Proton decay at the end of the Universe

[Gary Menzel]

TL;DR Summary

If dark energy is causing the expansion of the expansion of the universe to accelerate...
and there does not seam to be a limit to this increase in expansion, what happens when lone protons are expanding so fast they their constituent quarks fly apart?

I wish this forum allowed indentation using tabs. Some of these questions are dependent on the answers to others. I have used outline numbers to indicate nested questions.

I have BA in physics and mathematics, 40+ years ago. I was thinking (always a dangerous thing). I had some questions. I was reading "The Physics Companion" A.C. Fischer-Cripps; where it says electric charge only come sin integer amounts and this made me think about quarks... I'm hoping someone else has already worked this through (or at least further). I'm not sure I have time and energy enough to take the graduate level courses to try to work this out myself. I've spent the last 40 years working in gas and liquid measurement.

In an sufficiently rapidly expanding universe when/if protons are torn apart by the expansion:

1) Is this impossible; is there a limit on how rapid the universe can expand on a sufficiently small scale in the neighborhood of lone proton?
What about quantum tunneling (if the neighborhood is small enough).

1.1) Will the properties of the vacuum be such that additional quarks will not then form to complement the bare quarks? Would bare quarks become stable? Does vacuum energy cool down? Presumably it must in an expanding universe.

2) If not, then how hot would the formation and subsequent additional stripping of the quarks be?

2.1) If hot enough and continuing long enough, would this constitute a quark plasma such is supposed to have existed early during the big bang?

2.1.1) Would it be a "small bang" or another "big bang" (how long could it continue before there was enough mass to slow the expansion sufficiently)?

2.2) If cooler, would the formation be enough to decelerate the universe?

2.2) Where would the energy come from? I assume it is vacuum energy, at least in part, if a "bang", occurs.
2.2.1) Does this impose a limit? I assume it is an effective transmutation (Decay, phase change, ...?) of dark energy if deceleration occurs.

 

[PeroK]

Summary:: If dark energy is causing the expansion of the expansion of the universe to accelerate...
and there does not seam to be a limit to this increase in expansion, what happens when lone protons are expanding so fast they their constituent quarks fly apart?

If dark energy is a constant vacuum energy density, then there is no expansion of bound systems like a proton or even a galaxy cluster. The accelerated expansion applies on the largest cosmological scale only.

There is an alternative theory of an increasing dark energy (called quintessence), which may result in a "big rip" scenario.

 

[Ibix]

Summary:: If dark energy is causing the expansion of the expansion of the universe to accelerate...
and there does not seam to be a limit to this increase in expansion, what happens when lone protons are expanding so fast they their constituent quarks fly apart?

1) Is this impossible; is there a limit on how rapid the universe can expand on a sufficiently small scale in the neighborhood of lone proton?

It depends. With vanilla dark energy it's impossible - some systems (like galaxies) are tightly bound and remain so. With a variant usually called "quintessence" spacetime curvature increases without bound leading to a "Big Rip" in finite time where even protons are ripped apart (assuming quantum gravity doesn't intervene).

I think the rest of your questions fall under "we'll get back to you when we have a quantum theory of gravity". We're pretty sure GR isn't valid when spacetime curvature is significant on the same scale as particles.

 

[Gary Menzel]

It depends. With vanilla dark energy it's impossible - some systems (like galaxies) are tightly bound and remain so. With a variant usually called "quintessence" spacetime curvature increases without bound leading to a "Big Rip" in finite time where even protons are ripped apart (assuming quantum gravity doesn't intervene).

I think the rest of your questions fall under "we'll get back to you when we have a quantum theory of gravity". We're pretty sure GR isn't valid when spacetime curvature is significant on the same scale as particles.

Thanks.

So dark energy implies distant things get further apart faster, but close in, not so much?
Are galactic clusters considered bound systems? How close is close? Where is the edge? What is the curvature there? It would have to be not- changing and this sounds meta-stable.

I don't see quantum gravity happening in my lifetime. It was an open question when I was an undergrad. Still this scenario would offer a boundary check (can it answer these questions) on such a theory. I'm not sure I believe any of the string theory variants have a chance. They seam to me too much like a mathematician's (BA in Math as well) existence proof ("there exists a geometry such that...").

 

[PeroK]

Thanks.

So dark energy implies distant things get further apart faster, but close in, not so much?
Are galactic clusters considered bound systems? How close is close? Where is the edge?

There is no edge. The solar system, for example, has a certain mass density and a certain amount of vacuum. The mass dominates and nothing will change over time.

The universe as a whole, however, has a much lower mass density and is expanding. As it expands the vacuum energy dominates more and more.

Ultimately the expansion comes from the Friedmann equation, which applies at the cosmological scale. But not at scales where gravity dominates because of locally high mass density.

 

[Ibix]

So dark energy implies distant things get further apart faster, but close in, not so much?

An ideal FLRW model has everything being exactly the same density everywhere at all scales. In that case any two points at rest with respect to all the matter around them, no matter how close, move apart. But reality isn't like that - density fluctuations mean that some regions were slightly over-dense and the matter tended to collapse, forming stars and galaxies. So "how far away is cosmologically far away" depends where you are and how big a density fluctuation you're in. The universe is pretty uniform at scales above 100Mpc, if memory serves.

Still this scenario would offer a boundary check (can it answer these questions) on such a theory.

I don't understand what you're saying here. By the time we could test quantum gravity in a Big Rip scenario we'd be a bit short of time...

 

[Gary Menzel]

If dark energy is a constant vacuum energy density, then there is no expansion of bound systems like a proton or even a galaxy cluster. The accelerated expansion applies on the largest cosmological scale only.

There is an alternative theory of an increasing dark energy (called quintessence), which may result in a "big rip" scenario.

An ideal FLRW model has everything being exactly the same density everywhere at all scales. In that case any two points at rest with respect to all the matter around them, no matter how close, move apart. But reality isn't like that - density fluctuations mean that some regions were slightly over-dense and the matter tended to collapse, forming stars and galaxies. So "how far away is cosmologically far away" depends where you are and how big a density fluctuation you're in. The universe is pretty uniform at scales above 100Mpc, if memory serves.

I don't understand what you're saying here. By the time we could test quantum gravity in a Big Rip scenario we'd be a bit short of time...

A macro (i.e. galaxy) bound system would have a characteristic radius. Inside this the system is bound. Outside it is not. The density is the mass per unit volume (taking into account the additional curvature created by the mass). Presumably there is a critical density/mass (as a function of its temperature and radius required for this system to be considered bound. The system is probably hotter than the background and is radiating energy (cooling in some sense). Is the radius shrinking as is cools simply due to the cooling (because it is radiating energy and losing mass but at an even decreasing (long term) rate, or is it shrinking more (and the asymptote of the shrinkage curve is zero) or less (density decreasing faster than temperature requires), in which case the system may not be bound on a macro level after all. It seams to me we ought to be able to measure this (though we are probably looking at very long time frames to determine the effect).

Probably not our own galaxy as the study object, but perhaps one of the others in our cluster? Or maybe we need one even further away. First an evaluation of the time scale involved would be undertaken (and published) along with the assumptions as to theory and measurement (so that even if not feasible with existing tech, it would be easier to reexamine with advances in technology and refinement in theory).

This might, thereby set a limit on whether we will get isolated clumps of dark matter (with perhaps hydrogen, helium, cold neutron stars (no black holes since they evaporate according to current theory) - or a Big Rip. The time scale to determine this is probably very long, but measurement accuracy is improving without increase understanding and technology. I will admit however with our current methods of funding, unless these measurements can be performed as a part of a project doing sometime shorter term this will be difficult. Getting a grant for a 1000+ year study is unlikely except maybe through a NGO, and even then it would probably require an NGO dedicated to this cause. The theoretical work required to delineate the particulars of the study could start now, however, and might yield insight into other processes as well.

The question (leaving out the eldritch horror) is, to quote Lovecraft, "and with strange aeons even death may die" true? General Relativity says no, Quantum and Statistical Mechanics say yes, from what I understand.

Aside: The funding question is kind of like in genetics, more study is devoted to organisms with short generational cycles, since if you are doing a study on an organism with a 30+ year reproductive cycle (oak trees, or coconut palms for instance) you have to hope that your graduate student's graduate students (F2 generation of sorts) will complete the research. This was one of my mother's (the geneticist) rants. Molecular genetics has only somewhat changed this. Studies still need to be performed with F2 generations (back crosses of hybrids to see if the phenotypes segregate) to define the traditional definition of species. Wolves and dogs can cross bread with fertile hybrids, but if these hybrids bread, you tend to get either wolf-like or dog-like progeny. Thus they are considered separate, but closely related, species.

If there is a flaw (other than practicality/funding/tenure) in my reasoning, please let me know.
Otherwise, put a graduate student on it... and so on, unto the nth generation. Though not full time, there is still tenure.

Thanks for talking with me.

 

[Ibix]

A macro (i.e. galaxy) bound system would have a characteristic radius. Inside this the system is bound. Outside it is not.

No - whether a system is bound or not is a matter of comparing the kinetic energy of the components to the binding energy. It doesn't have anything to do with size or density. There are bound systems of wide ranges of sizes.

The rest of what you are saying seems to me to be you rushing into what you believe are the implications of something that you don't seem to have defined particularly clearly. Or if you have defined it then you have not communicated it clearly, because I still don't really understand what you are trying to argue.

What determines whether or not we get a Big Rip is nothing to do with density fluctuations and bound or unbound systems. The key parameter is the way the energy density of the dark energy/quintessence changes as the universe expands. If the density falls or stays constant we do not get one. If it rises, we do. As far as I'm aware our measurements are not yet sufficiently precise to rule out any of these three options.

 

[kimbyd]

Thanks.

So dark energy implies distant things get further apart faster, but close in, not so much?
Are galactic clusters considered bound systems? How close is close? Where is the edge? What is the curvature there? It would have to be not- changing and this sounds meta-stable.

I don't see quantum gravity happening in my lifetime. It was an open question when I was an undergrad. Still this scenario would offer a boundary check (can it answer these questions) on such a theory. I'm not sure I believe any of the string theory variants have a chance. They seam to me too much like a mathematician's (BA in Math as well) existence proof ("there exists a geometry such that...").

A system is bound if its constituent members are orbiting one another, essentially. It's a little complicated because for very large systems they might never have actually completed an orbit, but their trajectories will nevertheless keep them together into the future.

The existence of dark energy changes the distance at which this tends to happen, but does not stop it happening altogether.

 

[Buzz Bloom]

There is an alternative theory of an increasing dark energy (called quintessence), which may result in a "big rip" scenario.

I do not mean to offend anyone, but I frequently find it confusing when I see the ambiguous word "theory" in the context of scientific discussion. The online Merriam-Webster [ merriam-webster.com/dictionary/theory ] gives nine definitions. I think it would be very helpful to the reader if the usage included a choice among the various definitions. An alternative method of clarity might be to use the synonym "conjecture" or "speculation" and reserve "theory" to mean the #1 definition.

With respect to the quote above, I hope someone (or several participants) would clarify the intended meaning (based on the cited dictionary or any other source) of "theory" in the quote.

 

[Ibix]

With respect to the quote above, I hope someone (or several participants) would clarify the intended meaning (based on the cited dictionary or any other source) of "theory" in the quote.

I'd suggest that it's better not to put too much weight on a particular word. You'll end up with a lot of pointless fighting over whether such-and-such an idea is "generally" accepted and what we mean by "accepted" and "plausible". By all means ask how confident we are in any particular idea.

As I understand it, you can characterise the type of accelerated expansion with one parameter which I think Wiki calls $w$. If $w<-1$ then you have quintessence, if it's exactly $-1$ you have a cosmological constant, and if it's greater than that you have dark energy. Current measurements have the value being approximately $-1$, with some error bars (I don't know how large, but no option is excluded with much confidence - though a Big Rip in less than billions of yearsis excluded with enormous confidence).

I think everyone is confident in the maths - quintessence gives a Big Rip, the others don't. Whether dark energy/quintessence is actually a thing or really some hint of new gravitational theory or something else (in which case the maths is irrelevant) I don't think anyone is really confident. Let alone where exactly $w$ actually lies.

Edit: I see I have the terminology wrong. What I'm talking about is "phantom energy", which is one type of a more general concept called quintessence. I don't think it really changes anything I said to answer you.

 

[PeterDonis]

With respect to the quote above, I hope someone (or several participants) would clarify the intended meaning (based on the cited dictionary or any other source) of "theory" in the quote.

A more specific word would be "model": the general theory being used (General Relativity, or more specifically the class of solutions to the Einstein Field Equation used in cosmology, the FRW spacetimes) allows a continuous infinity of specific models, obtained by picking particular values for parameters. The "big rip" scenario comes from a particular subset of those models, the ones for which the parameter $w$ has a value less than $-1$.

If $w<-1$ then you have quintessence, if it's exactly $-1$ you have a cosmological constant, and if it's greater than that you have dark energy.

"Dark energy" and "cosmological constant" are often taken to be synonymous, or at least the latter is often taken to be a special case of the former.

Also, the "dark energy" behavior (accelerating expansion instead of decelerating expansion) is only found for $-1 \le w < - 1/3$. For $w > - 1/3$, you have decelerating expansion. "Matter" (or more precisely "cold matter") has $w = 0$, and "radiation" (which includes "hot matter", i.e., matter which is relativistic) has $w = 1/3$.

 

[Ibix]

Also, the "dark energy" behavior (accelerating expansion instead of decelerating expansion) is only found for $-1 \le w < - 1/3$.

I knew -1/3 came into it somewhere. Thanks.

 

[PeroK]

What is this quintessence of dust?