortest route between two points. In the same way, a planet or light ray moves along the "shortest" line in its four-dimensional world.

So far, three things have been discovered in which Einstein's theory of general relativity receives experimental proof as opposed to the theories of Newton. These differences are not great, but are measurable. In the first place, according to Newton's theory, the planet Mercury moves in an ellipse about the sun. According to Einstein's theory, Mercury moves along an ellipse, but at the same time the ellipse rotates very slowly in the direction of the planet's motion. The ellipse will turn about forty-three seconds of an arc per century (a complete rotation contains 360 degrees of an arc and 360 X 60 X 60 seconds of an arc). This effect is rather small, but it has been observed. Mercury is nearest to the sun and the relativistic effect would be still smaller for other planets.

If we take a picture of part of the heavens during an eclipse of the sun and near the eclipsed sun, and then take another picture of the same part of the heavens a little later, the two photographs will not show identical positions for all the stars. This is so because, according to general relativity, a light ray sent by a star and passing near the rim of the sun is deflected from its original path because the sun's gravity curves space. The effect of gravity on light is also the reason why black holes are invisible. The gravitation in a black hole is so strong that light cannot escape from it.

Physicists have known for more than a hundred years that when some elements are heated to incandescence they give off a pattern of spectral lines (coloured lines), which can be examined through a spectroscope. According to the Einstein theory, the wavelength of light emitted from a massive object will become longer because of gravitation. This results in a shift of the spectral lines towards the red end of the spectrum; this type of red shift is called gravitational red shift. If we examine the spectral lines of an element on our earth with the spectral lines given off by the same element on the sun or on a star, the spectral lines of the element on the sun or star should be very slightly shifted toward the red end of the spectrum, compared with the spectral lines of the same element on our earth. Experiment has confirmed this shift. In 1960, two American physicists, R. V. Pound and G. A. Rebka, Jr., detected the red shift resulting from the earth's gravitational field. They measured the effect of altitude on the frequency of gamma rays.

Conclusion- The theory of relativity is a truly wonderful theoretical concept that cleanly defies many of the facts of classical physics.

How ever scientists are still trying to confirm this theory and some success has also been achieved, as some scientists believe that velocity of light is not same even in vacuum or space.

Answer 8

No, but here is an article on gravitation. I couldn't find anything on gravity as a curvative of space or time.



In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. Gravitation is one of the four fundamental interactions in nature, the other three being the electromagnetic force, the weak nuclear force, and the strong nuclear force. Gravitation is the weakest of these interactions, but acts over great distances and is always attractive. In classical mechanics, gravitation arises out of the force of gravity (which is often used as a synonym for gravitation). In general relativity, gravitation arises out of spacetime being curved by the presence of mass, and is not a force. In quantum gravity theories, either the graviton is the postulated carrier of the gravitational force[1], or time-space itself is envisioned as discrete in nature, or both.



The gravitational attraction of the earth endows objects with weight and causes them to fall to the ground when dropped (the earth also moves toward the object, but only by an infinitesimal amount). Moreover, gravitation is the reason for the very existence of the earth, the sun, and other celestial bodies; without it matter would not have coalesced into these bodies and life as we know it would not exist. Gravitation is also responsible for keeping the earth and the other planets in their orbits around the sun, the moon in its orbit around the earth, for the formation of tides, and for various other natural phenomena that we observe.





The gravitational force keeps the planets in orbit about the sun.Contents [hide]

1 History of gravitational theory

2 Newton's law of universal gravitation

3 Gravitational potential

4 General relativity

5 Specifics

5.1 Earth's gravity

5.2 Equations for a falling body

5.3 Gravity and astronomy

5.4 Gravity versus gravitation

6 Applications

7 Alternative theories

8 See also

9 Notes

10 References

11 External links







[edit]

History of gravitational theory

Since the time of the Greek philosopher Aristotle in the 4th century BC, there have been many attempts to understand and explain gravity. Aristotle believed that there was no effect without a cause, and therefore no motion without a force. He hypothesized that everything tried to move towards their proper place in the crystalline spheres of the heavens, and that physical bodies fell toward the center of the Earth in proportion to their weight. Another example of an attempted explanation is that of the Indian astronomer Brahmagupta who, in 628 AD, wrote that "bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow".



In 1687, English mathematician Sir Isaac Newton published the famous Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and them answer pretty nearly." Most modern non-relativistic gravitational calculations are based on Newton's work.



[edit]

Newton's law of universal gravitation

Main article: Newton's law of universal gravitation

In 1687 Newton published his work on the universal law of gravity in his book Philosophiae Naturalis Principia Mathematica ( Latin:Mathematical Principles of Natural Philosophy). Newton’s law of gravitation states that: every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If the particles have masses m1 and m2 and are separated by a distance r (from their centers of gravity), the magnitude of this gravitational force is:





where:



F is the magnitude of the gravitational force between the two point masses

G is the gravitational constant

m1 is the mass of the first point mass

m2 is the mass of the second point mass

r is the distance between the two point masses

To see the change in gravity on earth based on the altitude (r in the above equation) based on real examples, you can use the eXtreme High Altitude Calculator



[edit]

Gravitational potential

The above equation leads to the equation for the work done in moving a mass from a radius R to infinity, which is obtained by integrating the force of gravity over this distance:





The work done when moving a mass from infinity to a radius R is therefore



and this is known as the gravitational potential energy.

Using the Earth as an example, the work done in moving a mass from the Earth's surface to infinity is given by:





where G is the universal gravitational constant, m is the object's mass, re is the Earth's radius, and me is the Earth's mass.



[edit]

General relativity

Main article: Introduction to general relativity

Newton's conception and quantification of gravitation held until the beginning of the 20th century, when the German-born physicist Albert Einstein proposed the general theory of relativity. In this theory Einstein proposed that inertial motion occurs when objects are in free-fall instead of when they are at rest with respect to a massive object such as the Earth (as is the case in classical mechanics). The problem is that in flat spacetimes such as those of classical mechanics and special relativity, there is no way that inertial observers can accelerate with respect to each other, as free-falling bodies can do as they each are accelerated towards the center of a massive object.



To deal with this difficulty, Einstein proposed that spacetime is curved by the presence of matter, and that free-falling objects are following the geodesics of the spacetime. More specifically, Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations whose solutions give the components of the metric tensor of spacetime. This metric tensor allows to calculate not only angles and distances between space-time intervals (segments) measured with the coordinates against which the spacetime manifold is being mapped but also the affine-connection from which the curvature is obtained, thereby describing the spacetime's geometrical structure. Notable solutions of the Einstein field equations include:



The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact enough objects, this solution generated a black hole with a central singularity.

The Reissner-Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with two event horizons.

The Kerr solution solution for rotating massive objects. This solution also produces black holes with multiple event horizons.

The cosmological Robertson-Walker solution, which predicts the expansion of the universe.

General relativity has enjoyed much success because of how its predictions have been regularly confirmed. For example:



General relativity accounts for the anomalous precession of the planet Mercury.

The prediction that time runs slower at lower potentials has been confirmed by the Pound-Rebka experiment, the Hafele-Keating experiment, and the GPS.

The prediction of the deflection of light was first confirmed by Arthur Eddington in 1919, and has more recently been strongly confirmed through the use of a quasar which passes behind the Sun as seen from the Earth. See also gravitational lensing.

The time delay of light passing close to a massive object was first identified by Shapiro in 1964 in interplanetary spacecraft signals.

Gravitational radiation has been indirectly confirmed through studies of binary pulsars.

The expansion of the universe (predicted by the Robertson-Walker metric) was confirmed by Edwin Hubble in 1929.

[edit]

Specifics

[edit]

Earth's gravity



Southern Ocean gravity fieldMain article: Gravity (Earth)

Every planetary body, including the Earth, is surrounded by its own gravitational field, which exerts an attractive force on any object that comes under its influence. This field is proportional to the body's mass and varies inversely with the square of distance from the body. The gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is approximately 9.81 m/s² or 32.2 ft/s². This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.81 m/s (around 22 mph) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.81 m/s after one second, 19.62 m/s after two seconds, and so on. According to Newton's 3rd Law, the earth itself experiences an equal and opposite force to that acting on the falling object, meaning that the earth also accelerates towards the object. However, because the mass of the earth is huge, the acceleration produced on the earth by this same force is negligible.



[edit]

Equations for a falling body

Main article: Equations for a falling body

Under normal earth-bound conditions, when objects move owing to a constant gravitational force a set of kinematical and dynamical equations describe the resultant trajectories. For example, Newton’s law of gravitation simplifies to F = mg, where m is the mass of the body. This assumption is reasonable for objects falling to earth over the relatively short vertical distances of our everyday experience, but is very much untrue over larger distances, such as spacecraft trajectories, because the acceleration far from the surface of the Earth will not in general be g. A further example is the expression that we use for the calculation of potential energy of a body = mgh. This expression can be used only over small distances from the earth. Similarly the expression for the maximum height reached by a vertically projected body,"h = u^2/2g " is useful for small heights and small initial velocities only. In case of large initial velocities we have to use the principle of conservation of energy to find the maximum height reached.



[edit]

Gravity and astronomy

Main article: Gravity (astronomy)

The discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our solar system, the mass of the sun, the distance to stars and even the theory of dark matter. Although we haven't traveled to all the planets nor to the sun, we know their mass. The mass is obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters.



[edit]

Gravity versus gravitation

It is important to note, in some contexts, that gravitation is not gravity, per se. Gravitation is a phenomenon independent of any particular cause. Some theorize that it is possible for gravitation to exist without a force; according to general relativity, that is indeed the case. In common usage "gravity" and "gravitation" are either used interchangeably, or the distinction is sometimes made that "gravity" is specifically the attractive force of the earth, while "gravitation" is the general property of mutual attraction between bodies of matter. In technical usage, "gravitation" is the tendency of bodies to accelerate towards one another, and "gravity" is the force that some theories use to explain this acceleration.



Gravity was rather poorly understood until Isaac Newton formulated his law of gravitation in the 17th century. Newton's theory is still widely used for many practical purposes, though for more advanced work it has been supplanted by Einstein's general relativity. While a great deal is now known about the properties of gravity, the ultimate cause of gravitation remains an open question and gravity remains an important topic of scientific research.



[edit]

Applications



Shot Tower, 1856 Dubuque, IowaA vast number of mechanical contrivances depend in some way on gravity for their operation. For example, a height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip or a water tower. The gravitational potential energy of water supplies hydroelectricity can also be used to power a tramcar up an incline, using a system of water tanks and pulleys. Also, a weight hanging from a cable over a pulley provides a constant tension in the cable, including the part on the other side of the pulley to the weight.



Examples are numerous: For example molten lead, when poured into the top of a shot tower, will coalesce into a rain of spherical lead shot, first separating into droplets, forming molten spheres, and finally freezing solid, undergoing many of the same effects as meteoritic tektites, which will cool into spherical, or near-spherical shapes in free-fall. Also, a fractionation tower can be used to manufacture some materials by separating out the material components based on their specific gravity. Weight-driven clocks are powered by gravitational potential energy, and pendulum clocks depend on gravity to regulate time. Artificial satellites are an application of gravitation which was mathematically described in Newton's Principia.



Gravity is used in geophysical exploration to investigate density contrasts in the subsurface of the Earth. Sensitive gravimeters use a complicated spring and mass system (in most cases) to measure the strength of the "downward" component of the gravitational force at a point. Measuring many stations over an area reveals anomalies measured in mGal or microGal (1 gal is 1 cm/s^2. Average gravitational acceleration is about 981 gal, or 981,000 mGal.). After corrections for the obliqueness of the Earth, elevation, terrain, instrument drift, etc., these anomalies reveal areas of higher or lower density in the crust. This method is used extensively in mineral and petroleum exploration, as well as time-lapse groundwater modeling. The newest instruments are sensitive enough to read the gravitational pull of the operator standing over them.



[edit]

Alternative theories

Main article: Alternatives to general relativity

Historical alternative theories



Aristotelian theory of gravity

Le Sage's theory of gravitation (1784) also called LeSage gravity, proposed by Georges-Louis Le Sage, based on a fluid-based explanation where a light gas fills the entire universe.

Nordström's theory of gravitation (1912, 1913), an early competitor of general relativity.

Whitehead's theory of gravitation (1922), another early competitor of general relativity.

Recent alternative theories



Brans-Dicke theory of gravity (1961)

Induced gravity (1967), a proposal by Andrei Sakharov according to which general relativity might arise from quantum field theories of matter.

Rosen bi-metric theory of gravity

In the modified Newtonian dynamics (MOND) (1981), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations.

The new and highly controversial Process Physics theory attempts to address gravity

The self-creation cosmology theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation.

Nonsymmetric gravitational theory (NGT) (1994) by John Moffat

The satirical theory of Intelligent falling (2002, in its first incarnation as "Intelligent grappling")

Tensor-vector-scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein

electrogavitics, magnetogravitics, gravity wave harmonics: electrogravitics: (eg. see books published by integrity research institute [1]) basic principle: electrons push, protons pull - using this principle, Nikola Tesla predicted gravitational repulsion in the 1880s, experimented with it in the 1890s, & designed the cigar shaped aircraft in the early 20th century. The Biefeld-Brown effect (1923) demonstrates this & Thomas Townsend Brown later designed asymetric capacitors suchas the disc shaped aircraft with a negatively electrical charged (repulsion) plate on the bottom & the positively charged (attraction) plate on top. gravity wave harmonics (eg. see book: How to Build a Flying Saucer and Other Proposals in Speculative Engineering, T.B. Pawlicki): gravity is a wave like any other - all the planets rest at harmonic intervals in a standing wave from the source of the wave, the sun.

Answer 9

Get a flat sheet of rubber, pinch it in one position from the bottom, if you rolled a ball around the cone that formes, then that is how that it is imagined that mass causes gravity.