Relativity and Cosmology

Jorrie,

Over the past week I've done a lot of calculations to try to demonstrate that there is no need for a cosmological constant to explain the expansion rate and accelerated expansion of the universe. I hoped to find that increased "clumping" of matter over time could explain the acceleration. But for better or worse, no matter at what level I tested the amount of clumping (atoms, stars, galaxies, clusters, superclusters), none generates enough expansion to match the observed rate. The supercluster level comes closest, producing about 1/30th of the necessary expansion rate. Smaller levels of clumping are orders of magnitude more short of the mark.

So reluctantly I'll accept the need for the cosmological constant.

Accordingly, here is a revised "Flatness Theorem":

1. Theorem 1: The geometry of the universe is perpetually flat.
2. The universe has been characterized by an interaction horizon since early on, so unless the universe was always flat, it is almost infinitely improbable that any fortuitous combination of circumstances could account for the degree of isotropic flatness we observe today. Therefore, the universe must always have been flat, and by extension it always will remain incapable of diverging from flatness.
3. Theorem 2: Rest Mass preserves flatness by causing expansion.
4. The rest mass (or static energy) of matter and radiation expresses gravitation, which causes curvature of space. This curvature must be offset in order to maintain flatness. Vacuum expansion is the mechanism that maintains flatness.
5. Theorem 3: Space reacts to the presence of static energy by spontaneously producing new vacuum space.
6. Every Kg of mass causes local space to spontaneously "produce" (whatever that means) new vacuum space. In total across the observable universe, this new vacuum space is produced at a rate equal to the "escape velocity" of the universe. I calculate that new vacuum volume presently is being created at the rate of about 2x10⁶³ cubic meters per second.
7. Theorem 4: The cosmological constant = the rest mass of vacuum.
8. A cosmological constant is needed to explain the high observed production rate of new vacuum. For example, I calculate that the sum of the rest masses of the estimated 10 billion galactic superclusters accounts for the production of a mere 6.3x10⁶¹ cubic meters of new vacuum per second.
9. The vacuum of the present universe alone (without including any matter or radiation) in aggregate posseses the correct mass to account for the full vacuum production rate of 2x10⁶³ cubic meters per second.
10. Given that the vacuum mass alone accounts for the accelerating expansion rate, there is no need to attribute special characteristics to the vacuum, such as "dark energy" or "negative pressure."
11. I propose (but haven't tried to calculate) that vacuum mass is simply the "average" mass of the virtual particles which continuously pop into the universe via quantum pair production, multiplied each particle's (very short) average lifetime before annihilation.
12. Theorem 5: The Flatness Theorem provides a consistent model for inflation, expansion, and accelerated expansion.
13. Inflation is just a name given to an (arbitrarily) brief initial period of hyper-expansion prompted by the precipitation of mass into the universe via quantum fluctuations. The expansion rate tracked the astronomically high vacuum production rate needed to maintain flatness at a time when all of the universe's mass was compacted into a microscopically tiny volume.

Jorrie, I would appreciate if you could help me calculate one thing: What was the volume or radius of the universe at the inflection point when the aggregate vacuum mass exactly equaled the aggregate rest mass of matter?

I couldn't find "quantum pair production" in wikipedia. Could you please direct me to a definition.

Sure, try this on "Pair Production:

http://en.wikipedia.org/wiki/Pair_production

And:

http://en.wikipedia.org/wiki/Electron-positron_annihilation

Hi Jon.

Yep, this is much closer to accepted theory now. There are a few aspects that may be very debatable, but I'll leave that to other contributors for now.

"... help me calculate one thing: What was the volume or radius of the universe at the inflection point when the aggregate vacuum mass exactly equaled the aggregate rest mass of matter?"

It's easy from the Friedmann equation, because per your requirement, it must be when Ω_m/a³ = Ω_v.

For Ω_m= 0.27 and Ω_v=0.73, this gives a~0.718. Multiply by the comoving radius of the observable universe (about 46 Gly) and you get ~33 Gly radius. This corresponds to about 9.45 Gy age, which one can only get from an integration of the Friedmann energy equation (what my spreadsheet does).

Jorrie

Thanks Jorrie.

You said: Ω_m= 0.27 and Ω_v=0.73. So the equation uses today's ratio, not the Ω_m= 0.5 and Ω_v=0.5 that would have been the ratio .55B years ago?

Hi Jon.

"So the equation uses today's ratio, not the Ω_m= 0.5 and Ω_v=0.5 that would have been the ratio ?"

Yep, that's how those Ωs are defined: today's actual densities as a fraction of today's critical density. (But where did you get ".55B years ago" from?)

The denominators (aⁿ) in the Friedmann equation sort out the epoch dependencies - how else?

Note that I have included the curvature term (first one under the √), to sort out things when today's Ωs do not add up to unity (open or closed universe). In the flat case, that term becomes zero of course.

Jorrie

Hi Jorrie,

Sorry, I meant 0.425Gy ago...

I built a spreadsheet for the Flatness Theorem. I adjusted the volume ratio between superclusters and voids to 0.07, which made their new vacuum production rates add up properly to the total new vacuum production rate of the universe. With the adjusted numbers, superclusters presently produce 0.13133 of the total new vacuum production rate, and vacuum mass produces the rest.

The good news is that the spreadsheet also works well with the universe at the age of .945Gy, the inflection point you calculated Jorrie. I am fairly confident that the spreadsheet will work at any point in the history of the universe, including during inflation. Obviously the average volume of superclusters will need to be adjusted smaller starting at some point in the distant past, but I'm not aware of any formula for doing so. I guess I can calculate it backwards from the spreadsheet.

Hi Jon.

"Sorry, I meant 0.425Gy ago..." and "...the spreadsheet also works well with the universe at the age of .945Gy, the inflection point you calculated ... "

I guess these are just typos. My post gave an age of 9.45Gy for matter-vacuum energy density equality, which is about 4.25Gy ago.

Jorrie

Hi Jorrie

Yes, typos. Your decimal places are correct.

I did some more adjusting. At the present, the volume ratio between superclusters and voids needs to be .09, and superclusters produce .166 of the total vacuum production.

At 9.45GY, superclusters produce .348 of the total.

Hi Jon, you wrote: "At the present, the volume ratio between superclusters and voids needs to be .09, and superclusters produce .166 of the total vacuum production."

I'm not sure what these figure of yours mean. It is hard to find the ratio between supercluster volume to void volume. Using a rough guess that our Virgo supercluster is about average in size and then taking Astronomy Answers values:

In a radius of ~400Mpc, there are 130 superclusters, with Virgo's volume 1.2 x 10⁴ Mpc³. If I work out the volume of 130 such superclusters as a fraction of the 400Mpc radius volume (2.7 x 10⁸), I get ~0.006 to 1.

So the total supercluster volume may be around 0.6% of the total volume of the observable universe.

Jorrie

Hi Jorrie:

According to Wikipedia: "... the total number of super clusters in the universe is believed to be close to 10 million." http://en.wikipedia.org/wiki/Supercluster

In the same article:

"... superclusters are now understood to be subordinate to enormous walls or sheets, sometimes called "super cluster complexes", that can span a billion light-years in length, more than 5% of the observable universe. Super clusters themselves can span several hundred million light-years."

In my calculations, I use the term "supercluster" to mean all of the coherent mass structures that aren't voids. That includes sheetwalls and filaments. I run my calculations as if these "superclusters" are 10⁷ identical spheres, but of course that is only partially accurate. It's just the best I can do with the facts at hand.

Since Wikipedia indicates that voids contain around 10% of the matter of the universe, I assigned the other 90% to what I refer to as "superclusters". Wikipedia says that voids are thought to constitute 95-98% of the volume of the universe. However, it isn't clear whether that includes any of the sheet walls, filaments, isolated galaxies, and other assorted riff-raff. In any event, in my spreadsheet, the "best fit" I can achieve (which is very close), is putting "superclusters" at 91% of the matter and 9% of the volume. I am optimistic that my calculation helps to nail this ratio down.

You'll be happy to know that I got the Friedmann equation to work properly after you pointed out that the "scale factor" a = radius. For some reason I had thought it related to volume.

I'd like to now run my spreadsheet at the inflection point where Ω_m = Ω_r, which I understand is at about t=10⁵. Can you help me calculate the radius and age more accurately? My calculation yields a radius of 1.02x10³m, but I'm not confident I'm doing the math correctly.

Hi again Jon.

"In my calculations, I use the term "supercluster" to mean all of the coherent mass structures that aren't voids. That includes sheetwalls and filaments. I run my calculations as if these "superclusters" are 10⁷ identical spheres, ..."

I rather take a large sphere of known volume and try and 'count' the number of superclusters in order to calculate their total volume, as I referenced before.

"Since Wikipedia indicates that voids contain around 10% of the matter of the universe, I assigned the other 90% to what I refer to as "superclusters"."

I seem to recall that the 10% was the average matter density of the voids in relation to the overall matter density. If this is so, your assumption has no grounds - it also depends on the void:supercluster volume ratio. Also remember, that they talking matter density, including dark matter, but excluding vacuum energy.

"I'd like to now run my spreadsheet at the inflection point where Ω_m = Ω_r, which I understand is at about t=10⁵."

From a 'pedagogical pov', density parameter Ω_m cannot equal Ω_r, because they have fixed values. I suppose you are referring to real densities, i.e., the time when ρ_m = ρ_v. This is calculated just like the ρ_m = ρ_v case, only with Ω_m/a³ = Ω_r/a⁴ from the Friedmann equation.

With Ω_m = 0.27 and Ω_r = 8.35E-05, it gives a = 8.35E-05/0.27 ~ 3E-04, giving an epoch radius for the present observable universe of ~1.3E+23 m. My integration gives an age of the universe at that expansion factor of ~2.8E+04 year (T₀ + 28 thousand years).

Jorrie

Jorrie, thanks for the calculation. And for sending the spreadsheet. I'm happy to send you mine if you want it.

My spreadsheet assumes that vacuum mass (a term I prefer to vacuum energy) is spread evenly throughout the voids, at the normal density. I also assume that the matter found in voids is the same percentage of dark matter and baryonic matter as the universe as a whole. Not that it makes a difference for my purposes what kind of matter it is, since it all has the same mass. I'm calculating mass in Kg, not densities.

Here's an excerpt from an article about the Bootes Void. http://www.acceleratingfuture.com/michael/blog/?p=69

• It is known that about 98% of the volume of the universe is consumed by intergalactic voids. The universe is made up of superclusters forming thin "walls" around these huge voids, perhaps reminiscient of the way organisms consist of cells whose main density lies in walls enclosing cytoplasm. (But in contrast to the way that atoms' primary concentration of density is located in the nucleus.)
• Of course, certain things can be found within the void, mostly in the form of energy. The extragalactic background light (EBL) and cosmic microwave background radiation (CMB) fill up the void. Interestingly, there is no gap in the cosmic background radiation in the region of the void. The void almost certainly contains a lot of dark matter and energy, perhaps even at densities no different than those found within superclusters. This means that dark galaxies and dark energy stars can probably be found. And, of course, the void is filled with endless quantities of virtual particles, which are created and annihilated constantly on the smallest timescales.

I have another source that says voids comprise 95-98% of the universe, but I can't find it right now. Obviously there's got to be a wide margin of error. For example, are voids defined to include the vacuum of their boundary regions which are gravitationally bound to neighboring clusters? For my purposes, I think it makes sense to consider such bound vacuum regions to be part of the "superclusters" they are bound to. Thus increasing the supercluster-to-void ratio.

Hi Jon.

Pleasure and yes, I'll like to look at your spreadsheet. Since CR4 mail doesn't allow attachments, I think, I'll send you my personal email address in a CR4 mail.

I'll accept the 98% voids by volume for now. Sticking that into some calculations for the present observable universe of 46 Gly radius yielded this:

Vacuum mass-energy, spread evenly over whole observable universe: 2.5 x 10⁵⁴ kg

Matter mass-energy, 90% in superclusters and 10% in voids: 9.3 x 10⁵³ kg

Void mass energy = 98% x 2.5 x 10⁵⁴ kg + 10% x 9.3 x 10⁵³ kg = 2.54 x 10⁵⁴ kg.

Supercluster mass-energy = 2% x 2.5 x 10⁵⁴ kg + 90% x 9.3 x 10⁵³ kg = 8.87 x 10⁵³ kg.

This makes the voids weigh in at 65% and superclusters at 35% of total mass-energy. One can say roughly two thirds to voids and one third to superclusters.

Does this tally with your calcs in some way?

Jorrie

Jorrie, sorry for the delay in responding. As I tried to clean up my spreadsheet, I found that it no longer generates the results I had thought. In fact, I'm at the point of giving up on the idea that superclusters or any other discrete clumping of mass-energy can generate enough local escape velocity to make a significant contribution to the total expansion rate of the present universe.

There are multiple ways to calculate measurements for expansion driven by mass-energy. The method I selected is the simplest I could think of. At any instant in time, flatness requires that the universe is always expanding at the rate of its own "escape velocity", the Einstein-de Sitter curve. Of course, that becomes a self-reinforcing loop since the expansion creates more mass-energy in the form of vacuum mass-energy, which in turn drives more accelerated expansion. That's what I mean when I say that the Einstein-de Sitter curve keeps moving outwards (or upwards). And yes over time as you said it does come to approximate a pure de Sitter curve (insignificant matter and radiation content).

First I calculate the observable universe's escape velocity "from itself" using the formula V_esc = (2Gm/r)^1/2.

Then I calculate the incremental radius by which the universe expands in 1 second as being equal to its escape velocity (in m/s). I use the formula for approximating the volume of a "shell" around a sphere, which is 4πr² x (shell's radial thickness). I set the "shell's radial thickness" equal to 1 second's worth of expansion at the escape velocity. That yields the incremental volume of expansion in cubic meters per second.

By this means, I calculate that the universe presently is expanding at 2.49x10⁶³ m³/s. Like you, I calculated the combined mass of the voids at .1 of total matter + .98 of total vacuum mass-energy. I calculated the individual mass of each of 10⁷ superclusters at .9% of total mass + .02 of total vacuum mass-energy. I calculate the volume expansion caused by an individual supercluster, then multiply it by 10⁷ to total up all superclusters.

The expansion numbers I calculate are 2.12x10⁶³ m³/s for the voids and 1.78x10⁶² m³/s for the superclusters. Not enough to sum to the expansion rate of the universe as a whole. Morever, playing around with the spreadsheet tells me that adjusting the supercluster/void ratio won't solve the problem unless 90% of the matter is put into the voids -- which makes their density indistinguishable from the superclusters, obviously a useless scenario.

So now I'm trying a new tack. I think the Flatness Theorem still is useful even if expansion can be calculated only at the level of the total universe. So I'm creating a new spreadsheet for that, which I'll send to you when it's ready.

I've calculated that the expansion rate for the universe at 9.45Gy (the matter/vacuum inflection point) = 1.1x10⁶³ m³/s, and at 28,000 years (the radiation/matter inflection point) = 9.93x10⁵⁷ m³/s.

Hi Jon.

I think you do the volumetric expansion rate a bit wrong by means of your "shell method". The best is to simply take ΔVol= 4/3 Pi (R₂-R₁)³ and divide it by ΔTime. The present observable cosmos has a proper radius of ~4.35x10²⁶ and R is increasing at ~10⁹ m/s.

Remember that you can also not just stick 10⁹ m/s inside the brackets, because then you are dividing by time³. You have to calculate the real volume increase and then divide by time.

For the present observable universe I get a volumetric expansion rate of ~7x10⁷⁰ m³/s. Also check your 'inflection point' or rather 'energy equality' radii; I think they are similarly wrong.

Jorrie

Oops!

The formula ΔVol = 4/3 Pi (R₂-R₁)³ is wrong for similar reasons than what I mentioned above. Should read: ΔVol = 4/3 Pi (R₂³ - R₁³).

I think my results were right, because I did not use the offending formula.

Jorrie

Jorrie,

I can't use your ΔVol formula for calculations, because my spreadsheet doesn't support enough significant digits to yield a non-zero number in the parentheses.

So unless you have another suggestion, I'm going to use an approximation formula which is slightly more accurate than the one I used previously, ΔVol = Δr*4Pi(r+Δr/2)².

I don't understand your point about about s³. In my calculations, s=1 always, so s = s² = s³. So m³/s³ = m³/s² = m³/s.

Using 4.34x10²⁶ for the radius of the present observable universe, and escape velocity = 9.59x10⁸, I calculate ΔVol = 2.28x10⁶³.

Hi again Jon.

Another Oops! Yea I had a blunder in my spreadsheet and when I calculated it your way, I got your answer.

I then found and corrected the error in my spreadsheet and it now gives your answer as well, give and take a little bit. Sorry about that. (I get 2.25x10⁶³ m³/s, due to slightly different constants).

I get around the lack of significant digits by just working it out over a longer time (like 100 million years or so) and then scale it down again. Your approximation seems good to me as well.

Jorrie

Jorrie,

My spreadsheet has now put the final nail in the coffin of any idea that Gravitational Binding Energy (GBE) has any direct correlation with the expansion rate. GBE calculated for the universe as a whole produces too fast of expansion, and GBE calculated from the sum of superclusters is way too low. I even tried adding in the GBE of the supermassive black hole in each galactic center, but it only partially closed the gap.

But, good news, the universe's ΔVol driven by the "escape velocity" of total rest mass almost exactly equals the ΔVol calculated from the Hubble formula, Δr = H_o(bar)*r_univ.

In fact, by working backwards from the Hubble formula, I calculate that a more precise figure for the true mass of the universe is 3.16x10⁵⁴Kg. That makes the escape velocities calculated by both formulas equal.

Jon

Hi Jon.

Yep, I think it's not for nothing that the cosmologists struggled for almost a century now to get to a model that works out (fit all present observations).

"I calculate that a more precise figure for the true mass of the universe is 3.16x10⁵⁴Kg. That makes the escape velocities calculated by both formulas equal."

The two equations must give the same answer, that's true. The real value is probably uncertain by 10 to 20%. Remember, the present radius and H_o(bar) are interdependent and not very certain. They fit the ΛCDM model (I see they also call it the 'Double Dark' model), but the absolute values are model dependent...

I just use rounded numbers, i.e. Ho=70 km/s/Mpc and critical density 10^-26 kg/m3, giving a mass of ~3.54 x 10⁵⁴ kg. We are both close enough for all practical purposes...

Jorrie

Jorrie,

Yes, but it also confirms for me that matter, radiation, and "vacuum energy" are just 3 different forms of the same thing. Another "equivalence principle."

"Vacuum Junk" differs from "regular" dark matter in that it doesn't "clump" at all, which means that gravity has no effect on it. And it doesn't travel at relativistic speeds. So it isn't matter and it isn't radiation.

By process of elimination, it must be comprised of virtual particles.

"By process of elimination, it must be comprised of virtual particles."

You may well be right, but AFAIK, scientists could not (yet) find virtual particles with the right properties, not even theoretically.

It seems that they have a better chance of finding the dark matter particles in the LHC quite soon.

Jorrie

Jorrie,

Further to Vacuum Junk (vacuum energy):

As I understand it, a virtual proton/anti-proton pair has a combined mass of 1.7x10^-27Kg, and an average lifetime of 10^-25 seconds.

So if each cubic meter of vacuum has a mass of 10^-26 kg/m3, that means that each such cubic meter need produce a mere 10²⁶ virtual proton/anti-proton pairs per second to account for the total mass of Vacuum Junk. And that's not even counting the contribution of virtual electron/positron pairs.

Seems to me that the vacuum is hardly breaking a sweat!

Jorrie,

Further to my last post:

It's interesting to note that the rest mass/energy of the vacuum (7x10^-27 kg/m³) is about 10¹⁴ stronger than the radiation of the CMB, which I calculate at 4x10^-40Kg/m³. So why would cosmologists be confident that the CMB is anything other than a tiny "shadow" of the astronomically more intense vacuum energy?

Hi Jon.

"Seems to me that the vacuum is hardly breaking a sweat!"

AFAIK, this is one of the biggest headaches of the quantum physicists - the extreme weakness of the present vacuum energy. Quantum field theory predicts a 'zero point energy' (zpe) of the vacuum that is immensely larger than what is observed on cosmic scales. Something probably cancels out the zpe almost completely, but what?

Jorrie

Hi Jorrie,

I want to return to the cosmic energy chart you posted on 8-16:

I'd like you to think about potential energy in a different way. I think that potential energy should = -((Static Energy) + (GBE_initial - GBE_current))

Conceptually, total potential energy represents the kinetic energy that would be released if the universe were allowed to gravitationally collapse. By definition, until the point at 9.55Gy where vacuum mass/energy exceeds matter mass, the universe is increasing its potential energy as expansion causes matter to become ever more dispersed. If there weren't any vacuum mass/energy, expansion would cause potential energy to continue increasing until all of the initial GBE, 10¹⁵⁰ joules, is worked down to the point where it equals the static energy of matter, 10⁷¹ joules. At such point as the initial GBE were reduced nearly to zero, no more potential energy could be gained through expansion (without vacuum mass/energy).

Moreover, it seems to me that vacuum mass/energy is "non-compressable". For example, if the universe were enabled to collapse gravitationally, the density of the vacuum mass/energy would not increase. Instead, the corresponding portion of the vacuum energy would simply disappear along with the volume of vacuum space it formerly occupied.

In that sense then, expansion caused by vacuum energy/mass should not be thought of as adding any potential energy to the universe, at all. Because it could never be converted into kinetic energy via gravitational collapse. So vacuum energy has no intrinsic potential energy.

The picture is less clear to me with respect to the GBE of vacuum energy, but intuitively it ought not to have any intrinsic binding energy, for the same reason it doesn't have intrinsic potential energy.

So, my conjecture is that the GBE line should continue downwards after 9.55Gy at approximately the same slope it had before that (I think it approaches but never reaches zero). The potential energy line should start at 10-¹⁵⁰, and slope downwards parallel to the (extended) GBE line, until it approaches, but does not reach, the 10^-300 line.

It seems reasonable that the distant future universe, characterized by ultra-low matter density, will possess virtually no binding energy and will have gained a commensurate amount of potential energy.

Jorrie, oops, I screwed up.

I was confused by the fact that potential energy is always negative. So an increase in potential energy means it becomes less negative, not more negative.

But I think my conjectures about GBE and vacuum mass/energy are still valid. Vacuum mass/energy has no intrinsic GBE or potential energy.

Therefore, the GBE line would remain as I described. The potential energy line would be as you drew it up to 9.55Gy, and then would continue as a straight line until it approaches, but does not touch zero.

Also, although static energy (the rest mass of matter and radiation) is used to calculate potential energy, I don't see why it is additive to GBE. The effect of declining rest energy should be seen only as a change in the slope of the curve, not in its absolute value.

Finally, it would be interesting to find a way to calculate the time when GBE/c² will exactly equal the static mass. I think it is sometime in the near future, because my calculations show that the GBE/c² of the universe presently is at least 9.2x10⁵⁴kg, while static mass = 3.16x10⁵⁴. I don't know any easy way to calculate a true GBE number for the universe though, since in theory it should be added bottoms up from every level of matter clumping. The tops down calculation is meaningless, because the density of the universe at small scales is far from homogeneous.

Hi Jon.

Yep, you may be right. I'm starting to realize that potential energy and GBE are perhaps invalid concepts for the universe at large, as the Physics Forums guru slapped my hands for denying.

The collapse phase of a vacuum energy driven universe is a thorny one, since with a positive cosmological constant, it can never happen.

"Finally, it would be interesting to find a way to calculate the time when GBE/c² will exactly equal the static mass."

I guess you meant densities, because the mass-energies never decline, but I don't catch your drift here...

Jorrie

Jorrie,

Well, I just don't think GBE is very important to the expansion of the universe. My latest "bottoms up" calculation, which sums the GBE at levels of Stars, Super-massive Black Holes, Galaxies, Clusters, and Superclusters, and even adds in the nuclear binding energy of "metal" atoms for good measure, still generates a combined total GBE/c² of only 1.66x10⁵¹Kg. That number is 3 orders of magnitude smaller than the total rest mass of matter in the universe.

Given that GBE is increasing over time as clumping continues, I doubt that GBE could possibly have been significant to the expansion rate calculation at any recent time in the universe. And if you go far enough back, it probably is rendered insignificant by the total rest mass of radiation.

I think that at all times, total potential energy of the universe merely = -(GBE), so it isn't of significant magnitude either, in the context of the big picture.

The "expansion energy" line on your graph represents the energy needed to "disperse" the universe's rest mass at its "escape velocity" of 9.85x10⁸m/s. I think the resistance to that dispersion comes almost entirely from the inertia of the rest mass, not from its gravitational binding.

Intuitively, that reflects the low mass density of the vacuum, and the relative insignificance of total binding energy at the level of superclusters and below.

Jorrie,

It occurs to me that whether you consider the "midlife" expansion of the matter-dominated universe to reflect residual momentum from a single impulse (cannonball) or ongoing self-propulsion responding to inertial mass (rocket engine), you still need to hypothesize a missing "force" or "energy" to supply the expansion vector.

I can't say that I have a clear idea what manner of physical reality that expansion "force" or "energy" represents, but here is an analogy for my theory that incremental expansion is spontaneously produced as a reaction to the universe's inertial mass:

Picture a massive quantity of oil deposited carefully (no ripples) onto the surface of a perfectly still, infinitely broad body of water. Then watch (preferably in slow motion) as the oil's own weight causes the radius of the oil slick to expand, at first very quickly, then slowing over time.

The cosmological constant can also be factored in by pouring additional oil onto the expanding surface. The amount of additional oil added per second is equal to the Δarea of the oil slick per second. So obviously the amount of additional oil/second increases rapidly over time, and the expansion rate of the oil slick increases.

Of course this a limited analogy. It is only 2-dimensional, and may ignore some details such as surface tension (analogous to GBE?). And any coherent oil slick will have a minimum thickness of at least 1 molecule, so it cannot expand infinitely as the universe seemingly can.

That latter point raises an interesting question: As the average mass density of the vacuum has fallen towards the cosmological constant, is the observable universe still a coherent "thing", or has it already "fallen apart" into many separate "clumps" that mostly don't experience any current interaction with their neighboring clumps anymore? They may still be receiving "photon postcards" from each other's past, of course. I think coherence is a slightly different concept than the interaction horizon of a homogeneous universe. In the latter, the current interaction horizon can be shifted arbitrarily to any observation point, whereas in the former, current interaction horizons extend only to the gravitational-binding boundary of each clump.

Jorrie, further to the last point on my prior note (which was not the main point of the note!):

If the "interaction horizon" is defined as a distance at which we can receive a one-way signal from a source (without even being able to reply to the signal), apparently such horizon presently = redshift 0.68 = 1.93Gpc = 5.96x10²⁵ meters. That is 30x the radius of the Local Supercluster @ 1.9×10²⁴ m.

So our supercluster has not yet become entirely functionally isolated from a subset of the other observable superclusters.

Nevertheless, since superclusters apparently aren't gravitationally bound to each other, they are irrevocably on the road to mature as fully independent universes. So while they are unbound from the mothership but still able to communicate with it, it seems plausable to call them "juvenile" or proto-universes. At a time in the distant past when they apparently were still gravitationally bound to the mothership, we can refer to them as "embryonic" universes.

There is a good paper on calculating various universe horizons at:

http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v565n1/54136/54136.html

There also is a handy redshift/distance calculator at:

http://astronomy.swin.edu.au/~elenc/Calculators/redshift.php?Ho=71&v1=1000&z1=0.68&v2=1000&z2=0.001

Hi Jon.

Thanks for the links and the spreadsheet. Will look at them in due course. I normally use Gott's paper and his very useful logarithmic maps of the universe.

Note that the z=0.68 indicates the present limit of 2 way communication, while the one-way causal contact is at some z=1.7 at present.

"So while they are unbound from the mothership but still able to communicate with it, it seems plausable to call them "juvenile" or proto-universes."

I would not call them that - by the time each supercluster is isolated from the rest, they are probably not too far from the 'degenerate phase', where all the mass-energy gets turned into radiation, if one believes Roger Penrose.

Jorrie

Hi again Jon.

"As the average mass density of the vacuum has fallen towards the cosmological constant, is the observable universe still a coherent "thing", or has it already "fallen apart" into many separate "clumps" that mostly don't experience any current interaction with their neighboring clumps anymore?"

Ever since inflation ended, there were a virtually infinite number of 'regions' that had no interaction possibilities with neighboring regions due to the distances between them being vastly larger than what light could have travelled since inflation. Isn't this the same thing?

Jorrie

Jorrie,

From my first post yesterday:

"I think coherence is a slightly different concept than the interaction horizon of a homogeneous universe. In the latter, the current interaction horizon can be shifted arbitrarily to any observation point, whereas in the former, current interaction horizons extend only to the gravitational-binding boundary of each clump."

One aspect of my distinction is that at some point in the future, the "generic" interaction horizon will be shorter than the radius of a supercluster, but despite that we'll continue to be able to interact within the entire area of our gravitationally bound supercluster. In that sense, each supercluster eventually becomes a permanent (or very, very long term) and relatively static observable universe of its own.

In contrast, any observation point located outside the gravitationally bound area of a supercluster will eventually have a very short event horizon and will not be able to interact with any supercluster.

Anyway, this subject is too philosophical to be important. I think it is relevant to my oil-on-water analogy, because the one-molecule minimum thickness of an oil slick may cause the slick to lose its unified coherence and drift into discrete, individually coherent patches. As the density of the universe drops over time, it similarly loses its unified coherence, and its superclusters will drift apart into discrete, individually coherent patches.

However, the oil-on-water analogy doesn't provide a strong analogy for the local coherence-maintaining force of supercluster gravitational binding. It would, if the oil had significant surface tension holding a slick together up to a certain maximum stable size (counterpart to an individual supercluster's stability size limit).

Jorrie, you'll recall that we had a discussion several months ago about the theoretical possibility that the universe is not expanding, but instead all of its contents are shrinking. I responded to support Guitarhunter's mention of the idea. Now I have uncovered a reference to this idea from the 1930's, by the famous British astronomer Arthur Eddington (who was one of the first to suggest that stars are powered by hydrogen fusion). Here is an excerpt from his book "The Expanding Universe: Astronomy's 'Great Debate', 1900-1931 (p.88-92), in which he muses about George Lemaitre's recently published work regarding the Big Bang:

=========================================================

"All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom".

It is our instinctive outlook that we are always the same; it is our environment that changes. As with Anatole France's dog Ricquet—"Les homes, les animaux, les pierres grandissent en s'approchant et deviennent enormes quand ils sont sur moi. Moi non. Je demeure toujours aussi grand partout ou je suis."

Is not the expanding universe another example of distortion due to our egocentric outlook? Surely the universe should be the standard and we should measure our own vicissitudes by it. We se a relative change, and cry out that the universe is dissolving; as well might the growing child, who sees the familiar home becoming smaller, be dismayed at the vanishing property of houses and furniture.

The argument sounds plausible, but I do not deem it true. Even if our standards are held responsible for the expanding of the universe, they cannot be held responsible for its bursting. Moreover our constant standards are not necessarily puny. I have mentioned (p. 72) one cosmical dimension which remains constant, namely the radius of curvature R_s of empty regions of the universe. Since it stands in a constant ratio to the metre, it can be used equivalently. This is in fact the ideal cosmical standard and judged by it the universe changes whilst we remain true to size.

Although I do not think the suggestion goes very deep or that it has any philosophical moral, I will follow it for my last escapade in our new playground. Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever-decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man's life is becoming briefer; his threescore years and ten are an ever-decreasing allowance. Owing to the property of geometrical progressions an infinite umber of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.

We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing."

====================== end of excerpt ===================

Wow. Deep. Thank you Jon for turning that up. I am humbled to have my idea associated with one of the great thinkers. His analogy "cosmic spectator" and our role as a "microscopic blur" really cuts to my feelings of our position in the infinite cosmos and the role or existence of a god. The translation of the french:

The men, the animals, the stones grow while approaching and become enormous when they are upon me. Me, no. I always remain tall everywhere I am.

It's a reference to perspective, which seems to be the point of Mr. Eddington's (and my/our) idea.

Hi Guitarhunter,

Thanks for the translation. It's very powerful in its own right. One of the fun things about the astronomers and physicists before around 1950 is that they mixed equal parts of observation, math, broad speculation, and philosophy. Einstein did it as much as anyone. Nowadays it seems like cosmology theory is increasingly limited to computerized processing of ultra-complex observational data, and use of abstract math to invent new quantum particles to plug every gap. How can any of us hope to weigh in on the theoretical merits of yet another hypothetical particle?

Somebody famous (I forget who) said that a new perspective is worth 80 points of IQ. I for one am happy to take advantage of that formula, because if I stick to speculative theories, it puts a natural floor below my otherwise subterranean cosmology IQ. But the cosmology experts are on to that trick, too...

Hi Jon.

Yea, I recall that we eventually agreed that if one just takes today's observation at face value, one can 'reverse' it to a 'shrinking model' and everything will stay the same. Except that extrapolations become troublesome, e.g., sizes blow the Planck limit.

My guess is that Eddington wrote those words with his tongue in his cheek...

Jorrie

Hi Jorrie,

Maybe he was tongue in cheek, but Eddington was an avid theoretical speculator himself. I believe his personal theory was that the early universe was perfectly homogeneous, and that homogeneity is equivalant to nothingness, so it was natural that the early universe could spontaneously appear out of nothing. Hey, why not!

In a similar bout of speculation, Einstein seemed fascinated with what he referred to as the "eliptical" universe, which had the geometry of a mobious strip. So light would circle all the way round it and come back to the start, but upside down. Until the event horizon eventually cut off the circulation. My guess is that if he had lived long enough for observational evidence to show that the universe is flat, he would have been extremely disappointed.

Johannes Kepler of course lived in a much more religious era. His mathematical theory apparently was inspired directly from by his religious/philosophical instincts, applied to some basic observations about electromagnetism, as Wikipedia reports:

"Within Kepler's religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from De Magnete (1600) and on his own work on optics. Kepler supposed that the motive power (or motive species) radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Perhaps this assumption entailed a mathematical relationship that would restore astronomical order."

Our current appetite for speculative, mindbending theories doesn't seem so different from how most of the historical scientists thought. I hope that our current generation of mainstream cosmologists hasn't lost that. As I said, they seem fixated on the mathematics of inventing new hypothetical particles, and new scalar fields for existing particles. For example, from what little I understand about the theory of inflation, it involves a couple of twisting backflips by a hypothetical particle, followed by some front flips and a splashless entry into the pool. All other possible explanations are mathematically excluded (until they devise an even more complex set of particles and scalar fields). The complexity of this new regime more and more resembles pre-heliocentric orbital mechanics.

Hi Jon,

Thanks for the exerpt from Eddington (good refresher).

I especially liked your twisting forward/back flips, etc. in order to try to fill endless gaps (they are endless, you know). This scientific "marching in step" has taken on a life of its own, not that it shouldn't be pursued, but at what cost? All the mathematics and cosmology conceivable cannot take the place of what something like music can do for the soul in creating the inspiration, the exuberation, to pursue things like math, cosmology, physics and so on. Lets admit it, humanity has its own passion, rooted deep within itself, above and beyond the physical sciences. It is what drives us in our attempts to achieve greatness.

Sorry to get too philosophical, but your post sorta brought in on.

Anyway, back to the topic? Is there really any difference as to whether we (the universe) is expanding or contracting? Seems like the net effect would be the same. Besides, is there any way (at all) to prove one or the other?

From the excerpt you posted from Eddington: "I have mentioned (p. 72) one cosmical dimension which remains constant, namely the radius of curvature R_s of empty regions of the universe. Since it stands in a constant ratio to the metre, it can be used equivalently."

Looks to me like there's no proof here at all because R_s would always be the same since just as the metre changes, so does the empty regions of the universe change proportionately. I fail to get this one. Help me if I missed it.

Anyway, your point is well taken. Please continue.

-John

Hi John,

I don't think there is any difference between us shrinking or the universe expanding. If there was a difference, then one of the two theories must be wrong! Since it's all relative, in theory BOTH the universe could be expanding and we could be shrinking at the same time. Or any variation that keeps the relative scales consistent with observations.

We may never be able to know which is which. But, never say never in this business. Scientists have proven some things that a mere 20 years earlier were considered impossible to ever prove.

To me, the most interesting aspect of the alternative perspective would be to figure out which constants would change and which would remain the same. Like the speed of light, for example. I think there would be some very weird adjustments to physics. Someday I'd like to spend time working it through, even if the whole exercise is probably imaginary. Analyzing an alternative model generally provides some new insights even about the traditional model.

Jon, you said "To me, the most interesting aspect of the alternative perspective would be to figure out which constants would change and which would remain the same. Like the speed of light, for example."

I think the problem is that we can not figure out which constants remain "constant relative to everything else". Even c, although we consider it constant, is only so relative to us. If our environment (the universe) changes; distances change proportionately; then c is also relative, even though it remains, to us, a constant. There's no solution to this one, I'm afraid.

-John

Hi John,

You may be right. But I think that in the "shrinking" model, some constants may remain constant. It's worth thinking about, anyway.

Jon

Hi Jorrie,

Please see my post to Jon.

Regarding the Planck limit, seems like it would change proportionately to everything else. I don't see any way to prove expansion or contraction. Seems like it really comes comes down to Descartes; I think, therefore I am. Prove me wrong.

Hi John.

Can you really conceptualize that your body is shrinking and what's more, shrinking at an increasing rate, forever... (at least as far as the atoms in your body are concerned)?

I can't. It may be interesting to toy with, but why bother with such an extremely metaphysical idea? It gives no new insights as far as I can see.

Jorrie

Hi Jorrie,

You're right, of course, but it seems like the more knowledge I acquire, the smaller I feel. Does humility have anything to do with science?

-John

Hi John; "Does humility have anything to do with science?"

It was said by some big scientist (I forgot who), paraphrased as: "novices are mostly so sure of themselves and experts so full of doubt..."

Jorrie

Hi JJ,

"Regarding the Planck limit, seems like it would change proportionately to everything else."

We can't assume this, since it follows quantum laws which may not apply to larger things. If something could be compared to it, we could prove expansion or contraction.

For what it is worth, Isaiah 42:5 says that the Lord stretched out the heavens, which seems to fit with an expanding universe,

S

The following is a quick summary of a new model that I've advanced: The Dominium

The model begins with the same set of premises and conditions that were originally set forward and given the moniker, the "Swiss Cheese" model. In other words, at Big Bang creation, matter and antimatter were created equally, however, distribution was slightly random. Statistically, some areas would have greater concentration of one type over an other ("perturbations" or "imperfections" depending on which author you follow).

The Dominium model takes this core idea and adds one truly new hypothesis: matter/antimatter repulsion. As a result of like attracts like/opposites repel forces, the once heterogeneous mixture would be expected to undergo the process of "Self assembly"--as commonly noted in hydrophobic/hydrophilic extremely heterogeneous mixtures. As a result of self-assembly, the original matrix of the Universe became more organized rather than heading towards more chaotic (as is the case of self-assembly heterogeneous mixtures at the nano and atomic level)--in other words, this model assumes that classic understanding of entropy is flawed. Not all systems become more chaotic. This has been shown over and over again at the atomic, molecular, and nano levels, why couldn't this also apply at the galactic? With this solution, we achieve results consistence to observable phenomena: a uniform distribution of mass and flat event horizon.

Opposites-repel can also be used to predict and describe many other observed "anomalies." For example, the solar wind. With this new model, a clear and simple explanation for this phenomenon is forthcoming. Positrons produced through fusion are repelled by the extreme mass of the sun. As a result they are driven toward the surface. Along the way, some will annihilate. At some point densities and energies become low enough that they gravitationally self-sort (becoming miscelular positron packets MPP) and become immiscible with the surrounding matter. Although immiscibility prevents further annihilations, it does not prevent interaction. The MPP are continually pushed forward by the repulsion from the Sun's matter, while this occurs they would be expected to push matter in front of them forward. Hence the solar wind. Question: why haven't WIND or SWEPAM solar wind probes measured the presence of positrons in the titer? Answer, because these probes are matter-dense objects, and because gravitational effects are felt at very large distances, the positrons of the MPP would avoid the probes, therefore, you would expect to NEVER record their presence in the solar wind.

The actual model is quite long. Anomalies accounted for by this new model also include "dark matter," nebulae formation, the reason supermassive galactic central black holes stopped growing at one point in their development, explanation of the Tunguska event, and many more.

For a free download of the abridged version (91 pgs) go to http://www.hasanuddin.org/viewtopic.php?t=3&sid=6709b63831e91b0f6d8a4b99be6570c1

Or if you're really interested, the full book (194 pgs) is at online bookstores.

PS: Two words of caution. 1) It's written in lay language in the tradition of Sagan & 2) There is a truly ominous implication: mini black-holes are predicted to be stable... right now LHC at CERN is a hair's breath away from creating a mini black-hole