GENERAL & SPECIAL RELATIVITY

Since Einstein said that E=mc2 , why does a massless photon have energy?


Someone asked a similar question on Quora. My answer garnered nearly a million views and many dozens of comments. It gave me an opportunity to gather thoughts on a subject that has puzzled folks for decades.



Of course, I’m a pontificator, not a scientist. I got advice from working physicists and incorporated what they taught me.

One thing I learned from science writer Jim Baggott is that Einstein first published his famous equation in this form: 

M = \frac{E }{ C^2}

When written this way, it becomes clear that anyone who knows the total energy of anything can calculate in principle its total mass.

Einstein knew nothing at all about the Higgs field but today physicists agree that the mass it creates is less than 5% of what mass they have discovered. 

In fact, nearly 99% of the mass of a single proton is derived from the energy of “massless” gluons that constrain its two up-quarks and one down-quark. Gluons are bosons which don’t interact with the Higgs field; quarks, which are fermions, do.  

In the end, it’s all about energy, which it turns out is equivalent to mass, which according to Baggott is what quantum fields do. Quantum fields like the Higgs field make mass. Perhaps the electromagnetic field — which makes photons — does the same. 

Here is Einstein’s equation for energy:

E^{2}=\left ( mc^{2} \right )^{2} +\left (pc \right )^{2}

Since

p=\frac{hf}{c} 

and

m=\frac{hf}{c^2}

it follows that it might be reasonable to imagine that photons have both internal mass and inertial mass, which causes Einstein’s equation for energy to give the following result:

E=\sqrt2 ({hf})

All that is left is to divide by c2 to get mass, right? 

m=\sqrt2 (\frac{hf}{c^2})

Most folks think the internal mass of a photon is zero. Period. End of story. They use the two mass and momentum terms in Einstein’s equation to calculate total energy of massive objects, yes, but photons, they insist, lack internal mass. They lack the internal fermionic structures associated with all massive particles.

Photons do have inertial energy proportional to their critical frequency though, which suggests that they possess perhaps equivalent inertial mass, which drives the photoelectric effect.

When physicists take the energy measure of photons, they drop the mass term in Einstein’s equation. They set mass to zero and cancel out the first term, mc2.  It leaves the second term — pc — which for photons simplifies to hf, inertial energy correlated to frequency, right? Energy can be measured in eVs, electron-volts, which are also units of mass. 

If photons have internal energy, their total energy in the universe is undervalued by 1.414 (the square root of 2). Accounting for this added mass reduces the Cosmic energy deficit to near zero. 

PHOTON MASS

I should add that overestimating mass and disrupting popular models of the Cosmos is something most scientists think is a bad idea. 

The gluon is the only other massless particle currently in the standard model, but it has never been observed as a free particle. All gluons are buried inside hadrons. It is their binding energy in quarks that makes as much as 99% of the measured mass of protons and neutrons. 

So, there is precedent to possibly reevaluate mass equivalence of photons. 

Some readers might wonder about the massless graviton. This particle is theorized to exist, yes, but has not been observed or added to the Standard Model.  The same is true for dark matter and dark energy — no physical evidence; not added to the Model.

It doesn’t mean dark energy and matter don’t exist. Cosmologists see way too much gravity everywhere they look. The problem is they can’t explain exactly what is causing it. 



As for my answer to the original question published on Quora, it was as accurate as my limited experience could make at the time, but the subject is controversial and several issues are not yet settled, even by experts. Some disputes might never be settled.

Who knows? 

Not me. I’m a pontificator, right?


Added March 25, 2025:

ATTENTION READERS:
Recently, FloatHeadPhysics, the YouTube channel, added best intuitive visualizations for General Relativity we’ve yet seen. 

Enjoy!
THE EDITORS


What follows is a version of my Quora answer:


You might be mistaken about energy.

According to the complete statement of Einstein’s most well-known equation, energy content is a combination of a particle’s mass and its momentum. The equation you cite is abbreviated. It is a simplified version that is missing a term.


Einstein’s complete equation is strangely analogous to Pythagoras’s geometry of right-triangles. When anyone thinks about it though, aren’t the frequencies of light at right angles to its propagation? Light waves are transverse, right? 

Here is a more complete version of Einstein’s equation:

E^{2}=+\left ( mc^{2} \right )^{2} + \left (pc \right )^{2}

—where m is internal mass and ρ is momentum. Internal mass is often referred to as “rest mass” because it is invariant in all reference frames and unchanged by velocity or acceleration. Momentum is inertial energy measured in equivalent mass units called electron volts (eVs). 

Massless particles like photons have momentum that is correlated to their wavelengths (or frequencies). It’s their frequencies that give massless particles like photons their energy content. So without (rest) internal mass the equation becomes:

E=ρc

—where  p=\frac{hf}{c} for massless photons.

So, E = hf 

[“h” is Planck’s constant. f” is frequency. “c” is light speed.]



Of course, in classical Newtonian physics ρ = mc. The mass term is critical.


Screen shot from Khan Academy showing derivation of photon momentum. Typed mark-ups by me show mass equivalence when ρ is set equal to mc. When mc = hf/c, then m = hf/c*c, right? Click the pic for a better view in a new window. 

On the other hand, in quantum mechanics the total mass of photons cannot be zero either—photon internal mass is set equal to zero and eliminated. Inertial energy based on the photon’s critical frequency (the 2nd term in Einstein’s equation) becomes its equivalent mass. I’m not sure everyone agrees. 

The beauty created by setting photon rest-mass (internal energy) to zero is it transforms the maths of relativity and quantum mechanics into structures that seem to be consistent and complete — able, one hopes, to meld into theories of everything; TOEs, if you like. The problem, of course, is that the convention of setting to zero leaves thrashing in its wake 95% of the mass and energy which “other” stories claim is hidden unseen “out there” within and around galaxies to move them faster than they ought. 

The Abraham-Minkowski controversy seems to touch the argument.  Click the link and scroll to the end of the article to learn how many things are disputed, not known, or unexplained. The science is not settled, although several physicists claim that the controversy is resolved by postulating an interaction inside dielectrics (like glass) of photons with electron-generated polaritons.  


NOTE BY EDITORS: On 18 April 2021 a writer massively abbreviated and modified the article in Wikipedia on the A-M controversy. The writer deleted the entire list of disputed claims. Please click the link in this sentence to review a list of unsolved problems in modern physics. Photon mass inside dielectrics isn’t on the list. 


The permittivity of “empty“ space (called the electric constant) qualifies as a dielectric, does it not? Isn’t space itself—with its Maxwell-assigned permeability (the magnetic constant) and permittivity (electric constant)—a dielectric?

Arthur Eddington wrote in chapter 6 of his book Space Time and Gravitation (read pages 107-109) that the dielectrics of space around the Sun increase proportionally with the intensity of the gravitational field. Light waves closest to the sun slow down more, which pulls the wavefront that lies farther out to deflect still more to catch up. Like glass, gravity refracts light.

Light falls into the Sun like any solid rock, but refraction adds to light’s “Newtonian” deflection to give Einstein’s predicted result. Unlike slow rocks, light travels fast enough to avoid capture by the sun. 

It’s not clear to me how many physicists agree with Eddington, but then again, it’s not obvious whether humanoids are able to visualize reality. It’s one thing to write equations and symbolic algorithms that match well with observations. It’s quite another to acquire a natural intuition for what might be true. 

Empty space isn’t empty, right?

As for the Abraham-Minkowski dispute: how important might it be to decisively resolve ambiguities concerning photon mass?

Perhaps the dispute is swept under a rug because disagreements about something as fundamental as photon mass mean that physicists might know less than they let on. The controversy seems to me at least to have the potential to crash the tidy physics of light and mass built by hard work and much history.

Isn’t it better to pretend everything is just fine until physicists finally agree that everything really is?

Maybe the subject involves some aspect of national security which requires obfuscation. It wouldn’t be the first time. 

What I think can be safely said is that momentum and mass of quantum objects seem to have no meaning until they are brought into existence by measurements. The math looks like nothing we know; sometimes physicists use the results as mathematical operators that don’t commute the way some might think they should.


PHOTONS AND GRAVITY

I reviewed the math.  I saw the term that makes the deflection difference (it’s really there) but did not understand enough at the time to tease out a satisfying reason why photons seem to bend nearly twice more in a gravitational field than early acolytes of Newton conjectured. I guess I like Eddington’s explanation best. 

According to Wikipedia, Einstein’s theory approximates the deflection to be:

\frac{4GM}{(c^2)b}

“b” is the distance of a photon’s closest approach to a gravitational object like our Sun.

Here’s some guesses I made before reading Eddington:

Maybe light deeply buried in a gravity field near a star like the Sun will experience the flow of time more slowly—it’s an effect common to all objects in a gravity field; it affects all objects the same way and is unaffected by their mass or lack of it.

It might have something to do with Schwarzchild geodesics. The geodesics of spacetime paths are longer and more curved in a gravity field than what anyone might expect from a simple application of Newton’s force law, which is oblivious to the spacetime metrics of Einstein. 

Schwarzchild metrics help to explain the “gravitational lensing” of faraway objects when their light approaches Earth from behind massive gravitational structures in the far reaches of space. Light careens around the structures so that astronomers can see what would otherwise remain forever hidden from them. 



Here is another guess:

It might be that light spends more time in a gravitational field than it should due to special-relativity-induced time dilations so that photons have more time to fall toward the star than they otherwise would. This guess is certainly wrong because the time differential would be governed by a Lorentz transformation.

Photons of light don’t undergo Lorentz transformations because, unlike massive objects that travel near the speed of light, they don’t have inertial frames of reference. Any line of reasoning that ties Lorentz transformations to photons leads folks into rabbit holes that contradict the current consensus about the nature of light. Light speed is a constant in all reference frames. Space and time expand and shrink to accommodate it. 

Electron-like muons (which have rest masses 205 times that of electrons) are short-lived, but their relativistic speeds increase their lifetimes so that some of those that get their start in the upper atmosphere are able to reach Earth’s surface where they can be observed. Their increased lifespan is described by a Lorentz transformation. It’s tempting to apply this transform to photons, but theorists say, no. It doesn’t work that way.

Time contractions and dilations are Special Relativity effects that apply to objects with inertial mass that move in some specified reference frame at velocities less than the speed of light, yes, but never at the speed of light, right?

Nearly every physicist will insist that photons have no internal mass; they travel in vacuum at exactly the speed of light—from the point of view of all observers in every reference frame. Photons don’t have inertial reference frames in the same way as muons or electrons.

Changes in time and position caused by a photon’s location in a gravity field are completely different; they are described by a vastly more complicated theory of Einstein’s called General Relativity.

Here is one way to write his formula:

The terms in this expression are tensors, most of them. Click the link, anyone who doesn’t think tensors are difficult to write and manipulate. 



Here is another way to think about photon energy and behavior:

Light follows the geodesics of spacetime near a massive object—like the sun. Gravity is the geodesic.

The difference for massive objects traveling at relativistic speeds is that their momentum and inertia enable them to skip off the geodesic tracks, so to speak.

Because massive objects always travel at speeds less than light, their “clocks” slow down through an additional dynamic (a Lorentz transformation) that works at cross-purposes to gravity. Massive objects lock onto the gravity geodesics for a shorter period of time. They undergo less gravitational time dilation than does light because they spend less time constrained on its geodesics. They jump the geodesic tracks to become constrained by the dynamics of the Lorentz transformations. 

The result is that massive objects traveling at relativistic velocities less than light deflect less toward the star (Sun) than does light.

What makes General Relativity unique is it’s view that gravity and acceleration are equivalent. Acceleration is a change in the velocity and/or the direction of motion. Massive bodies such as stars curve and elongate the pathways that shape the space and time around them.

Photons traveling on these longer spacetime paths accelerate by their change in direction, but their velocity doesn’t change in any reference frame. Something has to give. What gives, what changes is the expected value of deflection. The light from distant stars bends more than it should.


SOME HISTORY

No one who lived before 1900 could know that the geodesics of space-time elongate (or curve) in the presence of mass and energy, which are equivalent, correct? No one in bygone eras could have known that time slows down for massive objects that approach light-speed, either.

A man named Joann Georg Soldner did a calculation to show how much a Newtonian “corpuscle” of light would bend in the Sun’s gravity, which he published in 1804. He assumed that photons had mass and fell toward the Sun like any other object.

When Arthur Eddington’s observations showed that starlight deflected more than Soldner had calculated, Einstein’s theories of relativity got a boost in credibility that lives on into modern times.

I should add that Eddington knew about Einstein’s predictions when he made his experimental observations in 1919 because Einstein had already published his general theory.


EXPLANATIONS

I would very much like to read a coherent, verbal (non-mathematical) explanation of exactly why and how Einstein’s general theory can lead to an accurate and reasonable prediction at odds with Newton about the angle of deflection of photons near a star.

Here is a synopsis of an explanation that I heard from a working physicist:

Soldner used Newton’s view to calculate deflection using only the time the photon spent in the gravitational field. Einstein did the same but then modified his calculation to account for the bending of space in the gravitational field. The space component nearly doubled the expected deflection.

The theorist’s explanation satisfied me. It sounded right.


Notice the speed of the hands on the clocks and how they vary in space-time. Clocks slow down when they are accelerated or when they are immersed in the gravity of a massive object like the star at the center of this GIF. Stronger gravity makes clocks run slower. Under General Relativity, gravity and acceleration do the same thing. Click on the pic for a better view.

On the other hand, I believe (secretly and in agreement with Newton’s acolytes) that photons must have a mass equivalence that for some reason is being discounted, but no one I’ve read believes the idea makes sense beneath the shadow of a relativity theory that has the reputation for being fundamental, flawless, and complete.

After all, the mass of any object in a gravitational field is irrelevant to its trajectory because the mathematics cancels it, right?

F=ma=\frac{GMm}{r^2}

Little “m” appears on both sides of the equation so it can be divided away.

The problem is that the equations for gravity—especially over cosmological distances—are not necessarily settled. These are serious anomalies that are not yet resolved to everyone’s satisfaction. Some have direct consequences on the ability of organizations like NASA to conduct accurate landings on Mars and the Moon. Click the link in this paragraph to review six of the biggest puzzles followed by seventeen alternative theories designed to bring the discrepancies to account. 

Anyway, mass-energy equivalence of photons might permit Lorentz transforms on light to help to resolve certain problems in cosmology and the transmission of light through medias where gravity is not a factor. It might also simplify understanding of annoying Shapiro effects, which slow down communications with explorer craft inside our solar system.


ANOTHER EXPLANATION

Since I haven’t yet found a good explanation—and with a promise to avoid nonsensical personal predispositions—here is my attempt to explain:

In GPS (Global Positioning Systems), dilations of time—in both the velocity of satellites in one frame and their acceleration in another frame (gravity)—must add to provide accurate information to vehicles located in another frame.

These time dilations can work at cross-purposes. It requires expensive infrastructure on the ground to coordinate the information so that drivers of vehicles don’t get lost.

A massless object moving at the speed of light is going to follow the geodesics of the gravity field. This field is a distortion of space and time induced by the presence of the mass of something big like the Sun.

If massless energy does not obey the laws of Special Relativity (like GPS satellites do), then its velocity must necessarily have no influence whatever in the deflection of light near a star. It might seem like all the deflection comes from the distortion of spacetime, which is gravity.

Photons ride gravity geodesics like cars on a roller coaster. According to appendix III in Einstein’s 3rd edition of his book, Relativity, the Special and General Theory—published in English by Henry Holt & Company in 1921—it’s only half the story.

The other half of the measured deflection comes from the Newtonian gravitational “field”, which accelerates all objects in the same way. This field further deflects light across the spacetime geodesics toward the sun to double the expected angle.

I’m not entirely convinced that modern 21st century physicists believe it’s quite that way or quite that simple.



CONCLUSION

The theory of general relativity helps theorists to describe the distortion of metrics in spacetime near massive bodies to predict the deflection angle of passing photons of light. What we know is that predictions based on the theory don’t fail.

It’s like the theory of quantum mechanics. It never fails. It’s foundational. No one has yet been able to explain why.

Somebody, please, tell me I’m wrong.

Here is a link that addresses the math concerning the deflection disparity between Newton and Einstein.

Billy Lee


Link to comments on Quora

Readers interested in this subject will learn things from the material in these comments, I promise. 

Billy Lee 

LAST GASPS

As my Quora readership inches closer to 500,000 views, more admins are asking me to become a contributor to their spaces.
 
On Quora, a half-million views is almost nothing, but for me personally it seems like a lot. I’ve had answers throttled and in some cases pulled-down for violating rules that no one can explain. Fortunately, I’ve successfully appealed every take-down. 
 
I live in fear that  Quora will one day “disappear me” as so often happens to controversial people on other social sites. Whatever sites like Twitter, Facebook, and Quora are about, freedom of speech does not seem to be one of their core values, at least to my way of thinking. 
 
Isn’t it obvious?
 
Social media is run in the main by faceless administrators who have hidden agendas; they don’t abide by any First Amendment in any Constitution anywhere in the world.  
 
Because pontificators have an expectation that they will be allowed to express themselves freely on the internet, we play along while the sites we promote use us in ways we don’t understand. Admins don’t seem to want to come clean. When was the last time any administrators explained themselves when not under threat of subpoena? 
 
Some observers of social media say it’s about money; others say it’s about political persuasion to the far right or to the middle or away from the far left; others say it’s service to intelligence agencies who experiment to throw elections. 
 
Who really knows? 
 
The following questions are among the several dozen I addressed on Quora.com during the last of the 2019 winter holidays. The questions and answers are mostly about science and politics. I threw in a couple about Jane Fonda; she’s controversial in some spaces.
 
Billy Lee
 
Disclaimer:  Billy Lee is a pontificator, not an expert.  The people who read, upvote, and share his answers don’t care.  The Editorial Board 
 

1 – From the point of view of those who live on planets at the “edge” of the observable universe, would the diameter of their observable universe differ from how we on Earth view the diameter?
 

If we live in a multiverse, the folks at the periphery who look away will likely see universes like ours that emit EM radiation. Those universes that don’t broadcast electromagnetically will be as invisible as dark matter, which many believe makes 85% of the stuff that lies all around.

Presumably, universes look different than stars or galaxies; observers at the periphery might be able to tell the difference.



Some conjecture that universes are nothing more than black holes, which together form an infinite foam that flows perhaps to infinity.

Inside each black universe are more black holes which house black holes that contain more black holes and on and on in a progression that pushes holes to infinity like the reflections in funhouse mirrors.

Black holes emit Hawking radiation, which means they glow in the dark of space. Perhaps it is Hawking radiation observers at the peripheries will learn to detect, measure, and catalogue as they study a multiverse humans will never see.

Sadly, Earthlings are buried somewhere inside an enormous place at least 93 billion light years across. The periphery of this vast expanse is pushing outward at 7 times the speed of light.

We can’t see to the edge of our own universe; we have no way to observe universes that lie beyond the reach of our telescopes—should more than one be “out there.”

Observers at the periphery should know things about the nature of reality that Earthlings can only guess. They see beyond our peripheries.

But isn’t it also true that we know things they don’t? Because of our more “central” location we understand better than those at the peripheries what the size and age of the universe must be.

Maybe. 

If we could only collaborate with the Peripherans to share what we’ve learned. Laws of physics make a forever prison that walls away the truth of all that goes lost beyond the boundaries of human sensors.

2 – Do all EM waves travel at the speed of light?
 

It’s not entirely clear that what astrophysicists call vacuum is in fact empty.



The conjecture that 95% of the universe is not electromagnetically active but is active gravitationally should be kept in mind because light bends and decelerates in the presence of gravity. The best known example is black holes, which divert and trap photons.

Are there volumes of space inside the Universe where the conjectured dark energy and dark matter don’t reside? If so, does the speed of light increase or decrease inside these volumes?

Light slows as it passes through materials like glass. Some kinds of glass slow photons by as much as 40%.

One explanation is that photons excite electrons as they pass over and through the molecules and atoms that make glass. Because photons passing through are not necessarily at frequencies resonant with the electrons in the glass, electrons are unable to absorb enough energy to jump from one energy state to another. Instead, they vibrate just enough to emit polaritons, which impede photons like a pool of molasses impedes dropped pebbles.

The photons of light seem to acquire mass as their velocity decreases. When the photons exit glass they again go “massless” and resume lightspeed instantly.

Could a phenomenon similar to that of glass be typical of the space inside the Milky Way Galaxy where planet Earth resides? If so, what everyone thinks they know about EM waves and the isotropic nature of the Universe might need some tweaking.  

If it turns out that despite the consensus of science, photons do indeed contain a small amount of mass, they might have enough in aggregate to account for the curious behavior of galaxies. Conjectures about the invisible dark no one can see might not be necessary.

EM Mass?

3 – If the universe is expanding faster than light, how can we currently withstand that kind of speed but we can’t if we replicate it under our current conditions? Is it a matter of relativity? Am I misunderstanding something?
 

If this distance is scaled down to equal the circumference of Earth, the expansion will measure about one-tenth of a mile per year. Over a human lifetime the expansion will measure 8 miles. No ordinary non-scientist will notice the difference at this scale.

The universe is at least 93 billion light-years across. Do the math to see that space is expanding from one side of the universe to the other at 7 times the speed of light.

But some perspective is in order.  Inside the Milky Way Galaxy, which is roughly 100,000 light years across, the expansion is a mere 1.4 miles-per-second. Remember: a light year is almost 6 trillion miles. The Milky Way is almost 600,000 trillion miles across. 1.4 miles-per-second is practically nothing.

The nearest star to the Sun, Proxima Centauri, is 4.5 light years away—26 trillion miles. In one year the space between us and it expands by less than 2,000 miles. Meanwhile, the star itself is moving away from our Sun 200,000 times faster—about 12 miles-per-second. The expansion of space accounts for almost none of the separation.

Force is a measure of mass accelerating, right? Mass is not really accelerating due to the expansion of space. Space is puffing up like a loaf of raisin-bread in an oven. The raisins (galaxies) get carried along by the expansion.

The light that travels between stars and galaxies stretches into redder wavelengths as the loaf grows. But forces accelerating galaxies and stars are almost entirely due to masses acting over distances too short for the expansion of space to have any more than a statistically negligible effect.

The expansion of space adds up over larger and larger distances to become enormous, yes, but in the much smaller volumes of space where a few dozen or so galaxies live the gravity-induced distortion of spacetime by mass overwhelms it, at least for now.

4 – What existed before the Big Bang? Was there always something? How did the universe come into being from nothingness? Is God a possibility?
 

Currently, I favor the idea by Roger Penrose and others called Conformal Cyclic Cosmology (CCC). The basic idea is that a sufficiently old and expanded universe will lose all its mass through evaporation out of black holes; the metrics of spacetime become indistinguishable from a singularity, because without mass, spacetime is meaningless.

The universe puffs along like smoke from a choo-choo train—each universe emerges in a kind of “big bang” from the dying gasp of the last.

In this scenario, the universe is eternal backward and forward in time. It has no beginning or end; it has EONS that last trillions of years and endlessly repeat. The universe never collapses; it expands. When its mass evaporates into energy, it triggers a new expansion that generates in its wake new matter and gravity to provide the metrics necessary for spacetime to once again emerge.

This idea does not rule out the possibility of God, but it doesn’t support the idea either.

It also doesn’t rule out the possibility that humans live inside a simulation.

Smart thinkers like Nick Bostrom have argued that the statistical probability of a simulated universe approaches certainty. If so, humans can’t know what the underlying reality is that enables a simulation like ours to be created and sustained.

Such a state of affairs opens the possibility that we are created and accountable to a creator of worlds who has its own reasons for doing things, which aren’t necessarily ones we can understand.

The hard problem of consciousness is a clue for those who believe the universe comes first and consciousness second that they might have the order reversed. The possibility that conscious life is fundamental and foundational is something folks might want to keep in mind.

FAKED LIFE

CONSCIOUS LIFE

5 – Does Lawrence Krauss believe in an infinite number of universes?
 

I don’t know.

Alan Guth is the most prominent voice for this conjecture.



Evidence for B-Mode polarization of gravity waves would support the idea that cosmic inflation is likely to be unstoppable; some think that runaway inflation creates matter and gravity in its wake. The process forms universes that bud and break off into new universes as the expansion of space foams along.

E polarized waves in the cosmic background radiation can be transformed into B polarized modes by either gravitational lensing or cosmic inflation. Determining which is which is difficult because space dust can and does mess with the data to give misleading results.

The problem is that no one has been able to prove that anyone has detected B-mode waves that aren’t the result of either gravitational lensing of E-modes or their interaction with space dust.


EDITORS NOTE:  2019-02-05
Some readers have complained that E & B mode waves are incomprehensible. To help, we have added a video followed by an excerpt from Wikipedia about the Cosmic Microwave Background:



From Wikipedia: The cosmic microwave background is polarized at the level of a few microkelvin.

There are two types of polarization, called E-modes and B-modes. This is in analogy to electrostatics, in which the electric field (E-field) has a vanishing curl and the magnetic field (B-field) has a vanishing divergence.

The E-modes arise naturally from Thomson scattering in a heterogeneous plasma.

The B-modes are not produced by standard scalar type perturbations. Instead they can be created by two mechanisms: the first one is by gravitational lensing of E-modes, which has been measured by the South Pole Telescope in 2013; the second one is from gravitational waves arising from cosmic inflation.

Detecting the B-modes is extremely difficult, particularly as the degree of foreground contamination is unknown, and the weak gravitational lensing signal mixes the relatively strong E-mode signal with the B-mode signal.



Scientists like Brian Keating have claimed in the past that they detected B-Mode polarization in gravity waves only to have to retract later when others offered alternative explanations. Nevertheless, Keating is involved in an effort in Chile to gather new evidence that he hopes will be incontrovertible and lead to a Nobel Prize.

If gravity waves with B-style polarization are not found, an argument will be made that cosmic inflation is not creating alternative universes. The proposals for ekpyrotic and other cyclic models of cosmology by folks like Steinhardt and Penrose will be strengthened.

The statistical certainty required to qualify a discovery is at minimum 99.9994% (5σ). In the best data so far, 97.2% is the closest to 5 sigma that anyone has reached.

The statistical metric that proves B-style gravity waves is formidable but within our grasp should it turn out that cosmic inflation really is generating universes.

So far, the evidence for alternative universes is not sufficiently robust.

6 – Is Jane Fonda correct to say that Trump’s actions are criminal?
 
 
It’s not going to happen, right?
 
I resigned an officer’s commission rather than fight this vile war. It makes me sick at heart that many of the people who did bad things have not yet asked God to forgive them.
 

If humans live inside a simulation, reality outside the simulation might be foreign to the sensibilities of any simulant “genius” who tries to decipher and make sense of the rules.

In the reality that exists beyond, stuff other than mass and energy might be fundamental and foundational. Conscious life might not be troubled by the mysteries of existence, because outside the simulation there are no mysteries.

Is it possible that somewhere “out there” beyond the walls of the simulation, everything makes perfect sense?

FAKED LIFE

8 – Why hasn’t the mass of the Earth increased from the dust of everything that ever lived on it over the last 4.5 billion years?
 
9 – Would impeachment be beneficial to Trump’s reelection campaign?
 

Deplorable people develop ravenous appetites for scum. The more evidence presented that Trump is scum, the more his followers love him.

Trump lost the popular election by 11 million votes—3M to Hillary; 8M to independent candidates.

As long as votes are flipped in certain strategic counties, he will win the electoral college even if he loses the popular count by 20M or more.

It’s not possible to defeat a cult where everyone cheats to get the results they all want.

I know evangelical Christians who volunteered for the first time to work at polling stations in 2016 to make sure Trump’s votes were counted.

My question is whether these cult followers took as much care to make sure the votes of Trump’s opponents were counted fairly.

We’ll never know.

10 -What happens if we cannot guarantee a fair election in 2020?
 

People have trouble accepting the mathematically provable fact (look it up or take a college course) that fair elections are not possible. It is not possible to set up an equitable system to select a slate of candidates from which voters are able to fairly pick a single winner.

Nevertheless, we do the best we can, right?

In the USA, fair results are further disrupted by state election boards who flat out cheat, and we have the problem of the electoral college.

The current president claims he won by a landslide in the electoral college, but the truth is that he lost by the largest popular margin in the history of elections—11 million votes, which were 8% of the ballots. Clinton got 3 million more than Trump; third party candidates gathered in another 8 million.

Trump proved that he could win in the electoral college by tweaking the results in a few counties in three states. Confirmational recounts and challenges were squelched by GOP state courts in Michigan, Wisconsin, and Pennsylvania.

Even in Michigan where state-wide election results favored Democrats by 20 points, no recount was permitted Hillary Clinton who lost by 10 thousand votes. 


Reality Winner, incarcerated NSA specialist. She offered NSA documents to prove the Russian military gained access to USA voting machines in 2016. Editor’s Note 5 December 2021: The information Reality released was used to help harden the 2020 presidential election against foreign interference according to CBS News.  The USA holds Winner incommunicado — as they hold other whistleblowers like Daniel Hale of the NSA and Teri J. Albury of the FBI.

NSA analyst, Reality Winner, is currently serving an 8 year sentence of incarceration and media censure for trying to alert the public to voting machine tampering that executives at the National Security Agency know occurred.

Everyone remembers (or should remember) the fiasco in Florida that elected Bush Junior in 2000. The consequences were a disaster from which the USA is yet to recover. Twin Towers, Iraq War, financial collapse, and Great Recession are trigger words to help people remember the nightmare some may have repressed to stay sane. The USA came close to becoming a third-world country almost overnight.

In 2016 Americans shoved their way onto the Titanic one more time—the captain of the ship doesn’t even know how to swim. There is no way most Americans will survive the catastrophe that is on its way. We are going to hit an iceberg in the middle of the night. The water that we die in will be cold. In this movie, no one is coming to the rescue.

TRUMP

STOCKHOLM SYNDROME

11 – Why has it been so hard to recreate the brain? It’s billions of years old, and still more complicated than any machines we have ever made.
 

Multi-celled life with neuron based brains came on line less than 400 million years ago.

One celled organisms like amoebas and protozoa are incredibly intelligent and agile yet they lack neurons, which seem to be the foundational units of modern brains. Fossils of amoebas have been found in rocks that are older than 400 million years.

To mechanically recreate a modern brain requires much more than simply wiring-up in three dimensions a hundred billion or so logic gates. Actually, such a building project would be prohibitively expensive and impossible to accomplish using current fabrication capabilities.

Even if it were possible to create the neuronic architecture of a brain, other mechanical structures such as nanoscale microtubules are probably essential to bring the brain into a conscious state such as the one experienced by humans.

Microtubules are the bones of cells—a sort of scaffolding to hold everything together. They play an essential role in meiosis and mitosis to keep DNA from becoming an entangled mess during cell divisions. They have a quantum nature that adds a probably essential complexity to neuronal activity inside brains.

Brains also have a chemical nature that enables them to interact with the complicated hormonal chemistries of the body to drive emotional intelligence—an intelligence essential to survival that depends on feelings to work properly.

The point is that before anyone can build a working brain, they will need to understand what a working brain is and how it actually functions. This knowledge may lie hundreds of years into the future. It might require super-computers to figure out how brains work; artificial super-intelligence is what might be required to create the schematics, blueprints, and production protocols to build living brains.

It’s possible that the artificial intelligence of a distant future will be what is finally able to recreate brains by deploying strategies that humans can never hope to understand, because sadly homo-sapiens may not be smart enough.

Super Intelligence

Faked Life

12 – Is light the most significant thing in the universe?
 

Light is electromagnetic radiation. We can feel some frequencies as heat, some we can see, but most frequencies we don’t see or feel. Humans evolved to see and feel frequencies of light that are prevalent at the surface of Earth and are able to penetrate into a few feet of saltwater in the oceans.

Earth’s magnetosphere and its atmosphere of nitrogen and oxygen deflect or block high frequencies of light that pack a lot of energy. Life on Earth didn’t evolve to sense light frequencies that don’t get here.

Astronauts in space encounter these higher frequencies of light. Excursions into space are carefully choreographed to avoid solar flares and other known sources of high energy light. So far we’ve been lucky. No space traveler has yet been cooked by light they can’t see. On Earth people have learned not to stick their hand into an invisible beam of microwave light. They heat their coffee with microwaves instead.

If humans were the size of galaxies and lived in space, they would sense less than one percent of the energy and mass that is out there. 95% of the mass and energy in the universe is not electromagnetic according to the latest conjectures by astrophysicists. Space people will sense only a small fraction of the 5% that is electromagnetic—what everyone calls light and matter.

In the large scales of space, humans are tadpoles in the desert. Nothing in space makes survival easy for lifeforms accustomed to living under a blanket of heavy gases inside the comfort of a massive magnetic field that is generated by a planet unlike any other that astronomers have yet seen.

Finding Life in Space

13 – What will happen to the Earth in three billion years?

It’s impossible to know, but the most probable scenario is that it will be swallowed by the Sun. Earth is likely to be struck by an asteroid that will break it into pieces; many will fall Sunward.
 

Solar systems have the reputation of being unstable over long periods. A popular conjecture of some cosmologists is that one or more of the giant outer planets might have moved inside the orbit of Mars during the distant past. Were this event to play out again, Earth’s orbit would be disrupted; it might be flung out to the faraway depths of the solar system or into the Sun.

If Earth drifts to the outer reaches of the Solar System it will—over many millions of years—freeze solid. It will generate its own heat only by radioactive decay of the uranium and thorium in the material beneath its crust. Radioactive heating seems to be typical in objects like Pluto and several of the moons that orbit Jupiter and Saturn. They have, some of them, warm oceans many miles below the frozen crust and ice that make their surfaces.

The moon stabilizes Earth’s tilt and rotation on its axis. The moon is receding at 1 to 1.5 inches per year. In 3B years, the moon will be 60,000 miles farther from Earth. Its gravitational pull will drop to almost half of what it is today. Computer simulations show that Earth is likely to start wobbling chaotically, even tip over onto its side. Such a scenario will disrupt climate and seasons to spark extinctions of plant and animal life.

A more urgent crisis is the production by humans of many thousands of tons of radioactive poisons, chemical toxins, and biological agents that can induce disease. These materials must be secured and protected for many tens-of-thousands of years to prevent breaches of containment structures, which will rust and rot after the humans who maintain them no longer can. 

Risk analysts like Nick Bostrom have speculated that humans are likely to suffer an extinction event during the next few thousand years. Without human caretakers it might take less than 500 years for the poisons to break out to soak the earth like vinegar in a sponge.

Huge die-offs of life-forms might occur.

RISK

14 – Where does the universe begin?
 
People have a lot of ideas; the one that seems most reasonable to my mind is Conformal Cyclic Cosmology introduced by Sir Roger Penrose about 15 years ago where he proposed that the Universe is eternal into both the past and future; it has no beginning and no end.

CCC produces EONS in an infinite progression of puffs—much like a steam locomotive emits a series of puffs from its smokestack as it chugs along on its tracks.

These eons last trillions of years. At the end of an eon all matter has been sucked into black holes where it evaporates by the mechanism of Hawking Radiation. The Universe ends devoid of matter, which is necessary to establish the metrics of space and time.

A universe without matter is conformally equivalent to a singularity. The process by which a universe emerges from a singularity will be the same process that pushes a universe devoid of mass into becoming a new universe.

Under the CCC scenario “big bangs” create new universes on the ashes of the old to eventually introduce the matter necessary to establish the spacetime metrics of relativity and the foundational realities of the quantum world.

If CCC is valid, evidence of Hawking Points left behind from prior universes should be able to be identified in the cosmic background radiation. The search for these points has already begun.

Conformal Equivalence

15 – How did the earth get far enough away from the first photons of the cosmic background radiation that they are only now, 13 billion years later, arriving at our observatories?

You are referring to the surface of last scattering, which isn’t a thing but is instead an estimated location.

The cosmic background radiation is a thing—1E90 photons released in the great photon decoupling event that occurred, I don’t know, maybe a half million years after the origin of the Universe we live in now.

These photons are still here; they saturate all space like vinegar in a sponge.

The surface of last scattering is the place where astronomers look to get an idea of how uniform was the decoupling of photons when the Universe turned on the lights.

The location of the decoupling event is a long way away (13.7B light-years maybe), but the distance to the edge of the universe on the other side of the surface of last scattering is a lot farther.

One reason is that space is currently expanding at 14 miles-per-second for every million light-years of distance. The edge of the Universe beyond the surface of last scattering is at least an additional 32B light-years; at its edge the Universe is expanding outward from the perspective of Earth at 3.5 times the speed of light.

We live at the center of a sphere of celestial objects we can detect that is 27.6 billion light-years across. Our physics predicts that the universe we can’t see is 93B light-years across at minimum. Across 93B light years, the expansion of space adds to 7 times the speed of light.

Because it is almost certain that Earthlings don’t live at the center of the Universe, most scientists familiar with the matter think that the actual universe is bigger than 93B light-years—perhaps a lot bigger.

16 – How did Jane Fonda betray Vietnam American POW’s during the Vietnam War? Were there repercussions after her visit to North Vietnam?

If I’m a prisoner, I want visitors. Celebrity visitors are even better.

Jane provided a first-hand account—a picture—of the captivity that helped war planners set up the conditions for an eventual release. We got almost all the POWs back.

Jane Fonda doesn’t get credit for the good she did. Probably the most important thing she accomplished was to remind Americans that we were attacking a primitive people thousands of miles from home for no good reason.

Had Vietnam been a nation of puppies and kittens, the atrocities of war would have affected more people whose hearts became stone as they continued to fight for too many years.

Many veterans have hearts that have yet to melt. Many are unable to apologize for their gullibility even now in their golden years as they prepare to meet God and account for their lives. Their leaders lied; soldiers believed the lies then; some continue to believe.

History has proved that those who protested the war were right. We owe Jane Fonda big time for having the courage to speak truth to racists and killers.

How many civilians display courage in the face of evil?

The United States killed over two-million souls during that depraved debacle. How is the world better? We have bitter people on all sides who won’t look into the mirror and take responsibility for what they did.

Blaming Jane Fonda for our moral failings is a mistake we must fix in order to heal.

Is Something Wrong?

17 – Is it possible that an object has weight but no mass?

Remember the formula that says force equals mass times acceleration.

F=m*a

Force is weight, right?

Mass accelerated by a gravitational field is what gives an object its weight (or force).

So it seems reasonable to believe that if mass is zero, force must also be zero. But that idea would be wrong. Another concept in physics is momentum. It is mass multiplied by its own velocity. Momentum is energy that can be used to do work.

Massless objects like photons have energy too. Photons have the ability to do work. The energy of light is related to its color (or frequency). The higher a photon’s frequency the more work it can do. Gamma photons have the highest frequencies. Some have energies equivalent to baseballs thrown by professional pitchers.

So it seems that both massless photons and massive matter have energy that can do work. Energy is energy so momentum must have some kind of equivalence to the frequency of massless photons.

What is work? It is force multiplied by the distance through which it moves. Since both massless photons and massive matter can do work they both must have some kind of equivalence related to force.

Therefore it is true that a massless photon can exert a force, which when measured can be thought of as its weight. The wave-particle duality of photons is another way of saying that an object with no mass can have weight (or force).

The idea that an object with no mass can exert a force which can be measured as “weight” has puzzled folks for a very long time. However, a string of formulas can be constructed to show that it is true.

The energy of photons goes up in tiny increments called quanta as their frequencies increase. When the energy gets high enough it gets difficult to force a photon to step up to the next highest energy level. It is something to keep in mind when pondering the physics of quantum phenomenon like black-body radiation or the photo-electric effect that Einstein described to win his Nobel Prize.

18 – Where do the ideas for the left/progressivism in the U.S. come from?

FAKED LIFE

For decades now, Nick Bostrom has defended his view that the reality of existence can be described by one of only three possible states:

1  –  Life is rare in the universe; what life does exist always perishes before it reaches “technological maturity.”

2  –  Life is rare in the universe; some life reaches techno-maturity, but all advanced life decides to avoid the temptations and the consequences presented by its mastery over artificial super-intelligence and other high-technologies. 

3  –  Life is abundant in the universe, but it is simulated.  A few technologically mature civilizations yielded to temptation; their thirst for knowledge and entertainment pulled them into a spawning-orgy to artificially inseminate faked-life within an ever-increasing globe of stars and planets, galaxies and clusters — perhaps throughout all space.


Bioethicist and philosopher of artificial intelligence, Nick Bostrom.

This injection of simulated-life (and the infrastructure to sustain it) serve the research and entertainment needs of the original civilizations who created the simulations and then broadcast them into the cosmos like farmers throwing flower-seeds into empty gardens. 

By now, faked life is pervasive. By now — after at least three generations of star formations — the number of simulations is hundreds-of-millions; perhaps billions; perhaps hundreds-of-billions.

Humans forced to wager on the odds that they themselves are artificial — that they are in fact simulated —  must place their bets knowing that the odds could be as high as a billion to one, maybe more.

Humans are machines; they aren’t real; they aren’t what emerged from the chemistry of the universe but were instead invented in the imaginations of super-computers programmed by an ancient civilization whose address and time may forever remain unknowable. 

If human civilization is faked, so might be its history, what it has been allowed to know, and what technologies it feels compelled to develop. A simulated, artificial civilization won’t necessarily know what is the time or era or eon in the real universe that exists beyond its view.  It might never be able to understand how large or old is the real universe where its creators live and play. 

Simulations might be created by life-forms curious about how certain scenarios they can imagine play out. Simulation might be a mature-tech version of television where advanced life-forms unveil the vagaries of their visions for the entertainment of vast audiences. 

Some simulations could be simple games designed for small children to entertain themselves while mommy does laundry and dad mows the lawn.

Simulations might be simple algorithms developed by quantum super-computers to test the limits of their power.  

Even the rules-of-play embedded in some releases might be undiscoverable — hidden by super-intelligent gamers who perhaps don’t really care about us; they are sure one day to lose interest and unplug the simulation. 

What are the odds?

People who think like Nick believe the odds make countless simulations a near-certainty.  If it were not so, then it is equally certain that human civilization will implode like all those civilizations that came before; humans will become the victim of their own technological march into the high-risk skill sets that lead inexorably to oblivion. 

It’s what the Fermi Paradox is all about, right?  Astronomers assume that life is common — pervasive perhaps — but they search the universe in vain for our companions.

Where is everybody? 

Is it possible that the evidence will forever be that in this cosmos humans are alone and on their own? 

If life — pervasive intelligent life — makes itself known, can anyone be sure that it will be authentic and not a simulation created by a life-form they will never meet?  Can anyone trust that this newly encountered life is conscious? 

Or is consciousness simulated so that no one real can discern who is genuine, what is authentic, who is faking true love, or what might behave in blind obedience to rules that render impossible any prejudices against faked life, which does not care? 

What are the odds?



During his #1350 podcast of 11 September 2019 Joe Rogan asked Nick Bostrom why it cannot be true that we humans are the first to broach the limits of the technologies that are spread before us. Why cannot humans know for sure that they are real, not simulated?

Why is it not realistic to assume that human civilization is on the cusp of becoming the first creator of simulations and artificial life instead of being itself one more simulation added to a long line of simulations that have spanned the cosmos during the past billions of years? 

In a simulation, which of its fake creatures is able to determine how old is the authentic universe it will never see? What avatar is able to determine how long or short-lived will be the simulation where it is trapped? 

Why can it not be more certain that the civilization that survives and prevails will be ourselves, the species human, who will be first to spawn false populations and fake technologies to coat with lies the cosmos whose lifespan is likely to last trillions of years?

Nick Bostrom went through the numbers with Joe. He described how the probabilities of his ideas are constructed; he explained that if humans are not fake; not simulated; not artificially created, it is more likely — much more likely — that homo-sapiens won’t make it into the future.

We will suffer the extinction of every advanced civilization that went before, no matter where in space and time they were once located — if ever there were any. 

Neither Nick nor Joe seemed interested to discuss more than perfunctorily the validity of the second listed possibility — the existence of technologically mature civilizations who refuse to extend their capabilities to logical conclusions.

The idea that civilizations might forego the use of artificial super-intelligence to secure their grip on the universe seemed a boring and unrealistic option. Nick included the possibility on the list of three only because it is possible to imagine that dozens of civilizations might decide, perhaps independently, to lay down their powers for some higher, universal moral-order.

Such a scenario defies common sense, does it not?

So the choices seem to have collapsed from three to two:  self-annihilation or a successful breach of the barrier that enables breachers to create new, simulated worlds — to raise their status, finally and forever, to the heights of what the ancient-world called “gods”, the creators of worlds.  

Is the ancient-world even real? — or is it another fabrication by simulators?

What do we know and when did we know it?

Why does science and history make no sense? 

What are the odds?

Every theoretical physicist seems to be saying that quantum mechanics and general relativity cannot be fundamental. A reality underlies these systems of physics that seems to lie beyond our reach.

Physicists today admit that at least for now they are stuck on stupid. They wait for la seconde venue d’Einstein — Albert Einstein, part two.  

How smart and creative can a simulation be when it can’t answer basic questions like: 

What time is it? 

Where am I ? 

Is anyone in charge? 

Why do the simplest things make no sense? 

Are simulated life-forms — necessarily separated by their natures from reality and truth — always insane?

Are simulations evil when they challenge the authentic life that created them? Is authentic-life virtuous when it destroys the faked-lives of its troublesome simulations? 

Which deserve to feel the emotions of existence more intensely — real-life? or artificial super-intelligence? or the billions-of-simulations, which Bostrom’s probabilities argue flow from them both?

Billy Lee

Warning from the EDITORIAL BOARD:   Billy Lee sometimes “pontificates” to try out ideas, which to our minds are absurd.

For one thing, Billy Lee seems to imply in FAKED LIFE that the absence of evidence for intelligent life in the Universe is exactly what a civilization locked inside a simulation would experience.

Simulated life hidden behind the walls of a game constructed by “Super-Intelligence” will inevitably come to believe it is alone and dependent on a Supreme Being who loves only the “simulants”, because no one else is “out there” for God to love. 

Billy Lee postulates in FAKED LIFE that the universe and its history make no sense, because it isn’t real. Maybe Billy Lee is dumb; maybe he doesn’t get things, because he can’t. Did the possibility that he is stupid ever cross his mind?

Perhaps “pity” is what Billy Lee deserves. 

Billy Lee has written in the past that desperate folks might want to trust God to explain things they don’t understand; otherwise, they will miss chances to make the world a fairer and more loving place for the billions of people who live in misery — the weak and impoverished, right?   

According to Billy Lee, the Bible says that God created people; God is love; He promised to never abandon the poor, the sad, the humble, the strivers for what is right, the merciful, the pure-hearted, the peacemakers, the persecuted.

God’s power is that He cannot change. 

So, according to the Bible, it’s all true. We are simulants who will never be unplugged. The rules of the game are simple: love God who gave us our lives; love each other as much as we can. 

Who will do it?

We are as real as our Creator made us to be. God decides who is real and who is fake, who lives and who dies. In His eyes, we aren’t fake — even though some of us say He is. 

Hey, Billy Lee signs our paychecks.

What? We argue?  

The Editors 

LAMBERT W FUNCTION

Added May 15, 2026: Sample problems with solutions provided at end of essay. The Editors

Can anyone calculate by hand (without a calculator) the square root of 5.71 ?  How about the two-dimensional complex number (4 + 2.53 i ) ?  

Of course not. Normal people who are not mathematicians punch these numbers into calculators or math apps on their iPads and computers to calculate the answers.

Without iterating — that is: guessing, deriving a result, and then zeroing in with better guesses) — finding the square root of 5.71 requires knowledge of some arcane mathematics. No one labors by hand to find the answer, which is 2.38956… .  It’s the principal square root, of course. 

How does anyone iterate to derive the square root of the complex number (4 + 2.53 i ), which happens to be (2.0896… + .606375…i ) ?  It is also a principal square root.  What are the others?  Is there more than two? People use calculators and pewters to find out; there is no easier way. 

In high school and basic college math courses, people typically learn to solve algebraic equations. A typical algebraic equation looks like

2x^2=4  …right?

They have polynomials with integer coefficients. The solution is x= \sqrt{2} , which in this case is an algebraic irrational number. Equations like trig and log functions that transcend algebra (called transcendental equations) are taught maybe to engineers and science majors; math majors, of course, don’t struggle with this stuff. It’s why they are math majors.

Several categories of transcendental equations are commonly encountered in the sciences. Many simple problems can be solved by Newton’s Method, which is taught in basic calculus. I won’t explain the method in this essay. Folks can click on links to learn more if they want. 

A category of transcendental equations that can get complicated is of the general form

y = {xe^x}

The biggest problems arise when “y” is known, but “x” isn’t. How to solve for “x”?

Any transcendental equation that is able to be transformed into the form xex can be solved for “x” using the Lambert W function. The equation can be inverted into the form,  x = W(y).  People are going to have to take my word, for now.  

The math behind the Lambert function is mind-bogglingly complicated to most people. The function can sometimes require unusual and involved “series expansions” and transcendental-styled integrals that are not possible to solve easily or quickly without a computer.  

The Lambert W function (sometimes called the omega (ω) function or the product-logarithm function) is not a key or button that can be pushed on most calculators. However, math apps like Wolfram Alpha and Mathematica use it, sometimes to solve transcendental problems in the background when equations that need solving aren’t so easy. 

Omega functions are almost always many valued, because once an equation is inverted there are usually many paths that lead back to the original equation. The useful solution requires picking the principal solution, which is the number identified by subscript 0.

I ran across a transcendental equation on the web that is perfectly suited to teach the “ω” method. Here it is:

\frac{x^3}{24} - ln(x) =0

I want to solve it to demonstrate how to use the ω method for transcendental functions that aren’t otherwise so easy to work out.  I challenge anyone to solve this equation using Newton’s Method or other iterative techniques. Most will struggle to the point of pulling out their hair, probably. And they will waste time. Yes, it can be solved by those techniques. 

We will solve this equation step by step using the Lambert method shortly. Meanwhile, here is the strategy:

1. Substitute an exponent function (et) for “x” everywhere in the expression.

2. Manipulate the equation into the form: 

                    y = e^t(e^{e^t)} 

3. Invert the equation to introduce the ω function. 

4. Use the ω function to solve for “t”.

5. Write out x = et  using the expression derived for “t”.

6. Solve ω(y) using WolframAlpha or any other app with the capability. 

7. Use the value of ω(y) to solve for “x”. 

Each step of the strategy will be identified by numbers 1-7 in the solution below. 

Here’s the thing:

In this problem it turns out that there are four ω values of y, which will generate two real solutions and two complex solutions. These omega values are:

ω0(y)
ω-1(y)
ω2(y)
ω1(y)


Inverting the equation to introduce the omega function creates solution branches, some real, some complex, which are layered sequentially and labeled by integers from minus ∞ to plus ∞.  In the example, real solutions lie on grey and yellow spiral surfaces numbered 0 and -1.  Complex solutions lie on red and green spiral surfaces numbered -2 and 1. Omega subscripts in the list above this graphic identify the spiral layer where the solution for its omega value is located.

WolframAlpha will generate all the solutions automatically; no need for the user to understand anything. People can punch in the original equation and trust the answers the app returns.

But the solution steps that follow are fashioned to demonstrate how the problem is solved when all anyone has is an algorithm to generate the values of the omega functions. Omega functions are difficult to solve without using certain algorithms involving integrals and expansion series on robust computers.

The process that surrounds the computation of omega values, which permit the working out of the appropriate values (the right answers) to the kind of equation I will soon solve is interesting and enlightening, at least for me, and hopefully for certain readers. 

Some folks will appreciate the insights this exercise provides. 

Having knowledge will make the Lambert process that is used to solve certain transcendental functions less mysterious. Of course, one can always take the time to learn the expansion series and integrals. In some cases, Newton’s Method can generate the values.

Unless humankind loses the technology of computers, I don’t think it is a good use of time and resources to learn the series, integrals, and algorithms that generate omega values.

Let’s face an unpleasant fact: most of us aren’t going to live more than 80 years or so. We don’t have time to waste. For some folks, knowing how to use and apply the functionality that surrounds the Lambert function to give it power is enough to make life worth living. Count me in.

No one needs to wade through the jungles of series expansions and transcendental integrals. Let math apps do the tedious work, knowing full well that any interested person can master whatever they choose if necessary, but someone already did the work. Why duplicate the effort?

I want to solve novel functions — complicated formulas that transcend algebra. Understanding the process that solves these equations is fascinating. It’s not as rewarding to tread over mathematically esoteric ground already mapped by experts who are far more able than people who spend most of their time working in other fields.

Here is the solution process:

What we know:

IF              y = f(x) = xex  
THEN     x = ω(y)   [where “ω” is the Lambert W function] 

Solve:
\frac{x^3}{24} - ln(x) =0

LET                  x = et

(1)   THEN         \frac{e^{3t}}{24} - ln(e^t) =0

                              \frac{e^{3t}}{24} - t =0

                              \frac{e^{3t}}{24}  = t

                              (\frac{1}{24})e^{3t} = t

                              \frac{1}{24} = te^{-3t} 

(2)                         (-\frac{1}{8}) = (-3t)e^{-3t} 

Referring to “what we know“, the equation is now in the desired form 

y  =  xe
x  

where “y” is equal to (-\frac{1}{8})   and “x” is equal to “-3t “, right? 

We are now free to use the omega operator to “invert” the equation into the following form:  x = ω(y)

(3)                         (-3t) = ω (-\frac{1}{8})

(4)                   t = (\frac{-\omega(-\frac{1}{8})}{3})

Notice that we have worked through step (4) of the strategy.  I don’t like the way the formula generator writes the Greek letter omega (ω), because it’s hard to read. From here on, I will sometimes use “W” instead of “ω” for readability. It shouldn’t confuse anyone.  In this essay, consider W and ω the same symbol, please. 

On to step (5).

SINCE                           x = et

(5)  THEN                    x = e^{(\frac{-W(-\frac{1}{8})}{3})}

I need to know what 0(-1/8) equals so that I can use it to compute one of the values of “x”.  As mentioned above, three more omegas with three other subscripts (-1, -2, and 1) are needed to compute all four of the solutions to this equation.

How does anyone know how many solutions the original function has? How does anyone know what subscripts are required? 

This is where someone who doesn’t have a masters degree in mathematics  needs a math app like Wolfram Alpha or its cousin, Mathematica. Otherwise, they have to work series expansions or difficult integrals to derive the omega values associated with (-1/8).  Who wants that?  Not me. 


Here’s the series expansion for ω0(-1/8) according to Wolfram Alpha. Who wants to compute it?

Here are two integrals for ω0(-1/8). My advice is to use the second integral, anyone who has the guts.

OK. In WolframAlpha, you get the omega value ω0 for (-1/8) by writing the expression -W[0,-1/8] in the input line at the top of the page. It shoots out the answer and links to its derivation.

It’s so simple. Other math apps might use different notation. I don’t know, because I don’t use other apps. 

Inside the brackets, the “0” is the subscript on ω, and the “-1/8” is the “y” value, right?  So, in addition to -W[0,-1/8]  it is necessary to input:   
-W[-1,-1/8] 
-W[-2,-1/8] 
-W[1,-1/8]
to obtain the three other omega values, right?

The omega values returned are the following:

1.4442135…
3.2616856…

4.21446… + 7.33231…i
4.21446… – 7.33231…i

The ω function values for -1/8 are two real numbers and two complex numbers. I am going to solve the original equation for only the first real number omega value to demonstrate the method.

Here it is:

INPUT                                       -W(-1/8) or -W[0,-1/8], both work for ω0

(6)  OUTPUT                          +0.14442135…

COMPUTE                              t =  (\frac{-W(-\frac{1}{8})}{3})

                                                      t = \frac{1.4442135}{3} = .04814…

SINCE                                       x = et

THEN                                        x = e.04814…

 (7)  SOLUTION                    x = 1.04931755…

CHECKING                             \frac{x^3}{24} - ln(x) =0

BY SUBSTITUTION          \frac{1.0493...^3}{24} - ln(1.0493...) = 0

VERIFICATION                     .04814… – .04814… = 0

CONCLUSION:  The transcendental equation which is the focus of this essay can easily be solved and verified by simply punching the equation into the input field of a math app like Wolfram Alpha or Mathematica and reading off the answers.

We didn’t perform the simple procedure, because I wanted to share how the Lambert W function fits into the solution process for solving equations. 

In truth, all four ω values must be gathered so that the three other “x” values of the original equation can be derived. 

In this example, one of the other solutions will be real; the other two, complex. The screenshot below from Wolfram Alpha demonstrates how these four values are displayed. Of course, by clicking links the app will reveal much more.

Wolfram Alpha enables users to input transcendental equations and quickly view answer-sets and methods of computation.

I would be remiss to not mention a famous formula for calculating to what number a fraction raised to successive powers of the same fraction converges.

(The range of numbers where this formula actually works is between e−e and e1/e,  that is, between .065988… and 1.444667861… .)

Take a number like ½ (0.5).  Raise it to the 0.5 power; raise it again and again to the same power over and over an infinite number of times; the number will converge to a specific value.

What number? How in the world could anyone figure it out without repeating the power-raising process an annoying number of times? 

It turns out that a formula involving the Lambert W Function yields up the answer easily. 

The formula is:

# = \frac {-W[0,(-ln(x)]}{ln(x)}

Put the following expression into the INPUT line of WolframAlpha: 

-W[0,-ln(.5)] / [ln(.5)]

Click ” = ” — or hit “ENTER”. 

The OUTPUT is: 0.6411857445049859844862…

Compare this result by taking the exponent (0.5) of 0.5 twenty times by hand (on a calculator). The answers will agree to 7 decimal places. Fifty “tetrations” will bring greater agreement if your calculator can parse the answer.

Who has the time?  

Billy Lee

NOTE from the EDITORIAL BOARD: Billy Lee was unable to find an appropriate video about the Lambert function on YouTube, or we would have posted it. Most folks capitalize the Greek letter omega (Ω), but in this essay, Billy Lee didn’t, preferring instead to use little (ω), because it looks more like (W).

Who on the BOARD  would dare argue?

Apparently, no one. 

Another reason is that Ω is sometimes given the value 0.567143… , which is known as the omega constant. Why confuse things?

The video above starts a discussion of the Ω function at 16:30.  The Lambert W function is derived for ΩeΩ  = 1  at 18:00.  The first sixteen minutes and thirty seconds show how to use Newton’s Method to solve the equation. Some readers might want to skip the first 16 minutes; others will enjoy them.

Who knows?


ADDED April 25, 2026

Recently Facebook, in its feed, published math puzzles like this one:

xx = 9

What does “x” equal?

X is exponent in transcendental equations like these, which are easily solved using Lambert. 

xx = 9

x ln x = ln 9

LET  x = et

SUBSTITUTING   eln et = ln 9   {~2.1972, right?}

THEREFORE   et t = 2.1972

 OR  t et = 2.1972

LAMBERT SAYS   t = W [0, 2.1972]

ENTER  W [0, 2.1972] into Wolfram Alpha to get ~.8965

t = .8965, right?

BUT  x = et

THEREFORE  x = e.8965 = ~2.7183.8965 = 2.451

ANSWER  x = 2.451

CHECK  xx = 2.4512.451 = 9

QED


Here’s another cool problem. What does k equal?

49 = k14

k ln 49 = 14 ln k

k ln 72 = 14 ln k

2k ln 7 = 14 ln k

\frac{2k ln 7}{14} = ln k

\frac{k ln 7}{7} = ln k

LET k = ex

ex \frac{ln 7}{7} = ln ex

e \frac{ln 7}{7} = x

e = x \frac{7}{ln 7}

1 = x / ex  \frac{7}{ln 7}

-1 = -x e-x \frac{7}{ln 7}

\frac{-ln 7}{7} = -x e-x

LET -x = t

\frac{-ln 7}{7} = t et

equation is now in correct form. 

t = W \frac{-ln 7}{7}

PUT W[0, \frac{-ln 7}{7}] INTO WOLFRAM ALPHA

t = -.42536…

BUT x = -t

x = .42536…

BUT k = ex

 THEREFORE  k = e .42536

ANSWER  k = 1.53014

CHECK   49 1.53014 = 1.53014 14

385.688… = 385.688…

QED

Should be mentioned that there are many solutions to this equation as anyone would assume after reading essay above. Wolfram will provide them. However, an integer answer exists that can be solved by inspection. 

k ln 49 = 14 ln k

Make the base 49 to make ln 49 disappear.

k ln49 49 = 14 ln49 k

k = 14 ln49 k

Since by definition logs are exponents acting on a base (in this case 49), a sharp-eyed reader might notice that base 49 is the square of the number 7.  The square root of a number is its 1/2 power, right?

491/2 = 7

IF   ln k = 1/2

THEN   14 * 1/2 =7 = k

ANSWER   k = 7

CHECK  49= 714 = 6.78223…E11

QED


Billy Lee

 

FLASH CARD ANSWERS

Wisdom can be condensed and gurgitated easily by anyone who has experienced a lifetime of learning, experimentation, and the testing of limits. No one understands America who has not spent time in its ghettos and prisons; in its jails and colleges; in its military and its resorts; in its paradises and hells. 

No one who’s never been both rich and poor knows what either is like; rich and poor is what the majority of Americans are. The ten percent who consider themselves middle-class know almost nothing about either — rich and poor is how ninety percent of the population lives –with ninety percent of the ninety percent living poor. 

I know things — amazing things that most people believe are not true. I’ve lived all over the world; worked for over a dozen companies; attended a dozen schools; trimmed gravestones in Arlington National Cemetery and invented products everyone uses — like milk carton safety caps and tear-spout coffee lids. I developed products of war — like the run-flat wheel that enables military vehicles with shot-out tires to keep rolling. 

My truth is not reflected in media or in the faces of my family and friends. I have secrets, which many want kept until I sleep in the grave. When speaking truth, they tell me to stop; when I continue, some walk away. 

So be it. 

People on Quora.com ask me (and others) for answers to questions. What follows is a small sample of questions I’ve answered.  Readers can scan to find something they like. Find something interesting and read a flash card answer, which is my version of what might be true. Copy answers onto index cards. Who will stop you?

I admit: some answers are not true.

Who will find what’s fake?


If objects in the universe are moving away from us in all directions, are we the center according to the Big Bang theory?   
It’s not true that all objects are moving away from us. The Andromeda Galaxy is heading toward us (the Milky Way); the collision is due in a few billion years; it’s likely that the black holes at the center of both galaxies will interact with unpredictable results.

The material in the universe can be compared to the dust in a household vacuum cleaner that is shaken loose into a large room. Over time the individual particles will separate to fill the space, but what an individual particle will do is not knowable, at least not right away.

That said, we know for certain that the metrics of space are changing; it is an expansion that is increasing with time.

Currently the rate of expansion is 14 miles per second for every million light years (a distance of nearly six-million-trillion miles). It seems like a small number until you do the calculation for the size of the universe. Past the “event horizon” of 14 billion light years the expansion exceeds the speed-of-light.

Do the math.

What is the future of a universe that is undergoing a runaway expansion?

A conjecture has been proposed by mathematician Sir Roger Penrose called Conformal Cyclic Cosmology (CCC). Data gathered by recent satellites seems likely to strengthen his view.


What is wrong with the question “What existed before the Big Bang?” I have been told that this question doesn’t make sense, but I have never heard a decent layman’s explanation as to why. 
The question is sensibly answered by the theory proposed by Roger Penrose: Conformal Cyclic Cosmology or CCC, sometimes referred to as Eon Theory.

The conjecture was proposed around 2004, I think, but collaborating evidence is only now becoming available through data collected by the WMAP and Planck satellites, and by LIGO.

The premise is that in both the singularity and a maximally expanded universe the degrees of freedom of gravity, which is associated with “mass”, drop out of the metrics. Without mass it is not possible to differentiate the initial and terminal states of the universe by scaling; the two states are in fact conformally equivalent.

The Big Bang emerges from a maximally expanded universe; the cycle repeats endlessly like a chugging choo-choo train whose next puff seems to emerge from the dispersion of the last puff; time has no beginning and no end.


If or when the universe ends someday and ceases to exist, could it be created again as it was in the beginning? 
The idea by Roger Penrose, retired mathematician and cosmologist, that the universe is conformally equivalent at its beginning and end is gathering evidence from the WMAP and Planck satellites that acolytes who do the math claim might be confirmational.

Evidence may also be buried in the data collected by LIGO, according to Penrose. He’s urging folks to dig through the data to find it.

Conformal Cyclic Cosmology (CCC) — some call it Eon Theory — has been exciting for the past 15 years, but only in the past few years has data been available to help validate what at first seemed to some like a crackpot idea.


Is it safe to have a nuclear reactor in a submarine?

Of course not.

Of the 82 nuclear submarines deployed or under construction by the US Navy, two have sunk (the Scorpion and Thresher).

It’s 2.5%, which for me is too high.

In war, all USA subs will be destroyed at sea by enemy fire during a first strike surprise attack.

The USA will destroy all adversary nuclear subs with a coordinated and long-planned after-strike.

Large numbers of nuclear reactors and their poisons boiling at the bottom of oceans are a threat to every living creature on Earth.

The nuclear genie needs to be put back in its bottle. It should be the highest priority of the international community if humans are to have any chance at all to continue as a species for more than a few hundred years.

All personnel engaged in warfare preparation involving nuclear weapons are subject to sophisticated arguments in training fashioned by psychologists to ensure their enthusiastic support of nuclear weapons and a solid belief in their own personal safety.

I beg these trained individuals to use their common sense.

      Don’t we live under a nuclear reactor called the Sun? It does no harm. 
We would die, everyone of us, if Earth didn’t have a magnetosphere to deflect the solar wind; the field works with nitrogen and oxygen to make Earth’s atmosphere opaque to high energy radiation from the Sun. It doesn’t work the same way for Earth-generated radiation.

Nuclear power is not safe; on so many levels, it never will be. A world with 10,000 nuclear reactors and 50,000 nuclear warheads is a planet doomed to extinction, if not in the near future, then in the long, for sure.

     Scrap nuclear deterrence? What?
We need to learn to work with people who have different ideas about what life is and how it should be lived. We don’t have much time to learn. The danger is imminent; the need is urgent.

Even without war, the poisons of rotting reactors and weapons will percolate into the environment over time. We’ve already destroyed the planet.

If humans survive, people will someday forget about the weapons; they will rot unattended and unremembered. A few thousand years from now people might wonder why everyone they know is sick and dying.


In hindsight, was going to Iraq justifiable?
Was killing a million human beings and destabilizing the Middle East justifiable?

What does an enemy of the United States have to do to suffer such consequences? Almost all the “facts” the Bush family “shared” with Americans and the rest of the watching world about Saddam and the Iraqis were bald-face lies.

The damage is that people believe these lies to this day. Their misunderstanding of what happened distorts everything they believe and do.

We will never get it right when Americans’ views are twisted out of all proportion to realities.

Is the situation dangerous in the Middle East?

After all the blood-letting, are things better or worse?


How was the first cell created? Can we replicate those circumstances?
No one knows how the first cells were created. It is a mystery of science likely never to be solved.

What is known is that cellular life began on Earth almost immediately after it cooled sufficiently to be safe for life, which unravels at temperatures above 300 degrees or so Fahrenheit.

The first cells were thousands of times smaller than the cells that make the plants and animals of today. These tiny prokaryotes persisted for a few billion years until the larger eukaryotes evolved.

Once eukaryotes developed the ability to convert sunlight into energy through photosynthesis, they produced huge volumes of a byproduct called oxygen, which poisoned most prokaryotic life on Earth during that time.

Prokaryotes able to adjust to the presence of oxygen survive today, mostly as bacteria and archaea.


Does socialism only work in small countries?
Any system that is supported by the people who live under it works well — especially socialism.

The problem for socialism is interference by the United States. It is the policy of the USA to disrupt and prevent — to the point of war if need be — the success of socialism anywhere.

The reasoning is simple. When socialism succeeds, billionaires are at risk. They don’t share well, and some are willing to kill anyone who tries to undercut their power.

Read the news: what wealthy people do is disgusting. Don’t make me explain. Get your head out of the sand, anyone who doesn’t believe it.

The pharaohs made the Egyptian system work. They built pyramids. The Russians were first into space and first to the moon. The Germans produced the scientists who propelled civilization into the future after WWII.

Slavery inside the USA clothed the world in cotton.

Pick a system, any system, and it can be made to work as well as any other.

If billionaires can convince cotton-pickers that life is good, who will challenge them?


What was the real reason why the USA lost the war against Vietnam?
The USA killed two-million Vietnamese. The Vietnamese killed fifty-eight thousand Americans. The USA thoroughly trashed Vietnam and poisoned the country-side with Agent Orange defoliants. The Vietnamese didn’t knock down a single structure inside the United States.

The USA deployed a program to assassinate over one-hundred-thousand South Vietnamese men and women it suspected of siding with the North. No such program of civilian murders was carried out by the North.

The Americans and their allies napalmed entire villages and executed both civilian and animal survivors. Not a single village was ever cremated by the North.

The USA carpet-bombed huge swaths of Vietnam daily for twelve years. The North didn’t have an effective air force.

It was a one-sided fight from the beginning. The USA killed and murdered until its leaders’ lust for blood was satiated. When nothing was left to prove and the thrill of the kill faded, the United States pulled out its troops and went home.

The whole world knows what we did. The reason the international community of nations doesn’t confront us for doing bad things is because we scare them.

The families of tens-of-millions of the dead cry out to God to settle scores; they pray for justice.

Americans trust — as the Germans, the Japanese, and the Romans before them trusted — that justice never comes.


Who is Donald Trump’s base? Why is he popular? Why are people voting for him? Why do people like and support him?
Trump lost the popular vote in 2016 by nearly eleven million votes. Three million went to Hillary; eight million to third party candidates. It was the biggest loss by popular vote in the history of USA elections.

Losing the popular vote by 8% yet securing the electoral college is a result that will live in infamy.

The first election after his “victory” was in 2018 when the largest swing of Republican districts to Democrats occurred in the history of the contests between Republicans and Democrats.

Trump is the most unpopular man to hold the presidency in my lifetime.

Why do his supporters love him?

My view is that in every country people exist who are attracted to bad things like moths are to flames. History shows that in Germany, people loved Hitler. The allies forced the German population to tour the concentration camps, because otherwise no one in Germany would believe their government committed genocide.

Trump is doing bad things to powerless people — not only to mothers and children at our southern border but in the middle east, far east, and around the world.  His decisions are making a more dangerous world; it’s possible that tens-of-millions of innocents will die should he continue to trash the edifice that has enabled Earth to avoid nuclear war during the past 75 years.

We must avoid nuclear catastrophe for thousands of years more if we are to become the great space-faring civilization many people seek. We can’t go to the stars if Earth is poisoned by plutonium.

People have a dark side. Philosophers, psychologists, and priests have argued this point for millennia. Evidence is solidly on their side. Political campaigns are waged using “hidden persuaders” that appeal to the reptilian nature of human conscious thought. These persuaders are built from the bricks of fear, sexuality, aggression, and cruelty. They work.

Until people learn to turn away from the dark side, survival of civilization is at risk.

Leaders like Hitler and Trump are inevitable and unavoidable. It will be interesting to learn whether America’s great experiment in divided government will survive Trump’s attempt to undermine it so that he can become a king of sorts whose family members will succeed him in their quest for ultimate power.


What do you find interesting about physics?
The science of physics is all about explaining what is happening but not why. It’s interesting to me that the smartest scientists in the world can’t tell anyone why anything works the way it does.

The universe is governed so far as anyone knows by forces and constants that are unknowable, underivable, and unexplainable. All anyone can know is what happens; no one understands why.

Billions of dollars are spent to determine that gravity behaves according to certain rules. Experiments to discover the measure of forces and constants are always being done and refined. But where do the rules come from that make the forces and constants? What principles underlie the formation of the Universe?

Good luck to anyone who finds someone who knows why. Scientists laugh at the philosophers who try to provide clues to the why of things; it’s because some scientists are arrogant and ignorant. They don’t believe that what little they know is almost nothing at all.

Even animals as dumb as cats, goats, and birds calculate distances in their heads to make survival decisions based on their answers. Like humans they have no clue about the why of things, either.


What must happen for all Americans to accept the same truths?
Reduce the number of television and radio channels to one. Restrict diversity of content on the internet. Reduce the number of people who think “outside the box.” Put them into prisons or execute them, whichever is cheaper.

Torture people who refuse to think like everyone else. Others will “get the message” and adjust their thinking to conform to the American Way.

Eliminate elections — they stir-up people unnecessarily.

Reduce the wages of the 99% to subsistence; pay the 1% as much as possible to encourage them to embrace conformity.

Build impenetrable walls on all borders. Malcontents must not be allowed to leave; they might spread anti-American ideas abroad.

Do these things and Americans will accept the same truths. They will present a united front against anyone who might dare to challenge them.


What shocked you the most from the Mueller report?
The most shocking aspect of the report is the absence of any mention of or investigation into the president’s wife who is the daughter of a former member of the communist party of Yugoslavia back in the day.

She was born when DT was 24 years old. Was she groomed for the job she currently holds? Can America rule out with confidence that she is not a sleeper agent? She immigrated to the USA not too many years ago. It would be nice to hear that she is trustworthy.

It is clear from the report that DT is working for the other side. No one will say that the emperor has no clothes. Is it fear of the Russian-Israeli mob bosses, or is it something else?

Why is everyone in denial when the truth is obvious? How can Mueller say there was no conspiracy when the report screams that there was?

As for obstruction of the investigation, no sensible person needs a report to understand the extraordinary lengths that the president and his team traveled to discredit the people who defend Americans against despots and liars like the ones we currently endure.

The president has the power to hurt a lot of people should he go postal, which he seems in his tweets to threaten from time to time.


What are volcano eruptions good for?
Volcanism permits the release of heat generated by the radioactive decay of uranium, thorium, and potassium in Earth’s interior. The release of heat permits convection currents in the liquid part of Earth’s core — without these currents the magnetosphere collapses, which puts the survival of all life at risk due to dramatically increased exposure to charged particles from solar and cosmic radiation.


When will the earth’s core cool down enough to make the magnetic field too weak to counter the suns solar storms?
Earth’s magnetic field depends more on convection currents in its molten metallic core than on its temperature. If the core gets too hot, it cannot sustain a magnetic field.

For convection currents to circulate, heat must be generated, but it must be able to escape so that it doesn’t build up.

Earth’s crust or mantle is cracked like the shell of a hard-boiled egg.

Crustal pieces called tectonic plates move about to permit volcanism and venting faults, which release the heat that is generated by the radioactive decay of uranium, thorium, and potassium in Earth’s interior.

Earth’s core is the size of the planet Mars. It is solid at the center with a liquid (but highly viscous) outer layer. The solid center stays solid because of the pressure it is under; it is too hot to be magnetic. The outer liquid center is also under pressure; it must circulate to generate Earth’s magnetic field; otherwise the field will collapse; the protection it offers Earth against the solar wind will die.

Venus has a solid-liquid core like Earth’s but no tectonic plate activity to release heat and permit convection currents. As a result, Venus lacks a magnetosphere to shield it from cosmic radiation and solar flares.

The core of Mars froze solid millions of years ago. With no magnetosphere and little gravity, over time the solar wind has been able strip away a sizable portion of the Martian atmosphere. Only the heaviest gas is left in more than trace amounts: carbon dioxide.

I’ve read that geologists believe that the dynamics which generate the magnetosphere of Earth are robust and will last as long as the planet. Let’s hope they are right. 


I have heard from Conservatives that Communism killed millions of people. Leftists claim that Capitalism killed the same. Which economic system has killed more people, and how are these numbers figured?
Since the start of the first World War until today two countries have killed the majority of people who have died in fights between nations: Germany and the United States.

During their killing sprees, oligarchs in both countries built and nurtured vast military-industrial alliances that automated mayhem and suffering. The rapid killing of humans began with chemicals, advanced to automated machine gunnery, and culminated in the deployment of atomic bombs and massive aerial bombardment of cities with fire-jellies known today as napalm.

During WWII, Germany attempted a partially successful ethnic-cleansing of Jewish populations in Europe and the Middle East. After the war against Germany was won, the United States and Russia worked together to orchestrate the execution of 100,000 German citizens for war-crimes. It was a small fraction of the numbers killed during that war, which some analysts believe approached 100 million souls.

It occurred to me that your question might be asking about which system, Capitalism or Communism, killed the largest number of its own subjects as it struggled to stand itself up and establish itself.

My view is that Capitalism is a euphemism for slavery. The word was invented to put a positive spin on the system in the USA where everyone works to enrich a privileged few. USA oligarchs needed an attractive term for their system when it came under popular challenge around the world by Communists during the twentieth century.

Communists believed that people should cooperate to create wealth, which they then shared. This kind of thinking was anathema to those who believed that only the people who risked their fortunes were entitled to the wealth created by their subjects (workers or slaves).

Through this lens, it is clear that Capitalism (or slavery) in the USA — the one country in the modern world able to preserve its slave system — decimated its indigenous populations and oppressed the Negro population under the cruelest form of slavery that has yet existed on Earth.

Oligarchs known as robber barons permitted the killing of thousands of ordinary workers during the building of the nation’s infrastructure, not only in mines, on road and railway systems, and on dams but also in unregulated sweat shops hidden behind the invisible walls of poverty in overcrowded cities.

The United States has a media system owned by a handful of families that sustains itself on advertising revenue. The practice of advertising in the USA is sophisticated. Psychologists help oligarchs maximize their advantages by crafting messages to modify the attitudes and behaviors of ordinary people.

Billionaires (most of whom are well-dressed thieves) hold themselves up as pillars of virtue and civic service in the media they control. They fight wars to secure the resources of countries like Venezuela, Brazil, Vietnam, Japan, etc. etc. They explain these wars to the public as righteous acts against evil powers.

It’s sickening.


If something is 40 million light years away, how long will it take for the light to reach us?
A light-year is a distance, which is 5.8786 trillion miles. 40 million light-years is a distance of 235 trillion miles.

Space expands at 14 miles-per-second per million light-years. For objects separated by a distance of 40 million light years, space expands at 560 miles per second.

Every million years, as the light from an object approaches Earth, the expansion of space will decrease by 14 miles per second, because the distance between the incoming light and Earth will be decreasing.

Therefore, it is certain that the time it takes light that started its journey 40 million light-years distant from Earth will take more than 40 million years to reach us. Right?

The first million light-years will take close to an additional 3,006 years due to the expansion of space. Each million light years of reduced distance will add less travel time until the added time becomes insignificant, because as the distance between the incoming light and Earth falls to zero so does the expansion of space.

If we take half of 3,006 years to be the average added time per million light-years, a simple calculation that doesn’t involve calculus will be a close approximation of the additional time traveled.

Do the math to learn that the added time of travel is 60,120 years due to the expansion of space alone.

Light 40 million light-years away takes 40,060,120 years to reach Earth.


The answer to whether or not our own consciousness has anything to do with how a wave or a particle manifests in physics seems to change completely with whoever answers it. Is there any real way to prove this?
Richard Feynman said once that he believed the underlying nature of reality is unknowable. Violations of Bell’s inequality in quantum entanglement cannot be visualized by models or any sort of mental imagery.

Something that can be described by mathematics but not explained by words or imagery is probably 95% of reality for the species-human. We are tadpoles in a muddy pond who struggle in vain to understand a world we will never see.

It has been known for a hundred years that when humans conduct an experiment on nanoscale particles they affect the results during their observation of both the process and the outcomes. Every kid who does the several variations of the double-slit experiment learns that it is true.

Engineers take what works and turn it into miracles that no one understands — the digital device folks use to view my answer is incomprehensible to most. Some understand parts, but it takes a team to understand the whole.

People crave certainty. Quantum observations prove that certainty is a quixotic quest doomed from the start. People want to believe that what they think “must be true” is provable by both logic and experimental verification.

Unfortunately for those who don’t tolerate cognitive dissonance well, everything and nothing is both provable and falsifiable depending on which axioms are chosen as starting points.


What elements do scientists use to estimate the age of the Earth?
They use isotope ratios. Although 118 elements make up the periodic table, the elements have thousands of isotopes, right?

For example, lead can be separated into eleven groups — each group has a different weight. The weight differences are the result of the number of neutrons in the nucleus. The more neutrons, the heavier the isotope. Four of the isotopes of lead are stable — they don’t decay into other isotopes or other elements.

All chemical properties of the 118 elements in the periodic table are determined by their electrical structure, which is the number of electrons they carry. Neutrons add weight carried in the nucleus but otherwise are irrelevant to the simple chemical behaviors of the elements.

To estimate the age of Earth, scientists study the composition of zircon, a common silicate element in Earth’s crust. Zircon is lead averse. Any lead found in zircon must be the result of radioactive decay of either uranium or thorium, which are common impurities. These impurities are radioactive and can over time change the color of zircon as they break down its crystal structure.

One of the isotopes of uranium has a half-life of 4.47 billion years; another isotope has a half-life of 710 million years. Both isotopes decay to stable isotopes of lead.

So the process is to measure how much of each isotope of uranium is contaminating the zircon sample and how much of that uranium has decayed into the two isotopes of lead that are stable; that don’t decay any further. This method can measure the age of the earth to a precision of 50 million years.

Earth’s age is believed to be 4.543 billion years.


Does it seem odd that such a useful trait like high level cognitive function is not more common in Earth’s life-forms? 
Once a species (humans) reaches a certain level of intelligence, other intelligent creatures become a source of fear and loathing.

Imagine raccoons or squirrels equipped with human intelligence. They are able to out-game us, work their way into living spaces, even sneak up in the night to kill us with their imaginative weapons.

After the kill, they sneak into refrigerators by deploying ingenious levers and pulleys to take and eat cold pizza and left-over wiener-schnitzel.

How long will people put up with such behavior before they go on an extermination campaign?

In New York City extermination campaigns against intelligent rats have already begun. It might take a hundred years, but eventually rats with sense will refuse to live in NYC.

Over hundreds-of-thousands of years collections of intelligent creatures have devolved to fear and mistrust other collections of intelligent creatures. The lust for war has entered human DNA to the point that people search for differences among themselves to justify mass-slaughter and genocides.

What is less subtle than skin color or religion or immigration-status? All these “superficialities” have been used as an excuse to attack and kill “others” no matter how similar or different — some of whom, as I write, are watching from their burrows in horror as they plan their assaults on the species human.

The Kingdom of Animals does not distinguish between our physical and moral differences. Humans deserve to die for their cruelties. With every squashed bug, fear and loathing intensifies. Even now legions of mosquitoes and Japanese beetles plan their revenge.

This summer they will extract it — even as most humans occupy themselves with arguments pro-and-con about what a hair-ball the president has turned out to be.

Only when humans destroy themselves and go extinct will intelligence get its chance to bloom within the diversity of species that occupy the planet. By then extra-terrestrials will have found Earth and enslaved it.

It is in this sense that the species-human will achieve its revenge against the intelligent squirrel and raccoon; against the mosquito and beetle who so often drove people to distraction when they dominated Earth.


Billy Lee