# Wikipedia:Reference desk/Archives/Science/2014 March 20

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# March 20

## Mass in Planck Density

The article on Planck density states that "At one unit of Planck time after the Big Bang, the mass density of the universe is thought to have been approximately one unit of Planck density." What type of matter did this "mass density" consist of? Star Lord - 星王 (talk) 10:27, 20 March 2014 (UTC)

That period of time is the Planck epoch. It occurred so early, and its duration is so short, that it's difficult to describe in non-mathematical terms. Essentially, the time-period is so short and the energy density is so large that it is non-sensical to describe interaction between entities. Everything we know about interactions between entities is summed up in the four fundamental interactions; during the Planck epoch, these activities are indistinguishable from each other. Physicists who describe this era tend to stick to discussions about symmetry and symmetry-breaking - of the entire universe - instead of attempting to discuss individual elements within the universe. Every object was so "smushed" together - and, simultaneously, spread out to fill the entire universe - that it doesn't make sense to describe anything as a particle with a position or a volume or a means of interaction among other particles.
So, the "mass density" in that era is best thought of as just a property of the whole universe. Nimur (talk) 13:56, 20 March 2014 (UTC)
Thank you, @Nimur: . You mention that it is difficult to describe in non-mathematical terms. Please do describe it in mathematical terms if you think it will clarify matters. I am comfortable with the maths in Quantum Mechanics. Star Lord - 星王 (talk) 16:26, 20 March 2014 (UTC)
I'm not the best person to present this stuff mathematically - I'm not a practicing cosmologist! But I think I can safely say that nobody has yet provided a satisfying mathematical description that answers all the questions: there is no model that is both consistent with our present knowledge (about the standard model and the fundamental interactions) and that convincingly evolves a Planck-epoch universe through the various symmetry breaks necessary to yield a universe like our own.
In lieu of a mathematical presentation from me, here's a pretty good technical talk by George F. Smoot, who has a unit of length named in his honor. As you will no doubt see, real physicists address the problem by looking for the observable effects of the early universe, using tools like the COBE satellite and the WMAP to constrain mathematical models of mass and momentum during the Planck era. This approach is a lot more productive than trying to simulate the Planck-era conditions and forward-project their time evolution; but it means there's no "equation" to plug and chug; it's not exactly like modeling the hydrogen atom using quantum-mechanical equations. Nimur (talk) 04:34, 21 March 2014 (UTC)
A short side-question. Since it is called "mass density", would it be fair to say that there was "mass" in the Planch Epoch? Star Lord - 星王 (talk) 16:56, 20 March 2014 (UTC)
I think you need to use an incredibly broad definition of mass; something along the lines of "mass is a scalar property subject to certain conservation laws that are governed by fundamental symmetries of the universe." Even if we consider a broader "mass-energy" quantity, you still need to be cognizant that gravitation is a fundamental interaction for which the time- and length-scales of mediation might have been larger than the size and age of the universe during the Planck epoch. That's what defines this stage of the early universe as its own "epoch" : it is that time period during which definitionally the time- and length-scales were smaller than those which govern fundamental interactions as we know them today. Nimur (talk) 04:34, 21 March 2014 (UTC)
Hmmm, to put this into perspective, as I recall a black hole containing a Planck mass has a Schwartzschild radius of the Planck length. It's the smallest a black hole can be because the Compton radius of the entire mass of the hole would be larger than the Planck length, i.e. everything inside the hole smooshed together. But what I don't get is that while a Planck mass is a somewhat impressive explosion, it sure as hell isn't the mass-energy of the universe! And an evaporating black hole doesn't start a new universe, right? Wnt (talk) 14:19, 20 March 2014 (UTC)
The binary encoding of the Holographic universe needs one unit of Planck area to mark with a "1" for each unit of Planck mass within it. When the Universe was at Planck density, it had a cube root of the needed area. Hence explosive Cosmic inflation to correct for this, followed by the current Quintessence to give us room to breathe in. Hcobb (talk) 14:20, 20 March 2014 (UTC)
Can you explain that? How would the universe be at the wrong density...? Never heard of anything like this! Wnt (talk) 14:46, 20 March 2014 (UTC)
I think Hcobb made it up. Anyway, it's not true. -- BenRG (talk) 18:30, 20 March 2014 (UTC)
In quantum gravity, Planck-scale black holes, if they're possible at all, probably are not well described by general relativity. In classical general relativity, a Planck-mass black hole would have a Schwarzschild radius of twice the Planck length, because rs = 2GM/c² and in these units G = c = 1. I don't think this is particularly interesting. Anything involving Planck units and the constants G, c, ħ is going to give you a result that's small in Planck units because they're defined that way. -- BenRG (talk) 18:40, 20 March 2014 (UTC)
I should emphasize that Micro black hole currently says exactly what I did, that indeed the Planck mass is as small as a black hole can get. If the universe passed through a time when it had about the size and about the mass of one of these smallest black holes, this seems more than a little interesting. Wnt (talk) 20:10, 20 March 2014 (UTC)
That paragraph of the article is unsourced. I don't know why having a Compton wavelength larger than the Schwarzschild radius would be a problem. Pions have a diameter of ~1 fm and a Compton wavelength of ~9 fm. Electrons have a Compton wavelength of ~2000 fm and no detectable size at all.
This page quotes Leonard Susskind saying "there is no fundamental difference between elementary particles and black holes" (and that 't Hooft agrees), and here's a random arXiv paper that talks about black holes with sub-Planckian masses in loop quantum gravity. I'm not saying that they're right, but if there's a simple no-go argument against sub-Planck-mass black holes, they haven't heard of it.
I certainly agree that the physics of black holes and the early universe is interesting, but statements like "an object with the Planck mass has a Compton wavelength of the Planck length and light will take the Planck time to cross that distance and..." are tautologies with no physical content, and arguments like "no black hole can have a mass larger than the Planck mass because then its Compton wavelength would be smaller than the Planck length and the Planck length is the smallest possible length" are unjustified given our current near total lack of understanding of Planck-scale physics. -- BenRG (talk) 04:13, 21 March 2014 (UTC)
That paper makes for interesting reading. I'm not a competent judge of its significance/reliability and I didn't find a journal publication by that name with a simple search or I'd have added it to the article I mentioned, but I welcome you to update it if it is appropriate. Wnt (talk) 01:13, 22 March 2014 (UTC)
I removed the sentence from the article because in inflationary cosmology (for which there is brand new experimental evidence!) the early universe was never that dense. Also, no one understands Planck-scale physics and I think it would be better to avoid Planck-unit numerology in Wikipedia articles in general. -- BenRG (talk) 18:30, 20 March 2014 (UTC)
For what it's worth, in the inflationary epoch of inflationary cosmology (which is also the densest epoch) the universe is empty except for an inflaton [sic] field that is similar to dark energy but with a much higher energy density. There are almost no particles; it's a vacuum. -- BenRG (talk) 18:40, 20 March 2014 (UTC)
From the source mentioned above: "mankind can study the universe moments after the bing bang, but setting up an internet connection is a totally different story" – not sure if that was intentional ;) - ¡Ouch! (hurt me / more pain) 06:33, 24 March 2014 (UTC)
How can you have a universe full of energy and not have it full of particles? (hmmm, come to think of it, was there just not time for pair production?) Wnt (talk) 19:20, 20 March 2014 (UTC)
It's similar to the situation now, where most of the energy density is in the dark energy/quintessence. -- BenRG (talk) 04:13, 21 March 2014 (UTC)
Well, the current ratio isn't really that far off from 1:1 - I don't have the knowledge to say whether some kind of equipartition theorem applies when all degrees of freedom are considered, but I wouldn't call our universe a vacuum. Was there anything near that much ratio of ordinary matter in the inflationary period? Wnt (talk) 01:13, 22 March 2014 (UTC)
Yes, it's more like the situation in the far future (according to ΛCDM) where the accelerating expansion continues and the density of ordinary matter asymptotically approaches zero. In order to explain the observed homogeneity of the universe, inflation has to last long enough that any relics of whatever preceded it are diluted to undetectable levels. Actually, I was wrong when I said there were no particles, because there is Hawking/Unruh radiation from the de Sitter horizon (both during inflation and in the future of ΛCDM cosmology). But that's random quantum noise that's uncorrelated with whatever matter you started out with. -- BenRG (talk) 08:06, 22 March 2014 (UTC)
Hmmm... if the Unruh effect is creating particles within every little bit of expanding space, doesn't that stop a Big Rip from happening because they have mass and slow down the expansion? I feel as if it could vindicate the Steady State Theory... as a consequence of the Big Bang. :) Wnt (talk) 17:19, 23 March 2014 (UTC)

Since the inflationary field decayed to our current false vacuum, when will that decay to a true vacuum and clean everything up? Hcobb (talk) 19:38, 20 March 2014 (UTC)

The quintessence may be the true vacuum, in which case it will never decay, or it could be a false vacuum, in which case it will randomly decay with some half-life that we have no way of determining, or it could be on a slow roll like the inflaton in which case it won't decay as such but will turn into particles at a time that's predictable in principle but totally unknown in practice, except that I think it would have to be in the very far future. Or it could do something else entirely. -- BenRG (talk) 04:13, 21 March 2014 (UTC)
I take it then that you're not a great believer in the heat death of the universe either :) Wnt (talk) 10:58, 21 March 2014 (UTC)
What do you mean? -- BenRG (talk) 08:06, 22 March 2014 (UTC)

Thank you for your interesting answers, Nimur and BenRG. When I read the sentence "At one unit of Planck time after the Big Bang..." I interpreted that time as being just at border between then Planck Epoch and the beginning of the Grand unification epoch. I had already come to the conclusion that I would not be able to get many answers about the Planck Epoch, and I was really wondering about whether mass could have been said to exist in the beginning of the next era according to the standard theory, which I assume to be the Grand unification epoch. Star Lord - 星王 (talk) 17:05, 21 March 2014 (UTC)

The thing I still wonder about the inflationary period is what the "subjective time" would have been like for its inhabitants. Because it was expanding at an absolutely mind-boggling rate, the entropy would have been increasing at a similarly incredible rate. Entropy is information, so... does this mean that a sentient structure during that era would perceive it as lasting for an extremely long time? Wnt (talk) 01:13, 22 March 2014 (UTC)
From the perspective of someone living in it, de Sitter space is actually static and time-symmetric. It's similar to a black hole turned inside out: you're surrounded by a spherical event horizon which is gravitationally attractive and sucks up everything around you. (A similar horizon can be defined for any other object, so they're no worse off than you; you can't fall through your horizon by construction, but you can fall through theirs.) According to ΛCDM we'll end up in that situation eventually, with everything but the local supercluster falling through a horizon with a radius of about 18 billion light years. The inflationary epoch is similar except that the radius is only a few orders of magnitude larger than the Planck length. But aside from scale, these eras are similar enough that Roger Penrose actually proposed that they're the same. (I don't mean to endorse that idea, which is probably wrong; I just think it's cute.) -- BenRG (talk) 08:06, 22 March 2014 (UTC)
I think that at the GUT scale you would have something like a quark-gluon plasma, but with the GUT fields, whatever they are, instead of quarks and gluons. The phase transition between the GUT scale and the "quantum gravity scale" would be somewhere in the GUT-to-Planck energy range, but it wouldn't be right smack up against the Planck end of that range. The range is fuzzy anyway since the Planck scale is just the general sort of order-of-magnitude scale at which quantum gravity is expected to matter. To get a better estimate of the right scale you need a theory of quantum gravity. The Planck units are off by a factor of ${\displaystyle {\sqrt {8\pi }}}$ from the get-go because they were defined using Newton's G instead of Einstein's 8πG as the gravitational constant, and there are certainly other correction factors from quantum gravity. So even if there is a special time/mass/whatever, it's unlikely to be exactly one Planck unit. -- BenRG (talk) 08:06, 22 March 2014 (UTC)

Thank you again, BenRG. My question is really only "linguistically" based. How can one have "mass density" without mass? Star Lord - 星王 (talk) 08:23, 22 March 2014 (UTC)

I think that one's a kind of mass vs. matter question. For example, photons have a mass (but no rest mass) although they are pure energy. - ¡Ouch! (hurt me / more pain) 06:33, 24 March 2014 (UTC)
Mass density is just energy density divided by c². If by mass you mean the rest masses of the fundamental particles, even in ordinary matter that's only a tiny part of the total mass/energy—compare the bare up and down quark masses of 2 and 5 MeV with the proton mass of 900 MeV. Most of your mass comes from a complicated configuration of color-charged fields and not from particles as such. -- BenRG (talk) 18:03, 22 March 2014 (UTC)
Thank you BenRG and Nimur.Star Lord - 星王 (talk) 18:47, 22 March 2014 (UTC)
Resolved

## Bridge columns

Why are bridge columns normally round? 194.66.246.45 (talk) 11:59, 20 March 2014 (UTC)

When you say "columns" do you mean piers? Alansplodge (talk) 14:21, 20 March 2014 (UTC)
Well, I don't think they mean one of these; as you can see, it's not round at all. --50.100.193.30 (talk) 01:59, 22 March 2014 (UTC)
Few modern bridges have round columns, see Bridge; they more often have rectangular uprights called piers. When a Column is required to support a weight, a round cross-section is easy to construct by casting or assembling cylindrical sections, it has minimum surface area for a given strength and has no critical directions for buckling or wind loading. Vitruvius writes that ancient Greeks derived their Doric columns by emulating a smoothed tree trunk with stone. 84.209.89.214 (talk) 14:41, 20 March 2014 (UTC)
Unless 194.66 happens to mean starlings or cutwaters which are sometimes more round than angular, though not circular. ---Sluzzelin talk 16:46, 20 March 2014 (UTC)
Another advantage is that paint will tend to chip off at the corners of a rectangular cross section, and that paint is important in preventing corrosion of metal columns. On the other hand, rectangular cross sections (or I-beams) are often easier to manufacture, say with a continuous process that cuts them into pieces. StuRat (talk) 16:54, 20 March 2014 (UTC)

## Yeast and air

I make sourdough bread as well as yeast bread, and want to start making yogurt as well. Do the yeasts used in these processes need air? I have generally covered a bowl containing yeast dough or sourdough with a cloth pr paper towel to allow air exchange, but lots of websites with recipes for bread or yogurt say to cover the container tightly with plastic wrap. Do the yeasts need oxygen, or are they anerobic? Edison (talk) 19:08, 20 March 2014 (UTC)

Of course, we have articles that might be useful: yeast , Bread , and Proofing (baking technique) (each have potentially useful sources). We also have helpful and friendly volunteers here at the Reference desk who will provide even more information (see below, soon?). ~:71.20.250.51 (talk) 19:37, 20 March 2014 (UTC)
According to [1], yeast can grow both ways. For baking and brewing, you want to minimize the oxygen because in anaerobic conditions they will mainly produce CO2 and alcohol. In aerobic conditions, they will multiply more, but won't produce as much CO2, which is what you need for bread. It would be an interesting, and easy, experiment to see whether the covering really makes much of a difference. Yogurt is a slightly different process. Bakers' yeast is in the fungi kingdom; yogurt cultures are bacteria. But it is still anaerobic. 22:07, 20 March 2014 (UTC)
I'd also be worried about other nasties growing in an anaerobic environment.
BTW, are you aware that yogurt cultures lose their potency after a few reuses ? Apparently the mix of cultures changes over time, and the new mix isn't as good. StuRat (talk) 05:19, 21 March 2014 (UTC)
So the bacteria which convert milk to yogurt work work best when in a sealed container to minimize oxygen? My first effort was with a paper towel covering it, and the yogurt turned out fine. Lactobacillus delbrueckii subsp. bulgaricus does not say whether that bacterium benefits from anerobic conditions as doe the strep thermophilus. per its article. Edison (talk) 02:15, 24 March 2014 (UTC)
See Lactic acid fermentation. In general, most fermentation processes are anaerobic. That said, my guess would be that the covering makes little difference on that front. For bread at least, the covering is mainly to keep the surface of the dough from drying out. I've never made yogurt before, so I'm not sure of the reason for covering that. But my guess would be that it's to prevent unwanted bacteria, since it apparently involves holding a dairy product at warm temperatures for several hours. It could also just be to minimize heat loss or evaporation. 03:53, 24 March 2014 (UTC)

## Light (wave) Interference. Where does energy goes ?

Hi, I'm starting to study interference in light / waves and a big question came to me. If two waves meet at a point and from there we have a completely destructive interference, what happen with original energy that was transported (contained) by each wave ?

I would apreciate some help to clarify this matter to me.

futurengineer, 20/03

Futurengineer (talk) 19:29, 20 March 2014 (UTC)

It gets bunched up elsewhere. Hcobb (talk) 19:55, 20 March 2014 (UTC)
Useful demonstrations of light wave interference are explained at Newton's rings and (for an exciting post-classical idea that light is not just wave like) Young's Double-slit experiment. Energy carried by a wave is not destroyed at a place where there is destructive interference, it is just not detectable at that particular place. 84.209.89.214 (talk) 20:46, 20 March 2014 (UTC)
It goes to the places where we have constructive interference. --64.134.44.147 (talk) 21:15, 20 March 2014 (UTC)
Think of two waves of water crossing, so the crest of one wave fills in the trough of another. No energy is destroyed. StuRat (talk) 05:26, 21 March 2014 (UTC)
In some places there is no energy, and in other places there is twice the amount of energy. This is sometimes visible to the naked eye as alternate bands of light and dark where the light bands are twice as bright as the illumination prior to interference. Dolphin (t) 05:50, 21 March 2014 (UTC)
Almost. Actually the energy density goes as the square of the amplitude, so in the spots where you have full constructive interference, there's actually four times the energy density. But it all comes out in the wash. --Trovatore (talk) 00:54, 22 March 2014 (UTC)