Relativity and Cosmology

Jorrie,

Why is only rest mass considered? Why is kinetic energy not considered?

Roger

Hi Roger.

Good question. The short answer is that kinetic energy is considered as part of the total static energy.

Note that the expansion of the universe does not contribute to this kinetic energy, but the kinetic energy of particles moving through space is considered as part of the static, non-expansion energy - actually, dark matter is at least partially made up of relativistic particles, moving through space at close to the speed of light.

Friedmann (ΛCDM) cosmology assumes a homogeneous distribution of baryonic and non-baryonic matter that is at rest relative to the CMB. The reason is that the rest energy of baryonic matter (mc²) dwarfs any kinetic energy of movement through space (~0.5mv²), since v << c.

I chose to rather not call the expansion energy of the cosmos 'kinetic energy' (as some books do), because of this distinction and (sometimes) confusion. The expansion energy is in the 'stretching' of space, not in the movement of bodies.

Jorrie

Jorrie,

Your new post is great. I'm humbled that you mentioned our discussion!

One suggestion: I have not encountered the terms "static energy" and "expansion energy" before. I think I understand why you used those terms in preference to other alternatives, but they need more explanation about what they are. I interpret "static energy" to mean the total rest mass of matter and radiation; and "expansion energy" to mean the total kinetic energy of matter and radiation.

As I think about this more, it might be useful to create a variation on this chart. The variant chart would use 5 colored lines to separate out the contributions over time of (a) "V_rest", the accumulation of rest mass of vacuum energy, (b) "M_rest", the rest mass of matter, (b) "R_rest", the rest mass of radiation, (d) "G_bind", the gravitational binding energy of mass and radiation, and (e) "G_pot", the gravitational potential energy of the universe.

I'm not sure whether (d) is depicted in some way on your chart or not. But it seems to me that should be depicted, because over time it converts to potential energy (and therefore is conserved) in the same manner as (b) and (c) convert to potential energy. I think (e) can be partially calculated from your chart.

(a) V_rest: The accumulated rest mass of vacuum energy is near, but slightly above zero at the end of inflation (due to the accumulation of some vacuum energy during inflation). Due to the log time scale, the slope of the line starts out flat, and then curves up more and more steeply. It crosses the M_rest line at around 5Gy, and becomes nearly vertical, reaching 10₁₄₅ joules within a couple Gy after the present, slightly ahead of the red and blue lines shown in your chart, with no end in sight.

(b) M_rest: The rest mass of matter has remained pretty constant since the end of inflation, except that it has declined slightly as the ambient temperature of the universe has cooled very considerably. At the present time it would be approximately 2.7 X 10⁶⁹ joules, I think.

(c) R_rest: This could be called the kinetic energy of radiation, but I think rest mass means the same thing, in the sense that it measures the gravitational mass of the radiation at e=mc². I think this line would start after inflation at about (10⁹⁵ - 2.7 X 10⁶⁹ joules), comprising nearly all of the initial rest mass energy, except the part comprised of the M_rest, and the tiny bit comprised of the rest mass of accumulated vacuum energy. It would decline very quickly due to redshift. I think it's fair to say that the decline represents not energy loss, but conversion to potential energy. I presume that's true because if the universe could be magically forced to contract, this energy would be reconverted to kinetic energy via blue shift.

(D) G_bind: The total gravitational binding energy starts out very large at inflation and decreases over time, but I don't know how to calculate it in joules. The initial amount would be defined as the amount of kinetic energy that would be required to instantly pull all of the quanta of matter and radiation in the (then small) universe apart until they are infinitely distant from each other. Adding to the complexity, as the universe continues expanding infinitely, G_bind doesn't approach zero, because the steady accumulation of V_rest actually causes G_bind to increase faster and faster.

(E) G_pot: Due to expansion, gravitational potential energy is created by the conversion of some M_rest , R_rest, and G_bind into equal amounts of potential energy. At any point in time, the potential energy resulting from such conversion is equal to the amount of kinetic energy that would be released if all the matter and radiation were magically forced to instantly smash back together. Contrary to my recent "thought experiment" on the other blog, I now submit that the decrease in G_bind over time contributes exactly an equal amount of G_pot. Therefore, the accumulation of vacuum energy does not change the total energy balance of the universe. Thus I no longer see vacuum energy as a mechanism to "repay" the deficit of potential energy caused by the "borrowing" of matter and radiation from the cosmic sea during inflation. The chart could show that such initial borrowing causes G_pot to start out after inflation at negative 10¹⁴⁵ joules. I note that while R_rest almost fully repays its "deficit" over time by red shifting its rest mass towards zero, M_rest "cheats" the universal energy balance by clutching tightly to its rest energy into the foreseeable future. Why would the universe permit itself to be cheated by such a cheap trick?

Another question: Does it make any sense that G_bind and G_pot are additive to the sum of rest energies, or does that constitute double counting, or perhaps adding apples and oranges?

Also: Intuition tells me that the supplemental hyper-expansion driven by the accumulation of vacuum energy will itself neatly fit into an Einstein-de Sitter curve. If new vacuum energy ever were to stop accumulating, the expansion rate would immediately begin to decrease in accordance with an Einstein-de Sitter curve. But so long as the creation of new vacuum energy is ongoing, the expansion curve continues to be "bumped up" incrementally, and the rate of expansion increases.

Thanks jonmtkisco, all those definitions helped me to get my head around this really huge subject. I cope reasonable well with Newtonian physics but I am not confident with "Relativity" or "Cosmology"or "Chaos". Having a confirmed set of definitions is a great start.

Hi Jon - "Your new post is great. I'm humbled that you mentioned our discussion!"

You 'stirred' quite a bit and made us dig deeper into these matters.

"I have not encountered the terms "static energy" and "expansion energy" before."

My reply to Roger above gives my perceptions on the meanings. My physics friends convinced me to steer clear from 'rest energy' and 'kinetic energy', because they are slippery concepts on a cosmic scale. I hope I made it clear to Roger that they are somehow included in the 'static energy'.

As far as showing of the components of cosmic energy on the graphs, yes one can, provided you can define them. In the light of the above, I cannot quite agree with your definitions, but I'll give it a thought. One thing, 'potential energy' is just the negative of the expansion energy graph, way down 'below' the others. It 'kills' the energy axis scale if included on the same chart.

"Another question: Does it make any sense that G_bind and G_pot are additive to the sum of rest energies, or does that constitute double counting, or perhaps adding apples and oranges?"

Your G_bind and G_pot are positive-negative opposites (G_bind = -G_pot), so adding them has no meaning. What has meaning is to add expansion energy E_exp and potential energy E_pot and if you get zero, you have a flat cosmology. Any other value makes the cosmos open or closed.

Your last paragraph is essentially right, except that if the vacuum energy continues to work like we think it works today, the curve will never become an Einstein-de Sitter curve - in fact it will eventually approach what is called a 'de Sitter universe', which has no matter or radiation in it.

Essentially, the Einstein-de Sitter model just added matter energy to the mix, but no radiation or vacuum energies, which they assumed to be close enough to zero to be ignored.

Jorrie

`Hi again Jon.

On the 'chart variation' that you mentioned, I've used your 5 curves for the various components, just with slightly different names and definitions than what you proposed. From top to bottom in figure 1 they are:

Figure 1:

Expansion energy

The energy of expansion is essentially the total static energy times the expansion rate squared, similar to kinetic energy (½mv²).

Radiation energy

The radiation energy is what filled the observable universe and today makes up the cosmic microwave background radiation. The expansion of the universe reduces the radiation energy due to redshift of photons.

Matter energy

The constant ordinary (baryonic) and dark (non-baryonic) matter-energy of the observable universe. The matter density decreases with the expansion, but the total static matter-energy stays fixed.

Vacuum energy

Vacuum (or dark) energy has a constant density and hence the total vacuum energy grows with the expansion of the universe.

All of the above adds up to the 'static energy' of the observable universe. Vacuum energy has duel characteristics: it adds to the total static energy and at the same time adds to the expansion energy, keeping the energies in balance.

Potential energy

In the case of a flat universe, this is just the negative of the expansion ('kinetic') energy. It is plotted as -log(-potential energy) to show it in the 'proper' place for negative energy at the bottom end a log-log graph.

If the potential energy did not balance out the expansion energy right from the start, the universe forever has an open geometry (if too much expansion energy) or a closed geometry (if too little expansion energy).

I hope this clears at least some issues.

Jorrie

Thanks Jorrie, you're good at flipping out those new graphs!

I think your "static energy" definition is the same as the sum of my 3 rest energy definitions: M_rest + R_rest + V_rest.

I'm still having trouble nailing down what physical phenomon your "expansion energy" definition represents. Is it essentially the same as my gravitational binding energy definition G_bind? It looks like the same curve.

Do you agree that, most likely, the radiation energy (R_rest) "lost" through redshift is not truly lost, rather it contributes to the potential energy total? I justify this proposition with the presumption that if the universe could be magically forced to contract, the lost energy would be "regained" through blueshift of the remaining radiation energy. If on the contrary redshift losses were irrecoverable, absolute losses, that would seem to defy the conservation of energy. I guess either way it really doesn't change the yellow potential energy line noticeably.

The funny thing about these log based charts is that summing the values of multiple lines is visually meaningless. The line with the largest absolute value at any point completely dominates the math, so adding smaller value lines to it is no more than a rounding error and doesn't visibly move the line. It underlines the meaning of what the "radiation-dominated", "matter-dominated" and "vacuum energy-dominated" epochs represent.

Hi again Jon.

"I think your "static energy" definition is the same as the sum of my 3 rest energy definitions: M_rest + R_rest + V_rest."

Yep, essentially it is just definitions that differ, but: 'rest energy of radiation' does however not sit very well and as I wrote to Roger above, the static (non-expanding) energy includes the 'real' kinetic energy of matter matter moving through space. How does the "rest energy of the kinetic energy" sound? I rather call it static energy and expansion energy in my 'engineering spin'.

Cosmologists do not use these terms, because they never talk of the 'energy of the universe' - they cannot calculate it precisely at all (general relativity does not allow that). They will go as far as speaking of the "mass of the observable universe", but mostly they just talk mass density or energy density.

"I'm still having trouble nailing down what physical phenomenon your "expansion energy" definition represents. Is it essentially the same as my gravitational binding energy definition G_bind? It looks like the same curve."

Almost, but not quite. It is conceptually wrong to equate binding energy and expansion energy, because in an open universe, expansion energy exceeds binding energy and visa-versa for a closed one. In a flat cosmos expansion energy is equivalent to 'escape energy'.

"Do you agree that, most likely, the radiation energy (R_rest) "lost" through redshift is not truly lost, rather it contributes to the potential energy total?"

Yep. This is exactly why the potential energy curve rises during the radiation dominated phase. Obviously, the decreasing expansion rate makes the potential energy increasing faster than what the radiation energy decreases, but the energy balance is maintained.

Jorrie

Thanks Jorrie

Since I refuse to budge off of the Conservation of Flatness, in my model your definition of expansion energy will always equal gravitational binding energy.

Do you intend a literal physical interpretation of your term, i.e. that expansion energy measures the negative pressure "anti-gravity" that drives expansion according to the inflation/dark energy theory?

Also, you said:

"This is exactly why the potential energy curve rises during the radiation dominated phase. Obviously, the decreasing expansion rate makes the potential energy increasing faster than what the radiation energy decreases, but the energy balance is maintained."

Hmmm, it's hard for me to see that in the chart. Since your red curve is a mirror image of your yellow curve, the early rise in the yellow curve could just as well be attributable to a high initial expansion rate, as to the contemporaneous decrease in radiation energy. Since the expansion rate is squared in the formula, doesn't any given percentage increase in the expansion rate contribute a lot more to the slope of the yellow line than the same percentage decrease in radiation energy?

Hi Jon.

Yes, in the simplest flat models (ignoring relativistic effects), my expansion energy equals gravitational binding energy, which is the negative of gravitational potential energy. It is apparently not so in general relativity and I rather thrust the Friedmann equation to give me a (sort of) 'kinetic energy' of expansion, which must balance out the negative gravitational potential energy.

One can say that 'negative pressure "anti-gravity" ' is a physical mechanism to drive expansion and hence is a source of that energy. Remember, it is probably also the original physical mechanism and source of all the radiation and matter energies.

"Hmmm, it's hard for me to see that in the chart. Since your red curve is a mirror image of your yellow curve, the early rise in the yellow curve could just as well be attributable to a high initial expansion rate, as to the contemporaneous decrease in radiation energy."

The red expansion energy curve is similar to kinetic energy and hence is linearly influenced by any static energy change, just like ordinary kinetic energy (½mv²) is linearly influenced by any change in the rest mass. It is a bit hard to see on log-log graphs, but look again at equations 3, 5 and 6 in my Cosmic Energy page and you will notice that.

If you change the relative values of Ωr, Ωm and Ωv, while keeping Ωr+Ωm+Ωv = 1 (or just constant), the value of the bracketed factor changes (for any a ≠ 1). Keep Ho, Ro and ρ_c constant and both static energy Eo_(a) and expansion energy Ee_(a) change in magnitude. So both the values and shapes (slopes) of both curves must change accordingly.

But, always remember that these are only order-of-magnitude calculations...

Jorrie

Thanks Jorrie. I re-read the formulas but I still think my point is valid.

During the period from 10⁴⁵ up until time "0" on your chart, redshift contributed all but an infinitesimal percentage of radiation's original energy, 10⁹⁵ joules, back to the potential energy pool.

During that same period, your chart shows that the potential energy pool gained back all but an infinitesimal percentage of its original deficit, which was 10¹⁴⁵ joules.

In the context of an almost 10¹⁴⁵ joules gain in potential energy, the almost 10⁹⁵ joules contributed to that by redshift is utterly insignificant and would not visibly affect the yellow line. Also, the accumulated vacuum energy total at about 10⁵⁰ joules was even less significant.

Therefore, I conclude that the portion of the decrease in gravitational binding energy of matter and radiation during that period which was NOT due to redshift overwhelmingly dominates the shape of the yellow line. Thus the dominant contributor to the reduction in the potential energy deficit during that period was simply the increase in (average) distance between particles of matter and energy, (i.e. gravitational dilution per the inverse square law) caused by the explosive early expansion rate of the universe.

Hi Jon.

"During the period from 10⁴⁵ up until time "0" on your chart, redshift contributed all but an infinitesimal percentage of radiation's original energy, 10⁹⁵ joules, back to the potential energy pool."

Yep, that's right, but, the radiation energy was the dominant static energy that slowed down the expansion rate for the first 10⁵ years or so. Without it, the evolution of the universe would have been quite different to what is observed today.

We are essentially saying the same things in different words, e.g., your: "Thus the dominant contributor to the reduction in the potential energy deficit during that period was simply the increase in (average) distance between particles of matter and energy, (i.e. gravitational dilution per the inverse square law)..." is just another way of saying that 'most of the expansion ('kinetic') energy of the radiation dominated epoch was converted into gravitational potential energy.'

One thing that we must not lose sight of: by saying that the potential energy is negative is just a Newtonian convention, a matter of choosing a convenient reference point. The approximate relativistic view is that energies (potential and expansion) do not add up to zero, but to some constant positive value.

Actually, general relativity do not add energies like we normally do - it multiplies and divides, like Eq. 6.7, page 94 of How Orbits Work from Relativity 4 Engineers. Then, on the cosmic scale, the total relativistic energy do not even remain constant. Drat!

Anyway, it looks like we at least got to the bottom of the 'Newton gravitational well' now.

Jorrie

Jorrie,

Well I have to say that this discussion has been quite an eye-opener for me. First I was surprised to learn that 10⁹⁵ joules of radiation energy were simply lost by the universe through redshift. Then I was even more surprised that an astronomically larger 10¹⁴⁵ of gravitational binding energy was lost! But all of that is historical, as vacuum energy is refilling the energy bucket faster than ever.

This discussion has helped me to formulate a simpler and stronger version of Conservation of Flatness, which I will now call the Flatness Theorem:

1. Theorem 1: The geometry of the universe is, always has been, and always will remain, flat.
2. Since the universe has been characterized by an interaction horizon since early on, it is not possible for any contemporaneous phenomenon to achieve the overall flatness we observe today if the universe wasn't always flat. Therefore, the universe has always been flat, and by extension it always must remain so.
3. Theorem 2: Every joule of energy expresses equal amounts of gravitation and anti-gravitation.
4. By "energy", I mean static energy, ie, the mass-equivalent energy of matter, radiation, and vacuum energy. By "anti-gravitation" I mean what you call expansion energy.
5. Since gravitation acts to contract space, it causes clumping of energy on local scales. Since anti-gravitation acts to expand space, its local effects are masked by gravitation, but its smoothing effect is observed at larger scales.
6. Theorem 3: Anti-gravitation observes the same inverse-square law as gravitation.
7. This explains the shape of the Einstein-de Sitter curve, whereby the expansion rate falls as the distance increases. As distance increases, gravitational binding energy and anti-gravitational expansion both decrease equally.
8. Theorem 4: The preceding Theorems provide a consistent model for inflation, expansion, and accelerated expansion.
9. Inflation, expansion, and accelerated expansion were each caused by the interaction of the gravitation and anti-gravitation which each joule of energy brought with it when it first appeared in the universe.
10. Each of these 3 expansionary phases is defined by a simple Einstein-de Sitter curve when measured at an instantaneous point of time. As each quantum of new vacuum energy first appears in the universe, the overall Einstein de-Sitter curve for the universe shifts "upward" to account for that energy quantum's gravitation and anti-gravitation.

I think the Flatness Theorem ties several complex concepts together in a very simple way.

Well, I just posted the Flatness Theorem today and I already need to modify it. Here is a revised version of Theorem 3:

1. Theorem 3: Anti-gravitation does not express a physically observable repulsive force. In the presence of gravitation, anti-gravitation observes an inverse-square law, but compared to gravitation, its force at any given distance is multiplied by a constant >1.
2. The expansionary force of anti-gravitation exceeds the anti-expansionary force of gravitation by a constant positive amount. The resulting net expansion rate declines parabolically over time, but not to zero, in accordance with an Einstein-de Sitter curve.
3. Anti-gravitation probably is physically expressed as an ongoing production or emission of new quantum vacuum. Under the restraining influence of energy's own gravitation, the "net" new vacuum production rate declines over time, but not to zero. Hypothetically, in the absence of gravitation, the vacuum production rate would not decline over time.

Hi again Jon.

Apart from the issues with 'anti-gravitation' in my previous reply, your 'new 2.' is an example of how confused the issue may become in your model.

Vacuum energy contribution today exceeds the deceleration forces by an increasing amount, hence the expansion rate increases exponentially. Just after inflation, its influence was negligible.

Your 'new 3.' makes no sense to me at all. New vacuum energy is probably produced (at constant density) as space expand, but the rest...

My advice is that you check each of your postulates against standard cosmological theory, which agrees with ~99.99% of observations. If your postulate agrees with observation, but it differs in some significant prediction about something not yet confirmed, you may be on to something. Otherwise...

Jorrie

[1] The reference that I neglected to add to my previous reply: http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179v1.pdf , page 32.

Hi Jon.

There's not too much wrong with a 'flatness theorem', because there is a statistical chance that the universe was, is and will always be precisely flat. The best inflation theories predict exactly that. One must however note that nature does not necessarily agree; present observations indicate a slight statistical bias toward a 'just' closed universe (Ω=1.01±0.1).^[1]

I do however have serious misgivings about the way you define 'anti-gravitation', e.g., "By "anti-gravitation" I mean what you call expansion energy." and "Anti-gravitation observes the same inverse-square law as gravitation." and "As distance increases, gravitational binding energy and anti-gravitational expansion both decrease equally", etc.

My 'expansion energy' is just a form of kinetic energy (~½mv²) and it has nothing to do with anti-gravity. The flat Einstein-de Sitter model has zero anti-gravity, but a considerable expansion energy.

One can consider the vacuum energy of the ΛCDM model as anti-gravity (in a way), but it does not follow any inverse square law. In fact it somewhat destroys the old Newtonian inverse square law of gravity. If you look at cosmological equations, the square law is nowhere to be seen...

"This explains the shape of the Einstein-de Sitter curve, whereby the expansion rate falls as the distance increases. As distance increases, gravitational binding energy and anti-gravitational expansion both decrease equally."

If you replace 'anti gravitational expansion' just with 'expansion energy', I'll agree, but, as I said above, they are not interchangeable.

"Each of these 3 expansionary phases is defined by a simple Einstein-de Sitter curve when measured at an instantaneous point of time. As each quantum of new vacuum energy first appears in the universe, the overall Einstein de-Sitter curve for the universe shifts "upward" to account for that energy quantum's gravitation and anti-gravitation."

I'm afraid this statement may create false impressions amongst our reader. An Einstein-de Sitter curve has no acceleration, just deceleration, forever... The ΛCDM expansion curve changes smoothly from a decelerating to an accelerating form. If you 'shift a curve upward', it does not change its curvature (in the geometry sense). I know one can call a circle just straight lines from point to point, but why confuse the issue? Rather call a circle a circle.

If my 'expansion energy' still worries you, rather just call it the kinetic energy of expansion, which I avoided due to other issues. But it's better than 'anti-gravity'...

Jorrie

A minor erratum on my: "... present observations indicate a slight statistical bias toward a 'just' closed universe (Ω=1.01±0.1).^[1]"

The paper actually says: "Ω=1.02±0.2" No big deal though...

Jorrie

Jorrie, I don't want to confuse your readers. Hopefully it won't take them long to realize that about half of everything I write is wrong.

I agree with you that my Thereom #3 makes no sense, which has convinced me that #2 is wrong also. The answer must be simpler. Hopefully it's always darkest before the dawn, because here's a "new and improved" Flatness Theorem:

WARNING! WARNING! What follows is an ALTERNATIVE cosmology. READ IT AT YOUR OWN RISK!

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 it is almost infinitely improbable for any contemporaneous phenomenon to achieve the degree of overall flatness we observe today, unless the universe was always flat. Therefore, the universe always has been flat, and by extension it always must remain so.
3. Theorem 2: The expenditure of gravitational binding energy causes expansion.
4. Whenever two masses experience gravitational attraction force between them, a curvature field is applied to local space. This curvature must be offset in order to maintain flatness. Expansion is the mechanism to maintain local flatness.
5. Theorem 3: Local space reacts to the expenditure of gravitational binding force by spontaneously producing new local vacuum space.
6. The rate of production of new vacuum space is proportional to the amount of binding force experienced by the local space.
7. The newly produced vacuum space expands the local universe. It will continue doing so forever so long as binding energy continues to be expended. But if the distance between the two masses eventually increases, then the binding energy expenditure will decrease per the inverse-square law, and the production rate of new vacuum space will decrease accordingly. In a precisely homogeneous universe, this expansion would follow an Einstein-de Sitter curve.
8. Theorem 4: As the clumpiness of mass in the universe increases, the rate of expansion increases accordingly.
9. If the density of gravitational binding energy in a certain local region of space is high enough, the mass in the affected region will continue to clump. This causes the local production rate of new vacuum space to increase accordingly. If there is enough mass locally, clumping will reach the point where a black hole forms, and clumping will continue after that if more mass continues falling into the black hole. As the clumping continues, and local gravitational binding energy increases, the production rate of new vacuum and therefore the local expansion rate continue to increase.
10. Gravitation (like politics!) is an entirely local phenomenon because of the inverse-square law. It is not something that "averages" on large scales across the universe. Therefore, the net effect of clumping is to increase the total binding energy of the universe. For example, the binding energy in voids between distant galactic clusters is so low that as expansion vastly increases the distance between the clusters, the resulting decrease in total binding energy is tiny.
11. The net increase in the universe's total gravitational binding energy due to ongoing clumping causes the observed overall expansion rate to exceed the Einstein-de Sitter curve.
12. Theorem 5: Flatness is maintained through the current production of new vacuum space, not by the accumulation of previously produced vacuum space. Therefore, the universe will remain flat regardless of whether it is at "critical density."
13. Local space always produces new vacuum space at a rate that offsets the curvature field force of the local gravitational binding energy field. As vast amounts of vacuum space accumulate in regions of near-zero gravitational binding field, that vacuum space contributes virtually nothing to the flatness of the universe. It is irrelevant to this local process whether energy density is increasing or decreasing in other, distant areas of space. It is meaningless to "average" gravitational binding energy density at the large scale of the universe. There is no "critical density" of the universe in its entirety.
14. Theorem 6: The cosmological constant and "vacuum energy" do not exist.
15. The Flatness Theorem fully accounts for inflation, expansion, and accelerated expansion. There is no need to introduce another factor. Adding a cosmological constant would result in an expansion rate exceeding the observed rate.
16. Theroem 7: The ultimate fate of the universe depends on the stability of black holes.
17. The rate of expansion will continue to increase as long as clumpiness increases. The expansion rate will stop increasing once all mass has either fallen into ultimate clumps, or been dispersed to distances approaching infinity. It appears that the maximum expansion rate will be insufficient to tear the clumps apart, because the expansion rate always remains proportionate to the gravitational binding energy force. Once the universe attains its maximum expansion rate, it will continue expanding at that constant rate forever.
18. However... if it turns out that there is no limit on the ongoing contraction rate of black holes, then total binding energy will continue to increase, and the expansion rate of the universe will continue increasing forever.
19. On the other hand... if black holes eventually evaporate due to Hawking Radiation, then all mass will disperse towards infinite separation, and the expansion rate will decrease and approach zero.
20. There is no scenario in which the universe ultimately begins contracting, because gravitational binding energy cannot drop below zero.

So vacuum space is the waste "exhaust" produced by the "burning" of gravitational energy. If the human race wants to be more "green", we can reduce the rate of exhaust production by dispersing individually to the infinite corners of the universe!

Hi again Jon.

I think you will understand if I refrain from commenting on your "new and improved Flatness Theorem". Let's rather leave it at that.

Jorrie

Here's a revised version of Clumpiness Theorem #4 from my prior post:

1. Theorem 4: The expansion rate declined during the first 10¹⁰ years ("Dispersion Dominated Era") as the dispersion of the universe's mass due to expansion reduced gravitational binding energy faster than local clumping increased it. Thereafter ("Clumping Dominated Era") the expansion rate is increasing because local clumping continues, while intergalactic mass has become so dispersed that the absolute value of its decline in gravitational binding energy is becoming insignificant.
2. During the Dispersion Dominated Era, local galactic clumping of mass added to total gravitational binding energy, but on the large scale of the universe this increase was overwhelmed by the rapid dispersion of non-clumped intergalactic mass. This dispersion caused the net gravitational binding energy of the universe to decline by a factor of 10⁵⁰. The decrease in total gravitational binding energy during this era caused the expansion rate to decline accordingly.
3. The rate of decline of gravitational binding energy decreased throughout this era, ending the era at a rate of zero. This happened because intergalactic mass had become so dispersed that it had little gravitational binding energy left to give up, while local clumping continued to add binding energy.
4. During the present Clumping Dominated Era, the rate of decline in binding energy of intergalactic mass has declined below the rate of increase in binding energy caused by local clumping. Consequently, the expansion rate has begun to increase. In the future, intergalactic dispersion's negative contribution to total binding energy will become more and more insignificant. The expansion rate will increasingly be determined by the local clumping rate alone.
5. Gravitational binding energy (like politics!) is an entirely local phenomenon because of the inverse-square law. It is not something that can be "averaged" on large scales across the universe. Total binding energy can be calculated "bottoms up" only by summing the individual binding energies of all the local regions in the universe. Fortunately for our analysis however, total binding energy can easily be calculated "tops down" as a direct function of the observed expansion rate.
6. The redshifting of radiation as the universe expands causes total gravitational binding energy to decrease. However, the initial absolute magnitude of radiation density's contribution to gravitational binding was a factor of 10⁵⁰ less than the binding energy contributed by the initial density of matter and radiation. Therefore the expansion rate always has been dominated by the sum of the local densities of matter and radiation, and radiation redshift never has been a significant factor.

I was trying to edit points #5 and 6, but exceeded the 15 minute limit! Here's what I intended #5 and 6 to say:

1. It is reasonable to treate intergalactic mass (matter and radiation) as being evenly dispersed across the universe with homogeneous density. This allows us to "average" the effect of dispersion. However, the effect of clumping (like politics!) on total gravitational binding energy is an entirely local phenomenon because of the inverse-square law. It is not meaningful to "average" it together with intergalactic dispersion. The total binding energy of the clumps can be calculated "bottoms up" only by summing the individual binding energies of all of the clumps. Fortunately for our analysis however, total binding energy can easily be calculated "tops down" as a direct function of the observed expansion rate. Therefore the total binding energy of clumps can be calculated by subtracting the expansive contribution of the intergalactic dispersion rate from the total expansion rate.
2. The redshifting of radiation as the universe expands contributes to the decrease in gravitational binding energy caused by intergalactic dispersion. However, during the Dispersion Dominated Era the total joules of energy lost to redshifting was 10⁵⁰ times less than the total joules of gravitational binding energy lost by the universe. Therefore the redshifting of radiation never has been a significant factor in determining the expansion rate. The expansion rate always has been dominated by the relationship between the relative contributions of (a) the average intergalactic dispersion rate (ignoring the effect of redshift), and (b) the sum of the local clumping rates of matter.

I just want to stress again what Jon has said in his reply #23: "WARNING! WARNING! What follows is an ALTERNATIVE cosmology. READ IT AT YOUR OWN RISK!"

I do not endorse Jon's views and have asked him to shift our 'bickering' to private CR4 mail. If we can come to some conclusion, we can shift it back here again.

Jorrie

Oh no! This is not bickering. The only problem here is that there aren't many who can keep up enough to participate (like me). Alternative Cosmology? Now you're getting somewhere. Please do go on, even if i'm the only one sticking around. I try not to skim but I want to keep up, so I print out for further reading. Virtual particles remain constant while space expands? Gravity compensates for volume? You know what I'm going to say.

If you're going to "bicker", this is the place to do it. Stay and vent. No name calling.

Many thanks for the mental exercise (read: headaches) to this point, Tom C.

PS: Jorrie, is there a forum like C4 for Physicists? I think you mentioned this in passing.

Well, I'll second you on that guitarhunter. I very much enjoy the dialogue even though some of it goes right by me. Maybe by osmosis though...

-John

I'm with you guys. As yoga stretches the body cosmology stretches the mind, both make you take silly positions seriously.

Hi Tom.

I did ask Jon to start a new thread on his 'Flatness theorem', so that all can participate, but for some reason he declined. My only concern of having to deal with it on my 'mainstream' CR4 blog is that it may put off other 'mainstream oriented' people.

Actually, Jon declined on the grounds that there is already a Blog on relativity and cosmology (this one) and he does not want to duplicate it. This is however not a limiting factor. He can just open a discussion on Alternative Cosmology - any topic with even a vague connection to engineering goes here on CR4. Look at the many relativity and cosmology discussions that pop up as new threads every week.

Finally, there is a very good 'CR4' for physicists, called Physics Forums. It is however not a very friendly place for engineers, since they tend to treat us as 'not-knowledgeable'. They also slap your hands fast if you propose anything contrary to mainstream. I have seen many such treads quickly locked by the moderators.

If you ask questions about mainstream physics, they are pretty patient in answering and will also guide you to accepted, published material to read. I understand their almost obsessive reservation of the forum for mainstream science, because it will be chaos if they allow dissident theories there. I participate there now and then, but I only ask questions to test my understanding of the mainstream science.

Jorrie

It is rather entertaining to ask questions that don't always have complete answers. That gives us wiggle room to invent odd new theories! I'm glad that people want to think about such things.

I haven't run away, I've just taken the Flatness Theorem "off blog" while I do some calculations to see if it could make any sense.

Jorry, while I appreciate the suggestion that I start a new thread, I think it is clear to everyone that I make too many errors to be capable of hosting a discussion. It would be the blind leading the blind.

What we need is someone like you who actually knows what you're talking about. So here's my suggestion -- why don't you post one blog on your site, inviting people to keep all of their discussion of alternative theories limited to there. Then we can all vent, while avoiding "polluting" your mainstream blogs. And you can help keep us honest. Please consider the idea.

Thanks, Jon

Hi Jon.

"... why don't you post one blog on your site, inviting people to keep all of their discussion of alternative theories limited to there."

OK, I'll think about this one (on CR4 I guess you meant, not my own website, which is not yet WEB 2.0 compatible, meaning visitors can't post comments there). Give me a day or so...

Jorrie

Jorrie,

You've touched on something here I hadn't considered before.

The energy of a photon is E=hc/λ

where h is plancks constant, c is the speed of light, and λ is the wavelength of the light.

So as space expands, the Energy of the radiation decreases. For instance, if the wavelength of the radiation doubles, than the energy is halved. Where does that energy go? If I'm doing my calculation right, if the universe was filled with x-rays around big bang and is filled with microwaves (1.9mm) today, then there is a billion times less energy due to radiation. X-rays may be conservative too. If we say gamma rays then we're talking a trillion times more energy due to radiation then as opposed to now. Where did that energy go?

Conservation of energy demands it goes somewhere, but where? Jorrie, can you fill me in?

Another question. If photons are stretched (become less energetic), couldn't gravitons (if they exist) be stretched (become less energetic) as well? If they did, wouldn't that in essence lead to a weaker gravitational force at long distances?

Hi Roger.

"Conservation of energy demands it goes somewhere, but where? Jorrie, can you fill me in?"

I keep my sanity in this by considering the plain Newtonian balance or energies: kinetic energy (of expansion) + gravitational potential energy = constant. As the energy of the photons decreases AND the expansion rate decreases, the negative potential energy increases (becoming less negative) in order to keep the total energy constant. If the universal geometry is exactly 'flat', that constant is zero, of course.

Gravitons should suffer the same fate as photons, but I do not believe that they carry 'gravity', but only changes in the gravitational field (this is the semi-classical view - I know that the quantum physical view may differ from this).

So, gravity displays the inverse square law with distance, but the way the elusive gravitational waves (and gravitons) work may perhaps differ. The fact that neither has been directly detected does not help, of course...

Jorrie

Hi Jorrie,

Excellent post as usual. Figure 2 looks like I expected after previous posts and discussions, but Figure 1 looks extreme! I trust your math, but didn't expect such an extreme upward incline. If we are at the knee of the curve, then how can we be 4+ Gy after the expansion started in Figure 2? Is it just a scale difference?

"I wonder how the cosmologists would have interpreted this almost linear expansion curve. Probably not by bringing in 'dark energy', or would they?"

Considering the uncertainties of the recent cosmological measurements, the green curve would have not produced any conclusions. Dark energy would not have been brought in, but wasn't it theorized before the accelerated expansion was discovered?

S

Hi S, thanks.

It's just the log-log scale that creates the extremes. The problem is that with so many tens of orders of differences, it's impossible to view on linear graphs. If figure 2 is made log-log, it also has a super-slope in the far future.

"Dark energy would not have been brought in, but wasn't it theorized before the accelerated expansion was discovered?"

I'm sure you know that Einstein brought in vacuum energy (cosmological constant) to balance his 'static universe' energies. Then, when the universe was proven to expand, he withdrew that and believed Λ to be zero.

Everyone hoped and believed that Einstein was right, until the 1990s discovery of the increasing expansion rate almost flipped that apple cart. Lucky for them, cosmologists could just fall back on the Λ that the great man invented. Other forms of dark energy have since been theorized, but it looks like observations favor Einstein again.

Jorrie

Let's not forget the "Guitarhunter/Jonmtkisco Incredible Shrinking Matter Theory." [sniff, pops a pill] Your extensive blog was sourced from the radical contention that space dosen't expand but matter in fact shrinks, and now that it's established fact (in my mind anyway), prove it wrong!

Hi guitarhunter, I haven't forgotten about it, and I plan to think about it again sometime soon. But I'm finding it most helpful to try to learn how the accepted theories actually work. As you can see, that has been a handful for me!

Hi guitarhunter.

Oh no! Not that one again?

Anyway, I think we agreed in the other thread that you can view things like that of you want to make life difficult for yourself. Just exchange my 'expansion energy' for 'shrinkage energy'.

Jorrie

As I understand it (and I am certainly no expert), "dark matter" was invented to explain the discrepancy between the observed amounts of matter and energy in the universe compared to observed gravitational effects. But to me it is less of a "leap" to theorize that the gravitational constant varies across the universe than to theorize the existence of some unknown, unobservable kind of matter and energy. What proof do we have that those parameters we call "fundamental", or "invariable" (such as The Gravitational Constant) cannot fluctuate across the vast universe? Is there empirical evidence that G is the same everywhere? Or is the invariability of fundamental parameters so "fundamental" to existing scientific understanding that considering the alternative is intolerable?

Bill Morrow

I tend to agree. See the blog Cosmic 'train wreck' defies dark matter theories

Hi S, I tend to disagree with you! The 'train wreck' was a typical case of what can be describe as 'the journalistic principle of sensational headlines'.

The article is actually about evidence supporting dark matter and suggests that dark matter may even be stranger than what is believed today. It means dark matter has not been fully characterized, which is hardly surprising.

I actually believe there are many different particles making up dark matter. There are so many ordinary baryonic particles around and dark matter appears to more abundant than ordinary matter. So, why not?

J

Hi Jorrie,

I found the bullet cluster article to very interesting and significant. It seems strange to me that the unseen matter would not be particles that have been detected in 'atom smashers'. Are you ruling out all of those? For example, can it not be a bunch of neutrinos, or what about individual quarks that have not combined?

S

That's an interesting thought. All those leftover bits of cosmic sub dust particles amounting to mountains, invisible to see, but detectable. That, to me, sounds at least as plausibly as many other concepts I've heard put forward in cosmology.

Hi S, you wrote: "For example, can it not be a bunch of neutrinos, or what about individual quarks that have not combined?"

Neutrinos have some mass, it was found, but too small to account for the dark matter (when multiplied by the predicted quantity). Further, neutrino's are called 'hot dark matter' because of their speed that almost equal c. Such fast particles do not fit the structure formation theories, hence slow moving 'cold dark matter' (CDM) is the preferred type of candidate particle.

There is another puzzle: the bulk of CDM is thought to be non-baryonic, because there is a limit on the amount of baryonic matter that the inflationary BB could have produced. I think quarks are the basic building blocks for baryons, so that disqualifies them as the main contributor to the CDM.

The large hadron collider at CERN should become operational next year and could perhaps produce the WIMPs that is the 'best-buy' CDM particles that fit the theoretical 'budget'. We'll have to wait and see.

Jorrie

PS: I know little about particle physics, so I'm perhaps sticking out my neck here...

Hi Bill.

.... "dark matter" was invented to explain the discrepancy between the observed amounts of matter and energy in the universe compared to observed gravitational effects."

That's true. There are theories, like the 'modified Newtonian dynamics' (MOND) that does not vary the gravitational constant, but rather Newton's second law. Newer variants of it, like Tensor-Vector-Scalar gravity (TeVeS) is quite successful actually, but they all fail at some point to explain observations.

A changing gravitational constant has been though of and tested against observations and it failed. The only option that seems to explain all observations (so far) is to theorize that there is some matter that we cannot observe because they do not interact with photons - hence dark matter, consisting out of mysterious particles.

Dark matter has been indirectly observed by means of gravitational lensing in the collision of two galaxies in the Bullet cluster.

Jorrie

Hi Jorie,

Seems to me that if dark matter contributes to the total gravitational effect of clusters of galaxies such that it bends light, i.e., gravitational lensing, etc., then it must also, itself, be affected by gravity. If this is true, seems like dark matter would condense gravitationally into dark matter objects (planets, etc.) and be gravitationally pulled upon by the stars and planets that we are familiar with.

Except maybe, dark matter doesn't interact with itself like "light" matter does. In other words, maybe a mass of dark matter is not attracted to another mass of dark matter.

This article says "WIMPs may account for much of the "dark matter" in the universe, but because WIMPs do not usually interact with other matter, they slip through the universe undetected". If this is true, how can WIMPS gravitationally bend light as I said above?

I think when we detect WIMPS, if we do, we'll probably know a whole lot more about this elusive thing called gravity. Just my opinion.

Regards,

-John

Addendum to post #34:

In a nutshell Jorrie, How can dark matter/erergy affect the components of the universe so profoundly and yet, at the same time, be unaffected by the components of the universe.

-John

Hi John.

The nutshell answer to your: "In a nutshell Jorrie, How can dark matter/energy affect the components of the universe so profoundly and yet, at the same time, be unaffected by the components of the universe." is that dark matter does interact gravitationally with other matter and with light - hence it produces gravity and gravitational lensing.

Dark matter was originally postulated to explain the rotational dynamics of galaxies, with a halo of dark matter inside and (mostly) around galaxies. The extra gravitational 'pull' then explains the galactic dynamics. There is still no other mechanism known for that.

The idea is that dark matter particles do not interact with photons in the form of absorption or radiation - hence the title 'dark matter'. Further they are theorized to move straight through other matter, with only a very, very small chance of interacting at all. Hence they are very difficult to detect.

As I wrote to S above, well have to wait for the LHC at CERN to come on-line. Perhaps they will catch a glimpse of a WIMP.

Jorrie

Hi Jorrie,

Thanks for the reply. I realize that a lot of this is speculation, pending actual detection of certain particles, etc. and I understand why dark matter is called "dark". What really bothers me about the scenario is the seemingly "one-way" interaction that it has.

You said "[dark matter is] theorized to move straight through other matter, with only a very, very small chance of interacting at all". If this be the case, then, since it seems to have gravitational properties, how can it move through other matter without itself being affected by the matter that it moves through?

Please understand, I'm not arguing about dark matter (I'm not qualified). I'm just trying to understand what doesn't seem to make any sense. Again, my problem is dark matter doesn't interact with ordinary matter, yet it gravitationally affects (interacts with) ordinary matter. Makes no sense to me...

-John

Hi again John. Follow-on to my #37:

Confusion usually arises due to the fact that dark matter do not interact well with matter or photons in terms of collisions/absorption etc, but it does interact normally in a gravitational sense.

Another way to put it is that if a dark matter 'cloud' moves through a normal gas cloud, there is no or little friction, but they do attract each other gravitationally.

Hope this helps to clear the issue...

Jorrie

Thanks Jorrie, that helps.

observing that as the universe expands, the radiation and energy decreases... CMBR cosmic microwave background radiation, is theorized as the energy/ light particles echoing throughout the universe after the "big bang" if the CMBR truly is and was the initial energy that sparked the universe, and space time shifts along with it every so many billion years now... can it be calculated when it will shift down into lesser energy? will it effect us... so far we have evolved to live with it unconsciously.

Gravity/ dark matter? psh... Earth is a giant magnet. hot metal moving fast at the core with iron shell around it, nothing but a strong magnet, a large enough electro magnet will attract non-metallic/ biological material. we are just biological thinking viruses evolving and procreating on a giant rock magnet hurling through space.

Outside a dog a book is mans best friend, Inside a dog is too dark to read-Groucho Marx