Gravity and Space

 Gravity and Space - a heavy topic

What exactly is 'gravity'? Gravity is defined by the product of space and time. Or perhaps we could say that space is defined by the ratio of gravity by time. I kind of like this definition better. When we have nothing, imagine nothing, like opening your SolidWorks page and you have drawn nothing, no definition of scale exists no points of reference no direction, nothing. To have space you need at least three objects; two points and something to compare them with. If we had three points and defined the distance between A and B as 1 Gordinian distance then we measured the distance between A and C relative to the distance between A and B and found the distance to be 4 Gordinians then we have defined space but without time. The number of axis of that space has depends on the freedom that the manifold you are using allows you. In the case of SolidWorks you are only allowed 3 axis of freedom and things can be referenced by two angles and a radius or three co-ordinates relative to another.

We would have to keep track of the distances with respect to time to make measurements in space*time. But how would we measure time? Well, we require energy to do this.

Because everything comes from energy and if you differentiate energy with respect to time you get power, energy is the integral of power with respect to time so time comes from energy, it's a derivative. Power is the product of torque and spin. Space is also a derivative of energy as energy is also the integral of force with respect to distance. Force is a vector with three dimensions so therefore space is a derivative of energy also. Putting these two conclusions together we derive that space-time is a derivative of energy as is everything.

Time is meaningless without energy as time is derived from energy. When we break up energy into the components of power and time or distance and force, energy is simply the product of these two.

Energy = Position displacement x Time

Or more accurately...

E=∫∆P x dt

Another way to express energy in terms of force and distance is..

E=F x D

..more accurately..

E=∫F x dD

Where D is distance and Force (F), as vector with three assumed axis (there could be more), is the product of mass and acceleration (a)

F=m x a

..so from E = F x D ..

E=m x a x D

..and acceleration is velocity divided by time

a=V/t

..and velocity is distance divided by time..

V=D/t

..so then putting things together..

E=m x D²/t²

Another way to express energy using Planck’s constant and frequency is...

E=h x v

This is using Planck’s constant h which is 6.6260689366 * 10-34 * joule*sec (1 joule is 1 * kg * m2 * sec-2) which was used to define the energy of photons and v is the frequency of the photon.

The units of Energy is in kg*m²*sec^-2

So..

E = m x D²/t²

From this we can solve for time in terms of mass, distance and energy.

t=D*√(m/E)

E = m x c²*10^-7 joules/erg

t=D*√(m/(m*c²*10^-7 joules/erg))

t=D*√((10⁷ ergs/joule)/c² )

t=D/C*3.16227766*10³

From the above equation solved for time, the speed of light is used to define the dimension of time or if you solve for distance then the speed of light is also used. The constant 10⁷ ergs/joule is a unit-less number as a joule and an erg measure the same thing; energy. Space and time come out of the equations that include the speed of light. Space and time are coupled together, they are the same thing just a different face and are both defined by the electromagnetic field.

So what about gravity?

If we look at the universe from a far distance, then the energy is all at one point. One could say that the frequency gets higher and denser.

How is it that gravity can cause lensing?

It seems that the electromagnetic field rides on the surface of space-time. There is a field that can carry an electrostatic force and a magnetic force. These two forces are two faces of the same coin, and they are at right angles to each other. The field, like everything, is a product of energy and is spread throughout space. when it vibrates electromagnetic waves propagate through this field in quanta, we call photons. When there is no electromagnetic waves then the field is still. Only neutral particles without any charge such as neutrinos do not affect this field. As all atoms are made of protons along with electrons they affect and are affected by this field.

The Speed of Light in a Gravity Well

Light will appear to travel slower in gravitational fields. This is due to the fact that time will dilate, making clocks run slower and measuring devices to shrink. Time dilation is given by the following ..

t_d = √(() 1-2*G*M_o/(d_o*c² ))

.. where ..

d_o is the distance from the center of mass of the object with mass Mo, G is the gravitational constant and c is the speed of light in a vacuum.

When you use this formula to calculate the time dilation of an object near a black hole then you will get..

t_o = t_f /√(1-C_h/C_o )

.. where ..

t_f is the time for the object falling into the event horizon, t_o is the time for the observer, C_h is the Schwarzschild radius and C_o is the distance that the object is from that event horizon’s center. As you can see that as the object approaches the event horizon, the observed time will approach infinity, therefore making it impossible to observe the fall. The object will be effectively frozen just on the outside of the hole.

Due to this equation it is impossible for an object to fall into a black hole

Gravity and Anti-Gravity

Gravity may not only suck but it may also blow

The simplistic equation for gravity, Newton’s equation of the attraction of two bodies m1 and m2, has a secret, well maybe not so secret, glaring right at us giving us is a clue to dark energy. I’ll put the equation right here so we can look at it.

f_g = G x m₁ x m₂ / d²

Now this looks like a relatively simplistic equation, and it is in this format but, two things, it is only showing the gravitational pull on two bodies, we know that our solar system is made up of many bodies all affecting each other and that a planet is made from many discrete particles and they themselves are all pulling on each other. While the above equation is good enough for basic physics class and even getting a rocket to the moon, it is an oversimplification. The second thing is that it had a square, yes, right there in the denominator on the right-hand side and so would the expanded multi-body version of the same concept.

The squared distance means that the force exponentially decays with the distance between the masses and guaranteeing that the force f_g is always positive, mass is always positive. But, if the distance separating the masses is at another axis at right angles to the three axes of space that we are used to then d could have an i operator (√(-1)), a conjugate distance. This would give a negative value to f_g.

If f_g is negative, then it would generate a repulsive force meaning the masses would push away from each other. This would mean that the distance between the masses, d, is in another dimension.

Einstein's Field Equations'

Einstein’s field equations are dependent on the distribution of matter and energy in a region of space, where Newtonian gravity is dependent only on the distribution of matter. The fields described by general relativity, as we are aware of, represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating up the gradient of the field. If you are sitting in a rocket in space and fire the engine you will feel a force that is just like gravity which is caused by the inertia of your body if the rocket is accelerating, by Newton's second law. And while you are standing on the surface of the earth you are experiencing acceleration without motion, on the surface of Earth about 9.8 meters per second per second is your acceleration due to gravitational distortion of time-space. Generally, the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, the most well known being the deflection of light in a gravity field, the differences are minimal and so the Newton equation is adequate in this instance.

As I understand it the tensor description used up to n dimensions and the Einstein field equations set n=4, three of space and one of time. All three are treated like spatial dimensions so the time dimension is multiplied by c, the speed of light, to give it the same units as the other three dimensions.

G_uv - Λg_uv = kT_uv

Λ as the cosmological constant here and k is Einstein’s version of the gravitational constant. The cosmological constant is defined as the energy density of space, or vacuum energy, that arises in Einstein's field equations of general relativity. It is closely associated to the concepts of dark energy and quintessence.

Λ = 3 x H_g/c * Ω_Λ = (1.1056*10^-52)/(m²)

Ω_Λ (Omega Lambda)

Instead of the cosmological constant itself, cosmologists often refer to the ratio between the energy density due to the cosmological constant and the critical density of the universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted Ω_Λ, and is estimated to be 0.6889±0.0056, according to results published by the Planck Collaboration in 2018. H₀ = 67.66±0.42 (km/s)/Mpc (Mpc is mega parsec)

The value of k is...

k=8πG/c⁴

(G here is Newton’s gravitational constant not to be confused with G_uv) which is equal to 2.077 * 10^-43 / N

G_uv is a tensor field which is representative of the energy of the field and is the Einstein tensor. The variable g_μν is the metric tensor, T_μν is the stress–energy tensor, Λ is the cosmological constant and k is the Einstein gravitational constant. Newton’s gravitational constant is expressed in terms to convert units of mass² /distance² to units of Newtons (mass * distance / time²) a measurement of force. Einstein’s constant k units are time²/(distance x mass) or Newtons^-1

The Einstein tensor is defined as..

G_uv= R_uv - 1/2 x Rg_uv

where R_uv is the Ricci curvature tensor, and R is the scalar curvature. This is a symmetric second-degree tensor that depends on only the metric tensor and its first- and second derivatives.

Mathematically, spacetime is represented by a four-dimensional differentiable manifold M and the metric tensor is given as a covariant, second-degree, symmetric tensor on M, conventionally denoted by g. Moreover, the metric is required to be nondegenerate with signature (− + + +). A manifold equipped with such a metric is a type of Lorentzian manifold.

Explicitly, the metric tensor is a symmetric bilinear form on each tangent space of M that varies in a smooth (or differentiable) manner from point to point. Given two tangent vectors u and v at a point x in M, the metric can be evaluated on u and v to give a real number:

g_x(u,v) = g_x(v,u)∈R

This is a generalization of the dot product of ordinary Euclidean space. Unlike Euclidean space – where the dot product is positive definite – the metric is indefinite and gives each tangent space the structure of Minkowski space.

Is Gravity Quantum?

Most of us think so. It has always been a goal of physics to have a complete unified theory of everything and with quantum gravity, the graviton, would complete that goal. Though there are a few alternatives that don't directly go against the unified theory of the quantum they don't have the evidence either. One of the many issues is that gravity isn't really a force like the other forces are, so it seems. Gravity is all about space-time, and space-time is the stage on which all the particles strut their stuff as the actors.

In the normal QFT world, that stage stays fixed and unmoving throughout eternity, allowing us to focus on all of the interaction inanity. But general relativity tells us that the stage is an actor too and it bends and warps under the influence of the the other actors. That bending and warping redirects the actors' motions. And when we look back at our basic electron-photon interaction under a quantum field picture, we start to get migraines. We have to take into account not only every possible combination and permutation of photons and electrons interacting, but also all possible configurations of space-time underneath them! The quantum fluctuations fluctuate the space-time they are embedded in!

From an article By Charles Q. Choi on August 14, 2018 issue in Scientific American

The search for the graviton which is the proposed fundamental particle expected to be carrying gravitational force is a crucial step in physicists’ long journey toward a theory of everything.

Amazon Links to books on the subject>

All the fundamental forces of the universe are known to follow the laws of quantum mechanics, save one: gravity. Finding a way to fit gravity into quantum mechanics would bring scientists a giant leap closer to a “theory of everything” that could entirely explain the workings of the cosmos from first principles. A crucial first step in this quest to know whether gravity is quantum is to detect the long-postulated elementary particle of gravity, the graviton. In search of the graviton, physicists are now turning to experiments involving microscopic superconductors, free-falling crystals and the afterglow of the big bang.

The other fundamental force of quantum mechanics indicates that everything is made of quanta, or packets of energy, that can behave like a particle and a wave as demonstrated by the well known dual slit experiment. Detecting the hypothetical quanta of gravity would prove gravity is quantum. But because gravity is so extraordinarily weak to directly observe the extremely small effects a graviton would have on matter a particle used to detect a graviton using particle accelerators would have to be so massive that it collapses on itself and forms a black hole.

Theoretical physicist James Quach, of the University of Adelaide in Australia, has suggested a way to detect gravitons by taking advantage of their quantum nature. Quantum mechanics suggests the universe is inherently fuzzy—for instance, one can never absolutely know a particle's position and momentum at the same time. One consequence of this uncertainty is that a vacuum is never completely empty, but instead buzzes with a “quantum foam” of so-called virtual particles that constantly pop in and out of existence. He suggests that these entities may be any kind of quanta, gravitons included.

It was only a few decades ago that scientists found virtual particles generate detectable forces, the Casimir effect is one example. It is the attraction or repulsion generated between two flat surfaces placed very close together in a vacuum. These surfaces move due to the force generated by virtual photons coming into and out of existence. Also, other research suggests that superconductors may reflect gravitons more strongly than normal matter, so Quach did some calculations looking for the interactions that should occur between thin superconducting sheets in vacuum. This could indicate the Casimir effect due to gravitons. The resulting force is expected to be about 10 times stronger than that expected from the Casimir effect of photons.

A microchip was developed to perform this experiment. In the chip was two small aluminum-coated plates cooled to near absolute zero, they became superconducting. One plate with a movable mirror was fired at using a laser. If the plates moved because of a gravitational Casimir effect, the frequency of light reflecting off the mirror would measurably shift, a form of interferometry. Unfortunately, they failed to see any gravitational Casimir effect. This null result does not necessarily rule out the existence of gravitons—and thus gravity’s quantum nature. Rather, it may simply mean that gravitons do not interact with superconductors as strongly as prior work estimated, says quantum physicist and Nobel laureate

The cosmic microwave background radiation could be another strategy to find evidence for quantum gravity, the faint afterglow of the big bang, Cosmologist Alan Guth of M.I.T. says quanta of gravitons would fluctuate like waves, and the shortest wavelengths would have the most intense fluctuations. When the cosmos expanded immediately during the period of rapid inflation if the big bang, according to Guth’s widely supported cosmological model known as inflation, these short wavelengths would have stretched to longer scales across the universe. This evidence of quantum gravity could be visible as swirls in the polarization, or alignment, of photons from the cosmic microwave background radiation.

However, the intensity of these patterns of swirls depends very much on the exact energy and timing of inflation. “Some versions of inflation predict that these swirls should be found soon, while other versions predict that they are so weak that there will never be any hope of detecting them,” Guth says. “But if they are found, and the properties match the expectations from inflation, it would be very strong evidence that gravity is quantized.”

Another way to figure out if gravity is quantum by looking directly for quantum fluctuations in the gravitational waves, we have observed coming from black hole mergers, which, being gravity waves, are considered to be made up of gravitons that would be generated shortly after the big bang. Unfortunately, the Laser Interferometer Gravitational-Wave Observatory (LIGO) is not sensitive enough to detect these fluctuating gravitational waves that would have existed in the early universe, Guth says. A much more sensitive gravitational-wave observatory, perhaps in space could potentially detect these waves.

In a paper recently accepted by the journal Classical and Quantum Gravity, however, astrophysicist Richard Lieu of the University of Alabama, Huntsville, argues that LIGO should already have detected gravitons if they carry as much energy as some current models of particle physics suggest. It might be that the graviton just packs less energy than expected, but Lieu suggests it might also mean the graviton does not exist. “If the graviton does not exist at all, it will be good news to most physicists, since we have been having such a horrid time in developing a theory of quantum gravity,” Lieu says.

Perhaps gravitons don’t exist is another possibility.

Source of information is from.. Scientific American (Link to abo