Does Universe expands or collapses ?

If the total energy of the Universe = 0 = potential energy + kinetic and mass energy = 0

Than the potential energy has to be negative relatively to kinetic and mass energy. When is this case ?

The equation shows that gravitational potential energy is proportional to both mass and height. For example, raising two similar objects, or raising the same object twice as far, doubles the potential energy.

This assumption is mathematically exactly correct for a spherically symmetrical object (such as, to a reasonable approximation, a planet). It is not generally correct in other cases, though if the dimensions of an object are very small compared to the distance of separation then it is reasonable to consider it as a point mass and ignore the details of its shape.

With this simplifying assumption, integrating force over distance leads to the following general expression for the gravitational potential energy, U(g), of a system of two masses:

U(g)=integral [from h(1) to h(2)]Gm(1)m(2)/r^2 dr

U(g)=Gm(1)m(2)[1/h(1) – 1/h(2)]

If we try to calculate an "absolute" potential energy by setting the reference level at zero then the formula "blows up" with division by zero. In other words, we can only actually use this formula to measure the difference in potential energy between one non-zero separation and another.

In practice it is often convenient to take the reference level at infinite separation (i.e. h(1)=infinity), in which case the formula becomes:

U(g)= - Gm(1)m(2)/r

where r is now the distance between the centres of mass of the two objects (again noting the earlier caveats). For a small object above the surface of the earth, r is the distance from the object to the earth's centre (and similarly for other spherical bodies).

We see the minus in above equation because we calculate potential energy from infinity to a definite distance. The potential energy is related to the potential energy in the infinity.

When we calculate the total energy of the Universe and its potential energy is negative it means that we calculate it relatively to an infinite distance. The negative potential energy is when the matter comes from an infinity and collapses.

In cosmology it might be that a perfect empty space has an infinity small curvature. It started to collapse when the curvature becomes definite.
If it becomes enough sufficient dense the curvature of the gravitational potential energy might be transformed in a localized rest mass energy with its kinetic energy. Kinetic energy is repulsive and the rest mass matter expands then.

We observe a space recession because Vacuum becomes less energetic and less warped (curved). The Big Bang scenario is a consequence of the before collapsed space than.

Hello czeslaw:

I see you made a big, yet way common, mistake on the potential energy for a gravitational field. There are plenty of places where you can find support for this statement:

James Maxwell, Mr. Field Theory, was very bothered by it. This is a solution to the Poisson equation. The general solution is:

U(g) = k - M/R

See that k? It is important! In order to have the notion of energy in a field be consistent between the Maxwell equations and Newtonian gravity, U(g) must be positive, and k must be much bigger than M/R (I'll post the reference to Maxwell's analysis later, having trouble finding the URL). This stumped Maxwell. Einstein solved this by using some constants:

U(g) = 1 - G M/c² R

G is small, c² is huge, so this is always less than one except for black holes. This is the potential everyone should use every time because it gets the sign of energy right, where right means the one consistent with E and B fields. Do a force calculation by taking a derivative with respect to R and the constant drops, but it is necessary to get the meaning of energy to be the same.

This is such a common error, it is sad

doug

Isn't Wikipedia right ?
http://en.wikipedia.org/wiki/Potential_energy
"k" is very important. It depends on where is a zero point in a reference frame.
Notice that the gravitational potential energy has been defined so that an object very far from Earth's center (i.e. infinite r) has zero potential energy. This observation enables us to calculate in a simple way the escape velocity of any object sitting on the Earth.
http://theory.uwinnipeg.ca/mod_tech/node57.html

Hello czeslaw:

Wikipedia is one of many reputable places that does not have it right. I found the URL for this completely wonderful essay,
Why Maxwell Couldn’t Explain Gravity. I highly recommend a good read (even reread) of this paper. Newton had great insights into both gravity and light. Einstein had great insights into gravity and light. Maxwell, he only figured out stuff about light. Why did he get stuck? This article clearly explains the issue.

I must confess that I push on the implications in a way the author does not, namely that the only formally logically consistent way to write a potential is phi = 1 - 2 G M/c² R (I forgot the 2 last time, my bad). In my own proposal, I have phi = exp(-2 G M/c² R) whose Taylor series includes these two terms.

I have so much respect for Maxwell, and it was neat to understand where he had an issue. It is too bad this story is not more widely known. A field theory approach to EM and gravity cannot be constructed if wikipedia is right!

doug

Thank you Sweetser for a good link.
Energy is never negative. The potential gravitational energy is maximum in infinity. If they wrote it is equal zero, it means the zero is a maximum and every less energy would be with a negative sign relatively to this maximum energy. It is only a mathematical trick. Energy is always positive. It balances at a Schwarzschild Radius of the Black Hole. If there is more kinetic energy and "k" is greater than "2GM/c^2 R the object does not collapses.

I want to show in my thread that if Universe started of infinite low matter density (infinity low space curvature) it has its maximum potential gravitational energy than. It may reach a sufficient density locally where the potential energy might be transformed into a rest mass energy with its kinetic energy (our local Observable Universe with a critical density). It avoids a problem of singularity and space inflation. The potential energy is supplied from a bigger outside our local dense Universe. It avoids a problem of Dark Energy.
It is a Gedanken Experiment only.

Hello czeslaw:

I understand your goal, it is a good one. I am also glad we agree that for a classical system like the Universe (classical because no speeds are huge, no energy densities are high), we should only work with positive energies unless it makes sense to say something like the potential energy is negative.

In this equation:

potential energy + kinetic and mass energy = 0

we agree that the kinetic energy will be a positive number. The mass energy will also be a positive number. The only way this equation can equal zero is if the potential energy of the gravitational field is negative.

You have linked to a site that says plain as day that the energy of the gravity field should be viewed as negative. There is nothing wrong with sticking to those references, and we can politely disagree. For those who didn't read the Maxwell article (bad!), I'll map out the logic here because it is central to our technical disagreement.

We have a field theory for gravity governed by this equation:

∇φ(R) = ρ

This differential equation has the solution:

φ(R) = c M/R + k

[my bad: I switched c<-->k from the article] So that like charges attract, c must be negative. Most people who teach about gravity completely ignore the constant k - it is just a constant after all. If one where to take the potential in one spot, subtract a potential from another spot, k would drop. What wikipedia did implicitly (they certainly did not point it out) was to let k be zero.

What is the energy of a field? For an electric field, you get it by squaring E. The closer packed in your charges - even though they all repel, the higher the energy of the E field. Gravity appears to have the same property: bring all those masses in tighter, and you get more strength in the gravitational field. Square the energy of the field G, you should be able to get its energy (only in a classical field theory like Newton's or my work with GEM, not GR). This all sounds reasonable and even simple, until you have to account for like charges repel in EM but attract in gravity.

What Maxwell realized was if k was positive and super honking big, while c was negative, the energy of the G field and E field, and the repel/attracting stuff would make sense, there would be no need for a field with a negative energy. What Maxwell was unable to do was find some sort of equation whose solution had exactly those properties. That required the work of both Einstein and Schwarzschild to get a solution with the demands on a classical theory Maxwell demanded. It is so cool that Maxwell saw the necessary properties of a new approach to gravity.

The consequence of this view of the energy of E and G fields is that the potential energy must also be positive. Three positive numbers will never evaluate to zero unless all three are zero. Technically, the thought experiment is not valid.

doug

Three positive numbers will never evaluate to zero unless all three are zero.

I agree. That way the potential energy has to be on the begining. It might be stored in an infinite low space curvature or created in one moment and it is supplied now into our Observable Universe as a Dark Energy.

The potential energy extracted from a dense singularity seems very complicate for me.

Hello czeslaw:

I don't have any idea what these statements mean:

I have to have an equation to look at to feel really roped into physics. I do have some animations that also have technical information, but those animations have to be driven by equations. This is my own, well-defined issue: no equation, no understanding. I know how to write the metric for a weak gravity field (a baby step away from flat spacetime). I don't know about an infinite low space space curvature. Dark energy for me is equation free. If I was well versed in the research, I might know relevant equations.

Being old school, I think the singularities that Penrose and Hawking have shown exist in GR indicate where GR is wrong. If GR is flat out wrong for those particular domains, then I do not worry about the energy issues for said domains. That does not mean I have a replacement at this time, but I do have a concrete lead (in other words, equations to ponder).

doug

So is that an yes for expansion or a no to collapse?

__________________
"The beauty of that discussion of averages is that you don't have to be an expert in Apollo or in photography in order to see where this time study "analysis" breaks down. You just have to be, well...not an idiot." -JayUtah

Black Hole has a relation Mass/Radius=c^2/2G
The Mass increases proportional with a Radius M=R c^2/2G
An average density of the Black Hole D=M/V=M/aR^3=c^2/R^2 aG (a is const.numbers)
The average density decreases with R^2 much faster than Mass increases.
If Radius increases to infinity the density decreases to zero.
Ago an infinity time the density was nearly zero. In a certain place the entropy locally decreases and a distortion in a density causes a movement toward this distortion. It causes a local density decrease. After a certain time the density reaches a density of a Black Hole which may transfer a potential energy into a rest mass energy and Big Bang starts. The Big Bang is a local dense Observable Universe and it receives a potential energy from outside like an ordinary Black Hole.

It would be possible if the potential energy is transformed into a kinetic energy and it prevents to collapse into a superdense singularity.
The problem is how is the potential attractive energy transformed into a kinetic repulsive energy.

Hello Czeslaw:

Unfortunately I do not understand what you are saying. I will discuss the Schwarzschild metric which may be relevant, but it doesn't appear to work with your stance as I understand it.

The Einstein field equations are hard to solve. Einstein was not sure if anyone would in his lifetime. Schwarzschild made a series of simplifications that made it possible the very next year. He assume the source was static, spherical, non-rotating, and uncharged. Here is the solution in Euclidean coordinates, the coordinates used by astronomers:

ds² = (1+GM/2c²R))⁴ (dx² + dy² + dz²) - ((1-GM/2c²R)/(1+GM/2c²R))² dt² (MTW, eq.31.22)

In most technical books, the metric is written in the Schwarzschild coordinates because that makes the resulting metric look simpler, less to write. Both are correct. I chose the Euclidean coordinates for two reasons. First it is closer to what people who collect data must use. Second it shows that one should not put too much weight on how the metric is written.

The Schwarzschild singularity, or event horizon, is a coordinate singularity, meaning it depends on the choice of the coordinate system. There is a choice of coordinates where at R=2GM/c² nothing bad happens (no division by zero). It is impressive how much this coordinate dependent value gets discussed. Quantities that depend on the choice of coordinates are not deep insights. It would be interesting to know how much effort we are wasting on this coordinate dependent artifact.

To the extent that is it useful to consider the event horizon density where R=2GM/c², it does not represent a limit. It is easy to imagine something a million times more dense, and we have observational data that such massive small places exist at the centers of galaxies.

The Hawking/Penrose singularity where R->0 cannot be transformed away by a better choice of coordinates. They showed in the 60's that under a variety of conditions, the solutions to general relativity are singular. The problem with this is that things we can normally measure become undefined. That is why I do not like your phrase "superdense singularity": density cannot be defined at a singularity, so it is super undefined if anything.

It is my ATM opinion that Nature does not have the kind of Hawking/Penrose signularities that occur in general relativity. Czeslaw's speculations about the event horizon (it is worth consideration) appear closer to the mainstream that mine (the singularity indicates GR is wrong for this domain).

doug

Thank you Sweetser for explanation.
I am not sure if the Event Horizon could be created. Every stars are rotating and we use Kerr metric for a real Black Hole. Such a Black Hole has an ergosphere if it collapses.
You wrote a potential is phi = 1 - 2 G M/c2 R
It means there is more kinetic energy than potential gravitational energy in an object befor it collapses.
We observe that this heavy star receives more energy than emits and such a Black Hole grows only. How is it possible to create an Event Horizon if there is more kinetic repulsive energy than gravitational attractive energy ?

In a neutron star is a significant amount of binding energy (mass) and the mass of the neutron star is not only a baryon mass. There is a significant relativistic mass too.

I think Wiki has a nice article about the same, just in other words:
http://en.wikipedia.org/wiki/Magneto...lapsing_object

Thank you Svemir for this link. I have seen it before but it is much better now and larger.
I wrote a similar post on BAUT forum 7.August.2006
http://www.bautforum.com/archive/index.php/t-45357.html

My English is not so good and some people don't understand me. In Wikipedia is it writen in a proper English:

"Further, it is also known that realistic collapse of gravitational collapse must heat up the collapsing object and it must radiate out part of the energy gain due to release of gravitational energy during collapse. In the context of GR, this assertion has been made only in 2006[13].
Thus the quanta of "heat" i.e., photons and neutrinos generated within the collapsing object must move in increasingly curved trajectories as the continued collapse would proceed towards the z=∞ Black Hole stage. As a result they would increasingly fail to move out of the compact object due to its increasing self-gravity. In other words, the collapse generated radiation would tend to get trapped by self-gravity. This process of pure self-gravitational trapping during continued collapse has recently been elaborated.[14].

The outward PUSH due to radiation = Inward PULL due to gravity …(1)

In other words, sooner or later, at a sufficiently high z, the catastrophic collapse must be halted by the outward trapped radiation pressure and the object must become a quasi-static Radiation Pressure Supported Star (RPSS).

The existence of ECOs/MECOs is certainly not widely accepted at present.
But this is not necessarily because of any theoretical inconsistency or of any lack of observational evidence for ECOs. On the other hand, it could be so simply because the concept of a static Black Hole looks simpler and exact; and, also, four generations of astrophysicists and physicists have got used to working within the BH paradigm."

czeslaw