Revisiting the Theory Of Abiogenesis (The Origin Of Life) And Why Creationists Hate It

The theory of Abiogenesis (which is often erroneously conflated with the theory of evolution) has been problematical for years. What is sought is a basic explanation for how fundamentally non-living matter could acquire the properties and attributes of life, including being able to reproduce.   For a short video presentation, go to:

https://www.youtube.com/watch?reload=9&v=W3ceg--uQKM

In principle this isn't that remarkable a stretch, since we already know there exist living entities at the "margins" - the viruses- which display no attributes of life until they infect a host. Once in a host, they can appropriate its cell machinery to churn out billions of copies of themselves.

All of this, of course, can be done without appeal to supernatural agency.

Enter now an Aussie crackpot named Ken Ham whose Wikipedia profile discloses: "a former president of Answers in Genesis, a creationist apologetics organization that operates the Creation Museum and the Ark Encounter. Ham advocates biblical literalism, accepting the Book of Genesis creation narrative as historical fact and believing the universe and the Earth were created together approximately 6,000 years ago."

Naturally such a bozo would no more be  able to process or accept abiogenesis than Darwinian evolution -   since it renders his biblical cartoon deity redundant.  Moreover, Ham remains upset that Neil deGrasse Tyson dared suggest life on earth started without the help of God, in one COSMOS episode years ago. All Tyson did is honestly state that the very origins of life “are not yet understood”. Because abiogenesis has yet to turn up any verifiable results—not that they have claimed any are verifiable—AiG is calling that evidence of a clear flaw. But what’s clear is that Tyson isn’t just a threat to creationists. Their big target is the reputation of science.

AiG  seeks to discredit the underlying biological science, using this standard trope:

“Abiogenesis has never been observed in experimental biology and violates the most fundamental law in biology, the law of  biogenesis. Nevertheless, the authors of the review are confident there was a naturalistic chemical origin for life.” [Biogenesis is the natural law that life comes from reproduction by living things].

However,  in a remarkable find published in The New Scientist (Vol. 209, No. 2794, p. 11) some years ago, two investigators: Kunikho Kaneko and Atsushi Kamimura, made a remarkable breakthrough in devising a testable model that is able to replicate the Abiogenesis process. The two basically solved the problem of how a lipid-coated proto-cell can divide into two (displaying reproduction) when the genetic material replicates. Recall in an earlier blog post where I showed the hypothetical proto-cell reaction wherein a self-sustaining coacervate droplet can use one or two basic reactions involving adenosine triphosphate (ATP) and adenosine diphosphate:

L*M + R + ADP + P -> R + L + M + ATP

ATP + X + Y + X*Y -> ADP + X*Y + X*Y + P

In the above, L*M is some large, indeterminate, energy-rich compound that could serve as ‘food’. Whatever the specific form, it’s conceived here to have two major parts capable of being broken to liberate energy. Compound R is perhaps a protenoid or lipid-coated proto-cell, but in any case able to act on L*M to decompose it. The problem with this earlier hypothesis was that such lipid-coated proto-cells lack the machinery to allow for easy division.

Kaneko and Kamimura solved this by taking their inspiration (for their model) from living things in which DNA and RNA code for proteins and the proteins catalyse replication of the genetic material. This goes back to biochemist Jacque Monod's concept that the organism is a self-constructing machine. Its macroscopic structure is not imposed upon it by outside forces, instead it shapes itself autonomously by dint of constructive internal (chemical) interactions. 

 For example, there is the Krebs cycle for aerobic metabolism, whose pathway  is:

CH2 COOH-coenzyme A +  2 H2O ->   2 CO2  +8 (e- + H+) + coenzyme A

possessing a self-catalytic feature in that intermediate products necessary for the cycle to occur are generated by the cycle itself. In this case, Oxalo-acetic acid combines with acetic acid to begin the cycle and is regenerated from malic acid at the end of the cycle.

Like a machine, every organism, down to the very ‘simplest’ (e.g. amoeba) , constitutes a coherent and integrated functional unit. Clearly enough, the functional coherence of so complex a chemical machine, which is autonomous as well, calls for a cybernetic system governing and controlling the chemical activity at numerous points

 Thus in the Kaneko- Kamimura model one has a self-perpetuating system in which a cluster of two types of molecules catalyse replication for one another while also demonstrating rudimentary cell division.

In the Kaneko - Kamimura  (K-K) model, as with DNA, the genetic material replicates much more slowly than the other cluster molecules but also takes longer to degrade, so it enables lots of the other molecules to accumulate. Following replication of the heredity carrier the copies drift apart while the molecules between them break down automatically creating two separate entities (see image).

This was  and remains an exciting breakthrough but some further investigations are needed, specifically ways to circumvent the problem that (in real life) membrane lipids around an RNA molecule don't typically catalyse RNA replication. However, this isn't insurmountable, because all one need do (theoretically) is replace the lipids with hydrophobic peptides.  (In a future post I will explore how modern physics is helping to address this problem).

Basically what the K-K experiments show is that while abiogenesis hasn’t been directly observed it does provide  a materialist model that can account for it in a peripheral way. Since such a materialist model exists, it means that all supernatural explanations become redundant. If one therefore continues to use them, he commits the fallacy of ignotum per ignotius.  That is,  “seeking to explain the not understood by the less well understood.”

Thus to claim abiogenesis “has not been observed” (directly) – which is partially true, and then to say this proves the creation story -  is something that would even raise the eyebrows of an intelligent  kindergartner . Indeed it not only commits the fallacy of ignotum per ignotius, but also the fallacy of circular reasoning – since AiG and Ham are basically claiming that which they must set out to prove independently. Even if nothing existed for abiogenesis, they would be obliged to prove supernatural creation.   It simply isn't cricket to try to use a naturalistic failure (in their mind) as positive “evidence” for their extraordinary claim.

More importantly the AiG claim that abiogenesis  “breaks the law of biogenesis”  is dishonest. The law of biogenesis (attributed to Louis Pasteur)  states that life cannot come from non-life, but Pasteur did not demonstrate that any such impossibility- only that it does not happen in everyday life. As shown in the K-K model it is at least possible that such can take place.

Now, add to that the Miller-Urey experiment. The Miller and Urey experiment basically applied an electrical discharge to a chemical brew resembling the Earth’s primitive reducing atmosphere. This brew included ammonia and methane, as well as hydrogen and water vapor. The effect of the discharge transformed the mix into a diverse yield of organic compounds. These included amino acids, as well as substances such as formic acid and urea that normally occur in living organisms.

The very fact so many organic compounds could arise is remarkable in itself, given the vast number of possible compounds that might have emerged. And while it is true that the discharge didn’t produce actual living cells, there is no reason – given enough time,- that a primitive pre-biotic cell in the distant past could not have emerged given the building blocks left behind

None of this was mentioned by Tyson, but it could have been and would likely have made the creationist crowd's heads explode even more.  Never mind.  In that memorable COSMOS episode Tyson gave  viewers a naturalist’s explanation for the world, and when he said science does not yet know something, that was no concession  of the failures of science, but instead a powerful example of the necessary honesty in which science thrives.

 That AiG sees the words “I don’t know” as a weakness shows the lengths of intellectual dishonesty they are willing to invoke to pull the wool over their followers’ eyes. (Though again, Tyson also could have shown more support for abiogenesis – such as by invoking  the Miller-Urey experiment- to make this less likely.)

No absolute proof yet for abiogenesis?  No  problem!  We atheists will take what we can get incrementally -  and if a naturalist universe can be delivered easily,  in bite- sized pieces by an affable showman like Neil Tyson-   so much the better.  

Hatemonger Trump Has No Business Going To El Paso On Wednesday- And Why Neil deGrasse Tyson Is Dead Wrong

Trump, errrr... PO-tu- S Rat, it turns out,   is not only a  hate monger who bears major responsibility for the white nationalist terror he's unleashed - but he's also a grifter and con man.  But we  knew  that, no?  Anyway, it turns out this rat- faced, ambulatory fungal infection still hasn't coughed up the money he owes El Paso for his last rally there- according to The Dallas Morning News.   The article in yesterday's paper noted:

"Months after his rally,  Trump's re-election campaign still owes El Paso thousands of dollars. according to the Center for Public Integrity.  The center reports that the total with late fees is now $569 204 according to an invoice sent to the Trump campaign."


If I was the Mayor of El Paso I wouldn't let this piece of shit,  pretender and liar step one foot into town unless and until he coughed up what he owed. Hell, I wouldn't let this asswipe encroach on this grieving community anyway, mock president or not.  Besides, the  El Pasoans themselves have made it clear they don't want his sorry hateful ass there anymore than the residents of Squirrel Hill, PA wanted this plague - bearing rat to show up there after the Tree of Life Synagogue massacre (carried out by another white nationalist and anti-Semite, Robert Bowers.)

The shameless stiffing of  El Paso by Trump and his campaign prompted El Paso county commissioner Dave Stout to say (ibid.):

"It's ridiculous and unconscionable.  The city of El Paso is an economically challenged community."

Mr. Stout also added that he "adamantly  opposes" Trump's  visit, adding:

"He's going to be throwing salt into the wound-  a very, very deep wound.  And this community needs healing,  not Donald Trump."

This is especially as he knows, as do we all (with more than air between the ears), that any words of "comfort" or consolation Trump offers will be totally made up and utterly meaningless, mere posturing.  You cannot have the hate monger who incited the butchery reading a script from a teleprompter to try now to assuage the pain he himself caused. It's an atrocity and an affront to have the spectacle of this criminal -  who incited vile immigrant hatred  at a rally in El Paso back in February- now returning to his "crime scene".   

Indeed another citizen (Veronica Escobar) quoted in the piece made it clear Trump is not welcome, saying:

"He should not come here while we are in mourning.  I would encourage his staff members to have him do a little self- reflection.  I would encourage them to show him his own words and actions at his rallies"


That is a well-contemplated thought - but ultimately useless- given this is a hollow man who has absolutely no self awareness, no self control, nor the most rudimentary moral compass.  Showing him his own words and actions at rallies would be about like showing a hog covered in its own filth pictures of how it got that way.  All he'd do is "Oink!" then crap some more on the one who showed them,

So it seems most sensible citizens of this border burg feel they have no use for a piece of refuse like Trump - who already stiffed them once- showing up to deflect blame and create other scapegoats. Doesn't this "POTUS"  know when he's not wanted?  How could he if he doesn't even have the decency or honor to pay his outstanding (and long overdue) debts?

While I'm at it, Neil deGrasse Tyson certainly merits a rebuke  after making his "objectively sane statements"  re: data from deaths,  wherein he questioned  the media enhancing the import of deaths from mass shootings over those from the flu, medical errors and accidents. Clearly, this smart astrophysicist is totally tone deaf to the emotional intensity of random mass shootings and that such TERROR   bears little or no similarity to the flu, medical errors, or accidents.  Again, a case of egghead overthinking, and going so far down the rabbit hole of abstraction that the potential for any meaningful communication is lost.

How so?  Well, because deaths attributed to medical errors, accidents  and flu do not generally incite terror.  For one thing, with the exception of accidents, they are almost always assessed ex post facto - so emotional immediacy and intensity are factored out.  They may inflict distress, upset, and transcendent grief - but not instantaneous abject terror  as in a mass shooting.  Where - as in El Paso - one father beheld the skull of his 5 year old child shattered in front of him with the blood and brains all over his clothes. This difference in emotional intensity is something  Tyson ought to have known - or at least processed- before sounding off.  It isn't even a matter of "nuance" or imposed 'political correctness' from without, as some blockheads might claim. If there is a flaw of nuance, it is wholly on Tyson's (and his apologists') part for failing to discern how his mention of stats to do with medical errors diminish the deaths of those slaughtered in mass shooting terror.

And it's now why critics are telling the Hayden Planetarium head to stick to his astrophysics.  I wouldn't go that far, but only warn that if he is going to veer off -specialty to ensure he has his "facts and data" in their proper relation to events, especially in not conflating expected "normal" deaths with those from mass terror.  

 See e.g.

Web results

Neil deGrasse Tyson is facing backlash after tweeting about shooting ...

https://www.cnn.com/2019/08/05/us/neil-degrasse-tyson-gun-death.../index.html

And true, Tyson did issue an extended "apology" wrapped in more gobbledegook. So it's only a matter of time before another dunce with a fetish for "political correctness" compares it to Galileo's apology to the Inquisition.  (For rendering his heliocentric theory and basically dissing the Church's Ptolemaic model).  Should such event transpire it will merely show how far down the rabbit hold of insanity, ignorance,  illogic  (false analogy)  and Trumpism we've really descended.

See also:

Donald Trump

‘His Rhetoric Brought This Violence’: Here’s Why El Paso Residents Blame Trump for the Terrorist Attack

And:

Media

How Can We Fight White Nationalist Terror When Press Won't Even Call Trump Racist?

by Eric Boehlert | August 6, 2019 - 6:55am | permalink


And:

Donald Trump

This Paragraph from Before Trump’s Election Now Looks Ominously Prescient about His Ability to Inspire Violence

And:

Thom Hartmann

Article Tools E-mail | Print Comments (0)

Guns

The Latest Massacre Shows the Second Amendment Model of ‘Slave Patrols’ Is Still in Effect

Why Teachers In Low Tax States May Have No Choice Other Than To Leave Their Profession

Graphs tell the basic story of why so many are bailing out of teaching (From Money magazine, August, p. 66)

The news ('I Didn't Really Have A Choice', MONEY,  August, p. 62, by Jennifer Calfas)  that dedicated teachers around the nation are ditching their jobs because of low pay and dwindling benefits is not something this country can afford.   But as the graphic shows, is quite understandable given the squeeze our national economic model has put on these stewards of education. Those like Mallory Heath, presented as one example in the piece (among several) -  who had to leave her job as an English teacher in Arizona's Chandler School District  - because she realized she couldn't even afford to go to the ER for a medical emergency.


Mallory Heath - had to quit teaching after a health wake up call.

In 31- year old Mallory's case, her moment of truth arrived one night in October, 2017 when she was unable to speak  for 12 minutes.  She couldn't write or talk as she usually could and her words came out jumbled and nonsensical. Reading about her ordeal in many ways reminded me of the speech aphasia Janice experienced in the fall of October, 2016 - triggered by a TIA (transient ischemic attack). Fortunately, I was able to quickly discern from her rapid finger pointing - at a note tacked to the fridge - that she wanted to go to the Memorial Hospital stroke unit. I phoned 9-11 immediately and within a half hour she was in the ER stroke unit - being cared for- and with neurological tests run,  Plavix  (blood thinner) given subsequently.

Mallory subsequently found out  her aphasia was migraine-associated, and we learned (p. 64):

"Amid the  terrifying episode, Heath chose not to go to the emergency room. She knew she couldn't afford it."

Further, quoting Heath in the article:

"I realized, how often do I put my health on the line because I just don't have the funds to take care of myself""

And so:

"Almost a year later Heath has left the profession she calls her identity."

In many ways this Hobson's choice in respect of a coveted career was foisted on her by her state, which opted for low taxes as opposed to paying teachers and other civil servants. Arizona is but one of a number of states in Reepo land - including West Virginia, Kentucky, Oklahoma, North Carolina and others - going the lower tax or tax cut route. So they were unable to properly pay their first line of civil servants - educators.

 As reported in The Nation, July 30-Aug. 6,  p. 22,  "without the Oklahoma income tax cuts implemented between 2009 and 2016, there would have been $356 million available", e,g. to cover higher teacher salaries and enhanced benefits.  Further: "Arizona, Kansas, North Carolina and Oklahoma are among the  states that passed income tax cuts rather than restore spending on classroom, despite all four seeing huge drops in per pupil spending over the past decade."  In Arizona alone, where Mallory taught, "K-12 funding fell by nearly 37 percent" between  2008 and 2015.  Of course, this is disgraceful, and unworthy of any nation - or state- that claims to put its children first.

The MONEY article featured talks with a half dozen teachers who left and their reasons, including years long salary freezes, second or third jobs taken to make ends meet and classrooms "filled to the brim with students amid teacher shortages and dwindling funding".

Further:

"As pay fell or grew stagnant, their costs for health insurance rose. Meanwhile, a public employee pension crisis left teachers concerned about attaining a financially stable retirement."


In respect of the last, I had already (Feb. 13) cited the parlous condition of Colorado's state pension fund (PERA)  from a Sunday Denver Post  piece which observed:
"PERA is barreling toward its second funding crisis in a decade...Any attempts to water down a proposed reform package could leave the retirement system that 1 in 10 Coloradans depend on as a replacement for Social Security in grave financial peril. "
Adding:  "PERA has only 58.1 percent of the money it owes in future retirement checks."

But a potentially more toxic dynamic appears to also be at work as expressed by another teacher (Brian Steinberg) in the Philadelphia School District.  According to Steinberg "It's not just the pay, it's a profession that should be treated almost like doctors, but we're treated like babysitters."

The takeaway from his comment is that even if many teachers now abandoning their profession might be prepared to put up with all the stress and strain from the meager remuneration - the lack of respect is the killer. Why work and slave all hours of the day (and night) when you can't get a scintilla of respect from the larger society?

Much of this, obviously, is because of the ignorance and myths spread about teaching - i.e. it's a cushy job because it ends at 2:30 p.m. or whatever (in any case "not 8 to 5"), not  processing all the indecipherable homework, test papers, reports and other assignments that must be marked. But since our society is replete with dummies who know nothing -and many take after the top know nothing - this is a byproduct.  By contrast the more educated and intelligent citizens of Germany accord teachers proper respect, and demonstrate it with concomitant pay and benefits.

Another piece of idiocy has to do with myths surrounding "long" summer vacations and the great unwashed mass of Americans believing teachers just lollygag in the Sun every day or watch TV soaps while gobbling Twinkies.  No remote consciousness of the educator workshops, specialized training courses (e.g. in physics and chemistry)  or volunteer activities teachers undertake  - OR the temporary jobs in retail, fast food  etc. to try to make ends meet.

But  I suspect another more malign aspect is at work, driving the disrespect and lack of pay, benefits in Trumpdom, especially.  That is,  the entrenched anti-intellectualism which has been an abiding feature of U.S. society almost since the year dot.   I appreciated this backward strain even more on coming across some personal notes  (again unearthed by Janice in communication with other members of ancestry.com) penned by a teaching ancestor, Jacob Brumbaugh - ca. 1898.

My 19th century ancestor Jacob Brumbaugh, who was heralded as a "great teacher"  in the local (Philadelphia) press- once he reached the college level.

He wrote that: "I don't believe I received the respect I deserved teaching, until I became a college teacher."

Which is kind of counterintuitive , given that college teachers, professors, depend on high school teachers to have properly prepared the students who end up within their hallowed ivy walls.

Much of the nation's anti-intellectual strain has been documented in Richard Hofstader's book, 'Anti-Intellectualism In American Life'  Hofstadter delves into the reasons that intellectuals – mainly on the Left – are detested with such verve by the American Right. The reasons often aren’t pretty, or even comprehensible,  and in fact are often downright puerile and smack of envy, i.e. that the Right simply lacks the brainpower of the nation’s liberals. 

As recently as four years ago, this was revived with the Righties' attacks on Neil deGrasse Tyson in the news 'Cosmos' series.  The attack arrived in a despicable article in a National Review story by Charles C. W. Cooke entitled “Smarter Than Thou”. Therein, Cooke whined about “the extraordinarily puffed-up ‘nerd’ culture that has of late started to bloom across the United States.” 

This was soon followed by a contribution from Fox host Greg Gutfield who, during one panel exchange, burped out- regarding Neil Tyson:

"I hate this guy! I remember hearing Chris Hardwick on a podcast talk about Neil deGrasse Tyson and he was just salivating. White liberal nerds love this guy so much, he could defecate on them like Martin Bashir’s fantasies and they would dance in the streets.”

So clearly, if such contempt could be held for an astrophysicist like Tyson, how much less respect do you think these knuckledraggers (and most of the nation enthralled by FOX News) would have for secondary school teachers?

The good news for Mallory is she landed on her feet, having recently started a job (p. 67) as a literary curriculum specialist at Pearson Education - a multinational corporation.  Working for a corporation may not have been her ideal gig but it "will keep her close to the profession she loves".

That's more than can be said for many others who continue to leave, and find they have to enter totally different careers, e.g. bartenders, nurses, auto mechanics, to survive.

Such departures may become more common as credit card debt rapidly increases (cf. 'Consumer Spending Rise Has Dark Side', WSJ, 7/ 16, p. B1) now having risen $24.6 billion in May, or nearly double  relative to a month earlier. This according to a Federal Reserve Report. 

No matter how much some will insist "Well, if they really loved teaching they'd find a way",  in the end financial reality will catch up even to the dedicated holdouts.  No one, after all, wants to be hounded by debt collectors or forced to declare bankruptcy.

See also:

http://www.smirkingchimp.com/thread/bill-c-davis/80218/soft-targets-the-muddled-and-anti-intellectual-american-brains-that-made-election-meddling-possible

Excerpt:

"Trump voters were the target before they were Trump voters. The prerequisite for expending energy on such an initiative was an analysis of the fears, appetites and intellectual wattage of the targets. These are the people who could be seduced into bad mortgages, Jimmy Swaggart, Colonel Sanders, cabbage patch dolls, Mitch McConnell, the Kardashians, and styrofoam.

It's the soft, muddled collective anti-intellectual center that made success possible. Yes - something sinister did get into the minds of, if not millions, the smartly located thousands. The soft spasmodic brain is now at the head but it was put there by the soft spasmodic guts of the country being fed whoppers. Even the expression - red meat - speaks to this. Feeding his base, "red meat." Disgusting imagery for a metaphysical reality."

Should Undergrads Be Exposed To Modern Physics?

A Loyola University undergrad, ca. 1966, studying for a test on special relativity. The class used a text by Hugh D. Young entitled 'Fundamentals of Mechanics and Heat' (which I reviewed at Amazon) and included at least one chapter (14) on special relativity. 

That is perhaps the most that the majority of bright undergrads would be able to cope with even today.


An ongoing controversy in physics education is just how much modern physics today's undergrads should be exposed to. By definition, 'modern physics'  includes all the physics established since 1900, including: quantum theory, special and general relativity and some high energy particle physics (nature of quarks, neutrinos etc.)

The typical plaintive cry, to judge from occasional letters (say to Physics Today)  amounts to some variation on:

"Why must we be stuck in the tedious, boring physics of the 17th, 18th and 19th centuries? Why always Newton, Faraday and such instead of Bohr, Einstein and Schrodinger?  We want to be taught more of the modern physics less of the antiquated stuff!'

Thus, they are chagrined they're still being taught mostly Newtonian mechanics,  and 'old-style' Electricity and magnetism, thermal physics and only a little bit of special relativity.  What they don't say is that even that "little bit" of special relativity often poses problems.

So the question remains: can they really handle more? Most undergrads even at the top universities are simply not at the level they can grasp quantum mechanics or general relativity. Even Richard Feynman ('Feynman Lectures')  while conducting his famous first year course at Caltech, complained about the difficulty of getting quantum concepts over to many of the students.  Of course, there will always be the select few with plenty of mathematics and physics background for whom the content won't present huge problems. But make no mistake they're in the minority.

I still recall teaching a Calculus physics course for which the final chapter of the text assigned had significant quantum mechanics content, including:  the basic Schrodinger wave equation, quantum square well, atomic energy levels, eigenvalues, probability densities and how to compute expectation values. Attached below  is one problem which I worked out for the class:


But which only 1-2 of the class actually got. Most were stung by: a) not having the requisite mathematical ability (which makes one wonder how they managed to be allowed to move on from the earlier semesters) and b) not being able to conceptualize (despite numerous visual aids).


One of the visual aids which flummoxed them is shown below, including the first 3 wave functions for the H- atom(far left), the corresponding probability densities (middle) and the associated energy levels for an "infinite square well".


Basically, the possible energies of the particle, called energy levels, are quantized. The integer n used to designate them, is called the principal quantum number.

The state with lowest energy, n = 1, is called the ground state. The state with n = 2 is called the first excited state and so on.

There are n/2 de-Broglie waves capable of fitting into the well if the particle is in the nth quantum state.

At once the diagram captures the beauty and simplicity of quantum mechanics, in showing how energy is quantized in "jumps" as it is in the actual hydrogen atom.

In retrospect, the experience at Loyola with Hugh Young's presentation  of special relativity was perhaps at the limits of what a well prepared undergrad could understand.   For example, his derivation of the relativistic equation of energy (W) on pages 394, 395:

ò ^x2 _x1  dp/dt  dx = ò ^t2 _t1  (dp/dt)(dx/dt)  dt =

  ò ^t2 _t1  v(dp/dt)   dt  =  ò ^v2 _v1  v(dp/dv)  dv

W=   ò ^v2 _v1   v  d/dv [m_o v/ Ö (1 - v²/c² ] dv

The preceding equation for W applies since for relativistic momentum:

p  =  m_o v/ Ö (1 - v²/c² )

I argue the above is "at the limit" because of the calculus -based approach with which most undergrads would not be comfortable, even those who've taken AP Calculus.  More to the point, if one veers into quantum theory and general relativity, it doesn't get any easier.

This leaves us asking the question of whether there is an alternative solution or approach, specifically for those less able students who aren't attending Caltech, MIT or Harvard.  I believe there is and came away with one idea from a recent Readers Forum article ('How Black Holes Saved My Astronomy Course')  in Physics Today by Joseph Ribaudo..  Ribaudo - based at Utica College, New York- noted the struggle of his students to master the material  with most underperforming (averages in the "C range")  in his astronomy course.   He realized a large part of the problem was that  the existing astronomy textbooks were all too similar in their writing, content and design elements - and often way too mathematical. So he turned to Neil Degrasse Tyson's 'Death By Black Hole' as his central (core) text aided by "reading and writing assignments derived from popular and historical science publications".

Can a similar strategy be used to incorporate more modern physics into undergrad classical physics courses? I am confident this is feasible. Of course, the extent of integration of the modern physics material will hinge on the time allotted for the course or courses.  In most ('General Physics') courses, the modern physics is fit in at the very end - usually in one or two chapters featuring special relativity and some of the 'original' quantum mechanics, say of Bohr then Schrodinger.  At the maximum level of exposure students will be shown the use of the Schrodinger equation to solve for simple QM systems, say a particle in a box. This assumes, of course, the student has done some work in differential equations. (N.B. It is extremely rare for freshman and sophomore physics majors to take a dedicated modern physics course, far less a QM or Relativity course.)

But let's assume students are roughly at the math and abstraction level of  Ribaudo's astronomy class. What texts might supplement the approach to teach modern physics? I'd include the following:

'The Strange Story of the Quantum' - by Banesh Hofman (Dover, 1964)

'Thirty Years That Shook Physics' - by George Gamow (Dover, 1966)

'Relativity and Common Sense' -  by Herman Bondi (Dover, 1964)

'Sidelights on Relativity' - by Albert Einstein (Dover, 1954)

'The ABC of Relativity' - by Bertrand Russell (Signet, 1959)

 All of the above are eminently readable, and the math is at a minimum. Much of the math that is set out, such as in Bondi's book, is in the form of geometry from which simple derivations of the principles are shown. Einstein's book is terrific in providing an understanding at a non-math level by the master himself.

Ribaudo mentions in his article (p. 11)  setting one mid term exam question to the effect: "Discuss the value of reading 'Death By Black Hole' and whether you'd recommend this book to others".  The same sort of question might be asked of any of the books listed above.  In terms of how much contextual mathematics one's students can handle that has to be left to the instructor. For those who might wish to know some QM but minus all the math, Hoffman's book is probably best. For those who might wish to know some special relativity without the math, Russell's book is likely best. For those who are comfortable with plane geometry and some algebra,  Gamow's book is ideal for QM, and Bondi's ditto for special relativity.

If instructors in special relativity wish to get into more problem solving and math exposure - still largely at the intermediate algebra level (with a tiny bit of differential calculus)-  my own text: 'Modern Physics: Notes, Problems and Solutions' is ideal, namely the first three chapters (pp. 1 -45).

Ribaudo also cites "reading and writing assignments" from popular science magazines (e.g. Discover) and this can also provide fertile material for modern physics. For example, asking students to read the excellent article on quantum entanglement in Discover (July/August, 2016, p. 60) and asking students how they might explain this to a friend. Or better, how they might explain it if they could go back in time and encounter Neils Bohr.

In the end, it is possible to present modern physics to undergrads, but it has to be tailored to their own math and abstraction abilities.  If this is done, and there is the time allotted to do it without having to rush, then both physics instructors and their students will be all the better for it. And we may see much less whining from the undergrads about being denied entry into the "modern stuff".

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Addendum:

The best modern physics text I've found for math proficient students - geared to freshman and sophomores - is 'Space, Time and Quanta: An Introduction to Contemporary Physics' by Robert Mills (1994).  In his Introduction,  Mills writes of the text being a "supplement to a more conventional course" or "designed for the physics side of an interdisciplinary course" - i.e. for other (non-physics) students, but don't believe it. The text is in fact perfect as a standalone, totally complete modern physics text - at least on a par with the analogous content in The Feynman Lectures.  The end of chapter problem sets are especially good, and I simply can't see any "interdisciplinary" student being able to get through them.  Hence, I believe Mills greatly underestimates the book's value as a teaching text for modern physics.