General Relativity

Einstein worked (from) Newton’s equations describing matter and gravity: And he also changed a lot of it too, describing gravity in whole new terms to physicists. Newton’s law of gravitation is given as:

F = G M1M2/d2

Where G is the gravitational constant, m1 is mass one, and m2 is the second body with mass, and F was the force distributed between them. Also, Einstein worked with the already existing equation describing the laws between two masses m1 and m2, finding a square force that weakened over greater factors:
Charles Augustine de Coulomb in 1785 showed that the force of attraction and the force of repulsion between two electrically charged bodies and also between magnetic poles also obey an inverse square law. The force for two magnetic bodies are given as:
Fm = (1/µ)(p1p2/r2)
With what Einstein had in mind for this universe, which was pure curvature, he was able to use these concepts to create a geometrical vision of our cosmos. It described that matter was actually an energy:

E=Mc²

Which converts to the negative of E=Mc2m found by Dirac's Equation:

E=-Mc²+(E=Mc²) = 1022KeV of gamma energy

Through:

M=E/c²

Which is the reverse of E=Mc² and was first developed by Poncair. This scientist was also known for his remarkable work on relativity, and is often forgotten. In fact, General Relativity unifies the work of Poncair and Einstein in their theories describing Special Relativity with Newtons law of Gravitation.

Matter warped space, and time told matter how to move. And it can be said that time warped matter, and that matter told space how to act. This is because of Einstein’s equivalence principle, which covers a massive scope in his mathematically-genius work.

This next equation is Einstein’s field tensor, and you will most certainly learn it in a standard course of physics at college or university:

G_ab=kT_ab

This equation is very important, where the G_ab Einstein Tensor Factor, and the Stress Energy Tensor is given as and T_ab and k is a constant. This equation relates to the curvature of space and time, saying that stress energy is what causes the disturbance of spacetime. As we have seen, Einstein used Newton’s law of Gravity in his Field Equations, then we find the constant of k to have a value of:

Where π is pi, and G is the gravitational constant and k is a coupling constant, which will be most familiar as

k=8piG/c^4

The following equation which is an extension of the above equation connects matter with energy with the geometry of spacetime (on the left):

G^uv(-8 π G/c²)T^uv

But using the more well-known value of kappa, it gives the more recognized value of the above equation:

G^uv= 8 π G/c^4 |T^uv

A major consequence of General Relativity, is that it describes that time is dilated round strong gravitational fields. Tim can also be warped traveling through spacetime at very high speeds in long distances. We will explore that soon.

t’=t√1-2GMc²r

Where,
• t' = Time inside the gravitational field.
• t = Time outside the gravitational field.
• M= The mass causing the gravitational field.
• r = The distance from the center of the gravitational field.
• c = the speed of light in a vacuum 186,000 mps.
• G = The gravitational constant = 6.6742 x10-11 N m2 kg-2

From Pound and Rebka’s experiment in 1959 at the Harvard University, we know that the shift round in the gravitational distortions warp time only by infinitesimal standards. In order to measure the dilation with significant results, we have resorted to using atomic clocks. In other words, the life spans of particles could be experienced to be longer moving at very very high speeds. We can such particles, such as gold atoms to a fraction short of ‘c’, but we can never exceed that v>c because then we would require an infinite amount of energy… which is another successful prediction of relativity.

General Relativity was by far the more difficult to create, as it took Einstein so many more years to finish it. Special Relativity was also mathematically beautiful and so very straight forward when one began to appreciate it.

Special Relativity

Length Contraction and Relativistic Energy

In these relativistic principles, we need to know some concepts.

Minkowski’s flat vector spacetime is best used in physics today. It is given as (-, -, -, +) or (+,+,+,-) and with a matrix of, and in special conditions, can be written as (0,0,0,0) in zero-dimensions:

…..1000
…..0100
N=0010
…..0001-

The following equations are called ‘’Cartesian’’ coordinated systems, and they describe the distance between two points:

s² = (∆x)² + (∆y) ²

In a rotated system, we twist coordinates around in space, and we find them as a geometry of distance. The new coordinates are given as:

s² = (∆x′)² + (∆y′)²

Being almost identical math, they are easy to remember. In this case, we say that distance is an invariant of these equations. More interesting is that we learn that time is also an invariant of space.

Because of this, we can therefore find the following equation describing a spacetime interval:

s² = −(c∆t)² + (∆x)² + (∆y)² + (∆z)²

Where (t, x, y and z) are the coordinates of spacetime, because we can rotate space, and find a corresponding value with time, and this is why we say that space and time are one thing. All these equations lead to many more equations, just as Lorentz Boosts which derive from the mathematics described by Galileo, and his coordinates are given through the variables:

x' = x − vt
y' = y
z' = z
t' = t

This might sound very complicated, but it is relatively simple.

We should first start with rotational boosts, such as found in an x and y plain.

We are always taught that the rotational value θ is in fact a periodic invariant with a period with a value corresponding to 2π.

Now, the Boosts are in fact nothing but rotations in time and space. It can be put into a matrix, but i very much doubt my variables would show up here, so i shall continue just explaining.

The Boost parameter φ (found in the matrix), is in fact defined to infinity -00 to 00, totally in this direction. The rotation angles need not abide by such a rule, if my memory serves me correctly.

t′ = t cosh φ − x sinh φ
x′ = −t sinh φ + x cosh φ .

Here we have a set of Boosts, where the transformed coordinated are t' and x', and this tansformation has a moving value of x'. And therego, we say such a Boost has a velocity of

v = x/t= sinh φ/cosh φ = tanh φ

Before relativity, we never considered time as a vector of space. Now we cannot remove either, as it has been shown that time is a distance as well in space. To move through space, is to take a massive journey in time for us. In fact, time moves at the speed of light, and because we live in such a slow part of the universe, we cannot help but flow along with it.

Relativity was also developed to answer for optical phenomenon. One of these the Length Contraction of a physical body accelerating through spacetime.

The Length Contraction formula is given as:

L=L_0 (1-v²/c²)½

Here, L_0 is the proper length, and v is for velocity and c is for the speed of light. This equation shows that an object moving through spacetime is found to contract in length to the observer. Such paradoxes like, the pole and barn paradox are prime examples of this optical phenomenon.

So in short notation, we say that space contracts and time dilates by a factor of:

√(1-v²/c²)

As I explained, one example of Length Contraction is given by the pole-barn paradox. This is where a pole is traveling through space, and is physically contracted. If the pole is larger than the barn to begin with, and now it is shorter because of length contraction it can fit in the barn. Paradox is, how can a pole larger than the barn be length contracted so that it fits as it passes by? In this next set of equations, we work with a pole traveling through space which has a proper length of 20 meters. An observer moving at a speed v = 0.98 c will experience a contraction as shown:

L_0 = 20 m

L = L_0 (1 - v²/c²)½

= 20 [ 1 - (0.98)² ]½

= 3.98 m

If an object is accelerating through spacetime, it will experience a time warp. This is also been known to be called time dilation. If we experience time warps, then according to relativity this must also mean space warps.

We don’t experience space warps so much because we move so fast through time. In fact, we spend more time in the time dimension than we do in space. The time dilation formula is given as:

∆t=∆t_0/(1-v²/c²)½

In Einstein’s paradox, a moving spacetime traveler (twin one) is going at speeds short of ‘c’ arrives home having only aged a year or so, and on Earth his twin has aged considerably. In relativity, we learn that E=Mc2, and that energy can be transferred through angular momentum of a system, and the conservation of physics states that the loss of energy is equal to the gain of energy given as:

∆E=∆Mc²

Where mass gained is a loss in energy. And we also find that energy gained or lost, is equivalent to a gain in mass:

∆M=∆E/c²

Where L is the angular momentum, r is the position of the particle, x is the cross product and p is the linear momentum:

P=Mv

This shows, as it does in any text book, that momentum p is related to mass multiplied by the velocity v. The importance of this equation is that energy can only ever be transferred through angular momentum. So the particle is said to be given as:

L=r x p

And between two objects, one finds that one gains momentum and the other looses momentum, given as:

∆p1=-∆p2

Because everything is conserved, the state of momenta found prior to the transfer is equal to the momenta afterwards:

m1u1+m2u2=m1v1+m2v2

These equations are beautiful. I have also equated that if an end is desired by time and the cosmos, then somehow mass and energy is an illusion:

E=Mc²+E

And if ‘’c’’ is not equal to zero, which we know it isn’t, then we find through algebra that:

Mc2=0

This can be found to be true about this universe. All matter comes to zero when added with the energy in the vacuum:

(E=Mc²)+(E=-Mc²) = 0

So the converse can be accumulated:

M=E/c²+M

Then all energy comes to zero as well:

E/c²=0

The reason why this happens, is because we are adding all the matter and energy, about 10^80 particles ‘’pop’’ into existence, and when added to the negative energy of the vacuum produces a zero-total. The negative reservoir is called The Dirac Sea, and it is filled with negative spinning particles. In fact, Dirac postulated this sea using relativity. Virtual particles, like the kind found in this sea, don’t share the same properties as real energy:

E² = m²c^4

And is found to reduce to this instead of the normal energy and momentum formula:

E² = p²c² + m²c^4

… for when a particle is at rest p=0. Where p is momentum and c is the speed of light. This new relativistic outlook on the electron allowed Dirac to formulate his famous equations describing antimatter.

These relativistic formulae show that every time an electron ‘’pops’’ into existence, it leaves behind a hole. This hole is found to be its antipartner, the positron.

To measure the Kinetic energy of something, you must calculate it with the formula:

KE=E-E_0

And to measure the Kinetic energy of a high speed particle, we use the equation:

KE=Mc² - M_0c²

And the total energy is found as:

E=Mc² (1-v²/c²)½

And the rest energy is given in relativity as:

E_0=Mc²

Pure simplicity at its best. These equations have been the most influential in the world. These equations can describe the motions of little particles as well.

The complications of this are amazing. Time dilation in relativity means that a twin traveling off into the far reaches of spacetime a fraction short of c would return to earth hardly aged a year, whilst his twin is an old man. Einstein has shown the world of physics that time is not a fixed clock in the sky, and two events that are relative to each other will experience different times traveling at different speeds.

Vectors AND Scalars

In relativity, we find vector and scalar equations that describe in their own terms coordinates and fields.

For Vectors, we find that they describe:

Length, Area, Speed, Volume, Time, Mass, Energy Density, Pressure, Power, Temperature, Electric Charge and the Electric Potential.

For scalars, we find:

Displacement, Acceleration, Velocities, Force, Weight, Momentum, Torque, Electric Currents, Electric Field Strengths and Magnetic Field Strengths.

Even though they are described by different names, they are actually connected sensitively that one could say they are the same thing, because of magnetic and electric curl equations.
The electric constant (ε_0) has a value of 8.854*10-12Fm-1, and the magnetic Constant (μ0) has a value of 4π*10-7Hm-1.

Ouch!



Well, there's page one... I might post an intelligent reply in a week or two after I have had time to read that.

I'm sorry if it hurt I apologize.

Nevertheless, i was only hoping for a general discussion on the outcomes and prediction of general and special relativity.

What do i make of the equations, and what is universally-known?

''E=Mc²

Which converts to the negative of E=Mc2m found by Dirac's Equation:

E=-Mc²+(E=Mc²) = 1022KeV of gamma energy

Through:

M=E/c²''

It was known to Dirac, that if energy and matter where two sides of the same coin, then the reverse of each was capable. This gave rise to Dirac's equation, and the birth of antimatter from our perspective. E=Mc^2 is therefore the first indication that antimatter existed.

''This next equation is Einstein’s field tensor, and you will most certainly learn it in a standard course of physics at college or university:

G_ab=kT_ab

This equation is very important, where the G_ab Einstein Tensor Factor, and the Stress Energy Tensor is given as and T_ab and k is a constant. This equation relates to the curvature of space and time, saying that stress energy is what causes the disturbance of spacetime. As we have seen, Einstein used Newton’s law of Gravity in his Field Equations, then we find the constant of k to have a value of:

Where π is pi, and G is the gravitational constant and k is a coupling constant, which will be most familiar as

k=8piG/c^4

The following equation which is an extension of the above equation connects matter with energy with the geometry of spacetime (on the left):

G^uv(-8 π G/c²)T^uv

But using the more well-known value of kappa, it gives the more recognized value of the above equation:

G^uv= 8 π G/c^4 /T^uv.''

Says a very lot.

It says that matter, space, energy and time are all interlinked. In fact, according to Einstein, one cannot have a matter, energy, space or time, if one of these ingredients are taken away. This means that matter and energy is some kind of distortion in the vey fabric of space and time. In fact, if one removed all the energy and matter from the universe, space and time would instantly follow.

Matter is a longer lived fluctuation in space and time of a form of energy. It fluxes to this state through a method of freezing, even though there is no such thing as an absolute zero temperature in spacetime. But this is my interpretation, by saying an energy freezes into a certain state. The other idea right now is energy knots create matter fluctions. Other indications simply say that from one form, another is created.

''In these relativistic principles, we need to know some concepts.

Minkowski’s flat vector spacetime is best used in physics today. It is given as (-, -, -, +) or (+,+,+,-) and with a matrix of, and in special conditions, can be written as (0,0,0,0) in zero-dimensions:

…..1000
…..0100
N=0010
…..0001-

The following equations are called ‘’Cartesian’’ coordinated systems, and they describe the distance between two points:

s² = (∆x)² + (∆y) ²

In a rotated system, we twist coordinates around in space, and we find them as a geometry of distance. The new coordinates are given as:

s² = (∆x′)² + (∆y′)²''

Says that space and time are useless without each other. In fact, this is
what is said to have given birth to the notion that space and time are inseperable, because one cannot measure a space without a duration of time.

It is for this reason many physicists exclude that measurement is intrinsic to some intelligence. If there is no intelligence, then there cannot be anything such as a measurement. Both quantum behaviour and relativity point to the same conclusions: The universe is observer-dependant.

''I have also equated that if an end is desired by time and the cosmos, then somehow mass and energy is an illusion:

E=Mc²+E

And if ‘’c’’ is not equal to zero, which we know it isn’t, then we find through algebra that:

Mc2=0

This can be found to be true about this universe. All matter comes to zero when added with the energy in the vacuum:

(E=Mc²)+(E=-Mc²) = 0

So the converse can be accumulated:

M=E/c²+M

Then all energy comes to zero as well:

E/c²=0

The reason why this happens, is because we are adding all the matter and energy, about 10^80 particles ‘’pop’’ into existence, and when added to the negative energy of the vacuum produces a zero-total. The negative reservoir is called The Dirac Sea, and it is filled with negative spinning particles. In fact, Dirac postulated this sea using relativity. Virtual particles, like the kind found in this sea, don’t share the same properties as real energy:

E² = m²c^4

And is found to reduce to this instead of the normal energy and momentum formula:

E² = p²c² + m²c^4

… for when a particle is at rest p=0. Where p is momentum and c is the speed of light. This new relativistic outlook on the electron allowed Dirac to formulate his famous equations describing antimatter.''

... Points to a very strange concept, that everything in the vacuum should value a total zero.

The main problem is that the math of current research seems to suggest that there is a massive remainder even when everything is renormalized. I hold into the prospect that we might have the math wrong.

There's just a small part, to start off.

Since nobody has ever seen negative mass in a lab anywhere, the algebraic cancelation of plus and minus E=mc²...seems wrong. Postulating more things not seen doesn't seem to be leading physics towards realistic solutions, either in particle physics (the Standard Model) or cosmology. pete

__________________
A third rate theory forbids
A second rate theory explains after the fact
A first rate theory predicts...A. Lomonosov

I disagree with your analysis of the work. I do not refer to exotic matter - but rather how when a particle comes out of the Dirac Sea, it split's off a partner hole. In fact, just recently, there was a massive antimatter cloud discovered. And, what is also for my interest, was the massive hole found in the universe...

... What caused this? I think it was an early matter-antimatter collision.

Yes the antimatter cloud hovers around the galactic center. Many also speculate (self included) about a relation with antimatter production and black holes.
But I want to point out about clarity in wording to- the "hole" is not necessarily a "hole."

If I am reading you right, you speculate that the 'hole' is the result of a catastrophic meeting of matter/antimatter?
What leads you in this direction of thought? Have you read articles on that or is it your own speculation?

In the meantime, I am stillreading your equations from above head spins....

Yeh... I'm just babbling away. You see, big bang does not predict such a hole, but it could, since it does predict a matter-antimatter creation in equal distribution without any CPT-violation.

The words, ''Damn lucky,'' come to mind. Much like reality as we know it anyway.

I'm not sure that I follow "predicts matter antimatter in equal distribution" here.

If both were created in equal distribution- I can see catastrophic occurrences taking place in the early Universe.
Fact is we have a lot of matter right now and not much antimatter.

The current distribution observed demonstrates that matter and antimatter were not created in equal proportion.

The fact that antimatter can be created does not necessarily mean it will be created. Just that the creation is not strictly forbidden.

Quite right. Matter and antimatter SHOULD HAVE BEEN created in equal proportions due to quantum theory.

Why?

Except for violations of CPT parity!

__________________
Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

I can't do the math, but from what I read, antimatter WAS the hole in the Sea. Something about how the Dirac particles for say an electron had negitive charge but negative energy, the hole would have a positive charge and positive energy, that is, a positron. I could be wrong though.

__________________

No... you are right.

Poincaré.

__________________
"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

I apologize.