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alext87

Consequences of general relativity - gravitational waves

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In my lessons we have come across the Hulse-Taylor binary system. I have been 'researching' about why the binary system spirals in towards the common centre of mass and believe it is to do will gravitational waves produced by large accelerations of large masses in its orbit.

 

However, I am interested to have a simple understanding of how general relativity predicts gravitational waves and how to estimate how much energy is lost to them over a given time or orbit. By simple I mean with a mathematical base but not high university level please. I would be really grateful because it is hard to find sufficient explanation that is at my level on the internet. Thanks

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Well for a weak field we can consider the metric as a small perturbation from flat space-time metric

 

[math]g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}[/math]

 

Where the field h is not necessarilly a tensor, but a function added to each component of the Lorentzian metric. However, if we consider Minkowski space-time as a background, the field h will transform as a (0 2) tensor, so we can consider it as a tensor in such circumstances. If we now give ourselves an expression for the Einstein tensor in terms of our perturbed flat metric we can impose certain simplifying restrictions on h. These are the traceless-transverse gauge and the Lorentz (or de Donder) gauge, the latter being similar to that in classical electrodynamics. If we do this we end up with the weak field version of the field equations of general relativity which serves the basis of linearised field theory (linearised because we only one the terms linear in h)

 

[math]\left(\frac{1}{c^2}\frac{\partial}{\partial t}-\nabla^2\right)h_{\alpha\beta}=-16\pi T_{\alpha\beta}[/math]

 

Where T is the usual symmetric stress energy tensor of the generating field.

 

"A First Course In General Relativity"-B. Schutz has a good discussion on the treatment of gravitational waves in linearised field theory, including its detection and the energy radiated from bodies by their gravitational wave emission. Note that spherically symmetric bodies do not radiate gravitational radiation, as their quadrupole and higher moments vanish due to the symmetry.

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"The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a facility dedicated to the detection of cosmic gravitational waves and the harnessing of these waves for scientific research."http://www.ligo.caltech.edu/LIGO_web/about/

 

It is expected that some time during 2006 LIGO will detect a gravitational wave, thus proving (experimentally) that they exist. The only thing that would create gravitational waves big enough to be detected would be something in the order of a supernova collapsing or two black holes colliding, but it is still expected to happen some time this year.

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alext87: In my lessons we have come across the Hulse-Taylor binary system. I have been 'researching' about why the binary system spirals in towards the common centre of mass and believe it is to do will gravitational waves produced by large accelerations of large masses in its orbit.

 

However, I am interested to have a simple understanding of how general relativity predicts gravitational waves and how to estimate how much energy is lost to them over a given time or orbit. By simple I mean with a mathematical base but not high university level please. I would be really grateful because it is hard to find sufficient explanation that is at my level on the internet. Thanks

 

Amrit:

According to our research gravitational waves are a pur math speculation. They do not exist in the universe. Gravitational force is carried by the quanta of space that build up cosmic space.

 

see more: http://forum.physorg.com/index.php?showtopic=4802

 

amrit

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Thank you all for your comments and the links they have been very helpful. I particularly like to think of the entire system as a dynamic equilibrium but can anyone quantify (give a value to) the energy that is lost from the Hulse-Taylor pulsar binary from 'gravitational waves' as predicted by relativity? I appreciate that gravitional waves may be the wrong language to use but can not think of a better phase to describe it. Thank you.

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Thank you all for your comments and the links they have been very helpful. I particularly like to think of the entire system as a dynamic equilibrium but can anyone quantify (give a value to) the energy that is lost from the Hulse-Taylor pulsar binary from 'gravitational waves' as predicted by relativity? I appreciate that gravitional waves may be the wrong language to use but can not think of a better phase to describe it. Thank you.

 

 

You might want to check the references listed at the end of this page. The calculations might be included in one of them.

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hi alex energy that is lost by the Hulse-Taylor binary pulsar is because in one of star matter transforms back into the energy of space.

 

Diminishing of the speed of binary pulsar is caused by the transformation of matter back into the energy of cosmic space in the centre of one star of the binary pulsar. With transformation of matter into space the mass one stars is diminishing, and so also the speed of the binary pulsar is diminishing. There is no gravitational radiation, gravitational waves do not exist.

 

Decreasing of the duration of motion of the orbital period of the binary pulsar PRS1913+16 is the result of matter transforming back into space in the centre of one star. This diminishes the mass of the star, diminishing of the mass causes diminishing of the speed of rotation, with diminishing of the speed the duration of motion on the orbit is increasing.

 

see the whole story: http://forum.physorg.com/index.php?showtopic=4902

 

amrit

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amrit needs to come with a disclaimer: not to be confused with accepted physics principles.

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Hi Swansont

 

There is no need to write all this in latin

GW are a pure math speculation. why see below:

 

Ernst Mach about time:

It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive by means of the changes of things.

 

Albert Einstein about time:

Space and time are modes by which we think, not conditions under which we live." Time--the time that we know through clocks and calendars--was invented. http://www.britannica.com/clockworks/article.html

 

Roger Penrose about time:

The temporal ordering that we 'appear' to perceive is, I am claiming, something that we impose upon our perceptions in order to make sense of them in relation to the uniform forward time-progression of an external physical reality. http://www-groups.dcs.st-and.ac.uk/...ics/Time_2.html

 

Author about time:

In the universe one can observe only motion and not time. Time is a construction of the mind into which humans experience motion. Motion belongs to the Universe, time to the mind. Also “arrow of time” belongs to the mind. Universe itself is an a-temporal phenomena.

 

Julian Barbour gave his book title: The End of Time, The Next Revolution in Physics.

 

He has all reasons for this title. Existence of time as a physical reality has no experimental evidence. In all physical formulas symbol t means duration of motion. Universe is an a-temporal phenomena, time is of the mind, motion is of the universe. With clocks we measure duration of motion. The second is a unit with which we measure duration of motion. In 86400 seconds earth turn once around its axe. Second has no existence on it own, it came into existence when motion is measured by a clock. Second is a tool of the mind that man uses to measure duration of different motions. Motions by itself have no duration. Man give them a sense of duration by measuring them.

 

motion......perception (eyes)......elaboration (time)......experience (observer)

 

Motion is measured by clocks. With clocks we measure duration of the movement of body or particle regarding another body or particle. The speed of the motion depends on a density D of space. Density D in centre of planet or star is D = m x G, where m is a mass and G is gravitational constant. Density D is diminishing with the distance r on square from the centre of the star. Speed of time is increasing with the diminishing of density D. Clocks run faster on the top of the high mountain and slower at the sea side under the mountain. Density of space is higher at sea side and lover on the top of the mountain.

 

Density of space is increasing by going towards the sun. Time (speed of bodies and particles) is becoming slower by going towards the sun. That's the cause of "Mercury perihelion dilate".

 

2. Cosmic space is build up out of quanta of space QS. Gravitational force acts between quanta of space QS. Every QS attract the QS around it. Between QS near by the moon and QS near by the earth gravitation acts on the distance and instantly via QS that are between them. Gravitational force does not propagate into space, gravitational force is the force that builds up the space. In a similar way as the wall is made out of bricks. The cement between bricks is keeping together the wall, the gravitational force between QS is keeping together the space.

The strength of gravitational force depends on the density of QS that build up cosmic space. Density D of QS of a given volume of cosmic space depends on the density of matter contained in it:

 

formula 1: D = m x G

 

where D is the density of QS in the centre of the material object, m is the mass of the object and G is the gravitational constant. QS are “elastic”. Its density changes with the amount of matter. The gravitational force Fg between two material objects is given by the following relation:

 

Fg = (D1 x D2) / ( r on square x G)

 

where r is the distance between the centers of the two material objects.

 

Gravitational force Fg on material body or on a particle that has a mass m depends on the density G of space.

 

Fg = (m x D) / r on square

 

where m is a mass of a body or particle, D is the density if space in a centre of planet or star, r is the distance from the centre of the planet or star; r can be shorter or longer as t the radius of the planet or star.

 

In a centre of the planet or star Fg on a material object or mass particle is:

 

Fg = (m x D) m10^-2

 

Gravitational acceleration g in a given distance r from the centre of the planet or star is:

 

g = (m x G) / r on square

 

m is a mass of planet or star,

G is gravitational constant

r is a distance from a centre

 

 

According to the formula 1: D = m x G

 

g = D / r on square

 

where D is the density of space in the centre of planet or star and r is a distance from the centre

 

3. Relation between mass m of particle and density of space D into it is:

D = m x G

where G is gravitational constant. The density of space inside of the same atom is higher on the earth than on the moon, because on the earth the density of space is higher than on the moon. The same atom will have a bigger weight on the earth than on the moon. But its density D that defines its mass will remain the same. So by moving through the space the weight of particles changes, but its mass remains the same. Photon is an exception here. Around the photon there is no additional density D of cosmic space, so photon has no weight and no mass.

 

Energy of matter and energy of space inside of a material object or mass particle are in equilibrium, equal: Espace ( Es ) = Ematter ( Em )

 

Es = Em = m x cc, ( D = m x G)

 

where m is a mass of the object, c is speed of light, D is density of space around the object and G is gravitational constant.

 

Es = Em = (D x cc) / G

 

Energy of space Es inside of particle or material object depends on the density of space D.

 

First experiments that proves mass increasing of particles that moves fast were done about 100 years ago. The faster the elementary particle, the bigger will be its mass. We call that “The Relativistic Mass Increase”.

 

The formula E = 0.5m x vv shows the relationship between the increase in mass of the relativistic particle and its increase in kinetic energy.

 

In this formula we can change m with D/G and we will get the formula:

 

E = (0.5D x vv) / G

 

which shows clearly that the kinetic energy of particle depends on the density D of space into it and on the speed v

 

The mass of accelerated particle is increasing because the with the speed increasing the density around the particle is increasing.

 

Density of space is increasing also inside of the inertial system that moves with the higher speed regarding the inertial system that moves with the lower speed. This higher density of space causes the speed of clocks is slower into the faster inertial system.

 

Higher density of cosmic space inside of an fast inertial system is the bridge SR and GR. In SR the speed of inertial system causes the increasing of the density of cosmic space, in GR the mass causes the increasing of the density of cosmic space. “Inertial mass” and “gravitational mass” of a material object or particle are equal because the density of cosmic space in inertial mass and gravitational mass is equal.

 

Let’s say we are in a fast space ship that travels far away from the stars and planets in cosmic space with low density. With increasing of the speed of the space ship the density of cosmic space into it will increase. By attaining a certain speed the density of the space in the space ship will be equal to the density on the surface of the earth. Space ship travel than with this constant speed. We have two material bodies that are identical. Both of bodies will behave in exact the same way in the space ship and on the surface of the earth. The density D of space in both bodies is equal. This means the equality between inertial mass and gravitational mass.

 

4. Cosmic space is composed by quanta of space (QS) having the size of Planck length. Light is a physical event in which photons are "jumping" from one quantum of space to another in a Planck time. Cosmic space is a medium of light, inertial systems move through the cosmic space. That's why the speed of light is “maximum speed” in the universe and it is same in all inertial systems.

 

Light has a double particle-wave nature simultaneously. A single photon jumping from one quantum of space to another in its trajectory is the central part - particle. The “chain jumping” of the photon changes the frequency of the QS on its trajectory from its basic frequency to the frequency of the photon. The central part of the photon also changes the vibration of QS around its trajectory that is its circumference part - wave.

 

In a “double slit experiment” we can settle instruments and observe photon's particle-part or we can settle instruments differently and observe the wave's part of the photon.

When we settle instruments to observe a particle, we will observe (detect) the particle part of the photon, when we settle instruments to observe a wave, we will observe (detect) the wave part of the photon. Scientist (Observer) should not play any role in this experiment.

 

5. When a star has a mass of 3,2 masses of sun in its centre the density of cosmic space is so strong that gravitation overpowers all other forces. Matter transforms back into quanta of space (QS) that build up cosmic space.

 

Beyond Schwarzschild Radius gravity is so strong that prevails above all other forces. All elementary particles transform back into the energy of cosmic space. Matter and space are made out of the same “stuff”. Black holes are the “fabric” where matter transforms back into space. In big explosions of AGN space transforms back into matter.

Universe is composed by one energy. The basic packets of this one energy are QS. Energy is circulating continuously “space-matter-space-matter-…”. Universe is a self-renewing system. There was no beginning and there will be no end.

 

Schwarzschild Radius Rs is:

 

Rs = (2G x m) / (c x c)

 

G is gravitational constant

m is mass of the stellar object

 

According to the formula (1) D = G x m

D is the density of cosmic space in the centre of the black hole

 

Rs = 2D / (c x c)

 

Inside Rs gravitation has no direction, density of space does not increases towards the centre of the black hole. The area inside of Rs is a fabric where matter transforms back into the QS of cosmic space.

 

A mass has a weight when it is in a space where density changes, it has a direction. At the “weightless” Lagrange point between earth and sun happens that density D of space is stable, there is no change of density, no direction. So gravity is there because gravity is carried by the quanta of space QS, and QS build up cosmic space also at the “weightless point”. If it would be no gravitation at the “weightless point” earth would fly away long time ago.

A body at Lagrange point will not move, but this does not mean that gravitational force is not there.

 

Decreasing of the duration of motion of the orbital period of the binary pulsar PRS1913+16 is the result of matter transforming back into space in the centre of one star. This diminishes the mass of the star, diminishing of the mass causes diminishing of the speed of rotation, with diminishing of the speed the duration of motion on the orbit is increasing.

There is no gravitational radiation, gravitational waves do not exist.

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Some of the points Amrit is suggesting completely contradict what Professors of Physics have stated in their books! So I will trust the Professors.

 

Anyway in my reading I have come across an equation as follows:

 

T=(d/c)(d/R)^3 which can be used to estimate the time required for the binary system to coalense.

 

d - distance between centre of mass of the stars

c - speed of light

R - Schwarzchild radii

 

Can anyone please find values for d and R for the Hulse-Taylor binary? Does the value of d have to be the average? How can I work out the average because the velocity of the stars varies over one orbit - when d is small velocity is larger? Is the value of R to be used the schwarzchild meant to be the average of the two neutron stars? Thank you very much for all your help so far I really appreciate it.

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