Relativity! Please Clarify?

Question

What are the proofs for the conclusion that speed of light is not dependent on the motion of its SOURCE and MEDIUM? Please give detailed answers.

Answer 1

General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1][2] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational acceleration is the manifestation of the curvature of space and time. GR further call for the curvature of space-time to be produced by the mass-energy and momentum content of the matter in space-time. General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate space-time content and space-time curvature.

General relativity is currently the most successful gravitational theory, being almost universally accepted and well supported by observations. The first success of general relativity was in explaining the anomalous perihelion precession of Mercury. Then in 1919, Sir Arthur Eddington announced that observations of stars near the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. Since then, many other observations and experiments have confirmed many of the predictions of general relativity, including gravitational time dilation, the gravitational redshift of light, signal delay, and gravitational radiation. In addition, numerous observations are interpreted as confirming one of general relativity's most mysterious and exotic predictions, the existence of black holes.

In the mathematics of general relativity, the Einstein field equations become a set of simultaneous differential equations whose solutions are metric tensors of space-time. These metric tensors describe the shape of the space-time, and are used to obtain the predictions of general relativity. The connections of the metric tensors specify the geodesic paths that objects follow when traveling inertially. Important solutions of the Einstein field equations include the Schwarzschild solution (for the space-time surrounding a spherically symmetric uncharged and non-rotating massive object), the Reissner-Nordström solution (for a charged spherically symmetric massive object), and the Kerr metric (for a rotating massive object).

In spite of its overwhelming success, there is discomfort with general relativity in the scientific community due to its being incompatible with quantum mechanics and the reachable singularities of black holes (at which the math of general relativity breaks down). Because of this, numerous other theories have been proposed as alternatives to general relativity. An early and still-popular class of modifications is Brans-Dicke theory, which, although not solving the problems of singularities and quantum gravity, appeared to have observational support in the 1960s. However, those observations have since been refuted and modern measurements indicate that any Brans-Dicke type of deviation from general relativity must be very small if it exists at all.Treatment of gravitation
Two-dimensional analogy of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Note that the white lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime
Two-dimensional analogy of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Note that the white lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime

In this theory, spacetime is treated as a 4-dimensional Lorentzian manifold which is curved by the presence of mass, energy and momentum (or stress-energy) within it. The relationship between stress-energy and the curvature of spacetime is described by the Einstein field equations. The motion of objects being influenced solely by the geometry of spacetime (inertial motion) occurs along special paths called timelike and null geodesics of spacetime.

One of the defining features of general relativity is the idea that gravitational 'force' is replaced by geometry. In general relativity, phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion in a curved spacetime. So what people standing on the surface of the Earth perceive as the 'force of gravity' is a result of their undergoing a continuous physical acceleration caused by the mechanical resistance of the surface on which they are standing.

[edit] Justification

The justification for creating general relativity came from the equivalence principle[3], which dictates that free-falling observers are the ones in inertial motion. A consequence of this insight is that inertial observers can accelerate with respect to each other (Think of two balls falling on opposite sides of the Earth, for example). This redefinition is incompatible with Newton's first law of motion, and cannot be accounted for in the Euclidean geometry of special relativity. To quote Einstein himself:

"If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them." [4]

Thus the equivalence principle led Einstein to search for a gravitational theory which involves curved space-times.

Another motivating factor was the realization that relativity calls for the gravitational potential to be expressed as a symmetric rank-two tensor, and not just a scalar as was the case in Newtonian physics (An analogy is the electromagnetic four-potential of special relativity). Thus, Einstein sought a rank-two tensor means of describing curved space-times surrounding massive objects.[5] This effort came to fruition with the discovery of the Einstein field equations in 1915.[1]

[edit] Fundamental principles

General relativity is based on the following set of fundamental principles which guided its development.[2][6] These principles are:

* The general principle of relativity: The laws of physics must be the same for all observers (accelerated or not).
* The principle of general covariance: The laws of physics must take the same form in all coordinate systems.
* The principle that inertial motion is geodesic motion: The world lines of particles unaffected by physical forces are timelike or null geodesics of spacetime.
* The principle of local Lorentz invariance: The laws of special relativity apply locally for all inertial observers.
* Spacetime is curved: This permits gravitational effects such as free-fall to be described as a form of inertial motion. (See the discussion below of a person standing on Earth, under "Coordinate vs. physical acceleration.")
* Spacetime curvature is created by stress-energy within the spacetime: This is described in general relativity by the Einstein field equations.

(The equivalence principle, which was the starting point for the development of general relativity, ended up being a consequence of the general principle of relativity and the principle that inertial motion is geodesic motion.)

[edit] Spacetime as a curved Lorentzian manifold

In general relativity, the spacetime concept introduced by Hermann Minkowski for special relativity is modified. More specifically, general relativity stipulates that spacetime is:

* curved: Spacetime has a non-Euclidean geometry. In special relativity, spacetime is flat.
* Lorentzian: The metrics of spacetime must have a mixed metric signature. This is inherited from special relativity.
* four dimensional: to cover the three spatial dimensions and time. This is also inherited from special relativity.

The curvature of spacetime (caused by the presence of stress-energy) can be viewed intuitively in the following way. Placing a heavy object such as a bowling ball on a trampoline will produce a 'dent' in the trampoline. This is analogous to a large mass such as the Earth causing the local spacetime geometry to curve. This is represented by the image at the top of this article. The larger the mass, the bigger the amount of curvature. A relatively light object placed in the vicinity of the 'dent', such as a ping-pong ball, will accelerate towards the bowling ball in a manner governed by the 'dent'. Firing the ping-pong ball at just the right speed towards the 'dent' will result in the ping-pong ball 'orbiting' the bowling ball. This is analogous to the Moon orbiting the Earth, for example.

Similarly, in general relativity massive objects do not directly impart a force on other massive objects as hypothesized in Newton's action at a distance idea. Instead (in a manner analogous to the ping-pong ball's response to the bowling ball's dent rather than the bowling ball itself), other massive objects respond to how the first massive object curves spacetime.

[edit] The mathematics of general relativity

Main article: Mathematics of general relativity

Due to the expectation that spacetime is curved, Riemannian geometry (a type of non-Euclidean geometry) must be used. In essence, spacetime does not adhere to the "common sense" rules of Euclidean geometry, but instead objects that were initially traveling in parallel paths through spacetime (meaning that their velocities do not differ to first order in their separation) come to travel in a non-parallel fashion. This effect is called geodesic deviation, and it is used in general relativity as an alternative to gravity. For example, two people on the Earth heading due north from different positions on the equator are initially traveling on parallel paths, yet at the north pole those paths will cross. Similarly, two balls initially at rest with respect to and above the surface of the Earth (which are parallel paths by virtue of being at rest with respect to each other) come to have a converging component of relative velocity as both accelerate towards the center of the Earth due to their subsequent free-fall (Another way of looking at this is how a single ball moving in a purely timelike fashion parallel to the center of the Earth comes through geodesic motion to be moving towards the center of the Earth).

The requirements of the mathematics of general relativity are further modified by the other principles. Local Lorentz Invariance requires that the manifolds described in GR be 4-dimensional and Lorentzian instead of Riemannian. In addition, the principle of general covariance forces that mathematics to be expressed using tensor calculus. Tensor calculus permits a manifold as mapped with a coordinate system to be equipped with a metric tensor of spacetime which describes the incremental (spacetime) intervals between coordinates from which both the geodesic equations of motion and the curvature tensor of the spacetime can be ascertained.

[edit] The Einstein field equations

Main article: Einstein field equations

The Einstein field equations (EFE) describe how stress-energy causes curvature of spacetime and are usually written in tensor form (using abstract index notation) as

G_{ab} = \kappa\, T_{ab}

where Gab is the Einstein tensor, Tab is the stress-energy tensor and κ is a constant. The tensors Gab and Tab are both rank 2 symmetric tensors, that is, they can each be thought of as 4×4 matrices, each of which contains 10 independent terms.

The EFE reduce to Newton's law of gravity in the limiting cases of a weak gravitational field and slow speed relative to the speed of light. In fact, the value of κ in the EFE is determined to be \kappa = 8 \pi G / c^4 \ by making these two approximations.[2]

Einstein introduced an alternative form of the field equations to accommodate a static universe solution in his theory:[citation needed]

G_{ab} + \Lambda\ g_{ab} = \kappa\, T_{ab}

where Λ is the cosmological constant and gab is the spacetime metric.

The solutions of the EFE are metrics of spacetime. These metrics describe the structure of spacetime given the stress-energy and coordinate mapping used to obtain that solution. Being non-linear differential equations, the EFE often defy attempts to obtain an exact solution; however, many such solutions are known.

The EFE are the identifying feature of general relativity. Other theories built out of the same premises include additional rules and/or constraints. The result almost invariably is a theory with different field equations (such as Brans-Dicke theory, teleparallelism, Rosen's bimetric theory, and Einstein-Cartan theory).

[edit] Coordinate vs. physical acceleration

One of the greatest sources of confusion about general relativity comes from the need to distinguish between coordinate and physical accelerations.

In classical mechanics, space is preferentially mapped with a Cartesian coordinate system. Inertial motion then occurs as one moves through this space at a constant coordinate rate with respect to time. Any change in this rate of progression must be due to a force, and therefore a physical and coordinate acceleration were in classical mechanics one and the same. It is important to note that in special relativity that same kind of Cartesian coordinate system was used, with time being added as a fourth dimension and defined for an observer using the Einstein synchronization procedure. As a result, physical and coordinate acceleration correspond in special relativity too, although their magnitudes may vary.

In general relativity, the elegance of a flat spacetime and the ability to use a preferred coordinate system are lost (due to stress-energy curving spacetime and the principle of general covariance). Consequently, coordinate and physical accelerations become sundered. For example: Try using a polar coordinate system in classical mechanics. In this case, an inertially moving object which passes by (instead of through) the origin point is found to first be moving mostly inwards, then to be moving tangentially with respect to the origin, and finally to be moving outwards, and yet it is moving in a straight line. This is an example of an inertially moving object undergoing a coordinate acceleration, and the way this coordinate acceleration changes as the object travels is given by the geodesic equations for the manifold and coordinate system in use.

Another more direct example is the case of someone standing on the Earth, where they are at rest with respect to the surface coordinates for the Earth (latitude, longitude, and elevation) but are undergoing a continuous physical acceleration because the mechanical resistance of the Earth's surface keeps them from free-falling.

[edit] Predictions of general relativity

(For more detailed information about tests and predictions of general relativity, see tests of general relativity).

[edit] Gravitational effects

[edit] Acceleration effects

The acceleration effects are common to all accelerated frames of reference, and were described by Einstein as far back as 1907[3]. As such, they are present even in special relativity.

The first of these effects is the Gravitational redshifting of light. Under this effect, the frequency of light will decrease (shifting visible light towards the red end of the spectrum) as it moves to higher gravitational potentials (out of a gravity well). This is caused by an observer at a higher gravitational potential being accelerated (with respect to the local inertial frames of reference) away from the source of a beam of light as that light is moving towards that observer. Gravitational redshifting has been confirmed by the Pound-Rebka experiment.[7][8][9]

A related effect is gravitational time dilation, under which clocks will run slower at lower gravitational potentials (deeper within a gravity well). It is another way of perceiving that decrease in frequency of the gravitationally redshifted light. This effect has been directly confirmed by the Hafele-Keating experiment[10][11] and GPS.

Gravitational time dilation has as a consequence another effect called the Shapiro effect (also known as gravitational time delay). Shapiro delay occurs when signals take longer to move through a gravitational field than they would in the absence of the gravitational field. This effect was discovered through the observations of signals from spacecraft and pulsars passing behind the Sun as seen from the Earth.[12][13]

[edit] Bending of light
The most famous early test of the general theory of relativity was made possible by observation of the 1919 solar eclipse. According to Sir Arthur Stanley Eddington, starlight could be seen to bend around the sun as it made its way to the observer on earth.
The most famous early test of the general theory of relativity was made possible by observation of the 1919 solar eclipse. According to Sir Arthur Stanley Eddington, starlight could be seen to bend around the sun as it made its way to the observer on earth.

This bending also occurs in any accelerated frame of reference. However, the details of the bending and therefore the gravitational lensing effects are governed by space-time curvature.

Einstein was aware of this effect by 1911, but at the time he calculated an amount for the bending that was the same as predicted by classical mechanics given that light is accelerated by gravitation. In 1916, Einstein found that the amount of the bending in general relativity was actually twice the Newtonian value[2], and so this became a way of testing general relativity. Since then, this prediction has been confirmed by astronomical observations during eclipses of the Sun and observations of pulsars passing behind the Sun[14].

Gravitational lensing occurs when one distant object is in front of or close to being in front of another much more distant object. In that case, the bending of light by the nearer object can change how the more distant object is seen. The first example of gravitational lensing was the discovery of a case of two nearby images of the same pulsar. Since then many other examples of distant galaxies and quasars being affected by gravitational lensing have been found.

A special type of gravitational lensing occurs in Einstein rings and arcs. The Einstein ring is created when an object is directly behind another object with a uniform gravitational field. In that case, the light from the more distant object becomes a ring around the closer object. If the more distant object is slightly offset to one side and/or the gravitational field is not uniform, partial rings (called arcs) will appear instead.

Finally, in our own galaxy a star can appear to be brightened when compact massive foreground object is sufficiently aligned with it. In that case, the magnified and distorted images of the background star due to the gravitational bending of light cannot be resolved. This effect is called microlensing, and such events are now regularly observed.

[edit] Orbital effects

General relativity differs from classical mechanics in its predictions for orbiting bodies. The first difference is in the prediction that apsides of orbits will precess on their own. This is not called for by Newton's theory of gravity. Because of this, an early successful test of general relativity was its correctly predicting the anomalous perihelion precession of Mercury. More recently, perihelion precession has been confirmed in the large precessions observed in binary pulsar systems.

A related effect is geodetic precession. This is a precession of the poles of a spinning object due to the effects of parallel transport in a curved space-time. This effect is not expected in Newtonian gravity. The prediction of geodetic precession was tested and verified by the Gravity Probe B experiment to a precision of better than 1 percent[15].

Another effect is that of orbital decay due to the emission of gravitational radiation by a co-rotating system. It is observable in closely orbiting stars as an ongoing decrease in their orbital period. This effect has been observed in binary pulsar systems.

[edit] Frame dragging

Main article: frame dragging

Frame dragging is where a rotating massive object "drags" space-time along with its rotation. In essence, an observer who is distant from a rotating massive object and at rest with respect to its center of mass will find that the fastest clocks at a given distance from the object are not those which are at rest (as is the case for a non-rotating massive object). Instead, the fastest clocks will be found to have component of motion around the rotating object in the direction of the rotation. Similarly, it will be found by the distant observer that light moves faster in the direction of the rotation of the object than against it. Frame dragging will also cause the orientation of a gyroscope to change over time. For a spacecraft in a polar orbit, the direction of this effect is perpendicular to the geodetic precession mentioned above. Gravity Probe B is using this feature to test both frame dragging and the geodetic precession predictions.

[edit] Black holes

Main article: black hole

Black holes are objects which have gravitationally collapsed behind an event horizon. A black hole is so massive that light cannot escape its gravitational pull. The disappearance of light and matter within a black hole may be thought of as their entering a region where all possible world lines point inwards. Stephen Hawking has predicted that black holes can "leak" mass,[16] a phenomenon called Hawking radiation, a quantum effect not in violation of general relativity. Numerous black hole candidates are known. These include the supermassive object associated with Sagittarius A* at the center of our galaxy[17].

[edit] Cosmology

Main article: physical cosmology

Although it was created as a theory of gravitation, it was soon realized that general relativity could be used to model the universe, and so gave birth to the field of physical cosmology. The central equations for physical cosmology are the Friedmann-Lemaître-Robertson-Walker metric, which are the cosmological solution of the Einstein field equations. This metric predicts that the universe must be dynamic: It must either be expanding, contracting, or switching between those states.

At the time of the discovery of the Friedmann-Lemaître-Robertson-Walker metric, Einstein could not abide by the idea of a dynamic universe. In an attempt to make general relativity accommodate a static universe, Einstein added a cosmological constant to the field equations as described above. However, the resultant static universe was unstable. Then in 1929 Edwin Hubble showed that the redshifting of light from distant galaxies indicates that they are receding from our own at a rate which is proportional to their distance from us.[18] [19]. This demonstrated that the universe is indeed expanding. Hubble's discovery ended Einstein's objections and his use of the cosmological constant.

The equations for an expanding universe become singular when one goes far enough back in time, and this primordial singularity marks the formation of the universe. That event has come to be called the Big Bang. In 1948, Ralph Asher Alpher and George Gamov published an article describing this event and predicting the existence of the cosmic microwave background radiation left over from the Big Bang. In 1965, Arno Penzias and Robert Wilson first observed the background radiation.[20], confirming the Big Bang theory.

Recently, observations of distant supernovae have indicated that the expansion of the universe is currently accelerating. This was unexpected since Friedmann-Lemaître-Robertson-Walker metric calls for a universe that only contains visible matter to have a decelerating expansion. However, for a universe that is 4% baryonic matter, 26% dark matter, and 70% dark energy, the Friedmann-Lemaître-Robertson-Walker metric takes on a form that is consistent with observation. There is also an irony in that the dark energy can be modeled using Einstein's cosmological constant, but with a value that enhances the dynamic nature of the universe instead of muting it [citations needed].

[edit] Other predictions

* The equivalence of inertial mass and gravitational mass: This follows naturally from free-fall being inertial motion.
o The strong equivalence principle: Even a self-gravitating object will respond to an external gravitational field in the same manner as a test particle would. (This is often violated by alternative theories.)
* Gravitational radiation: Orbiting objects and merging neutron stars and/or black holes are expected to emit gravitational radiation.
o Orbital decay (described above).
o Binary pulsar mergers: May create gravitational waves strong enough to be observed here on Earth. Several gravitational wave observatories are (or will soon be) in operation. However, there are no confirmed observations of gravitational radiation at this time.
o Gravitons: According to quantum mechanics, gravitational radiation must be composed of quanta called gravitons. General relativity predicts that these will be massless spin-2 particles. They have not been observed.
o Only quadrupole (and higher order multipole) moments create gravitational radiation.
+ Dipole gravitational radiation (prohibited by this prediction) is predicted by some alternative theories. It has not been observed.

Answer 2

There is no proof, science can't set out to prove anything. We try to satisfactorily predict observations and experiements. All observations and experiments indicate that light travels at c in vacuum, and that this speed is independent of the source's motion. It's not a conclusion, it's just the way it is--found by measuring the speed of light and finding it's the same regardless of the sources motion. Check out the michelson-morley experiment, it's one of the most famous "failed" experiments ever done. (They were trying to determine the speed of light relative to a medium . . . it didn't work.)

Answer 3

Hi,
Your missing the fundemental point, there is no "proofs" there are pseudo logical arguments as to why, but not the how.
So Einsten had an idea that , if we did indeed allow light to have an unbounded speed, or indeed that it was possile to go faster, then the concept of time/future/past/ and information would all become meaningless, if we allow instaneous travel the every part of the universe would know about every other part at once.

So basically it makes sense for us that light is the speed limit of the universe. Hope that helps

Answer 4

By theoretical consideration, it has been derived that

The velocity of light in any medium depends upon the permittivity of the medium and permeability of the medium.

This shows that the speed does not depend upon the nature and motion of the source.

Using the values of these two constants for vacuum, the velocity of light in vacuum is calculated to be 3x10^8m/s.

The experimental value also agrees with this.

Unless the permittivity of free space and permeability of free space change, the velocity of light cannot change.

In any other medium these two are different and hence the velocity decreases in any other medium.

With out any physical concepts like permittivity and permeability, we can explain like this.

The light’s velocity decreases in a medium because the medium gives some resistance. In vacuum there is nothing to resist and hence it moves with the maximum velocity.. We cannot imagine any other medium which can allow the light to go with higher than this.

Constancy of speed of light
Suppose three things are emitted from a moving source.

1. An object. 2. A sound wave 3. A light wave

The speed of these three are measured by a stationary observer and an observer moving with a speed ‘v’ with respect to a stationary star.

If the object is thrown with a speed ‘c’, in the direction of motion, the stationary observer will measure its speed as c + v, the moving observer will measure it as v.
Note that the source determines the speed of the object.

In the case of sound, the speed of the sound depends upon the medium and IT IS NOT DETERMINED BY THE SOURCE. Whatever the speed of the source, the sound once emitted will have the speed destined in that medium (let us take the medium as air).

Therefore the speed of sound measured by the two observers depends upon the speed of the medium in which it travels.

Two extreme cases are possible.

The air in the moving frame is taken along with the frame; or it is stationary with respect to the stationary observer.

If the speed of sound in air is c, in the case in which air is carried along, the moving observer finds the speed equal to c and the stationary observer finds it equal to c +v.

In the case in which the air is not carried along, the moving observer finds the speed equal to c-v and the stationary observer finds it equal to c.

In the case of light, the speed is not determined by the source like sound. It travels in vacuum.

The speed of light in vacuum is c. The vacuum is not carried along with the frame.

Therefore, one will expect the second case of sound to happen; that is the moving observer is to find the speed as c-v.

Note that all other cases are not applicable to light.


In continuation of our speed about light,

“Contrary to our belief, it is not so”.

Both observers observe the speed as C. It is the theory of relativity.


In the case of a double star and satellites of Jupiter, it is verified that the speed of light emitted by these objects is always C, when they approach earth and when they recede earth.

Answer 5

In special relativity there is no proof of this, you assume that the speed of light is a constant, and then deduce everything we know from that.

The speed of light is constant, is the 1st principle of relativity.

Answer 6

people are answering your question wrong. There is proof. It is the fundamental experiment behind special relativity. Look at the Michelson Morley Experiment. You will see it.