a little help needed for an ignorant old man

[Brian W]

Hi all. heres my problem; when I throw a rock into a pond I see circles emanating out from where the rock enters the water. Barring unseen underwater obstructions and until the waves run into something else the rings are concentric and where the rock entered the water is the centre.

To my brilliant but ignorant mind that should also be the case for our universe. The whatever that caused the singularity to morph into our universe must also have had a wherever as well as a whenever.

To my way of thinking this wherever must be the centre of our universe but people keep on telling me everywhere is the centre.

HELP!
Brian

[Miaplacidus]

See, that's the problem with similes. You've got to pick the right one. What you're forgetting is that the rock contains the pool it is thrown into. A marginally more useful analogy is to a balloon that is being blown up with air, with the 3D universe represented by the stretching latex skin of the balloon, with all parts moving away from each other. Ceci n'est pas une pipe...

[ballaratdragons]

Hi Brian,
If there was a 'Big Bang' who's to say it went out in concentric spheres .

Look at any explosion, yes especially in space.

Are you familiar with the shapes of SuperNovae remnants? Notice none of them are concentric.
Yes many Planetary Nebulae look concentric. But they aren't if you look at them properly.

Explosions in space give us a small sampling of how any Big Bang could have reacted. All out of shape.
Personally, I can't see any Big Bang being as neat and ordered as 'rings in a pond'.

Which tells me that it would be fantasy to measure backwards and evenly to find a centre of origin. :thumbsup:

Just my Threepence Halfpenny :lol:

[Brian W]

okay that makes sense but there is still only one centre to the balloon.

[Brian W]

All-right even if it is not 'concentric' there would still be a spot where it all started and from which everything moved away from. And even today that spot could be findable?

The supernova irregularities make sense to me when I realize that there are any number of gravitational factors involved. But would those same factors be in play at the singularity when things were too hot to coalesce?

Plus as I understand it the 'Big Bang' may not have actually been an explosion but rather an expansion.
Brian

[CraigS]

The current Lambda CDM model (Standard Cosmology Model) takes into account present Cosmic Microwave Background Radiation (CMBR) measurements which indicate that the universe is flat - not ballon-like in shape. The ballon analogy was invented as an analogue to explain expansion of the universe. Everything expanded all at once including space just after the 'Bang'. An expanding flat rubber sheet is more applicable.

There is no centre. The explosion analogy is not applicable either as explosions do have a centre. They also result in collisions of the exploding particles as well as expansion of the space between others. We only observe expansion (via redshift) at the largest scales of the universe.

Cheers

[Brian W]

Aha! that is just what people keep telling me 'there is no centre' but even on a flat rubber sheet there is a spot that is the centre.

However ... would it change the parameters of the discussion if instead of 'centre' I was to refer to the single place where it all began?
Brian

[CraigS]

The Cosmological Principle (http://en.wikipedia.org/wiki/Cosmological_principle) underpins the Standard Model (which includes BBT). The principle states:



In other words, there are direct, measurable observations underpinning the Standard Model and the principles underpinning it. The rock in the pond model, ballon analogy, etc are not supported by any combined direct, observational evidence.

Cheers

[CraigS]

Correct .. even the flat rubber sheet model is deficient.

There is no geometrical centre in the BBT/expansion model because this still implies that something is not expanding which doesn't align with observations nor the Cosmo Principle.

The rubber sheet model helps to visualise the observable fact that no matter where you are located on the sheet, everything looks as though it is expanding away from everything else as it stretches. This more closely aligns with redshift observations.

Cheers

[Brian W]

Ok Craig I follow your argument with a few questions

(1) when I used to go sailing there were times that I was out of sight of land. Anyone else that was sailing out of sight of land would see basically what I was seeing. I get the idea that it all looks the same.

But I still do not see that that means there is no single spot where it all begins. Unless one was to take ethnocentricity to it ultimate limit.

(2) please explain to me the co-relationship between having a centre and not expanding.

It seems to me that there can be a centre in an ever expanding anything.
Brian

[CraigS]

Hi Brian;
Please excuse the sharpness of my responses (I'm a bit rushed today).

Ok. So … I guess there can be a centre in an ever expanding 'anything', if one chooses to go with the models originally suggested..

However, two testable consequences of the cosmological principle are homogeneity and isotropy. Homogeneity means that the same observational evidence is available to observers at different locations in the universe. Isotropy means that the same observational evidence is available by looking in any direction in the universe. A universe that appears isotropic from any two locations (for eg), must also be homogeneous.

If the universe is isotropic, the distance to the edge of the observable universe is about the same in every direction (ie: appears as a sphere - confirmed by CMBR observations in different directions). But every location in the universe sees the same view ... which may, or may not, overlap with our Earth centric view.

So, if every observer sees the same expansion (with redshifts) how can one determine where the centre is ? (I don't think this is possible).

I think the point here is, one either goes with the observable evidence, and model, and accepts that there is no identifiable centre, or one believes otherwise, with no observable evidence supporting that belief.

The original model of the BBT suggests that the original universe started from an infinitely small, infinitely hot (energy dense) point. It expanded into nothing. It's location or its centre is not determinable, if one goes with the Standard Model concepts of homogeneity and isotrophy which are based on observations.

Cheers

[noswonky]

In the balloon analogy, you have a balloon with dots on it representing galaxies. The two dimensional surface of the balloon represents three dimensional space. As the balloon expands, the dots (galaxies) move away from each other. In this analogy, where is the centre?

There isn't one.

Because this is a two-dimensional analogy of three-dimensional space, you can't say that the centre is inside the balloon. That would be the three-dimensional centre and that's not allowed in a two-dimensional model.

So asking where the center is in three dimensional space is like asking where the centre is on the SURFACE of a balloon. There isn't one.

Before the balloon began inflating, all the dots on the balloon's surface were close together - ideally infinitely close together. But once it starts inflating you can't point to a spot on the surface and say 'that's where the balloon started inflating'.

The key is that the expansion on the universe did not start at some point in three-dimensional space. Rather, space itself began tiny and got bigger.

[Brian W]

Craig, I got to go and ponder on this but I will be back.

Peter, couple of points
(1) the balloon is not overly good simply because 'space' is not two dimensional. To my poor way of thinking any three dimensional object must have a centre.

(2) you state that the key is that the universe did not start at some point in three dimensional space but that even 'space' started with the expansion.

To the best of my understanding science makes no claim about what was there before expansion. Nor how it started. And certainly not what it was like at the moment of beginning.

In any case I need to go and ponder cause this is really, at least for me so counter intuitive that I have trouble accepting it.

However I freely admit that the truth of no centre certainly does not rest on my ability to understand it.
bria

[Brian W]

Craig, I got to go and ponder on this but I will be back.

Peter, couple of points
(1) the balloon is not overly good simply because 'space' is not two dimensional. To my poor way of thinking any three dimensional object must have a centre.

(2) you state that the key is that the universe did not start at some point in three dimensional space but that even 'space' started with the expansion.

To the best of my understanding science makes no claim about what was there before expansion. Nor how it started. And certainly not what it was like at the moment of beginning.

In any case I need to go and ponder cause this is really, at least for me so counter intuitive that I have trouble accepting it.

However I freely admit that the truth of no centre certainly does not rest on my ability to understand it.
bria

[Archy]

Having seen the replies to your sensible question, one can't help but think that in science fiction as in Alice in Wonderland anything is possible

[CraigS]

Care to elaborate on where the "fiction" is ?

Cheers

[CraigS]

The point to be made here is that there is no 'truth' to be found anywhere on this. We're talking about something ~ 14 billion years old (observable) and (perhaps) infinite in expanse beyond that.

No-one will probably ever know the 'truth' about something as old and as big as this. (At least not in my lifetime).

If there is no truth … then there is no fiction.

The idea is try on: wrapping one's mind around the initial concepts and what follows is extraordinarily logical and rational. Most other alternative starting premises are falsified, pretty quickly, by the observational data.

I'd much rather spend my time pondering the Standard Model than an opinion unsupportable by linked observations.

Cheers

[Brian W]

Hi Craig you have just hit upon my dilemma.

(1) all of my observations tell me that any three dimensional object has a centre.

(2) my observations tell me the universe is three dimensional.

(3) therefore the universe must have a centre.

The above is nothing more or less than basic logic and as such cannot be denied. However as it is a tautology it does not of necessity about reality.

I suppose that I am having the same type of problem that someone who is working on a unified theory faces; how do you make the micro and the macro make sense together?

Oh well, as you say Craig one can only keep on keeping on.

Brian

[mswhin63]

I am tinking in relation to both puddle theory and baloon theory.

BB not yet proved what would happen to the air inside a balloon when you use a powerful compression to blow it up initially, after a while the compressor is turned down and everything inside is settling down. Is it possible the air inside is still moving quickly during this transition and some galaxies or whatever have bounced of the edge and heading towards the centre, air currents or gravity etc are flinging galaxies off in different directions or circulating around the universe. It is just another ignorant man idea.

The same could be said for the puddle as well but in a 2 dimensional.

As the first post is a simple analogy why not me :) So if it has already be said in a theoretical mathmatician language then please excuse me.

[sjastro]

The danger with any analogy is that while it may aid in visualization, taken literally it can lead to false conclusions. One needs to be very careful visualizing mathematical concepts.

The Universe has no centre, the observer is the centre. If a galaxy was receding from the "centre" of the Universe, then any observer in the line of sight of the receding galaxy will measure the same recession velocity.
This clearly violates Hubble's law which shows that the recession velocity is proportional to the distance between the galaxy and observer. This is based on observation.

Hubble's law is explained by having the receding galaxies fixed in space and allowing the space to expand. Hence galaxies recede as a function of the increasing scale of the Universe. In this scenario there is no absolute centre, each observer in the Universe can rightly claim to be the centre.

This leads to the cosmological principle as explained by Craig.

Regards

Steven

[CraigS]

Hi Brian;

Don't give up there, fella ! (Good to have you around !)

Glad to see Steven's words on this, also.

Hubble's Law is a kind of set in stone in astronomy circles.
It'd be a real nightmare to try and explain his observations in any other way!
Others have tried and some of the stuff they come up with from thereon looks positively screwy !

Let us know your thoughts.

Cheers and Regards

[mswhin63]

I suppose it will be difficult to locate the centre of the universe (the point equal-distant from the outer edge/s) until we actually see the edge of the universe. I understand the principle of the observer as the centre but that is the centre of observation not the centre of physical reality.

I always though maths was used to describe what we see not what we can't see. I suppose I got it all wrong. I watched the BBC - "Dangerous Knowledge" program and I suppose they died from trying to work out what they couldn't see, although they did live in difficult times. So yes we need to be careful with math.

[Alchemy]

I see where you are coming from Brian. The universe is 3 dimensional from our perspective and logic does dictate a centre, the problem is that because space is expanding it's indeterminable.

Ie.... If for example the centre of the universe was the Virgo cluster of galaxies you might argue it's not moving...... But we being off centre are, and the clusters 180 degrees opposite are expanding outwards from us also, the end result is both sides APEAR to be moving at the same rates. So should as logic dictates... a centre..... You can never find it.

[sjastro]

The Universe doesn't have a physical centre for the reasons I gave in my previous post. Neither does the Universe have an edge, the implications for that would be expansion into existing space. In other words metric expansion of space wouldn't occur and we wouldn't be able to explain Hubble's Law or the mechanism of cosmological redshift.



These guys worked in the field of pure mathematics. Pure mathematicians consider themselves artists, and probably had all the attributes of artistic temperment.
http://en.wikipedia.org/wiki/Mathematical_beauty

Not surprising some of them went the way they did.

Others went in more spectacular ways.
This kid died at the age of twenty, his ideas in mathematics were so advanced they were used in physics 120 years after his death.

http://en.wikipedia.org/wiki/%C3%89variste_Galois

Regards

Steven

[Steffen]

I reckon some of the confusion stems from the use of the term "centre". You can of course define any number of "centres" in a 3-dimensional space, such as centre of gravity, or geometrical centre, or centre of interest ;)

What doesn't have a centre (or point of origin) though is the expansion of the universe. Wherever you stand in the universe things are moving away from you as if you where right at the point of origin of the expansion. Any spot is as good (and as "central") as the next one.

Cheers
Steffen.

[CraigS]

Here's a thought .. perhaps what we're saying here, is that from today's observations, it is not possible establish a geometric centre of the universe.

This doesn't mean that at the instant of the Big Bang, the universe didn't have a geometric centre. After all, the theory points out that it was very small. However, all of the text I've read is also very careful to point out that we still don't understand much about the very early phases of the universe.

I think Brian may have already mentioned this, also.

So, it would only be speculation to talk about when the universe may, (or may not), have had a geometric centre. But it may have been possible, maybe even probable .. who knows ?

I have read that they have shown that it is possible that things may have been very chaotic in the very early stages (blue & red shifts randomly distributed).

Following this rationale, the points Brian is making seem reasonable.

Comments welcome .. this discussion, (being a different one to where I was coming from originally), however, is all very speculative.

Cheers

[Archy]

Where is the Science

[CraigS]

What is your definition of Science ?

[Archy]

I don't need to have a definition of science: Popper did it for me. If you don't understand my reference, give me your definition of science.

[The_Cat]

I don't know too many pure mathematicians who consider themselves artists !!:)

Re: Use of Galois fields (ie. finite field arithmetic) in physics ? Where ?

We use these in the design of error control codes - our CD players would not work without them !!

Jeremy

[OICURMT]

An oh-so-true statement. In Petroleum Engineering, we often calculate hydraulic tables as a 6-dimensional matrix. The maths are accurate, but trying to show an executive the results can leave them pondering for days if they don't have an engineering background.

Trying to display the results is equally challenging, as people are used to 3 dimensions (x,y,z). We augment the display via color (4th), saturation (5th) and transparency (6th).

OIC!

[sjastro]

I did pure maths as an undergraduate before switching over to applied maths.
Pure mathematicians see beauty in their work based on the originality, simplicity and logic, somewhat like an art form, the applied mathematician is far more phelgmatic.

I found pure maths excruciatingly boring, abstract and difficult, I think you need to be passionate to succeed.:)

Sorry the sample size is small but it is based on personal observations.

Galois made significant contributions to Group Theory. Group theory is used extensively in particle physics.

Regards

Steven

[Brian W]

Now this begins to become understandable. with 'space expanding' and galaxies more or less going along for the ride then I can begin to see where no 'absolute centre' makes sense.

Now a little more help if you please... is it permissible or sensible might be a better word, to talk of an' absolute beginning position'? Granted that it is not the absolute centre.
Brian

[sjastro]

Hello Brian,

Let's "look" at a very small object such as an electron. If we had the capability of observing electrons, the electrons would not appear as tiny spheres or points but as a "cloud" structure. This is quantum mechanics at work at small scales. The "cloud" represents the probability of finding the electron in a small region of space. It's impossible to pinpoint the exact position of the electron in space.

In the very early history of the Universe, the scale was small enough for the Universe to obey the laws of Quantum mechanics. For the same reasons as the electron, the beginning position would have been spread out over a small but finite volume of space instead of occupying a point in space time.
As the Universe expands so does this small finite volume of space, so it impossible to even define the region in which this beginning position could have occurred.

Regards

Steven

[CraigS]

It seems that it is hypothesised that even before the Universe obeyed the laws of quantum mechanics, space and time 'break down', which suggests that they may be approximations of something more fundamental.

At this time, it seems that dimensions wouldn't make any sense (nor units of time).

Interesting.

Cheers

[Archy]

How do you know?

[SkyViking]

I suppose the quite intuitive reasoning behind the original question is that the Big Bang was an explosion (as it is all too often depicted as) and therefore it must have had a centre, or merely that the Big Bang must have happened at a particular point in the Universe. The key point however is that everything, both space and time - essentially what we call the Universe - was created in the Big Bang, and thus it is impossible to define a position inside the resulting Universe for this event.

For example, imagine a new coordinate system that suddenly emerges and expands from a single point. That single point can only be defined relative to some other coordinate system, which must be outside the expanding one.
Likewise, any 'centre', 'beginning position', 'point of origin' (or what one might call it) for the Universe would have to be relative to something else that is outside the Universe itself. But what, if anything, which may or may not exist outside the Universe is of course pure speculation...

[Brian W]

Hi all, seems to me that all of this hangs upon the idea that the universe is finite. By this I mean that there is a beginning and an ending. As most of us have been directly influenced by the Judeo / Christian way of looking at things this is quite understandable. (please note that I am not bringing G-d into the equation just the idea that our culture limits the questions we can ask)

How would the questions and answers be effected, or indeed would they be, if we were to approach this from the cultural belief that the universe is infinite with no beginning and no ending?

If the big bang was simply the continuation of what came before... and in time what was started would move into what comes next?

Brian

[CraigS]

Brian;

This conversation has now drifted into philosophical areas, (which is OK .. and normal .. most threads in the Science Forum end up this way).
:)
My 2 cents worth on this is that I have no problems in thinking of the Universe as infinite, with no beginning and no ending. Neither have many other prominent scientists throughout history (Einstein, Fred Hoyle, etc, etc). Their ideas in these areas however, have tended to fall by the wayside in the light of hard data. They do make various reappearances in man-made hypotheses/theories which to a certain degree, contain some measure of 'consensus' or 'agreement'.

Such thoughts are as good as anything for having some kind of picture in one's mind about it all. At the end of the day, they are mostly opinions and as they say .. 'everybody's got one .. and they rarely make a big difference'. Big shifts mostly tend to happen upon observation of 'anomalous' phenomena.

As far as cultural influences on scientific thinking goes, many famous scientists also have had in the past, religious beliefs. We have discussed the Jesuit Scientists (http://en.wikipedia.org/wiki/List_of_Jesuit_scientists) previously, as an example. Another example is that the Pope also recognises (http://en.wikipedia.org/wiki/Pontifical_Academy_of_Sciences) the very scientists behind the mainstream thinking outlined in the response posts in this thread. This would seem to be evidence of sociological religious support for mainstream scientific thinking.

The main point I'd like to make from what you say is that modern science doesn't seek the 'truth'. Its about observing, theorising, seeking evidence, falsifying and refining then predicting. This is all about decoupling the false perceptions which humans generate from looking at the environment around us, from the cold reality of the physical world.

This approach has also culminated in a modern perspective which leans towards creation of the universe from nothing, with purely unthinking physical processes building what we see around us. I for one, have no problems living inside any of these dimensions of thought.

How about you ?

Cheers and Regards

[Brian W]

Hi Craig, apparently I do have problems with living inside some of these paradigms, else why would I be in this conversation?

One of the main beliefs in science is that energy can be neither created nor destroyed but simply changed. That being the case how does one get creation of the universe out of nothing.

That seems to break a very basic 'law'.

Brian

[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 (http://en.wikipedia.org/wiki/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]

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]

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]

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]

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]

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]

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]

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]

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]

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. :shrug:
(unless this applies to a total mass)

[sjastro]

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=Y9KT4M7kiSw&feature=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]

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]

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.



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]

Show me where newton used density instead of mass

[sjastro]

Go educate yourself George and stop wasting my time.

[bojan]

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.



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).

[CraigS]

Point taken.

And it works both ways. I'm not clear on your response above.

Responding to a call for help is part of community and contribution.

Confusion is part of learning. So is asking questions.

I do not live in fear of confusion.

Communication sorts this out.

Cheers

[Brian W]

Then there be people such as myself who with the clearest of answers find myself in a huge state of confusion!
Brian

[bojan]

OK..
Since the single picture is worth a thousand words, and because I think this fundamental issue must be resolved properly, I put some effort into attached drawing, to clarify things, the way I see them.

The gravitational energy well is represented with the curves, the masses are circles.
Small mass resides at the surface of the Big mass (or it is in the circular orbit).
m, M, small and Big mass, respectively.

Ee is the energy required to pull out the small mass out of the well.
Ep is potential energy of the small mass, and it equals zero (because the small mass is on the surface of the big mass - lowest energy state).
E_total = Ee + Ep (Ep is zero before collapse of the Big Mass)

F0 and F1 iare the indications of field strengths (only they are inverse proportional to the value of F1^2 )

Also, because this is the closed system, the total energy balance before and after any change (including collapse) must be the same, right?

If we allow the big mass to collapse from Ro to R1 and if we keep the small mass at the same distance from the gravity centre of the Big mass (Ro.. let's assume it is in circular orbit around Big mass), the things are now different in terms of:

1) the potential energy of the Big mass changed (the matter is now deeper in its energy well.. the individual particles will now need more energy to escape the gravity well, as correctly pointed out by Steven).

2) If the small mass remained at the same place (or circular orbit), it acquired potential energy (Ep) which came from collapse of the big mass (??).
However, Ee (escape energy from the well ) remained exactly the same. This is in contradiction to what Steven said earlier, citation is below:




The same goes for field strength at this point - it didn't change.

It would be good if someone could present the equation that fully accounts for energy bill in the system described above - I will try to do it later.

[CraigS]

That is so cool, Brian !

:)

We're all confused !!
Maybe we're all on the same playin' field after all .. that's a terrific place to learn from eachother !

:)

Having said that, Steven's answers are very clear to me, also.
We're lucky to have him around.
Oh and Bojan, also - thanks for taking the time and effort to outline things as you have. I'll have a look at your post when I get the chance. Thanks kindly, Bojan.

Cheers

[Brian W]

Hi Craig, two questions, are you self taught or did you pick this up in university? (if the first then there just might be hope for me) what is a 'bartelized' dob?
Brian

[bojan]

Hi Brian,
I am guessing the above question is for me :D

Have a look here on the website below:

http://www.bbastrodesigns.com/BBAstroDesigns.html#Computer_Operat ed_Telescopes

[sjastro]

A few points here. Ee is the kinetic energy. Since gravity is a conservative force E_total = Ee + Ep is constant everywhere for the small mass in the gravitational well.



It has nothing to do with the potential energy of the large mass. When the small mass moves up the well Ee is converted into Ep, that is the small mass KE is converted into potential energy. It is why E_total is constant.
Conversely if it moves down the well Ep is converted into Ee.



If the small mass has the value Ep=0 when the large mass contracts and remains at the same point in the deeper well, Ep is no longer zero. This means the small mass is performing work, that is KE is being converted into PE. The small mass loses KE equalling the difference in the depths of the well before and after contraction.

Hence Ee does not remain the same.

Regards

Steven

[bojan]

Hi Steven, thank you for your clarification.



OK so far.


Now we came to the sticky point (for me and for some others, I am sure). Even if the distance of masses centres remain the same?
So what is happening to the proposed circular orbit?
Or, does the shape of the well change, apart from just being extended downwards? The curve was supposed to indicate the energy as a function of the distance from the centre. If this is so then I've got it.. if not.. well then I have a problem :P
Because I always believed in a principle that the extended mass (star) can be replaced with point like mass of equal value, without small mass (planet) ever noticing the difference, for the purpose of orbit calculations (and that involves potential and kinetic energies of course - all according to classical mechanic)

[Brian W]

Ok now it is official, I started this thread looking for an explanation in simple English. Now we are into diagrams, algebra and serious philosophical chat... I'm lost!

But I am learning however for a while I am just going monitor the discussion but please do not stop cause I am loosing ignorance with each and every comment.
Brian

[CraigS]

Brian;

This is the Science Forum and these guys are discussing the science.

Feel free to interject any questions you may have. (They'll probably welcome the relief …)

Cheers

[sjastro]

I don't see the relevance of orbits in this discussion. I have been referring specifically to the separation of a small mass from a large mass. It is in keeping with the 2 mass model to explain the significance of the cosmological term "Omega". The well is based on this criteria.

The role of KE and PE in circular orbits is very different when compared to separating masses.

For circular orbits, the PE+KE =constant rule is also applicable. Orbits however do not have to exist in the lowest PE state. The PE of an orbit is proportional to the radial distance.
PE and KE are constant at every point in the orbit. Hence there is no conversion of PE to KE and vice versa. The only criteria for a closed orbit is that KE<PE.

Getting back to your original point, I agree, if you shrink the central mass, the orbit is unaffected.

Regards

Steven

[bojan]

Steven, thanks for your answer
Well, there is a relevance, because your later clarification created some confusion, I am sorry but I have to say this. And I only tried to sort it out taking another view angle, because confusion is not what we want to have here in science forum.
So, as far as orbits are concerned, that is exactly what I wanted to see.
Therefore, the conclusion is, the energy to remove the small mass from gravitational well in our little case is the same regardless the Big mass is shrank or not.
It is the energy needed to put the small mass from circular orbit around the Big mass into parabolic one.
Please correct me if I am wrong here and please show me where and why....

After this is sorted out, we can move to more complicated things, like omega.

[Archy]

Of course the bullet is not stationary, so what's your point

[Archy]

Have you guys ever heard of the Cavendish experiment

[Archy]

It has yet to be demonstrated that gravity has field lines or that is related to EMF, so how does Gauss come into it
so how

[CraigS]

Gauss' Law for Gravity (http://en.wikipedia.org/wiki/Gauss%27_law_for_gravity) … but of course, you would already be an expert on it.

[sjastro]

You are not comparing apples to apples.

In a circular orbit, the direction of the velocity is perpendicular to the central force. No work is being performed. This is opposite to the the mass moving radially in the field.

A circular orbit exists because it is in a dynamic equilibrium without having to be in lowest PE state, a mass in the field is in the most stable equilibrium when it is in the lowest PE state.

A circular orbit is subject to orbital inertia. The interaction of gravity with orbital inertia is very different when compared to the linear inertia of a mass moving in the field.

The energy supplied for converting a circular orbit to parabolic orbit is due to external non conservative forces. The KE+PE = constant rule no longer applies. This is contrary to the effects of gravity on the inertia of masses in the absence of external forces on which the Universe is modelled on.

Regards

Steven

[bojan]

OK, now I think I see where the difference is (and I hope it is more clear to others as well).

Summa summarum:
Our little system is not closed (it is open to external influence).
Universe is a closed system.
Thanks..

[CraigS]

Coming back to the origin of all this, (and because I'm a summary addict), for me, Steven's original statement in Post #43, condenses it all:



The words around this statement, (in post #43), fill in the details.

Cheers

PS: This post is intended to be kind of like a 'file note'. Cheers.

[Archy]

Is sarcasm the best you can do?