I think classical Newtonian mechanics has to be in the conversation.
There’s a difference between “wrong” and “incomplete”. Newtonian mechanics was incomplete, the Luminiferous Aether was wrong.
Future candidates for wrong include Dark Matter and Dark Energy and “String Theory”.
Dark matter has good evidence supporting it.
Not really. It just fills a hole, and has no strong evidence against it, as of yet. But, there are other contenders for that hole filling.
I’m not a big fan of theories that are consistent with existing observations, but are otherwise unverifiable in an end-to-end test. I suspect that much of what we think we know about the universe will be overturned when and if we ever are able to venture out far from our origin to investigate from other vantage points.
There are plenty of observations that cannot be explained without non-baryonic cold dark matter. The numbers for primordial nucleosynthesis, angular power spectrum of the CMBR, galaxy formation don’t work out without it. Also, the Bullet Cluster is strong evidence against modified theories of gravity as an alternate explanation.
Erik Verlinde’s entropic gravity theory looks like the best bet to me. I found parts of it extremely elegant, simpler than existing theories (he derives the properties of the macro- universe from little more than temperature, entropy, information, and the existence of a quantum realm whose properties don’t matter all that much) and it does away with gravity as a fundamental force. It also is a pretty good fit for observations without any tweaking at all, including I think the bullet cluster.
Paul, I’m not too impressed lately with Ars Technica’s science writing, especially physics; I’ll stick with Sabine’s take until further notice. She’s a good blogger and a well-respected physicist.
Well, Paul D.’s link is more up to date. Of course, since I am in no position to analyze the data for myself, if I must choose, I must make the choice based on faith. I do not like making choices based on faith.
IMHO, the data are simply too limited. For any given finite set of observations, there is an inifinte set of mathematical models which can be made to reproduce the observations to an arbitrary degree of precision. Maybe, out of that infinite set, a given set of researchers have picked the exact one that has the greatest affinity with natural reality. But, I wouldn’t bet my life on it.
“Hey, the elephant is a pillar,” said the first man who touched his leg. “Oh, no! it is like a rope,” said the second man who touched the tail. “Oh, no! it is like a thick branch of a tree,” said the third man who touched the trunk of the elephant. “It is like a big hand fan” said the fourth man who touched the ear of the elephant. “It is like a huge wall,” said the fifth man who touched the belly of the elephant. “It is like a solid pipe,” Said the sixth man who touched the tusk of the elephant.
The usefulness of a theory is in its predictive power, which allows us to utilize the theory to derive tangible benefits by bending nature to our wills. I just can’t get too excited about a theory that has no particular usefulness except in describing some remote phenomenon, and for which we cannot, at this time, have absolute assurance of its validity.
The author DEFINES a “wrong” theory as incomplete. The standard model is correct as far as it goes but it’s incomplete.
Luminiferous Aether.
It has to be the greatest wrong theory because it keeps on giving even after it is killed. Just a few years ago there was a serious proposal being floated that WIMPs (i.e. Dark Matter) would flow through our solar system in a sort of “WIMP wind”. And that the effects of that ought to be measurable in a fashion similar to that which was prosposed to detect the LA from Michelson-Morley days! A bad idea that keeps coming back deserves some type of special recognition!
WIMPs were a kind of CDM, but they are not the only kind that could work. WIMPs were favored by some because of prejudice from supersymmetry models (leading to a “WIMP miracle” of numbers and thermal cross sections working out), but SUSY has failed to be confirmed at LHC, and WIMPs of the necessary interaction strengths have been ruled out.
There was never anything for the ether except the prejudice that a wave equation must mean there’s something material that’s waving.
Yes, Chad was quite explicit in his definition that good theories that were wrong were recognized as such but still found useful. Aether was not.
Clearly, the presence of the ‘ether’ was the greatest wrong theory
FTA: “Newton’s gravity loses some points, though, because for most of that time, nobody had any idea that it was, in fact, a wrong theory. ”
Oh, I think they knew essentially from the beginning. The problem of instantaneous action at a distance led to Newton himself throwing his hands up, and proclaiming “hypotheses non fingo”.
Just because a theory has had some (very great, as he notes) successes doesn’t mean it’s “correct,” even if you slyly admit it’s incomplete. You could have said that about Newtonian gravity, until Einstein showed it was not incomplete, but simply wrong. Calling the Standard Model “correct, but incomplete” makes it the moral equivalent of Dan Rather’s “fake, but accurate” Texas ANG memo.
It’s fair to describe the Standard Model as a great achievement. But to balance its successes, it sometimes gives very wrong answers, or none at all. I’d put my money on string theory as being more incorrect (and at present, much less useful) than the Standard Model.
In the past, when physics theories have met brick walls, it’s been a sign that a revolution is in the offing, and I wonder if that’s the case for quantum physics today. Or, we might have simply reached the limits of what is knowable and testable by experiments we can conceive or perform, and our theories are simply showing the stagnation that must result.
In any case, scientific models are just that–models, or descriptions of what nature does. Nature doesn’t look at some list of equations we’ve cooked up and do what they say. Nature does its own thing, we just try to model that behavior with equations. As a cynic and empiricist, I’d say most every theory in physics is at best an approximation, and some are much better approximations than others. I do not demean or discount theory in physics; at a certain point, an approximation is so good, you can use it as if it’s correct. For example, using a series to calculate pi to 10 digits is certainly good enough for calculating the circumference of a circle, when your diameter measurement has only 3 significant figures. But it’s still an approximation, it’s not *really* pi.
What wrong answer does the Standard Model give?
The Standard Model doesn’t do well with dark matter (dark matter is not predicted, and as I understand it, additions to the Standard Model might be needed when/if a dark matter particle (there may be several types) is finally identified; the matter/antimatter asymmetry isn’t simply explained; the Standard Model didn’t allow for neutrino masses, and needed tweaking to allow for massive neutrinos. I was originally thinking of the cosmological constant being 120 orders of magnitude off from the predicted value, though that’s probably not the Standard Model’s fault.
Again, it’s very good, but to claim it “correct, but incomplete,” when you need to correct its errors…
I nominate Benjamin Franklin and his incorrect labeling of electrical charge. (To his credit, e had a fifty-fifty chance of getting it right, and guessed.)
This is a “wrong” theory that we’ve KNOWN to be wrong for a hundred years, and we still use it, and every single electrical engineer has to deal with electrons having negative charge every single day, and will until the end of (human) time.
At least we got which side of the road to drive on right.
If the MSM controlled culture can lable pro-liberty states “red” and pro-socialism “blue”, we can change the name of the electron charge if we can just get the NYT, WaPo, NBC, CBS, CNN etc etc to use the same procedure.
Asimov asserted that science doesn’t so much get things right as get things less wrong over time.
My theory is the ratio of unknown to known is always greater than one.
I guess writing an article called “15 Wrong Theories in Diet” would be like shooting fish in a barrel.
It would be a very difficult article to write. Having to pick just 15…
I can’t read the article because I run an ad blocker and refuse to whitelist Forbes (one of the worst embedded ad sites around), but I’ll nominate Aristotle’s impetus theory of motion as holding back progress in dynamics for well over a thousand years.
And Lavoisier’s proclamation that “there are no stones in the sky, therefore, stones cannot fall from the sky” was a serious impediment to observational astronomy and our understanding of the solar system by allowing meteorite observations to be dismissed and ridiculed out of hand.
Flat Earth theory is the winner by far. It’s known to be wrong for at least two millennia and yet, it’s still used in building construction and geography maps.
For purposes of building construction “flat Earth” works. It’s only over a larger area that it presents problems.
Actually “Flat Earth” doesn’t work – and isn’t, therefore, used – when designing bridges, especially suspension bridges.
That’s the point of these “wrong” theories. They work for the purpose of some niche even though they’re known to be wrong in general (with glaring flaws once you get away from the parameter space where the niche works). Flat Earth theory just has a few of the largest niches and one of the longest histories of known to be wrong.
epicycles
It worked well and predicted planetary motion. Except it was wildly complex. Reminds me of dark energy.
Dark energy has basically two free parameters. Epicycles had many more. You can think of them as Fourier coefficients.
But, that makes epicycles merely a phenomenological approach. A “Just So” story, with no cause and effect relationship. We cannot take an arbitrary configuration of masses and say how they will move relative to one another. We must fit the model to observations in time.
There is a danger, as physical models become ever more complex, that we will run into the same problem. With a rich enough functional basis, we can always fit observations to a greater or lesser degree of fidelity to a given expansion.
That is my concern with “Dark Matter” and “Dark Energy”. They are too kluge-like, without a fundamental reason for their existence except to fit observational data.
Well, yes. Epicycles were just curve fitting. At best, they observed “hey, look! we don’t need THAT MANY Fourier parameters”, which is just a way of saying the orbits are close to (but not exactly) circular.
Newton’s theory gave better predictions with fewer free parameters (basically, planetary masses, positions, velocities, and G). Better prediction with fewer “knobs” to do the curve fitting with is what physicists want to see. Dark energy has only two (really, only one, if you assume it behaves like a cosmological constant). This is pretty much the OPPOSITE of a complicated theory.
“Conservation of Energy” along with “Conservation of Mass” were theoretical models that worked great but led to immense errors. Because energy could not be created or destroyed, the Sun could be no more than a few hundred million years old. Hence the Earth could not be older, nor life on Earth more than maybe one hundred million years. Evolution, then, and much of geology, had to be incorrect according to “simple physics”.
With this model of the Sun and Earth, it was plain Mars may have once had life (and canals!) when it was hotter and before the Sun “ran down” to the current levels. Venus, on the other hand, must be hotter and wetter and hold more primitive life, currently, though it could be predicted to become Earth-like as the Earth itself exhausted its energy of formation.
Conservation of Energy meant “gradualism” was false. Past times must necessarily have been cataclysmic and violent, thrusting up mountains and tearing out chasms in moments of unimaginable upheaval. Plants and animals must have learned to adapt by choosing for themselves survival traits or “teaching” their progeny new forms. Geologists and paleontologists might have been called “deniers” of physics for insisting on some calmer, steadier, process.
Conservation of Energy meant our industrial society was doomed. We had already exhausted wood and whale oil, “rock oil” (petroleum) was mined out in nearly every surface of the Earth where it had cropped up, and coal required miners to go deeper every year, for diminishing return. Sorry, all you optimists, but it’s just simple physics. Your kids, or maybe your grandkids, will never reach the levels of attainment you’ve been lucky enough to enjoy.
A physicist contemplating the reports by chemists, such as the Curies, about radium, polonium, and other “something for nothing” sources of light, must necessarily and regretfully conclude that something was terribly and fundamentally wrong with the science of Chemistry itself. How could “scientists” report such results, so obviously in violation of the principle of Conservation of Energy? And how could such heretics be brought back into consensus on the topic?
“Conservation of Energy” along with “Conservation of Mass” were theoretical models that worked great but led to immense errors.
Ok, what errors did they lead to? I didn’t notice any mentioned in your post.
and before the Sun “ran down” to the current levels
To the contrary, the Sun is growing hotter. Turns out a higher concentration of heavier nuclei result in a denser, hotter plasma in the interior, which results in a slow build up of heat in the interior combined with more radiation emitted from the Sun’s surface.
Conservation of Energy meant our industrial society was doomed. We had already exhausted wood and whale oil, “rock oil” (petroleum) was mined out in nearly every surface of the Earth where it had cropped up, and coal required miners to go deeper every year, for diminishing return. Sorry, all you optimists, but it’s just simple physics. Your kids, or maybe your grandkids, will never reach the levels of attainment you’ve been lucky enough to enjoy.
Silly thing to claim when there’s 1kW per square meter of power in sunlight, which won’t exhaust itself for maybe a billion years.
The sun would also be growing hotter if it were powered by gravitational contraction, as they thought before nuclear fusion was discovered. This follows from the Virial Theorem, which says the internal energy of the sun = 1/2 the (negative of the) gravitational potential energy. As the sun contracts, it becomes more tightly bound, and therefore its internal energy and temperature must increase.
Because energy could not be created or destroyed, the Sun could be no more than a few hundred million years old.
This doesn’t follow at all. The Sun was thought to be tens of millions of years old because the Sun was thought to be powered by gravitational contraction. We all know it’s actually powered by nuclear fusion, and that fusion causes a conversion of mass to energy. But it’s possible to imagine something like nuclear fusion that would work even in a Newtonian universe where conservation of mass and of energy are two different laws. After all, nuclear reactions differ from chemical reactions in that they are much more energetic, but they both convert mass to energy in our relativistic universe (it’s just the change of mass in chemical reactions is too small to easily measure.)
I’ll add that it’s possible to imagine a Newtonian universe where the Sun is much OLDER than it could be in our universe. The energy yield of a reaction of matter in our universe is limited by the total energy content of that matter (mc^2), but there is no such limit in a Newtonian universe.
I think classical Newtonian mechanics has to be in the conversation.
There’s a difference between “wrong” and “incomplete”. Newtonian mechanics was incomplete, the Luminiferous Aether was wrong.
Future candidates for wrong include Dark Matter and Dark Energy and “String Theory”.
Dark matter has good evidence supporting it.
Not really. It just fills a hole, and has no strong evidence against it, as of yet. But, there are other contenders for that hole filling.
I’m not a big fan of theories that are consistent with existing observations, but are otherwise unverifiable in an end-to-end test. I suspect that much of what we think we know about the universe will be overturned when and if we ever are able to venture out far from our origin to investigate from other vantage points.
There are plenty of observations that cannot be explained without non-baryonic cold dark matter. The numbers for primordial nucleosynthesis, angular power spectrum of the CMBR, galaxy formation don’t work out without it. Also, the Bullet Cluster is strong evidence against modified theories of gravity as an alternate explanation.
Erik Verlinde’s entropic gravity theory looks like the best bet to me. I found parts of it extremely elegant, simpler than existing theories (he derives the properties of the macro- universe from little more than temperature, entropy, information, and the existence of a quantum realm whose properties don’t matter all that much) and it does away with gravity as a fundamental force. It also is a pretty good fit for observations without any tweaking at all, including I think the bullet cluster.
Quanta Magazine article
phys.org article
I think both of those link to his papers.
His theory may be wrong, and is certainly not complete, but it is quite interesting.
Sabine Hossenfelter has two good posts on Verlinde:
http://backreaction.blogspot.com/2016/12/can-dark-energy-and-dark-matter-emerge.html
http://backreaction.blogspot.com/2017/03/is-verlindes-emergent-gravity.html
Her take to date: still very incomplete and far too immature to be taken very seriously, but it is compatible with GR and worth of further work.
Also, she has some interesting work taking the Bullet Cluster off its pedestal as the dark matter poster child: http://backreaction.blogspot.com/2017/01/the-bullet-cluster-as-evidence-against.html
Cthulhu:
The Bullet Cluster is looking good these days. Science in action.
https://arstechnica.com/science/2017/09/science-in-progress-did-the-bullet-cluster-withstand-scrutiny/
Paul, I’m not too impressed lately with Ars Technica’s science writing, especially physics; I’ll stick with Sabine’s take until further notice. She’s a good blogger and a well-respected physicist.
Well, Paul D.’s link is more up to date. Of course, since I am in no position to analyze the data for myself, if I must choose, I must make the choice based on faith. I do not like making choices based on faith.
IMHO, the data are simply too limited. For any given finite set of observations, there is an inifinte set of mathematical models which can be made to reproduce the observations to an arbitrary degree of precision. Maybe, out of that infinite set, a given set of researchers have picked the exact one that has the greatest affinity with natural reality. But, I wouldn’t bet my life on it.
It’s like the parable of the blind men and the elephant:
The usefulness of a theory is in its predictive power, which allows us to utilize the theory to derive tangible benefits by bending nature to our wills. I just can’t get too excited about a theory that has no particular usefulness except in describing some remote phenomenon, and for which we cannot, at this time, have absolute assurance of its validity.
The author DEFINES a “wrong” theory as incomplete. The standard model is correct as far as it goes but it’s incomplete.
Luminiferous Aether.
It has to be the greatest wrong theory because it keeps on giving even after it is killed. Just a few years ago there was a serious proposal being floated that WIMPs (i.e. Dark Matter) would flow through our solar system in a sort of “WIMP wind”. And that the effects of that ought to be measurable in a fashion similar to that which was prosposed to detect the LA from Michelson-Morley days! A bad idea that keeps coming back deserves some type of special recognition!
https://en.wikipedia.org/wiki/Luminiferous_aether
Yes, he discusses both of those.
WIMPs were a kind of CDM, but they are not the only kind that could work. WIMPs were favored by some because of prejudice from supersymmetry models (leading to a “WIMP miracle” of numbers and thermal cross sections working out), but SUSY has failed to be confirmed at LHC, and WIMPs of the necessary interaction strengths have been ruled out.
There was never anything for the ether except the prejudice that a wave equation must mean there’s something material that’s waving.
Yes, Chad was quite explicit in his definition that good theories that were wrong were recognized as such but still found useful. Aether was not.
Clearly, the presence of the ‘ether’ was the greatest wrong theory
FTA: “Newton’s gravity loses some points, though, because for most of that time, nobody had any idea that it was, in fact, a wrong theory. ”
Oh, I think they knew essentially from the beginning. The problem of instantaneous action at a distance led to Newton himself throwing his hands up, and proclaiming “hypotheses non fingo”.
Just because a theory has had some (very great, as he notes) successes doesn’t mean it’s “correct,” even if you slyly admit it’s incomplete. You could have said that about Newtonian gravity, until Einstein showed it was not incomplete, but simply wrong. Calling the Standard Model “correct, but incomplete” makes it the moral equivalent of Dan Rather’s “fake, but accurate” Texas ANG memo.
It’s fair to describe the Standard Model as a great achievement. But to balance its successes, it sometimes gives very wrong answers, or none at all. I’d put my money on string theory as being more incorrect (and at present, much less useful) than the Standard Model.
In the past, when physics theories have met brick walls, it’s been a sign that a revolution is in the offing, and I wonder if that’s the case for quantum physics today. Or, we might have simply reached the limits of what is knowable and testable by experiments we can conceive or perform, and our theories are simply showing the stagnation that must result.
In any case, scientific models are just that–models, or descriptions of what nature does. Nature doesn’t look at some list of equations we’ve cooked up and do what they say. Nature does its own thing, we just try to model that behavior with equations. As a cynic and empiricist, I’d say most every theory in physics is at best an approximation, and some are much better approximations than others. I do not demean or discount theory in physics; at a certain point, an approximation is so good, you can use it as if it’s correct. For example, using a series to calculate pi to 10 digits is certainly good enough for calculating the circumference of a circle, when your diameter measurement has only 3 significant figures. But it’s still an approximation, it’s not *really* pi.
What wrong answer does the Standard Model give?
The Standard Model doesn’t do well with dark matter (dark matter is not predicted, and as I understand it, additions to the Standard Model might be needed when/if a dark matter particle (there may be several types) is finally identified; the matter/antimatter asymmetry isn’t simply explained; the Standard Model didn’t allow for neutrino masses, and needed tweaking to allow for massive neutrinos. I was originally thinking of the cosmological constant being 120 orders of magnitude off from the predicted value, though that’s probably not the Standard Model’s fault.
Again, it’s very good, but to claim it “correct, but incomplete,” when you need to correct its errors…
I nominate Benjamin Franklin and his incorrect labeling of electrical charge. (To his credit, e had a fifty-fifty chance of getting it right, and guessed.)
This is a “wrong” theory that we’ve KNOWN to be wrong for a hundred years, and we still use it, and every single electrical engineer has to deal with electrons having negative charge every single day, and will until the end of (human) time.
https://xkcd.com/567/
At least we got which side of the road to drive on right.
If the MSM controlled culture can lable pro-liberty states “red” and pro-socialism “blue”, we can change the name of the electron charge if we can just get the NYT, WaPo, NBC, CBS, CNN etc etc to use the same procedure.
Asimov asserted that science doesn’t so much get things right as get things less wrong over time.
My theory is the ratio of unknown to known is always greater than one.
I guess writing an article called “15 Wrong Theories in Diet” would be like shooting fish in a barrel.
It would be a very difficult article to write. Having to pick just 15…
I can’t read the article because I run an ad blocker and refuse to whitelist Forbes (one of the worst embedded ad sites around), but I’ll nominate Aristotle’s impetus theory of motion as holding back progress in dynamics for well over a thousand years.
And Lavoisier’s proclamation that “there are no stones in the sky, therefore, stones cannot fall from the sky” was a serious impediment to observational astronomy and our understanding of the solar system by allowing meteorite observations to be dismissed and ridiculed out of hand.
Flat Earth theory is the winner by far. It’s known to be wrong for at least two millennia and yet, it’s still used in building construction and geography maps.
For purposes of building construction “flat Earth” works. It’s only over a larger area that it presents problems.
Actually “Flat Earth” doesn’t work – and isn’t, therefore, used – when designing bridges, especially suspension bridges.
That’s the point of these “wrong” theories. They work for the purpose of some niche even though they’re known to be wrong in general (with glaring flaws once you get away from the parameter space where the niche works). Flat Earth theory just has a few of the largest niches and one of the longest histories of known to be wrong.
epicycles
It worked well and predicted planetary motion. Except it was wildly complex. Reminds me of dark energy.
Dark energy has basically two free parameters. Epicycles had many more. You can think of them as Fourier coefficients.
But, that makes epicycles merely a phenomenological approach. A “Just So” story, with no cause and effect relationship. We cannot take an arbitrary configuration of masses and say how they will move relative to one another. We must fit the model to observations in time.
There is a danger, as physical models become ever more complex, that we will run into the same problem. With a rich enough functional basis, we can always fit observations to a greater or lesser degree of fidelity to a given expansion.
That is my concern with “Dark Matter” and “Dark Energy”. They are too kluge-like, without a fundamental reason for their existence except to fit observational data.
Well, yes. Epicycles were just curve fitting. At best, they observed “hey, look! we don’t need THAT MANY Fourier parameters”, which is just a way of saying the orbits are close to (but not exactly) circular.
Newton’s theory gave better predictions with fewer free parameters (basically, planetary masses, positions, velocities, and G). Better prediction with fewer “knobs” to do the curve fitting with is what physicists want to see. Dark energy has only two (really, only one, if you assume it behaves like a cosmological constant). This is pretty much the OPPOSITE of a complicated theory.
“Conservation of Energy” along with “Conservation of Mass” were theoretical models that worked great but led to immense errors. Because energy could not be created or destroyed, the Sun could be no more than a few hundred million years old. Hence the Earth could not be older, nor life on Earth more than maybe one hundred million years. Evolution, then, and much of geology, had to be incorrect according to “simple physics”.
With this model of the Sun and Earth, it was plain Mars may have once had life (and canals!) when it was hotter and before the Sun “ran down” to the current levels. Venus, on the other hand, must be hotter and wetter and hold more primitive life, currently, though it could be predicted to become Earth-like as the Earth itself exhausted its energy of formation.
Conservation of Energy meant “gradualism” was false. Past times must necessarily have been cataclysmic and violent, thrusting up mountains and tearing out chasms in moments of unimaginable upheaval. Plants and animals must have learned to adapt by choosing for themselves survival traits or “teaching” their progeny new forms. Geologists and paleontologists might have been called “deniers” of physics for insisting on some calmer, steadier, process.
Conservation of Energy meant our industrial society was doomed. We had already exhausted wood and whale oil, “rock oil” (petroleum) was mined out in nearly every surface of the Earth where it had cropped up, and coal required miners to go deeper every year, for diminishing return. Sorry, all you optimists, but it’s just simple physics. Your kids, or maybe your grandkids, will never reach the levels of attainment you’ve been lucky enough to enjoy.
A physicist contemplating the reports by chemists, such as the Curies, about radium, polonium, and other “something for nothing” sources of light, must necessarily and regretfully conclude that something was terribly and fundamentally wrong with the science of Chemistry itself. How could “scientists” report such results, so obviously in violation of the principle of Conservation of Energy? And how could such heretics be brought back into consensus on the topic?
“Conservation of Energy” along with “Conservation of Mass” were theoretical models that worked great but led to immense errors.
Ok, what errors did they lead to? I didn’t notice any mentioned in your post.
and before the Sun “ran down” to the current levels
To the contrary, the Sun is growing hotter. Turns out a higher concentration of heavier nuclei result in a denser, hotter plasma in the interior, which results in a slow build up of heat in the interior combined with more radiation emitted from the Sun’s surface.
Conservation of Energy meant our industrial society was doomed. We had already exhausted wood and whale oil, “rock oil” (petroleum) was mined out in nearly every surface of the Earth where it had cropped up, and coal required miners to go deeper every year, for diminishing return. Sorry, all you optimists, but it’s just simple physics. Your kids, or maybe your grandkids, will never reach the levels of attainment you’ve been lucky enough to enjoy.
Silly thing to claim when there’s 1kW per square meter of power in sunlight, which won’t exhaust itself for maybe a billion years.
The sun would also be growing hotter if it were powered by gravitational contraction, as they thought before nuclear fusion was discovered. This follows from the Virial Theorem, which says the internal energy of the sun = 1/2 the (negative of the) gravitational potential energy. As the sun contracts, it becomes more tightly bound, and therefore its internal energy and temperature must increase.
Because energy could not be created or destroyed, the Sun could be no more than a few hundred million years old.
This doesn’t follow at all. The Sun was thought to be tens of millions of years old because the Sun was thought to be powered by gravitational contraction. We all know it’s actually powered by nuclear fusion, and that fusion causes a conversion of mass to energy. But it’s possible to imagine something like nuclear fusion that would work even in a Newtonian universe where conservation of mass and of energy are two different laws. After all, nuclear reactions differ from chemical reactions in that they are much more energetic, but they both convert mass to energy in our relativistic universe (it’s just the change of mass in chemical reactions is too small to easily measure.)
I’ll add that it’s possible to imagine a Newtonian universe where the Sun is much OLDER than it could be in our universe. The energy yield of a reaction of matter in our universe is limited by the total energy content of that matter (mc^2), but there is no such limit in a Newtonian universe.