a little help needed for an ignorant old man

[CraigS]

Hi Brian;

I'm also interested in this topic so I've done a lot of reading up on it to satisfy my own curiosity. I'd also like to share what I've learned, but I'm no expert. Perhaps others might help out (when they get the chance).

Having said this, all this is actually in accordance with the laws of thermodynamics according to Alan Guth (the grand-daddy of the inflation part of BBT). I'd suggest having a read up on his link in Wiki.

I'd also check out supercooling and phase transitions of false vacuums. Quantum mechanics suggests that the initial enery releases may have been from the breaking of symmetry. Good descriptions of all of this are in Wiki.

Hope this helps.

Cheers

[Brian W (Brian)]

Ok Craig, time to share some of your expertise. In the A. Guth article there is talk of 'omega' and how it needs to equal 1.

It is obviously a buzz word that I should know. What is it?
B

[sjastro]

Originally Posted by Brian W

Ok Craig, time to share some of your expertise. In the A. Guth article there is talk of 'omega' and how it needs to equal 1.

It is obviously a buzz word that I should know. What is it?
B

Imagine a very simple Universe composed of a very large mass and a very small mass. There is a gravitational force between the masses.
Suppose the small mass is at some fixed distance and kinetic energy is supplied to the smaller mass.

There are 3 scenarios.
(1) The kinetic energy is insufficent to overcome the gravitational potential energy. The small particle initially moves away from the larger mass but eventually stops and falls back towards the larger mass.
(2) The kinetic energy equals the gravitational potential energy. The small mass will move away from the large mass but it is being slowed down. Inertia however prevents scenario (1) from occurring.
(3) The kinetic energy is greater than the potential energy and the small mass moves away from the large mass without being slowed down.

Each scenario can also be described by the density of the large mass, since the gravitational potential energy varies according to density.

For scenario (2) to occur the density of the larger mass has a particular value. This is known as the critical density.
If the actual density of the large mass is less than the critical density than (3) occurs.
If the actual density of the large mass is greater than the critical density than (1) occurs.

Omega is simply the ratio of the actual density to the critical density.
If actual density equals critical density then Omega = 1.

This principle can be applied to our Universe. Omega descibes the effect of gravity on an expanding Universe and also the geometry of the Universe.

If Omega < 1, the Universe will expand forever. An open Universe.
If Omega = 1, the Universe will expand forever (even though it is slowing down slightly). A flat Universe.
If Omega >1, the Universe will stop expanding and eventually collapse. A closed Universe.

Our Universe is flat. This has been confirmed by the variations in the Cosmic Radiation Background hence Omega = 1.

In Cosmology Omega is more complicated as it goes beyond the density of matter. It is composed of a visible matter component (as described above), a dark matter component and dark energy.

Regards

Steven

[Archy (George)]

Steven, you say:
"Each scenario can also be described by the density of the large mass, since the gravitational potential energy varies according to density."

Where exactlyin Newton's law of gravitational attraction does density come in?

[Archy (George)]

Steven, you say:
"In Cosmology Omega is more complicated as it goes beyond the density of matter. It is composed of a visible matter component (as described above), a dark matter component and dark energy."

To cut out the mumbo jumbo, if I were to fire a bullet, I can calculate its trajectory without invoking dark matter and dark energy. Since earth and the bullet are part of the cosmos and the bullet's path can be calculated without invoking dark matter and dark energy, dark matter and dark energy are fictions.

[sjastro]

Originally Posted by Archy

Steven, you say:
"Each scenario can also be described by the density of the large mass, since the gravitational potential energy varies according to density."

Where exactlyin Newton's law of gravitational attraction does density come in?

Mass = Density X Volume.
You substitute the mass term for density X volume.

This is done for objects that are not expressed as point masses.

Steven

[bojan]

Originally Posted by Archy

Steven, you say:
"Each scenario can also be described by the density of the large mass, since the gravitational potential energy varies according to density."

Where exactlyin Newton's law of gravitational attraction does density come in?

Steven probably wanted to say "Each scenario can also be described by the density of the total mass, since the gravitational potential energy varies according to density."

Steven, please confirm.

[sjastro]

Originally Posted by Archy

To cut out the mumbo jumbo, if I were to fire a bullet, I can calculate its trajectory without invoking dark matter and dark energy. Since earth and the bullet are part of the cosmos and the bullet's path can be calculated without invoking dark matter and dark energy, dark matter and dark energy are fictions.

Your example is flawed because the bullet is travelling in space. The bullet is not stationary in space being carried along by the Hubble flow.

Steven

[sjastro]

Originally Posted by bojan

Steven probably wanted to say "Each scenario can also be described by the density of the total mass, since the gravitational potential energy varies according to density."

Steven, please confirm.

Bojan,

In the two mass Universe example, the large mass is an extended mass of radius r, the small mass is a point mass at the radius.

If the larger mass has a greater density this corresponds to a reduction in r (since density = mass/r^3).

The smaller mass is now closer to the centre of the large mass and is now at a different gravitational potential. It will require more KE to overcome the gravitational potential.

Regards

Steven

[bojan]

Originally Posted by sjastro

Bojan,

If the larger mass has a greater density this corresponds to a reduction in r (since density = mass/r^3).

The smaller mass is now closer to the centre of the large mass..

Could you please explain this in more detail ?
I don't get it how the distance can vary with density of the large mass only.
(unless this applies to a total mass)

[sjastro]

Originally Posted by bojan

Could you please explain this in more detail ?
I don't get it how the distance can vary with density of the large mass only.
(unless this applies to a total mass)

Mathematically if the large mass is very much greater than the small mass you can disregard the effects of the smaller mass.
For example the small mass is in the gravitational well of the larger mass, not around the other way.

The density of the large mass determines the depth of the well.
So if you shrunk the Earth down to a certain size, even though the mass remains the same, the gravitational well is deeper for the small mass to reside in. It would require more energy to get out of the well.

Regards

Steven

[bojan]

That's all OK, provided the small mass is on the surface of the big mass.
However, it is implied both masses are at some distance from each other.

If the big mass collapsed into smaller volume (increasing density), the field strength at the place where small mass is (was) is still the same.
Therefore, the energy required for small mass to be removed further (out of the g well) is still the same.
Unless the distance of the small mass changed.
But you said we are talking only about big mass density.. so I'm still not with you on this.

[avandonk]

Here is one very rational smart man explaining things. You can get a better idea from the animations of tesseract shadows or projections from 4D to 2D.

http://www.youtube.com/watch?v=Y9KT4...eature=related

And here for an animation.

http://www.youtube.com/watch?v=5xN4DxdiFrs

This is my pathetic contribution to show how we all live on the 'surface' of 4D space.

Bert

[sjastro]

Originally Posted by bojan

That's all OK, provided the small mass is on the surface of the big mass.
However, it is implied both masses are at some distance from each other.

If the big mass collapsed into smaller volume (increasing density), the field strength at the place where small mass is (was) is still the same.
Therefore, the energy required for small mass to be removed further (out of the g well) is still the same.
Unless the distance of the small mass changed.
But you said we are talking only about big mass density.. so I'm still not with you on this.

The model is based on the small mass residing on the surface of the large mass. This is because the small mass resides in the lowest possible gravitational potential energy state.

If you shrunk the large mass and kept the small mass at the same distance, the energy required to remove the small mass out of the well increases.
The reason for this is that small mass is no longer in lowest possible gravitational potential energy state. You require energy to keep the small mass at the same distance plus the energy to remove the mass out of the well.
The alternative is that the small mass drops to the lowest potential energy state in which case it is deeper in the well.

Regards

Steven

[CraigS]

Originally Posted by bojan

If the big mass collapsed into smaller volume (increasing density), the field strength at the place where small mass is (was) is still the same.

Hi Bojan;

This is similar to Gauss' Law for electric fields:

"The electric flux through any closed surface is proportional to the enclosed electric charge."

The smaller 'closed surface', encloses more 'field lines', (for a constant charge or gravity), thus the field strength goes up as the radius (r) of the 'closed surface' decreases. If the point mass stays at the same place, the potential difference between where the point is and where the shrunken 'closed surface' now is, is greater and thus results in a greater attractive force on the point. Hence a greater force is needed for it to escape.

The 'closed surface', I think, is the key in the model. The numbers of field lines passing thru this surface determines the field strength.

Hope this helps.

Cheers

[bojan]

Thanks guys.. I've got it now.

Originally Posted by sjastro

.....This is because the small mass resides in the lowest possible gravitational potential energy state.

If you shrunk the large mass and kept the small mass at the same distance, the energy required to remove the small mass out of the well increases......is no longer in lowest possible gravitational potential energy state. You require energy to keep the small mass at the same distance plus the energy to remove the mass out of the well.

I will stick to Steven's explanation as above, it is most precise..
I didn't realise that shrinking (collapse, increasing density) of the bigger mass changes the energy level distribution of the system.

EDIT:
Or, the the energy of the system remained the same, however due to collapse of the bigger mass, part of it's potential energy is converted into potential energy of the smaller mass.. Please confirm.

Guys, we have to be more clear in answers to some basic questions. Otherwise we are just creating confusion among some people..

[bojan]

BTW, while reading about GR, I noticed the term "pressure" is mentioned very often as contributor to total energy of the system.
For example, for object that moves at speeds close to C, due to dilation in the direction of movement, the pressure is also increased, and that contributes to the total energy of the moving body.. Is this correct?
I will supply the reference later, if I misunderstood something.
Is this "pressure" has something to to with what we are discussing here?

[Archy (George)]

Originally Posted by sjastro

Mass = Density X Volume.
You substitute the mass term for density X volume.

This is done for objects that are not expressed as point masses.

Steven

Show me where newton used density instead of mass

[sjastro]

Originally Posted by Archy

Show me where newton used density instead of mass

Go educate yourself George and stop wasting my time.

[bojan]

Originally Posted by CraigS

The 'closed surface', I think, is the key in the model. The numbers of field lines passing thru this surface determines the field strength.

Hope this helps.

Cheers

Err.. maybe.
However, if we stick to Gauss law, the field strength is determined by number of field lines per unit of surface (cm^2).. but the total flux (energy packed in the well) remains the same (because the big mass is the same in amount, regardless the change in density.
So your analogy is not quite correct, because the field strength at place where the small mass was is still the same.
However it appears that the potential energy of the small mass changed.
It came from the potential energy of the big mass which is now smaller, due to shrinkage.

So, after shrinkage of the big mass, and if we allow the small mass to fall to the lowes possible energy state, yes, we will have to use more energy to remove the small mass out of the well.

Originally Posted by sjastro

You require energy to keep the small mass at the same distance plus the energy to remove the mass out of the well.

So, the first part of the total energy of the small mass is already there (added by collapse of the big mass. The small mass didn't move).
I need only the second part (after "plus ") to remove the small mass from the well.
This is not more than needed before collapse of the big mass.


As I commented in my earlier post (maybe my remark went un-noticed because it was edited later), we should be more clear when answering questions like this. Cryptic and not well-enough explained answers, however correct, will just create a huge confusion among some people (including myself).