Category: Cosmology

Dodeca to The Rescue

On By rolcottIn Cosmology, General: Fun Stuff, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Days are getting warmer, so my walk around the park’s lake is at dawn. I’m enjoying the view when my phone blares out <bomPAH-dadadadaDEEdah>. Of course, the caller‑ID display shows 710‑555‑1701. “Good morning, Ms Baird. Surprised to hear from you again so soon. How is Project Lonesome coming along?”

“It’s been saved, thanks to your knowledge of antique Physics.”

“Antique??!?”

“Lenz’s Law was already nearly 200 years old in your time, Mr Moire, and I’m another 200 years on. Our engineers have to learn exponentially more than yours do. Things get lost in the welter so we missed the magnetic squirt‑out stumbling block. Anyway, armed with your hint I was able raise the issue early enough in the design phase that we could adjust.”

“Repulsion between opposed magnetic fields is pretty basic Physics. How will your people get around that?”

“By going from ten anti‑matter factory sites to twelve.”

“Huh? Your original design had ten current‑carrying tractor/pressor beams arrayed around the equator of Planetoid Road. That was a problem because currents in the beams would induce their own magnetic fields. The combined field would be perpendicular to the equator. Lenz’s Law says induced fields are in opposition to the black hole’s external field. Field‑field pressure would squeeze Road right out of the system. Twelve beams around the equator would make an even stronger magnetic dipole. How would that solve the problem?”

“It wouldn’t, but that’s not the configuration we’re looking at. Do you know what a dodecahedron is?”

“One of the Platonic solids — twelve identical pentagonal faces, lots of symmetry.”

“Right. So we’re going to center each AM factory in its own face of a dodecahedron plotted onto Road’s surface.”

“Ah, the symmetry’s nearly spherical so the induced fields won’t combine as a dipole. Cute.”

“It’s better than that, Mr Moire. The currents are pulsed, remember, and we didn’t expect to have all the factories running full‑out all the time. By varying individual pulse rates or even shutting down one or two factories we can control the strength and direction of our combined magnetic field. We can tweak that vector relative to the black hole’s field lines as needed to stabilize our position. We could even steer the planetoid around the system if we have to. All with zero fuel expenditure. Wins all around!”

“What about the spaceport?”

“Spaceport?”

“You’re making a lot of AM product here, and you’re going to need to ship it out to wherever Star Fleet needs it. That means Road will need a port and docking facilities and everything that goes with that. I had assumed that’d be at one of the poles. Zero rotational speed up there would would make for easy landings and take‑offs. But the new configuration would have the worldlet tumbling arbitrarily. No fixed poles. Where will you put the docks? For that matter, how else could you build and staff the factories in the first place?”

“That we did think about. Not even the original design included on‑planetoid docking. Landing a ship at either magnetic field convergence point would have been too risky. That’s why we were originally going to site all the AM factories at the equator. Putting them somewhere else is no problem because each factory will be assembled in space. Space tugs can drop it into any position and then flit away. Every AM factory will be fully automated, including the robots that will repair whatever needs repairing, so no staffing required.”

“But how will you get the AM away from the planetoid?”

“The usual way. The AM will be magnetically suspended in massive gamma bixonate cannisters transmitted by industrial‑scale transporters. The bixonate blocks the black hole’s field. Transporter range is limited near Lonesome’s steep gravity well, but we can orbit a transshipment facility close enough to be useful but far enough to be safe.”

“What if a transporter malfunctions? You wouldn’t want AM spraying around the transshipment deck.”

“Reception transporters for AM cargoes work from the outside in so the cannister’s integrity is complete before the AM signal exits the buffer.”

“I sense a promotion in your future.”

~ Rich Olcott

  • Thanks to Alex and Xander for keeping me on‑topic.

The Polar Peril

On By rolcottIn Cosmology, General: Fun Stuff, Physics: Black Holes and Relativity, UncategorizedLeave a comment

This park bench is perfectly situated for watching the summer solstice sun setting across the lake. I’m enjoying the view when <bomPAH-dadadadaDEEdah> blares from my phone. Number 710‑555‑1701 on the caller‑ID display evokes memories of a sultry stare and pointed ears…. “Good evening, Ms Baird. What’s new in the 23rd century?”

“Not much that I can tell you about, considering the Prime Directive. We’re taking a second shot at Project Lonesome. You may recall we’d identified an isolated black hole we called Lonesome. We were going to use two orbiting planetoids, Pine and Road, to generate electricity from its spinning electromagnetic field. Star Fleet’s anti‑matter synthesizers need that power.”

“Yes, I remember. Three‑body gravitational instability cost you Pine and your rank. Have you recovered the rank?”

“I’m only up to Lieutenant Commander so far, but part of the deal was that I’m back on Invigilator for a second shot at Lonesome. This time we’ve simplified the design. We had to, we only have Road to work with.”

“If I recall correctly, the idea was that the rotating field would induce electrical currents within conducting tractor beams strung between Pine and Road. How are you going to do that with only one orbiter? Relativity would be a challenge if you string something down to Lonesome.”

“We’re not stupid, Mr Moire, and we’re quite familiar with Relativity’s effects. I’ll give you an example your science is ready for. General Relativity says that time runs more slowly the deeper you go into a gravity well, yes?”

“Indeed. Our GPS time‑signal calibrations include an Einstein correction for reduced Earth gravity at satellite height. We have a movie, Interstellar, where gravitational time dilation was a major plot element.”

“A classic film. Even now we watch it occasionally. Consider this: on its own timeline, a star within its gravity well is younger than remote measurements say it is. The more massive the star, the greater the difference between experienced and apparent age.”

“Ooo, nice.”

“Counteracting gravitational discrepancies was a major challenge when we were developing transporter technology. Physics just doesn’t like teleporting a material object between different timescales, even through subspace. We finally gave up on that approach. What worked was transcribing the object into a subspace signal between pattern buffers. In the receiving environment we rebuild from the buffered signal and amorphous matter. Sometimes roundabout is the best path.”

“I’m with Bones on that—”

“Who?”

“Doctor Leonard McCoy.”

“Never heard of him. Must have been before my time.”

“Anyway, he’ll refuse to use transporters, convinced they’ll spray his atoms all over the Universe.”

“Way, way before my time, then. These days they’re as safe as your airplanes. Safer.”

“So what’s the new design?”

“The plan is to site ten plants around Road‘s equator. Each plant will have a free‑standing AM production facility teamed with two conductive tractor/pressor beams locked onto a floating plate of gamma‑phase bixonate. I’m allowed to give you those details because it’ll be a century before you’ll have bixonate production technology, much less gamma restructuring capability.”

“Why the special material?”

“At the nanoscale level, gamma bixonate’s surface is an array of corner‑cube mirrors that perfectly reflect electron waves back to their source. Meanwhile, the jagged edges between nano‑cubelets topologically obstruct local coherent magnetic fields. The combination is key to my Project Lonesome architecture. The power production cycle starts with injecting pulses of spin‑up electrons into one beam’s center where they’re trapped and streamed upwards. The black hole’s rotating magnetic field accelerates the electrons until they hit the bixonate nano‑cubelets that reflect them down the other beam. The reflection operation also flips the electron spin state so now the field accelerates them downward towards the factory’s energy receptors.”

“Double the acceleration effect.”

“Mm‑hm. We expect to achieve energies in the high exa‑electronvolt range, about a billion times what your CERN instrument can do. That’s plenty for AM synthesis.”

“One question.”

“Yes?”

“Have your engineers considered Lenz’ Law? Your immense electric currents will generate their own magnetic fields in opposition to the black hole’s. The induced fields will squirt Lone right out of the system.”

A sudden shocked pause, then the connection drops.

~ Rich Olcott

  • Thanks to Xander for a deeper Time question.

The Disk That Bent Space

On By rolcottIn Cosmology, Physics: Einstein, UncategorizedLeave a comment

<Author’s note — Side projects completed. Back to the fun stuff…>

“A cup of mud and a strawberry scone, please.”

“Sy! You’re back! Spent the winter months down in Bermuda with the onions and the eels, eh?”

“Not quite, Cal. A contract needed me on-site to monitor how well the company executed my recommendations. They did a pretty good job. They’re happy; I’m happy, paid and back home again. The weather here’s more to my liking.”

A hefty hand grabs my shoulder. “Hey, Sy, you’re back. Where ya been and how was it?”

“Sorry, Vinnie, my lips are sealed. You know how that works.”

“Yeah, I been there. Well, not there there, but. Anyways, I got a question I been saving up for you.”

“Always good to have a conversation-starter. Out with it.”

“Came from a Calvin And Hobbes comic strip some years ago but I saw it again on the internet. Calvin, that’s the kid who has a stuffed tiger named Hobbes but it talks, he’s sitting on the floor listening to something on his record player which tells you how old the strip is. His Dad comes over, points one finger at the disk’s edge and another at the label near the center. Got the picture?”

“Clear so far.”

“Dad leads off, ‘Both points make a complete circle in the same amount of time, right?‘ And the kid says, yeah, and Dad’s like, ‘But this point on the edge has to make a bigger circle than this point near the center so it has to move faster. Two points on the same disk move at different speeds but they both do the same revolutions per minute‘, and the kids goes to bed all frazzled.”

“Ah, the difference between angular speed and linear speed. The whole Earth turns once every 24 hours so Quito on the Equator does 1040 miles an hour but Helsinki up 60 degrees north goes half that.”

“Yeah, I know all about that stuff, I fly airplanes for a living, remember? That’s not my question.”

“Okay, what’s your question?”

“Suppose Calvin’s record speeds up until the label point’s going near the speed of light? What happens to the edge point?”

“Things get interesting, like Einstein-level interesting. On his way to General Relativity he did an important thought experiment about a disk like this. Sort-of like this.”

“Sort of?”

“Calvin’s disk represents a real material object, Einstein’s doesn’t. Objects made of matter have a limit to how fast you can spin them and it’s way short of lightspeed. Remember that time you were in here playing with that kid-toy top?”

“Gimme a sec… that was about centrifugal force, right, the kind that tries to shoot stuff straight out away from a spin center?”

“Sharp as ever, Vinnie. The centrifugal force per unit mass rises with the square of the rotation speed. Spin twice as fast, the force quadruples. Spin it faster and faster, eventually the outward force exceeds any material’s tensile strength. Chunks near the rim tear loose from the rest of the disk and it’s not a disk any more. Einstein imagined an infinitely strong disk that wouldn’t have that problem. In the kind of argument that good scientists love, Ehrenfest thought up a Special Relativity paradox that led Einstein to his big breakthrough.”

“A pair o’ docs, HAW!”

“Ha. Ha. We’ve talked about how Special Relativity says—”

“It’s gonna be frames again, ain’t it?”

“Relativity’s always about frames, Vinnie. Ehrenfest wrote that according to Special Relativity, the radius r of a disk doesn’t change when the disk rotates, but its circumference should be compressed to something smaller than 2πr which is non‑physical. Einstein replied that Ehrenfest had it backwards. In the disk’s rotating frame, you’d measure the circumference by seeing how many yardsticks you can pack around it.”

“Short yardsticks.”

“Millimeter-sticks, whatever. Einstein pointed out that when the disk spins, each yardstick gets shorter so you can pack in more yardsticks. Rotation doesn’t shrink the circumference, it expands it by warping space from a flat plane to a curved surface like a potato chip. Chasing that idea got him to curved space and General Relativity.”

~ Rich Olcott

  • Thanks to Alex, who asked the question.

Does Tomorrow Exist?

On By rolcottIn Cosmology, General: Fun Stuff, UncategorizedLeave a comment

Power’s back on. The elevator lets us out on the second floor where we proceed into Eddie’s Pizza Place. We order, find a table, and Cathleen cocks an eyebrow. “So, Anne, you’re a time‑traveler?”

“Lots of dimensions, actually. Time, space, probability… Once I accidentally jumped into a Universe where the speed of light was a lot slower. I was floating near a planet in a small system whose sun flared up but it took a long, long time for the flash to reflect off the planet behind me. Funny, I felt stiffer than usual. It was a lot harder to move my arms. I avoid cruising dimensions like that one.”

<The other eyebrow goes up> “Wait, what’s the speed of light got to do with dimensions? And why would it affect moving your arms?”

My cue. “Physics has a long‑standing problem with the speed of light and a dozen or so other fundamental numbers like Newton’s gravitational constant and Einstein’s cosmological constant. We can measure them but we can’t explain why they have the values they do. Okay, the speed of light depends on electric and magnetic force constants, but we can’t explain those, either — the rabbit hole just gets deeper. In practice, our Laws of Physics are a set of equations with blanks for plugging in the measured values. People have suggested that there’s a plethora of alternate universes with the same laws of physics we have but whose fundamental constants can vary from ours. Apparently Anne traveled along a dimension that connects universes with differing values of lightspeed.”

“I suppose. … But the arm‑moving part?”

“An effect of Special Relativity. Newton’s Second Law a=F/m says that an object’s acceleration equals the applied force per unit mass. That works fine in every‑day life but not when the object’s velocity gets close to lightspeed.” <jotting on a paper napkin> “I don’t see Vinnie nearby so here’s the relativistic equation: a=(F/m)×√[1–(v/c)²]. The v/c ratio compares object velocity to lightspeed. The Lorentz factor, that square root, is less than 1.0 for velocities less than lightspeed. This formula says a given amount of force per unit mass produces less acceleration than Newton would expect. How much less depends on how fast you’re already going. In fact, the acceleration boost approaches zero when v approaches c. With me?”

“If your factor’s exactly zero, then even an infinite force couldn’t accelerate you, right? But what’s all that got to do with my arm?”

“Zero acceleration, mm‑hm. Suppose your arm’s rest mass and muscle force per unit mass are the same in the slow‑light universe as they are in ours. The Lorentz factor’s different. Lightspeed in our Universe is 3×108 m/s. Suppose you wave your arm at 10 m/s. Your Lorentz factor here is √[1–(10/3×108)²] which is so close to unity we couldn’t measure the difference. Now suppose ‘over there’ the lightspeed is 20 m/s and you try the same wave. The Lorentz formula works out to √[1–(10/20)²] or about 85%. That wave would cost you about 15% more effort.”

<Both eyebrows down> “Have you tried going forward in time?”

“Sure, but I can’t get very far. It’s like I’ve got an anchor ‘here.’ I can move back ‘here’ from the past, no problem, but when I try to move forward from ‘here’ even a day or so … It’s hard to describe but as I go everything feels fuzzier and then I get queasy and have to stop. Do you have an explanation for that, Sy?”

“Well, an explanation but I can’t tell you it’s correct. Einstein thought it conflicts with Relativity, other people disagree. According to the growing block theory of time, the past and present are set and unchanging but the future doesn’t exist until we get there. Your description sounds like a build on that theory, like maybe the big structures extend a bit beyond us but their quantum details are still chaotic until time catches up with them. There are a few reports of lab experiments that would be consistent with something like that but it’s early days in the research.”

“As the saying goes, ‘Time will tell,’ right, Sy?”

“Mm-hm, lo que será, será.“

~ Rich Olcott

A Shot Through The Dark

On By rolcottIn Cosmology, General: Fun Stuff, UncategorizedLeave a comment

<THUNK!!> “Oh, dear. Is this the same elevator that you and Vinnie got trapped in, Sy?”

“Afraid so, Cathleen, but at least we had lights. This looks like a power outage, not a stuck door mechanism. Calling the building super probably won’t help. Hope you’re okay being stuck in the dark.”

“I’m an astronomer, Sy. A dark night’s my best thing. Remember the time we got locked with no light in my Mom’s closet?”

<chuckle> “Mm-hm. It was our pretend spaceship to Mars. We had no idea that closet had a catch we couldn’t reach. We were stuck there until your Mom came home. <sigh> We’ll have to wait ’til power comes back.”

<FZzzzzttPOP!!> … <then a voice like molten silver> “Oh, there you are, Sy! I’ve been looking all over for you. Who’s this?”

“Been a while, Anne. This is Cathleen. Cathleen, meet Anne. Anne’s an … explorer.”

“Ooo, where do you explore? For that matter, how did you get in here, and why is your dress (is it satin?) glowing like that?”

“Yes, it is satin, at the moment. It figures out whatever I need and makes that happen. It’s glowing because we’re in the dark.”

“I suspect your dress saved you when you met anti‑Anne.”

“Auntie Anne?”

“No, Cathleen, anti‑Anne, another me in the anti‑Universe. You might be right, Sy. It would have held anti‑Earth’s anti‑atoms away long enough for me to escape annihilation. Maybe I should explain.”

“I wish you would.”

“Wellll, I’ve got this super‑power for jumping across spacetime. Sy helped me calibrate my jumps and we even worked out how I can change size and use entropy to navigate between probabilities. So I explore everywhere and everywhen and that’s how I got into this elevator.” <brief fizzing sound> “Don’t worry, power will be back on soon but we’ve got time for Sy to explain my most recent experience.”

“Ah‑boy, now what?”

“Well, it seemed like a fun thing to do — go back to the earliest time I could, maybe even watch the Big Bang. I did some reading so I had an idea of what to expect as I dove down the time axis — gas clouds collapsing with glittering bursts of star formation, stars collecting into galaxies, galaxies streaming by like granular gas — so beautiful, especially because I can tweak my time rate and watch it all in motion!”

“And did you see all that?”

“Oh, yes, but then I hit a wall I couldn’t get past and I don’t understand why.”

“What were things like just before you hit the wall?”

“This was just beyond when I saw the very first stars turning on. There were vague clouds glowing here and there but basically the Universe became pitch black, no light at all for a while until the background started to glow with a very deep red just before I was blocked.”

“Ah. Cathleen, this is more your bailiwick than mine. Anne, Cathleen teaches Astronomy and Cosmology.”

“Just as a check, Anne, do you know exactly how far into the past you got?”

“Sorry, no. My time sense is pretty well calibrated for hours‑to‑centuries but this was billions of years. You probably know when I was better than I do.”

“On the evidence, I’d say you got 99.98% of the way back to your goal, nearly to the beginning of the Dark Age.”

“Dark Age? I’ve been there — 10th‑century Earth, bad times for everyone unless you were at the top of the heap but you wouldn’t stay there long. But I was too far out in space to see Earth. I couldn’t even pick out the Milky Way.”

“No, this was the Universe’s Dark Age, a couple hundred million years between when atoms formed and stars formed. Nothing could make new light. The Dark Age started at Big Bang plus 370 000 years when temperature cooled to 4000 K. The dark red you saw everywhere was atoms emitting blackbody radiation at 4000 K. Just 0.01% further into the past, the Universe was a billion‑degree quark plasma where not even atoms could survive. No wonder your dress wouldn’t let you enter.”

<THUNK!!> “Oh, good, power’s back on. We have light again!”

~ Rich Olcott

A Cosmological Horse Race

On By rolcottIn Astronomy: Multi-messenger, Cosmology, Physics: Einstein, Physics: Electromagnetism, UncategorizedLeave a comment

A crisp Fall day, perfect for a brisk walk around the park. I see why the geese are huddled at the center of the lake — Mr Feder, not their best friend, is on patrol again. Then he spots me. “Hey, Moire, I gotta question!”

“Of course you do, Mr Feder. What is it?”

“Some guy on TV said Einstein proved gravity goes at the speed of light and if the Sun suddenly went away it’d take eight minutes before we went flying off into space. Did Einstein really say that? Why’d he say that? Was the TV guy right? And what would us flying across space feel like?”

“I’ll say this, Mr Feder, you’re true to form. Let’s see… Einstein didn’t quite prove it, the TV fellow was right, and we’d notice being cold and in the dark well before we’d notice we’d left orbit. As to why, that’s a longer story. Walk along with me.”

“Okay, but not too fast. What’s not quite about Einstein’s proving?”

“Physicists like proofs that use dependable mathematical methods to get from experimentally-tested principles, like conservation of energy, to some result they can trust. We’ve been that way since Galileo used experiments to overturn Aristotle’s pure‑thought methodology. When Einstein linked gravity to light the linkage was more like poetry. Beautiful poetry, though.”

“What’s so beautiful about something like that?”

“All the rhymes, Mr Feder, all the rhymes. Both gravity and light get less intense with the square of the distance. Gravity and light have the same kinds of symmetries—”

“What the heck does that mean?”

“If an object or system has symmetry, you can execute certain operations on it yet make no apparent difference. Rotate a square by 90° and it looks just the same. Gravity and light both have spherical symmetry. At a given distance from a source, the field intensity’s the same no matter what direction you are from the source. Because of other symmetries they both obey conservation of momentum and conservation of energy. In the late 1890s researchers found Lorentz symmetry in Maxwell’s equations governing light’s behavior.”

“You’re gonna have to explain that Lorentz thing.”

“Lorentz symmetry has to do with phenomena an observer sees near an object when their speed relative to the object approaches some threshold. Einstein’s Special Relativity theory predicted that gravity would also have Lorentz symmetry. Observations showed he was right.”

“So they both do Lorentz stuff. That makes them the same?”

“Oh, no, completely different physics but they share the same underlying structure. Maxwell’s equations say that light’s threshold is lightspeed.”

“Gravity does lightspeed, too, I suppose.”

“There were arguments about that. Einstein said beauty demands that both use the same threshold. Other people said, ‘Prove it.’ The strongest argument in his favor at the time was rough, indirect, complicated, and had to do with fine details of Earth’s orbit around the Sun. Half a century later pulsar timing data gave us an improved measurement, still indirect and complicated. This one showed gravity’s threshold to be with 0.2% of lightspeed.”

“Anything direct like I could understand it?”

“How about a straight‑up horse race? In 2017, the LIGO facility picked up a gravitational signal that came in at the same time that optical and gamma ray observatories recorded pulses from the same source, a colliding pair of neutron stars in a galaxy 130 million lightyears away. A long track, right?”

“Waves, not horses, but how far apart were the signals?”

“Close enough that the measured speed of gravity is within 10–15 of the speed of light.”

“A photo-finish.”

“Nice pun, Mr Feder. We’re about 8½ light-minutes away from the Sun so we’re also 8½ gravity-minutes from the Sun. As the TV announcer said, if the Sun were to suddenly dematerialize then Earth would lose the Sun’s orbital attraction 8½ minutes later. We as individuals wouldn’t go floating off into space, though. Earth’s gravity would still hold us close as the whole darkened, cooling planet leaves orbit and heads outward.”

“I like it better staying close to home.”

~ Rich Olcott

A No-Charge Transaction

On By rolcottIn Cosmology, Crazy Theories, Physics: Light and Relativity, UncategorizedLeave a comment

“I ain’t done yet, Sy. I got another reason for Dark Matter being made of faster‑then‑light tachyons.”

“I’m still listening, Vinnie.”

“Dark Matter gotta be electrically neutral, right, otherwise it’d do stuff with light and that doesn’t happen. I say tachyons gotta be neutral.”

“Why so?”

“Stands to reason. Suppose tachyons started off as charged particles. The electric force pushes and pulls on charges hugely stronger than gravity pulls—”

“1036 times stronger at any given distance.”

“Yeah, so right off the bat charged tachyons either pair up real quick or they fly away from the slower‑than‑light bradyon neighborhood leaving only neutral tachyons behind for us bradyon slowpokes to look at.”

“But we’ve got un‑neutral bradyon matter all around us — electrons trapped in Earth’s Van Allen Belt and Jupiter’s radiation belts, for example, and positive and negative plasma ions in the solar wind. Couldn’t your neutral tachyons get ionized?”

“Probably not much. Remember, tachyon particles whiz past each other too fast to collect into a star and do fusion stuff so there’s nobody to generate tachyonic super‑high‑energy radiation that makes tachyon ions. No ionized winds either. If a neutral tachyon collides with even a high-energy bradyon, the tachyon carries so much kinetic energy that the bradyon takes the damage rather than ionize the tachyon. Dark Matter and neutral tachyons both don’t do electromagnetic stuff so Dark Matter’s made of tachyons.”

“Ingenious, but you missed something way back in your initial assumptions.”

“Which assumption? Show me.”

“You assumed that tachyon mass works the same way that bradyon mass does. The math says it doesn’t.” <grabbing scratch paper for scribbling> “Whoa, don’t panic, just two simple equations. The first relates an object’s total energy E to its rest mass m and its momentum p and lightspeed c.”

E² = (mc²)² + (pc)²

“I recognize the mc² part, that’s from Einstein’s Equation, but what’s the second piece and why square everything again?”

“The keyword is rest mass.”

“Geez, it’s frames again?”

“Mm‑hm. The (mc²)² term is about mass‑energy strictly within the object’s own inertial frame where its momentum is zero. Einstein’s famous E=mc² covers that special case. The (pc)² term is about the object’s kinetic energy relative to some other‑frame observer with relative momentum p. When kinetic energy is comparable to rest‑mass energy you’re in relativity territory and can’t just add the two together. The sum‑of‑squares form makes the arithmetic work when two observers compare notes. Can I go on?”

“I’m still waitin’ to hear about tachyons.”

“Almost there. If we start with that equation, expand momentum as mass times velocity and re‑arrange a little, you get this formula

E = mc² / √(1 – v²/c²)

The numerator is rest‑mass energy. The v²/c² measures relative kinetic energy. The Lorentz factor down in the denominator accounts for that. See, when velocity is zero the factor is 1.0 and you’ve got Einstein’s special case.”

“Give me a minute. … Okay. But when the velocity gets up to lightspeed the E number gets weird.”

“Which is why c is the upper threshold for bradyons. As the velocity relative to an observer approaches c, the Lorentz factor approaches zero, the fraction goes to infinity and so does the object’s energy that the observer measures.”

“Okay, here’s where the tachyons come in ’cause their v is bigger than c. … Wait, now the equation’s got the square root of a negative number. You can’t do that! What does that even mean?”

“It’s legal, when you’re careful, but interpretation gets tricky. A tachyon’s Lorentz factor contains √(–1) which makes it an imaginary number. However, we know that the calculated energy has to be a real number. That can only be true if the tachyon’s mass is also an imaginary number, because i/i=1.”

“What makes imaginary energy worse than imaginary mass?”

“Because energy’s always conserved. Real energy stays that way. Imaginary mass makes no sense in Newton’s physics but in quantum theory imaginary mass is simply unstable like a pencil balanced on its point. The least little jiggle and the tachyon shatters into real particles with real kinetic energy to burn. Tachyons disintegrating may have powered the Universe’s cosmic inflation right after the Big Bang — but they’re all gone now.”

“Another lovely theory shot down.”

~ Rich Olcott

Got To Be Good-lookin’ ‘Cause He’s So Hard To See

On By rolcottIn Cosmology, Crazy Theories, UncategorizedLeave a comment

I’ll be sorry when Acme Building’s management swaps out our old‑style door locks for electronic ones. Vinnie has such fun lock‑picking his way past my office door in the morning. “Morning, Vinnie.”

“Morning, Sy. Hey, I got a new Crazy Theory for you. Nobody knows what Dark Matter is, right?”

“Right. All we know is that it has about five times as much mass as normal matter so it participates in gravitational interactions. Some of it seems to gather in spherical halos around galaxies and some of it seems to collect in spikes near their centers. Cosmologists are arguing about whether or not Dark Matter is particles, much less how they’d be quantized. And we call it Dark because it absolutely doesn’t care about electromagnetism.”

“That’s what I thought. I remember you said if Dark Matter did play with light waves at all it’d block our view of the CMB. So yeah, absolute. Good.”

“I gather your theory is about Dark Matter.”

“Mm-hm. I thought of a way that all that mass could be hiding in plain sight except we can’t see it.”

“Alright, I’m listening.”

“Tachyons.”

“Come again?”

“Tachyons — particles that fly around faster than light. I read an article about ’em. Some people say they can’t exist but hear me out, okay? The reason they’re not supposed to exist is ’cause it would take an infinite amount of energy to boost something up past lightspeed. I got that, but suppose they were born above lightspeed, back when the Big Bang singularity had energy packed so tight the Physics laws we know don’t apply. A lot of particles got flung out below lightspeed, but maybe even more got flung out above it.”

“What does this have to do with dark matter?”

“I’m gettin’ there. The thing with tachyons is, the article said it’d take infinite energy to slow one down to lightspeed. A tachyon rock hits a slow rock, it don’t stop ’cause the slow rock don’t have the juice for that. The collision may take a little energy from the tachyon rock but that just changes its trajectory.”

“Mmm, those tachyon rocks can’t be a thing. The — what can I call it? slow matter?”

“The article called ’em bradyons.”

“Thanks. We know that 92% of all … bradyonic atoms in the Universe are hydrogens. Rocks are made of silicon, oxygen and other atoms that are even heavier. Everything heavier than hydrogen and maybe some helium was created by nuclear reactions inside a star. Tachyonic atoms zooming beyond lightspeed couldn’t gather together to form a star or even join one. No significant tachyonic fusion, no tachyonic rocks.”

“Okay, they all stay tachy‑hydrogen, still not a problem. The point is, there could be a lot of them and they could add up to a lot of mass. So the next thing I asked is, where would tachyons hang out? Gotta be around galaxies, but being tachyons going super‑lightspeed they can’t just hang, they orbit around the centers. They’d spend the most time where they go slowest which is where they’re farthest away ’cause that’s how orbits work. But they’d be thickest close in ’cause of gravity but that’s where they go fastest.”

“Cute, so you’re predicting galaxies with halos of tachyons, plus spikes of them at each center. That just happens to be the dark matter distribution the astronomers find.”

“It gets better, Sy. I’m not so sure of this because math, but it feels right. I don’t think tachyons can do electromagnetism things.”

“Why not?”

“No blue glow — you know, that blue glow in nuclear reactors when electrons go through the cooling water faster than light?”

“Cherenkov radiation, happens when fast electrons polarize the water. The polarizing slows light in water relative to a vacuum.”

“Right, but tachyons in space travel through vacuum. They ought to polarize the vacuum like what fast electrons do to water. Electromagnetic tachyons orbiting galaxies ought to make a blue glow but there isn’t one, so tachyons don’t do electromagnetism things and that makes them Dark Matter.”

“You’re going to have to do better than that, Vinnie. Absence of evidence just might be evidence of absence. Maybe they’re not there to begin with.”

~ Rich Olcott

Properties of Space

On By rolcottIn Cosmology, Physics: Electromagnetism, Physics: Waves, UncategorizedLeave a comment

Vinnie gives me the side‑eye. “Wait, Sy. Back there you said Maxwell got the speed of light from the properties of space. What does any of that even mean?”

“Do you remember Newton’s equation for the force of gravity between two objects?”

“Of course not. Lessee… the force’d be bigger when either one gets bigger, and it’d get smaller when the distance between ’em gets bigger and there’s some constant number to make the units right, right?”

“Close enough, it’s the distance squared. The equation’s F=Gm1m2/r². The G is the constant you mentioned. It does more than turn mass‑units times mass‑units divided by length‑units‑squared into force‑units. It says how many force‑units. For one pair of objects at a certain distance, turn the G‑dial up and you get more force. Make sense?”

“Yeah, that looks right.”

“The value of G sets the force‑distance scale for how two objects attract each other everywhere in the Universe. That value is a property of space. So is the fact that the value is the same in all directions.”

“Huh! Never thought of it like a scale factor. Space has other properties like that?”

“Certainly. Coulomb’s Law for the electrostatic force between two charged objects has the same basic structure, FE=–(q1q2/r²)/CE. In any units you like you replace the q‘s with object charge amounts and r with the distance between them. For each set of change‑ and distance‑units there’s a well‑researched value of CE to convert your charge and distance numbers into force‑units. Under the covers, though, CE is a scale factor that controls the range of the electrostatic force. It’s the same everywhere in the Universe and it’s completely independent of Newton’s gravity scale factor.”

“Hey, what about ‘like charges repel, opposites attract’?”

“That’s what the minus sign’s in there for. If the q‘s have the same charge, the force is negative, that’s repulsion; opposite charges make for positive, attractive force.”

“If there’s a CE for electric there’s gotta be a CM for magnetic.”

“Sort of. The electrostatic force doesn’t care about direction. Magnetism does care so the equation’s more complicated. You’re right, though, there is a similar universal scale factor we might as well call CM.”

<chuckle> “Electric, magnetic, I don’t suppose we could mix those two somehow for an electromagnetic scale factor?”

<grin> “Did you read ahead in the book? Yes we can, and Maxwell’s equations showed us how. If you multiply the two C‘s together, you get one over the square of the speed of light. Re‑arranging a little, c=√(1/CECM), so c, the electromagnetic scale factor for velocity, is based on those space properties. Einstein showed that no material object can have a velocity greater than c.”

“I’ll take your word for the arithmetic, but how does that combination make for a speed limit?”

“There’s an easy answer you’re not going to like — it’s a speed because the units come out meters per second.”

“That’s a cheat. I don’t like it at all and it doesn’t account for the limit part. Explain it with Physics, no fancy equations.”

“Tough assignment. Okay, typical waves have a displacement force, like wind or something pushing up on an ocean wave, that works against a restoring force, such as gravity pulling down. Electromagnetic waves are different. The electric component supplies the up force, but the magnetic component twists sideways instead of restoring down. The wave travels as a helix. The CE and CM properties determine how tightly it spirals through space. That’s lightspeed.”

“And the limit part?”

“Einstein maintained that anything that happens must follow the same rules for all observers no matter how each is moving. The only way that can be true is if space is subject to the Lorentz contraction √[1-(v/vmax)²] for some universal maximum speed vmax. Maxwell’s electromagnetism equations showed that vmax is c. Okay?”

“I suppose.”

~ Rich Olcott

  • * Vinnie hates equations even with regular letters, Greek letters make it worse. Hence my using CE and CM instead of the conventional ε0 and μ0 notation. Sue me.

Squaring The Circle

On By rolcottIn Cosmology, UncategorizedLeave a comment

Vinnie gives me the eye. “That crazy theory of yours is SO bogus, Sy, and there’s a coupla things you said we ain’t heard before.”

“What’s wrong with my Mach’s Principle of Time?”

“If the rest of the Universe is squirting one thing forward along Time, then everything’s squirting everything forward. No push‑back in the other direction. You might as well say that everything’s running away from the Big Bang.”

“That’s probably a better explanation. What are the couple of things?”

“One of them was, ‘geodesic,‘ as in ‘motion along a geodesic.‘ What’s a geodesic?”

“The shortest path between two points.”

“That’s a straight line, Mr Moire. First day in Geometry class.”

“True in Euclid’s era, Jeremy, but things have moved on since then. These days the phrase ‘shortest path’ defines ‘straight line’ rather than the other way around. Furthermore, the choice depends on how you define ‘shortest’. In Minkowski’s spacetime, for instance, do you mean ‘least distance’ or ‘least interval’?”

“How are those different?”

“The word ‘distance’ is a space‑only measurement. Minkowski plotted space in x,y,z terms just like Newton would have if he could’ve brought himself to use René Descartes’ cartesian coordinates. You know Euclid’s a²+b²=c² so you should have no problem calculating 3D distance as d=√(x²+y²+z²).”

“That makes sense. So what’s ‘interval’ about then?”

“Time has entered the picture. In Minkowski’s framework you handle two ‘events’ that may be at different locations and different times by using what he called the ‘interval,’ s. It measures the path between events as
s=√[(x²+y²+z²)–(ct)²]. Usually we avoid the square root sign and work with s².”

“That minus sign looks weird. Where’d it come from?”

“When Minkowski was designing his spacetime, he needed a time scale that could be combined with the x,y,z lengths but was perpendicular to each of them. Multiplying time by lightspeed c gave a length, but it wasn’t perpendicular. He could get that if he multiplied by i=√(–1) to get cti as a partner for x,y,z. Fortunately, that forced the minus sign into the sum‑of‑squares
(x²+y²+z²)–(ct)² formula.”

Vinnie’s getting impatient. “What is an actual geodesic, who cares about them, and what do these equations have to do with anything?”

“A geodesic is a path in spacetime. Light always travels along a geodesic. The modern version of Newton’s First Law says that any object not subject to an outside force travels along a geodesic. By definition the geodesic is the shortest path, but you can’t select which path from A to B is the shortest unless you can measure or calculate them. There’s math to tell us how to do that. Time’s a given in a Newtonian Universe, not a coordinate, so geodesics are distance‑only. We calculate d along paths that Euclid would recognize as straight lines. That’s why the First Law is usually stated in terms of straight lines.”

“So the lines can go all curvy?”

“Depends, Vinnie. When you’re piloting an over‑water flight, you fly a steady bearing, right?”

“Whenever ATC and the weather lets me. It’s the shortest route.”

“So according to your instruments you’re flying a straight line. But if someone were tracking you from the ISS they’d say you’re flying along a Great Circle, the intersection of Earth’s surface with some planar surface. You prefer Great Circles because they’re shortest‑distance routes. That makes them geodesics for travel on a planetary surface. Each Circle’s a curve when viewed from off the surface.”

“Back to that minus sign, Mr Moire. Why was it fortunate?”

“It’s at the heart of Relativity Theory. The expression links space and time in opposite senses. It’s why space compression always comes along with time dilation.”

“Oh, like at an Event Horizon. Wait, can’t that s²=(x²+y²+z²)–(ct)² arithmetic come out zero or even negative? What would those even mean?”

“The theory covers all three possibilities. If the sum is zero, then the distance between the two events exactly matches the time it would take light to travel between them. If the sum is positive the way I’ve written it then we say the geodesic is ‘spacelike’ because the distance exceeds light’s travel time. If it’s negative we’ve got a ‘timelike’ geodesic; A could signal B with time to spare.”

~ Rich Olcott