Month: July 2022

In vacuo veritas?

On By rolcottIn Cosmology, UncategorizedLeave a comment

“Let’s see if my notes are complete, Mr Moire. We’re crossed off two possible Universe finales — falling into a Big Crunch or expanding forever while making new matter between the galaxies to keep itself in a steady state. Or the Universe might expand to some critical density and then stay there but we mostly ruled that out because a twitch would push it to either crunching or expanding forever. Einstein’s Cosmological Constant might or might not be dark energy but either way, Friedmann’s equation predicts that the Universe will expand exponentially. Is that all the ways we could end?”

“Of course not, Jeremy. The far distant future’s like anything we humans don’t know much about, we make lots of guesses. Vacuum energy, for instance.”

“Anything to do with getting my roommate off the couch when it’s their turn to do the floors?”

“Very funny, but no. The notion of ‘vacuum‘ has a history. Aristotle said it’s empty space and that’s nothing and you can’t talk about nothing, but of course that’s exactly what he was doing. It wasn’t until Newton’s day that we developed dependable technologies for producing and investigating ‘nothing.’ Turns out that a good vacuum’s hard to find and even outer space is a lot busier than you might think.”

“Yeah, Jim in the Physics lab says he’s working with Ultra‑High Vacuum, a millionth of a millionth of an atmosphere, and the molecules left in the apparatus still cause problems.”

“Wonder how many molecules that is. Time for Old Reliable. <muttering> Avagadro’s Number, 22.4 liters, 10-12 atmospheres … Wow, there’s nearly 30 billion molecules per liter in his rig, a couple hundred times more if he chills it. <scrolling> This Wikipedia article says the solar wind runs only ten thousand protons per liter; interstellar medium’s about a tenth of that. But all those are physical vacuums. Theoretical vacuums are completely empty except they’re sort‑of not.”

“How could they be empty but not? Is that a Schrödinger joke?”

“No, but it does point up how the word has acquired multiple technical meanings. Newton’s concept of a vacuum was basically equivalent to Aristotle’s — simply a space with no matter in it. Two centuries later, Maxwell pointed the way to electric and magnetic fields which meant we needed to define a new vacuum with no such fields. Einstein added his proviso about the speed of light in a vacuum but that was okay. Then along came quantum and strings and several new kinds of vacuum.”

“Why would we need new definitions? Nothing’s nothing, isn’t it?”

“Not necessarily in theory, and that’s the point. For instance, you might use a Maxwell‑inspired theory to think about how a certain charged object behaves in a certain electromagnetic field. You can’t isolate the field’s effects unless you can add it to a theoretical space containing no objects or electromagnetic fields. Make sense?”

“And that’s a Maxwell vacuum? Seems reasonable. Then what?”

“Quantum theories go in the other direction. They start by assuming that Maxwellian vacuums can’t exist, that space itself continually produces virtual particles from their associated fields.”

“Um, conservation of mass?”

“Valid question. This may feel like dodging, but there’s math and experiment to back it up. What’s really conserved, we think, is mass‑energy. Particles, anti‑particles and energy fluctuations averaging to zero over finite time intervals. A dab of energy concentrated to create a particle’s mass? No problem, because that particle will be annihilated and release its energy equivalent almost immediately. To replace the Maxwellian vacuum, quantum theorists co‑opted the word to refer to a system’s lowest possible quantum state or maybe the lowest possible set of states, depending on which kind of calculation is underway. The cosmology people picked up that notion and that’s when the doom‑saying started.”

“Awright, now we’re getting somewhere. What’s their vacuum like?”

“From what I’ve seen, a tall stack of ‘if‘s and hand‑waving. The idea is that our Universe may not be in the lowest possible quantum state and if so, sometime in the next 188 billion years we could suddenly drop from false to true vacuum, in which case everything goes haywire. I’m not convinced that the Universe even has a quantum state. Don’t panic.”

~~ Rich Olcott

Generation(s) of Stars

On By rolcottIn Astronomy: Stellar Science, Cosmology, UncategorizedLeave a comment

“How’re we gonna tell, Mr Moire?”

“Tell what, Jeremy?”

“Those two expanding Universe scenarios. How do we find out whether it’s gonna be the Big Rip or the Big Chill?”

“The Solar System will be recycled long before we’d have firm evidence either way. The weak dark energy we have now is most effective at separating things that are already at a distance. In the Big Rip’s script a brawnier dark energy would show itself first by loosening the gravitational bonds at the largest scale. Galaxies would begin scattering into the voids between the multi‑galactic sheets and filaments we’ve been mapping. Only later would the galaxies themselves release their stars to wander off and dissolve when dark energy gets strong enough to overcome electromagnetism.”

“How soon will we see those things happen?”

“If they happen. Plan on 188 billion years or so, depending on how fast dark energy strengthens. The Rip itself would take about 2 billion years, start to finish. Remember, our Sun will go nova in only five billion years so even the Rip scenario is far, far future. I prefer the slower Chill story where the Cosmological Constant stays constant or at least the w parameter stays on the positive side of minus‑one. Weak dark energy doesn’t mess with large gravitationally‑bound structures. It simply pushes them apart. One by one galaxies and galaxy clusters will disappear beyond the Hubble horizon until our galaxy is the only one in sight. I take comfort in the fact that our observations so far put w so close to minus‑one that we can’t tell if it’s above or below.”

“Why’s that?”

“The closer (w+1) approaches zero, the longer the timeline before we’re alone. We’ll have more time for our stars to complete their life cycles and give rise to new generations of stars.”

“New generations of stars? Wow. Oh, that’s what you meant when you said our Solar System would be recycled.”

“Mm-hm. Think about it. Back when atoms first coalesced after the Big Bang, they were all either hydrogen or helium with just a smidgeon of lithium for flavor. Where did all the other elements come from? Friedmann’s student George Gamow figured that out, along with lots of other stuff. Fascinating guy, interested in just about everything and good at much of it. Born in Odessa USSR, he and his wife tried twice to defect to the West by kayak. They finally made it in 1933 by leveraging his invitation to Brussels and the Solvay Conference on Physics where Einstein and Bohr had their second big debate. By that time Gamow had produced his ‘liquid drop‘ theory of how heavy atomic nuclei decay by spitting out alpha particles and electrons. He built on that theory to explain how stars serve as breeder reactors.”

“I thought breeder reactors are for turning uranium into plutonium for bombs. Did he have anything to do with that?”

“By the start of the war he was a US citizen as well as a top-flight nuclear theorist but they kept him away from the Manhattan Project. That undoubtedly was because of his Soviet background. During the war years he taught university physics, consulted for the Navy, and thought about how stars work. His atom decay work showed that alpha particles could escape from a nucleus by a process a little like water molecules in a droplet bypassing the droplet’s surface tension. For atoms deep inside the Sun, he suggested that his droplet process could work in reverse. He calculated the temperatures and pressures it would take for gravity to force alpha particles or electrons into different kinds of nuclei. The amazing thing was, his calculations worked.”

“Wait — alpha particles? Where’d they come from if the early stars were just hydrogen and helium?”

“An alpha particle is just a helium atom with the electrons stripped off. Anyway, with Gamow leading the way astrophysicists figured out how much of which elements a given star would create by the time it went nova. Those elements became part of the gas‑dust mix that coalesces to become the next generation of stars. We may have gone through 100 such cycles so far.”

“A hundred generations of stars. Wow.”

~~ Rich Olcott

En Route to Spreading Out

On By rolcottIn UncategorizedLeave a comment

“Gee, Mr Moire, if Einstein and Friedmann are right, some day the Universe will expand exponentially and everything dies. Even Dr Mack says that’s a downer.”

“First, it’s not ‘some day,’ it’s already. We’ve got evidence that exponential expansion became the dominant process five billion years ago. The interesting questions are about what happens during the expansion and what the timeline will be. That’s all controlled by a single weird parameter so naturally the parameter’s conventional symbol is w. Each major component of the Universe has its own value of w and they combine to predict the future course of the Universe.”

“Weird sounds like fun. What is it, another difference like the Cosmological Constant minus that mass‑pressure stuff?”

“Good guess, but it’s not a difference, It’s a ratio, between different flavors of energy.”

“Kinetic and potential, I’ll bet.”

“That split seems to be a common theme in Physics, doesn’t it? In this case, you’re almost right if we stretch things. One of the energy flavors is mass, including both normal and dark matter. If you take the long view, every atom of normal matter will sooner or later break down so you can think of it as a packet of potential energy, pent up and waiting for release. Dark matter, who knows? Anyway, w‘s denominator is mass per unit volume. The numerator’s a little trickier. As you guessed, we need something related to kinetic energy and we slide into that sideways.”

“How so?”

“Well, most of the normal matter is very dilute hydrogen which we can treat like a perfect gas. That’s something we’ve got a good theory for. Per unit volume, gas particle kinetic energy is proportional to pressure and that’s what we use for w‘s numerator. Averaged over the volume of space the pressure‑to‑mass ratio w for matter moving at ordinary speeds is effectively zero.”

“Does dark matter follow the same formula?”

“We pretend it does.”

“How about photons? They don’t have mass so that ratio would be infinity.”

“True, but they do carry momentum and it turns out w is simply ⅓ for photons and neutrinos and anything else traveling at relativistic speeds. Then there’s the Cosmological Constant’s w, which is minus‑one. Since the Big Bang we’ve gone from radiation‑dominated to matter‑dominated to Constant‑dominated; the effective w has shifted from somewhat positive to zero and into negative territory. Thanks to the surviving photons and matter, though, we’re still at least slightly above –1.0.”

“What difference does that make?”

“Minus‑one is the boundary between fates for the Universe. More positive than that, gravity and electromagnetism are guaranteed to be stronger than dark energy. Expansion will move gravity‑bound objects farther away from each other, but the galaxies and each galaxy cluster will stay together. The supply of hydrogen that fuels new stars will peter out. Eventually all the stars will gutter out and disappear into the cold dark as they wait for their constituent atoms to decay. The whole process will take something like 1010¹⁰ years.”

“That’s dark, alright, but at least it’ll take a long time. What happens of w is more negative than minus‑one?”

“The Big Rip. If w is more negative than the threshold, dark energy will grow stronger with time. We don’t know of anything that would limit the growth. First dark energy overpowers gravity and allows the galaxies and stars to disperse. Then it overrides the electromagnetism that holds molecules and rocks together. Eventually even the weak and strong nuclear forces will be defeated — no more atoms. Depending on how extreme w is, figure something like 200 billion years, give or take an eon.”

“Wow. But wait, we’ve covered radiation and mass and the Constant and none of them have a w below the threshold. What can have a more negative w?”

“A hypothesis. If there is anything, pretty much all we have is a name, ‘phantom energy,’ which is even more tentative than ‘dark energy.’ People are working to evaluate w with data. Results so far are so close to –1.0 that we can’t tell if it’s above or below the threshold or just teetering on the brink.”

“Two hundred billion years or way more. No worries, hey?”

~~ Rich Olcott

Constant’s Companion

On By rolcottIn CosmologyLeave a comment

“It’s like Mark Twain said, Jeremy — ‘History may not repeat itself, but it rhymes.‘ Newton identified gravity as a force; Einstein proposed the Cosmological Constant. Newton worked the data to develop his Law of Gravity; Friedmann worked Einstein’s theory to devise his model of an exponentially expanding Universe. Newton was uncomfortable with gravity’s ability to act at a distance; Einstein called the Cosmological Constant ‘his greatest blunder.’ The parallels go on.”

“Why didn’t Einstein like the Constant if it explains how the Universe is expanding?”

“It wasn’t supposed to. Expanding Universes weren’t in fashion a century ago when Einstein wrote that paper. At the time everyone including Einstein thought we live in a steady state universe. His first cut at a General Relativity field equation implied a contracting universe so he added a constant term to balance out the contraction even though it made the dynamics look unstable — the Constant had to have just the right value for stability. A decade later Hubble’s data pointed to expansion and Friedman’s equations showed how that can happen.”

“I guess Einstein was embarrassed about that, huh, Mr Moire?”

“Well, he’d thought all along that the Constant was mathematically inelegant. Besides, the Constant isn’t just a number or a term in an equation, it’s supposed to represent a real process in operation. Like Newton’s problem with gravity, Einstein couldn’t identify a mechanism to power the Constant.”

“Power it to do what?”

“Think about universal constants, like the speed of light or the electron charge. Doesn’t matter where you are or how fast you’re traveling in which inertial frame, they’ve got the same values. If the Constant is indeed a constant, it contributes equally to cosmological dynamics from every position in space, whether inside a star or millions of lightyears from any galaxy. Every point must exert the same outward force in every direction or there’d be swirling. And it multiplies — every instant of general expansion makes new points in between the old points and they’ll exert the same force, too.”

“That’s what makes it exponential, right?”

“Good insight. It’s a pretty weak force per unit volume, weaker than gravity. We know that because galaxies and galaxy cluster structures maintain integrity even as they’re drifting apart from each other. Even so, a smidgeon of force from each unit volume in space adds up to a lot of force. Multiply force by distance traveled — that’s a huge amount of energy spent against gravity. The big puzzle is, what’s the energy source? Most of the astrophysics community nominates dark energy to power the Cosmological Constant but that’s not much help.”

“As Dr Prather says in class, Mr Moire, ‘You sound tentative. Please expound.‘ Why wouldn’t dark energy be the power source?”

“In Physics we use the word ‘energy‘ with a very specific meaning. Yes, it gets heavy use with sloppy meanings in everything from show business to crystal therapy, but in hard science nearly every serious research program since the 18th Century has entailed quantitative energy accounting. The First Law of Thermodynamics is conservation of energy. Whenever we see something heating up, a chemical reaction running or a force being applied along a distance, physicists automatically think about the energy being expended and where that energy is coming from. Energy’s got to balance out. But the Constant breaks that rule — we have no idea what process provides that energy. Calling the source ‘dark energy‘ just gives it a name without explaining it.”

“Isn’t the missing energy source evidence against Friedmann’s and Einstein’s equations?”

“That’s a tempting option and initially a lot of researchers took it. Unfortunately, it seems that dark energy is a thing. Or maybe a lot of little things. Several different lines of evidence say that the Constant constitutes twice as much mass‑energy as all normal and dark matter combined. Worse yet, as the Universe expands that share will increase.”

“Wait, will the dark energy invade normal matter and break us up?”

“People argue about that. Normal matter’s held together by electromagnetic forces which are 1038 times stronger than gravity, far stronger yet than dark energy. Dark matter’s gravity helps to hold galaxies together, but who knows what holds dark matter together?”

~~ ROlcott