Archive for the ‘Physics’ Category

A Few Thoughts on Melting Ice and Heating Water

December 11, 2018

Here’s a little known fact about all those melting glaciers and ice caps; the energy required to melt a kilogram of ice (basically going from -0˚C to +0˚C), uses up as much energy as it takes to heat a kilogram of water from 0 to 80˚C.

So, we really have no good idea when all the ice will melt, the caps and glaciers disappearing, but when they do, all that heat that wasturning ice to ice-cold water, maintaining a fairly stable 0˚C, is going to go into heating the same mass by 80˚C. One estimate says it won’t happen for 5000 years, but then, more recent articles seem to suggest that the melt rate is accelerating faster than expected. Time will tell.

One estimate (2005) states that there are roughly 30,000,000 cubic kilometers of ice on Earth that year. So, imagine that in some time X all that ice melts due to extra heat in the atmosphere. Fortunately, all that energy is being sucked up by the phase transition from ice to water. Unfortunately, in the next period X, all that heat is going straight into heating the 30,000,000 cubic miles of water up by 80 degrees Celsius. Not quite boiling, but close. If “X” equals 5000 years, we might be okay and reverse the trend. If “X” is 100 years, we’re screwed because a sizable fraction of our government is run by morons who see short-term financial gains and understand no science at all.

To put this into perspective for metric-challenged Americans, 80˚C is about 176 degrees Fahrenheit. A hot-tub at 110 degrees Fahrenheit is considered dangerously warm.

To add more perspective to the volume involved, all of North America is 24,709,000 square kilometers. This much 80˚C water could cover all of North American over 1 kilometer deep. I mean, it won’t, of course, it’ll just end up in the ocean where the heat will add to the rest of the heat accumulated over 5000 years in the rest of the ocean, and parboil all the life there, instead. You know, those tiny organisms that produce most of our oxygen.

Just sayin’, we should really get our act together and quit fucking around.

 

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Running a Stirling Engine Using the Night Sky

November 28, 2018

I’m a failed inventor. I get strange ideas, try them out, and usually discover that I either got my physics wrong or built my prototype poorly, or that someone beat me to the punch thirty or three hundred years ago. I created what I thought was a great factoring algorithm for huge numbers and found out that Fermat developed it first. That’s the way it goes.

So here’s the latest invention. It’s not really an invention so much as an interesting application of an existing device.

Is it possible to make a heat engine that runs off the thermal differential between the night sky and the heat radiating from the ground? Stirling engines can run using fairly small temperature differences, such as the ambient air and the heat in the palm of your hand. You can get one of these hand-driven Stirling heat engines from ebay for under $50.  The real question isn’t so much whether you can make a device that runs off the heat sink of the night sky, but how much of a thermal delta you could provide to that engine.

How cold is the night sky? I’ve read that on a clear night, it can provide a radiative heat sink of -70˚C. Yeah, that’s negative 70 degrees centigrade. Pretty cold. Those with a background in heat transfer physics know that the other two forms of thermal transfer are conductive and convective, and with the right glass or plastic covered chamber, you can minimize those thermal paths so that your heat source/sink sees only the -70˚C of the night sky. This is why some telescopes have a problem with their optics freezing up. Really. It also explains why some windshields frost up even though it doesn’t reach freezing temperatures outside, and other related phenomena.

The other side of your Stirling heat engine could be getting its energy from the radiation from the ground, say, about 15˚C. Or if you heated up a tank of water during the day, maybe 40 or 50˚C. You could run your engine easily with a delta of 100 degrees, though as you thermal guys know, the engine would be a lot more efficient at higher temperatures during the day shift.

But, the hypothetical question is if you could run an engine off the night sky. My speculative answer is “yes”. What’s nifty about the ability to do this? Well, instead of dumping HEAT into the atmosphere to generate energy, which every power source on Earth currently does, you are actually dumping COLD (a.k.a, removing heat) into the atmosphere to run your engine. The net heat loss of your engine is NEGATIVE.

So yeah, we could cool down the Earth and generate energy at the same time. Crazy, huh? The biggest problem with the idea is that you could generate a lot more energy a lot more efficiently using a hot solar Stirling engine during the day at the same cost, while dumping more heat into the atmosphere.

And cost seems to drive everything except our self-preservation instinct.

Does the Sun have a Positive Charge?

September 23, 2018

While I was reading about Venus’ atmosphere, and how the tremendous heat had split apart the hydrogen from water molecules and sent them off into space at escape velocity, I started thinking about the Sun’s plasma.

Hot gases are interesting, in relationship to how fast each molecule is moving. Small, light molecules move very quickly, while heavier molecules slog along at a slower pace in the same gas. So, in the formula  KEAVG=½ mv2=3/2*k*T, where k is Boltzmann’s constant and KEAVG is the average molecular kinetic energy, you can see right away that for a given temperature, the smaller the mass of the particle, the higher the velocity. So, if a particle in a gas is 100 times larger than another particle, you’d expect the smaller particle to be moving √100 = 10 times as fast.

So, back to the Sun. The Sun has a plasma atmosphere, that is, it’s mostly dissociated electrons and protons and other stripped atomic nuclei. Electrons are about 1/2000 the mass of a proton, so we expect that their average velocity in the atmosphere of the Sun is going to be √2000 faster that the average proton, or roughly 45 times as fast.

What this suggests to me is that, in the solar wind, most of the particles that actually reach escape velocity from the Sun (all suns) are going to be the electrons by a large margin. This also tells me that most of the particles that reach escape velocity from our galaxy are also going to be electrons.

So, some general figures to keep in mind; the escape velocity from our general region of the galaxy is about 537 km/s. Our Sun happens to be moving about 220 km/s around the perimeter, so particles would only have to be leaving our Sun’s heliosphere at about 317 km/s to escape the galaxy. The escape velocity from the Sun’s surface is around 618 km/s, and the solar wind (protons and electrons) supposedly passes by the Earth at about 400 km/s, though as we may discover, this isn’t exactly true. The escape velocity from the Solar System, if you start from Earth orbit, is only 42 km/s, much lower than the 400 km/s stream of particles flying by our planet.

I’m speculating that the solar wind consists of very fast electrons and much slower protons; if they were moving at the same speed, they would recombine into hydrogen. And since the electrons are moving much, much faster than the protons, I’m also speculating that a lot more electrons escape from the Sun than protons.

Over a long period of time, the Sun should become positively charged as more electrons than protons escape into interstellar space and intergalactic space.

One might look at the velocities, and think, well, hey, if the protons are moving at 400 km/s, they’re all going to escape the Sun’s gravity, too, and the balance of charge will be maintained! But they aren’t all traveling at this high speed; there’s something called the Boltzmann velocity distribution curve for particles in a gas, and some fraction of those protons aren’t going to make the necessary 42 km/s as they pass by Earth; they’re going to fall back into the sun. The electrons, as we noted, are probably moving 42 times as fast, on average, as the protons, so a much smaller number of them are going to be trapped by the Sun’s gravity. Likewise, a lot more electrons will escape our galaxy than protons.

Wow, the number 42 sure does pop up a lot. I wonder if that means anything?

Anyway, we speculate that a lot more electrons will escape from the Sun than protons. This would have some interesting side-effects.

The Sun, being positively charged, is going to be pushing and accelerating protons in the solar wind. The surplus interstellar electrons will be pulling on these same protons. Likewise, the motion of the electrons in the solar wind will be retarded due to the positive charge of the Sun. Eventually, I would expect some sort of balance, while still maintaining a net positive charge on the Sun. Somewhere out there in the heliosphere, the proton and electron velocities would finally match up, allowing them to merge into hydrogen.

I read recently that there is a yet-unexplained acceleration of the solar wind away from the Sun. Perhaps this charge imbalance is related to that.

So, we have a cloud of surplus electrons in between the galaxies. We have another cloud, probably denser, of interstellar electrons within our galaxy, between the suns. And we have positively charges suns stuck in this rotating cloud like a plum pudding. Over billions of years, I’d expect the intergalactic cloud to get denser, pushing the galaxies apart as one high-velocity electron wind smashed into others, and the field pushed the galaxies apart. Could this be interpreted as the acceleration of the separation of galaxies in the universe that we see and attribute to dark energy? I have no idea. Could the plum-pudding of positive charges (stars) imbedded in a rotating negatively-charged galactic cloud appear to be more massive than it really is, as it rotates within the universe’s own electron field? I also have no idea. I’m not an astrophysicist, or a plasma physicist, or any of the other useful fields that could actually answer these questions.

ADDENDA: I tried to look up velocity distributions for electrons and protons in a solar wind. The new Parker Probe, just launched, will probably be measuring this, and the GOES satellite and ACE measured this. Looking at the ACE SWEPAM experiment live data, it looks like electrons and protons have, on average, roughly the same electron-volt values, which, as I suggested earlier, would mean that electrons are moving a lot faster than the protons, which would give us results as described. But I don’t know how good the data is, or if I interpreted it correctly.

If you like this speculation, be sure to check out my SF short stories listed at my website.

Black Hole Evaporation versus CMBR

May 5, 2018

Black holes evaporate. At least, that’s what most physicists tell us.

What I stumbled into recently was a conjecture that they can’t evaporate beyond a certain point if the input is greater or equal to their output. This was mentioned on Quora by some physicist as a response to a related question. I thought it was interesting enough to mention it here.

Really large black holes are colder than the cosmic microwave background radiation (CMBR), which is about 2.73 degrees. The radiation going into a black hole is actually greater than the radiation leaving the black hole. The only way a black hole could radiate is if it’s very small and already radiating hotter than the CMBR (plus whatever particles fall into it, adding to its mass).

The limit where the size/mass of the black hole is equal to CMBR input is about 1% Earth mass, about 4×10^22 kilograms, based on Susskind’s formula and Hawking’s formula. This would create a black hole smaller than a millimeter. But black holes can’t even form without at least three or more Solar masses to begin with.

So, any black hole larger than a millimeter is going to keep growing. Presumably, primordial black holes smaller than 10^11 kg, created during the Big Bang, would have evaporated by now. This leaves a range of possible primordial black holes from 10^11 to 10^22 kg as possible existing evaporators, since they would be hotter than the background radiation.

However….

Primordial black holes would form because of high density and radiation. It would be crazy to think that their mass wouldn’t quickly grow far beyond Earth mass when surrounded by a buffet of dense gas and radiation. Just the nature of the formative process suggests that they will never radiate faster than mass/energy is added to them from their environment, and will always grow larger in size.

I really WANT them to exist, however. My next SF story kind of depends on it.

The Spacetime Diet: Redistributing the Fat of the Universe

October 29, 2017

If you’ve had your nose in spacetime physics at all, you’re familiar with the idea that when you move really fast, other objects look thinner. Or, relatively, you look thinner from the viewpoint of someone else’s reference frame.

This is called the Lorentz-FitzGerald contraction. When you observe a moving object, it appears shorter, or thinner, along the axis of its motion relative to you. Likewise, you appear thinner relative to the moving object (who does not feel thin at all). There’s a formula for this, but it’s irrelevant for the discussion below.

You also appear to gain mass (using a similar formula). This is also irrelevant for the following discussion, but I thought I’d toss it out there.

So here’s the rub. You will often hear someone say or write, “When an object nears the speed of light, the universe flattens to a thin sheet from the viewpoint of an observer on that object.”

Just to clarify, this is bullshit. If you are cruising along at near-light speed, then all matter, relative to your frame of reference, is moving in the opposite direction at near-lightspeed. That’s okay so far. Except, the universe is expanding. And the farther out you go, the faster it’s expanding, such that there are regions of space expanding away faster than the speed of light (the expansion of “space” is apparently able to ignore the whole “speed of light” limit thing; go figure).

So when you attain a certain velocity, you become stationary relative to another part of the universe that is moving away from Earth at the same speed. There is no shortening of length or thickness for that object, that part of the universe.

Take the Andromeda Galaxy for example, moving toward us at 110 kilometers per second. When we measure the galaxy in the direction of its travel, along its axis of motion, it’s foreshortened in that direction. Now, fire up your rockets so you’re traveling at 100 kilometers per second in the same direction, and Shazam! The entire galaxy poofs back out to its real shape in its own frame of reference that happens to coincide with your own. Relative to you, the Andromeda Galaxy is no longer moving.

So, back to the expanding universe; as your spaceship speeds up more and more, there’s always a part of the universe that’s moving at the same speed at which you are traveling (a comoving reference frame). It won’t look compressed or thinner or foreshortened at all. In fact, if we take the viewpoint that all parts of the universe are essentially equal, (that is, there is no “center” of the universe) then the universe doesn’t compress into a pancake at all as you near the speed of light; it’s just that the non-foreshortened part of it, the part that matches your current velocity, is farther and farther away from you. But the overall volume will appear unchanged.

 

Black Holes and Those Pesky Event Horizons

October 8, 2017

In Leonard Susskind’s book, The Black Hole War, page 240, he states, “To a freely falling observer, the horizon appears to be absolutely empty space. Those falling observers detect nothing special at the horizon…” In Amanda Gefter’s book, she points out that the distant observer sees the event horizon, while the falling observer detects no event horizon at all. Of course, she took a lot of her ideas from Susskind. In the meantime, Hawking treats the event horizon as a fixed boundary where virtual particles can split apart (Hawking radiation).

black_hole_2013_0

I think none of these is right. The idea between the “escape velocity being faster than the speed of light” is relative to the delta between the gravitation potential of the observer and the potential at the event horizon. From an infinite distance, we observe an event horizon at a certain radius. Should the event horizon suddenly disappear if we are in an inertial frame starting our fall into the black hole? Starting at what distance? A thousand miles? A light year?

The more likely result is that the event horizon moves inward as you approach it. You are in a deeper gravity well as you approach the black hole, thus the difference between your local gravity potential and that of the event horizon, to maintain a high enough value for the escape velocity to equal the speed of light, requires that the event horizon continuously move away from you (toward the singularity) as you move toward the singularity. You never quite catch up with it. There’s a Wikipedia article that says this explicitly, but then, it’s a Wikipedia reference (Event Horizon). Sometimes they’re wrong, but usually they’re dead-on.

An interesting consequence of this is that if you maintain a certain orbit near the event horizon, and your version of the event horizon is closer to the singularity than that of a more distant observer, then a photon just outside your observed event horizon could reach you just fine, even though it cannot reach the more distant observer. Having received that photon, you could transmit the data from it outward, (boosting the frequency) as the distance from your gravity well to the distant observer requires an escape velocity somewhat less than the speed of light. Is this a loophole?

Why, then, do we think that a photon below the event horizon (for the observer at infinity) can’t escape the confines of the black hole? Is it only because it would be red-shifted to a zero frequency? Or is that false?

Escape velocity is merely a calculation of the velocity required to go from one gravity potential to another. If you are already in a gravitational well (like the outer edge of the Milky-Way galaxy) with an escape velocity of 300km/s, this has no effect on the escape velocity from Earth (11km/s), or the velocity needed to orbit Earth (7.5km/s). Likewise, consider a photon trapped just beyond the event horizon as viewed from an observer at infinity. To the guy in orbit around the black hole, the difference in potential is much smaller, and his relative event horizon is closer to the singularity. Won’t he see that photon? Can’t he receive it from the domain outside his apparent event horizon, but inside the event horizon of the observer-at-infinity? And then capture the photon and retransmit it?

So, even though a photon by itself can’t escape the event horizon of the observer-at-infinity, an intermediate process (natural or human) could conceivably pass a photon up through overlapping light cones, even though the light-cones at either end don’t overlap. This might eliminate the question of whether information can escape a black hole or not. The infalling observer can see what’s happening beyond the outer event horizon, and pass the information on, since his own event horizon is even closer to the event horizon.

A Fool’s Physics

September 18, 2017

I’ve read a lot of physics in my life and have a lot more to read, a lot more to learn. It’s hard to read any general physics text without stumbling across some interesting tidbit that makes me sit back and ponder how that tidbit fits in with my mental model of the universe. Some things make sense, some don’t. When I heard of the Unruh effect, I was dumbfounded (to my understanding, this is the emergence of energy out of a vacuum relative to an accelerating object). When I learned that photons are their own antiparticles, I was confused. When I realized that the time component in the spacetime interval produces a hyperbolic curve in the formula, it was an enlightenment years in the coming. When I read that antiparticles are just regular particles going backward in time (Feynman, I think), that, too, messed with my mental models of the universe. To say nothing of dark matter, the accelerating expanding universe, and so on. So, I try to organize all this hodge-podge of apparently related information into a single model that makes sense. As most physicists will tell you, it is an insurmountable task. But, I am not a physicist, really. I have a Masters in Astronautical Engineering, and as Sheldon Cooper would tell you, I’m really just an engineer. I create mental models that make sense to me, but may not have any practical use or truth in the larger sense of things. But we all have to start somewhere. I’ll keep reading, and revise the incorrect bits as I go along.

In this log of ramblings, I’ll offer up a bunch of foolish ideas on physical reality. I’m a big fan of determinism, so be forewarned. I also think of time as an actual, physical dimension. If you happen to join me on this warped (!) journey of speculation, I’d love for you to tear my arguments apart, tell me what’s wrong, and perhaps help shape the speculations into something that makes a coherent sense of reality, or assure their demise.

Causality Paradox? What causality paradox?

September 11, 2017

I can’t call this real physics, this is just pure and wild speculation. I had a funny idea today about whether or not you can go back in time and shoot your grandfather, thus keeping yourself from ever being born. Ethical questions aside, I thought of a possible solution to the whole “paradox” issue.

First, if you aren’t familiar with the Grandfather Paradox, you can read up on the subject at Wikipedia at https://en.wikipedia.org/wiki/Grandfather_paradox.

Start with the idea that we are always travelling at the speed of light. You, the Sun, the Earth, your brother Bob, everything is travelling at the speed of light through the time dimension, all going the same direction so your relative speed is zero. This is a pretty common concept in modern physics, so I’m not going to expand on that here. Just more physics weirdness.

So, let’s say I get the dubious urge to go murder my grandfather at some time in the past, before I was born. Using some fantastic time machine, I go back in time to when Grandpa was just a young fella and shoot him. What happens then?

Well, imagine that space and time are a 4-dimensional matrix, but that changes made in the matrix can only propagate forward at the speed of light. Remember, that’s how fast we move through time. Eventually, the change (where I no longer exist) reaches the point where I would have gone back in time, but the particles that would have made up my body go shooting forward past that point and never go back. Well, they aren’t “shooting forward” so much as redirecting the world line of their old path at the speed of light. Now, instead of making a U-turn and heading toward their fate with my grandfather, the bullet-magnet, they continue forward in time. The old worldline going backwards collapses/disappears at the speed of light and eventually catches up to where Granddad is, and lets him live. I’m born again! And I foolishly decide, again, to go back in time and kill my granddad.

What does this result in? An oscillation. The world line shifts back and forth between the two realities, carrying the data from both possible realities, like a sine wave on a current. Just as a single electrical sine-wave can contain positive and negative values as it propagates through a wire, so can events toggle on a worldline as that worldline propagates through time. Even past the point where I made my fateful decision, the world line is toggling back and forth; both realities are true, taking their turn as the decision I made causes both of them to be real. The duration of this toggling or oscillation would be twice the duration of the time from when I went back in time to when I snuffed Gramps; the duration of the whole loop.

It’s my belief (not necessarily shared by many others) that we live in a four-dimensional space time that exists perpetually as a 4D matrix, and that what we perceive as our consciousness exists at each point along that worldline. There is the version of you that you perceive now, and the version that existed when you kissed your wife for the first time, savoring the moment you’ve forgotten. Kind of a repetitive immortality.

But what I’m suggesting above is that multiple realities can exist on a single worldline; you don’t need multiple universes dividing every time a critical decision is made or a quantum observation collapses a wave function, or a bit of antimatter goes back in time and changes an existing chemical configuration. Both events occur and exist on a changing, fluctuating, dynamic 4D worldline. There’s the version of you that remembers killing your Grandfather, and the version that never existed, propagating through time, one behind the other forever on the oscillating world line.

The normal view of a 4D worldline is of a static deterministic universe, bound by the future and past configuration of an unchanging worldline. Another view is that every decision, human or quantum, splits the universe into a multiverse, a crowded infinity of infinities. This version allows us to stick with one universe, but to modulate our worldline to allow multiple realities to exist along a single timeline.

Possibly, an outside observer could interface with either version of your reality, based on where he encounters your worldline from his own worldline. Could that be the “collapse of the wavefunction” we talk about? Good grief, that would make the Schroedinger’s Cat conundrum actually possible. Dead and alive! I always thought of it as complete nonsense.

One issue with this model is that each worldline, as it moves from one reality to another, may have to move instantaneously from the collapsed worldline to the new worldline. I think. No real way to test it, that I can imagine. Mmm…maybe pick a subatomic decay process that can have multiple durations, then have someone record the decay time data, then take off (with that data) somewhere at high-speed so your worldline is no longer in sync with the experiment’s original timeline, fast enough that the time separation is greater than the decay time variance. Then, come back and see if the recorded time is the same as it was before; you’ll have two sets of readings of the duration of a single decay, and they might not agree. Wouldn’t that be something?

 

Background Gravity – Time Dilation in a Flat Field

August 11, 2017

I got into an argument with a physics buddy not that long ago (a year, maybe), about gravity. We have an intermittent arrangement where we go drink beer and talk about physics at two or three pubs in San Luis Obispo. Usually, the physics becomes a little less coherent as the evening wears on.

One of the discussions centered on whether there is a “background field” of gravity or not, or whether it’s even sensible to discuss such a thing since, in an infinite field of equally distributed mass (or gas, or 1 atom per cubic light year, whatever), all the forces around you seem to cancel out. The mass of the universe to your left is equal in size to the mass of the universe on your right; you feel a net acceleration of zero. I argued that even though the field was “flat”, there was still a field there. He argued that a field implied a gradient; there is always a force.

We did not come to a satisfactory conclusion. It might merely have been the fact that we were defining the same terms in different ways in our heads. I’m not sure. I thought my argument was rock-solid.

So, here is my side of it.

Some of you are probably familiar with Newton’s Shell Theorem. It’s in his Principia Mathematica, and if I remember right, he solved it without using calculus. Basically, what it says is this; if you are inside a spherically symmetric shell of mass, then you feel no gravity pulling you any direction. It’s a bit non-intuitive. Let’s say the Earth is hollow, and the entire planet’s mass has been compressed into a thin spherical shell a few centimeters (or meters, it doesn’t matter) thick. If you are floating around in your Nike Space Suit inside this shell, you will not be pulled toward the center, or the inner surface of the shell, or anywhere else inside the shell. Wherever you are put, you will remain.

Personally, I think this is one of the coolest theorems ever.

It’s also true that if you are outside the surface of a spherically symmetric planet, then it doesn’t matter how dense it is, at a given radius you will feel the pull of a certain amount of gravity. If you are in orbit above the Earth, and the Earth suddenly becomes a black hole of the exact same mass, you will remain in orbit, totally unaffected by that change. That’s pretty cool, too. Given that the gravitational force is based on F=GMm/r2, this should be kind of obvious. Neither your mass (m) or the mass of the Earth (M) has changed, your orbital radius is the same, and G is the gravitational constant. Ergo, the density of the object you are orbiting at a radius “r” from the center of the object is irrelevant.

So, that was me drifting from the actual subject. Shell Theorem—let’s get back to that.

As you might know, the clock of anyone in a gravity field runs slower than that of a clock outside of that gravity field. This is called gravitational time dilation (and is equal to ∆t’ = ∆t √(1-2MG/rc2) for a non-rotating sphere). A person on Earth actually ages slower than a person in deep space, according to relativity. This was verified with clocks flying around the Earth in the Hafele-Keating experiment. Before you ask, yes, they took into account Earth’s rotational speed, the speed of the airplane (in both directions relative to Earth’s rotation) with regard to Special Relativity’s time dilation due to velocity. It was a nice experiment.

Let’s say we’re using a hollow Earth from Newton’s shell theorem. As you get closer to the Earth, you are in a deeper gravity well, and the outside observer sees your clock slow down. There’s a small hole in the planet, and you pass into the planet, where everything is pulling you in opposite directions equally, so you seem to feel no force. And yet, your time dilation effect does not suffer a discontinuity, jumping suddenly to that of the outside observer. You are in a denser gravity field, but a flat gravity field. [to the physics majors out there, for god’s sake, if my terminology sucks, please correct me]. Your time dilation will be just the same as if you were standing on the surface of the planet.

So now you have a flat gravitational field (no “force” pulling you in one direction, that is, all forces pulling you equally in all directions). And yet, even in this apparent lack of gravity, where you can’t actually tell that you’re in a gravity well, your time runs slower than the time of someone far from the planet.

I extended this argument to the rest of the universe. If mass was distributed equally around you, even though you felt no force one way or the other, there would still be a background gravitational field. Gravitational time dilation implies a gradient; for time dilation to be relevant, you need someone in a weaker gravitational field measuring your time. However, both the measured and the measurer can be in locally flat gravitational fields.

Does a flat gravitational field curve spacetime by itself? Or is it only the gradient between two different gravitational fields that curves spacetime? My general opinion is that you don’t need the gradient for the curvature of spacetime. If you have an infinite universe with equally distributed mass, then from some arbitrary center, it will appear to curve spacetime until it closes the dimensions of universe into closed loops, like the inside surface of an event horizon (though other arbitrary centers will have different, yet overlapping event horizons – a subject I will touch upon another day). Likewise, if you have a large, thin flat sheet of soapy water in the air, fluctuations are going to cause it to form bubbles, closing up the edges. In spacetime, there may be a similar tension (gravity?) that closes the edges together into a 4D hypersphere.

How would you test the curvature of space inside a shell? I’m not entirely sure. I think the universe we have is a good test case, however.

Particle Pair Production in Deep Space

August 6, 2017

Many of you know that a matter-antimatter reaction results in a pair of gamma rays. Fewer of you will know that you can take a couple of gamma rays, run them into each other, and get a pair of matter-antimatter particles. This has been done experimentally, and there’s a bit of data about it under “Two Photon Physics” in Wikipedia. Generally, if a subatomic reaction can occur, then it’s reversible. Maybe not statistically probable, but still reversible. This is a concept I used in a story I recently sold to Analog SF. In an area of space with high-density, high energy gamma rays, you’ll get a lot of positrons and anti-protons produced (more positrons, since they are 1/2000th the mass, of course), but there will also be some small production of antihydrogen if the antimatter doesn’t recombine right away with normal matter. And the antihydrogen may be neutral enough to survive and drift in deep space for a while, maybe long enough to be used as a resource.

Some reactions result in the release of more than two photons. A particle and antiparticle meet, three photons are emitted. The photons are lower energy, but the reverse reaction, 3 photons meeting, is a much, much lower probability than 2 photons (gamma rays) meeting. Still, on rare occasions, it might happen.

In fact, it’s my belief that if you have enough photons, even low-energy photons, passing through the same bit of space at the same time, you can also have pair-production, spitting out particles and antiparticles. One calculation for photons from the cosmic microwave background radiation (CMB) estimates 400 photons per cubic centimeter, average, plus whatever higher-energy visible light and gamma rays pass through from billions of stars. And there are a lot of cubic centimeters in a light-year (about 4.9 x 1050). Even if the probability of pair production is very, very low, I still imagine that it would happen on occasion.

As a side-note, the probability of a positron and electron meeting in deep space is very high, since they attract one another, while the probability of two gamma rays meeting at just the right time in just the right way is fairly low. The reaction looks symmetric, but the probability of it happening in a certain direction is much higher one way than the other. Ditto for any two-particle reaction that creates three particles. This contributes to the increased entropy of the universe and the “arrow of time”; there’s a preferred direction for these subatomic reactions to occur.