None of which excuses the word “proof.”
Yes, it is.
Yes. “Dark energy” is synonymous with “some force”, at least that’s the way I’ve seen the term used.
The OP seems to be asking for the paradigm shifts of science as described by Thomas Kuhn. Not all science works like that. Kuhn was clearly inspired by the huge changes in physics that had occurred. He was after all a physicist prior to turning to philosophy. And he felt that science advances like that.
Not everyone thinks that this is the rule, or even necessarily all that useful. Kuhn published this work in the 60’s at a time when the idea of bucking the establishment had a certain popularity. Not all philosophers of science were impressed with Kuhn, especially Karl Popper and Paul Feyerabend. I tend to feel that Kuhn misunderstood the point of Popper’s falsifiability, and thought that it was the mechanism by which a theory was overturned rather than understanding that is is the touchstone of a theory being scientific.
Science based upon the idea of a falsifiable hypothesis is now the mainstream view of what distinguishes science from other forms of knowledge. Popper was concerned with battling pseudoscience. In particular socialist ideology masquerading as a scientific reality, and psychology promoting ridiculous claims - Freud in particular. There is something of a curious irony that Kuhn’s hypothesis of paradigm shifts was itself bordering on psuedo-science. Especially his notion of parallel incommensurate theories.
The idea that a scientific theory is proven is not really part of Popper’s view of science. A theory is validated, and over time becomes more accepted as it proves useful. Useful means it is predictive, and hopefully it is predictive enough to build other science on. Any theory that is predictive has the eternal danger that one day a prediction will be wrong. That is the point. If the prediction resolutely remains wrong in the face of additional work, there is much rejoicing, and the possibility of new science opens up, with new theories that themselves must run the same gauntlet. They must be falsifiable, and over time may become validated by further experiment, and if they continue to be predictive, they may become accepted as a mainstream theory.
A lot of real science is the result of hard grind over decades of work from thousands of scientists. Kuhn called this “normal science”, but expected paradigm shifts - and competing incommensurate theories as part of the shift
My poster child for normal science is biochemistry. The advances and capabilities in the area would be considered science fiction only a few decades ago. Lots of surprises on the way, but surprises that improved understanding of the complexity, and sometimes overthrowing orthodoxy - but usually with a shrug of “ok now we know more” rather than a single identifiable paradigm shift. The overarching paradigm (if it makes sense to lump everything into one) has shifted enormously, but incrementally, on many fronts. The complexity of the area guarantees that this will be going for a very long time.
Khun’s incommensurate theories leading to an actual battle between old and new with a consequent paradigm shift generally doesn’t happen. Which is why this thread struggles to come up with much beyond the well known few.
Physics gets the attention in popular culture. And that probably skews popular views of science. There seem to be an order of magnitude more popular headlines about the underpinnings of physics than any other area of science reporting. Alternative theories get talked up as “the crisis in cosmology” or similar stupid headlines. Lamba CDM might be the accepted orthodoxy, but there is a queue of scientists hoping to be the one to push the next step, and if the stars align, maybe get a free trip to Stockholm. And the next step is very unlikely to be a hard fought battle between entrenched aging adherents and the new guard, but rather a - “well that was unexpected” and moving on. Expect a lot of scrutiny, and a few bruised egos, but modern science tends to move at a pace that does not reward obstinate digging in of heels.
When Arthur Eddington journeyed to Brazil to photograph the 1919 solar eclipse, he sought to validate the newly minted general relativity. His observations were more consistent with Einstein than Newton. (The effort and care that went into this was extraordinary, and the results were on the ragged edge of what was achievable. GR predicts an offset in star position twice that of Newton, and the offset is about one second of arc.) The observations were touted as a vindication of Einstein in the popular press. The reality was that they were consistent with GR and inconsistent with Newtonian gravity. That is not the same. But the fact that a testable (and falsifiable) prediction of GR had been validated was a big deal. What GR was not, was proven. And here we are 100 years hence. GR has withstood every test thrown at it. But that doesn’t stop us prodding and poking it looking for a crack or weakness. The expectation is that it will hold up. The hope is that one day it doesn’t.
No, nothing can be established with complete certainty. See Solipsism.
Maybe we are brains in a vat, and the world around us is a simulation. Maybe Pluto and neptunium are fantasies, and part of the simulation.
Maybe I’m the only real thing, and you are part of the simulation. How can I be certain?
What is reality anyway?
My hypothesis, or theory, or whatever others want to call it, is that every tenured physicist, from a major university, who today (say, since 2010) publishes peer reviewed research on related topics, believes that faster than light communication is impossible. I’m not saying the tenured physicists of today’s world are correct – although I have a suspicion they are – just that there is such as strong consensus that it’s a model for what a strong consensus looks like.
If my hypothesis is wrong, please provide peer reviewed research suggesting that. Maybe it exists and I will then have to modify my hypothesis!
As for there existing “something that’s always faster than light,” that’s a different question. “Something” is not the same as communication.
It’s worse than that - we know that GR has limitations, because some of its predictions for extreme situations produce impossible results (infinities). But so far, we haven’t found a usefully disconfirming observation - an observation that disagrees with GR and might point the way to something better.
The law of conservation of mass was proven to the limits of then-contemporary observation. Likewise the law of conservation of energy.
Both were then disproven.
Both are now seen as useful low-energy approximations of the law of conservation of mass-energy, which has been proven to the limits of our current observations.
Everyone agrees it’s impossible for us, you mean.
(“tenured physicist” … “major university” … “peer reviewed” … don’t worry, no one’s going to find any such thing, or hunt for it either.)
You might be interested in this: 2011 OPERA faster-than-light neutrino anomaly - Wikipedia. In this particular case, it was clear from the first preprint that the experiment was conducted in a way almost maximally susceptible to systematic oversights – a feature of their trying to do something the overarching project, OPERA, wasn’t made for – so it was easy not to rush to burning the old textbooks.
@Francis_Vaughan: Nice post.
On consensus: One will get difference senses of consensus across three populations: the lay public, researchers in the field broadly, and researchers in the very specific niche of that field. For the latter two, if someone knowledgeable asks someone deeply knowledgeable, “Hey, isn’t this just known?” they might hear back, “Welllllll, …,” followed by nuances that don’t usually warrant any mental load outside of the narrow research niche.
Actually, those first results were consistent with both, just slightly more consistent with GR. The error bars were too large to be definitive. But it was touted by the press as a resounding victory for Einstein, anyway.
Later results were better.
Under the definitions of “mass” and “energy” currently used by physicists, both are still conserved. But those definitions don’t entirely match the definitions that used to be used. For instance, a single photon does not have mass… but a pair of photons, so long as they’re not traveling in the exact same direction, do have mass. The total mass of a system is not just the sum of the masses of the components of the system.
True.
But preserving the law by changing the definitions arguably counts as deciding the original law was wrong (by the old definitions, mass and energy are not conserved, right?)
When someone speaks as an expert in their field on some well-established principle or methodology, you would be a fool to not listen to them.
When someone speaks as an expert in their field about some principle or methodology on the cutting edge of research, it’s fitting to ask if their expertise actually applies.
Scientists can be as blind to that reality as anybody else. Projecting one’s expertise beyond its actual amount is a common fallacy.
This dances around the adage known as Clarke’s First Law:
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
That’s what I was thinking of.
I even found an error in the Bad Astronomy book, where Plait writes that Polaris is really a system or six or so stars.
https://astronomy.stackexchange.com/questions/16290/how-many-actual-stars-are-polaris
Well, science marches on, the Hubble helps, and there are really only three in the actual Polaris system.
But note that does not mean Phil was 'wrong", just that Science moves, one, new discoveries are made, etc.
That’s I think the biggest hurdle that science has versus the general public and their understanding of how it works.
People tend to look for things to be understood and resolved. The scientist conception that what we know right now is only as good as the tools and data we’ve got right now doesn’t sit well with a lot of people- they do tend to view pointing out that Polaris is not one star, but six, and now three looks to them like scientists don’t know what they’re talking about.
This is because in everyday, nonscientific life, going back and forth like that is a sign that you weren’t prepared, didn’t do your homework, or whatever. It’s like when your mechanic says “It’s your spark plugs!” then comes back and says “It’s your ignition coils!” and then comes back a third time and says “It’s actually 3 spark plugs and the ignition module” Even though he may have done all the diagnostic work right, it looks like he doesn’t know what he’s doing and he’s fishing for a solution. People perceive stuff like this the same way.
Some is information control and how things are phrased. Careful phrasing and emphasis on how what we know is tentative and not firm is important, as is the timing of information release, so as not to actually proclaim something and “go back” on it several times.
Now the public generally doesn’t care if Polaris is one star or six; it’s one celestial object and that’s pretty much all that they care about. But for stuff like diseases, nutrition, etc… the way this stuff is released is important. Nutrition is one where it’s been especially obvious. Over my lifetime, several different things have been demonized and then reformed. Cholesterol, fat in general, sugar, animal fat, saturated fat, trans fats, carbs, and probably some others. And some of them flipped the previous understandings around 180 degrees. It makes for a certain skepticism toward all that guidance in me, and I happen to have a fairly good understanding of the process. I think part of it is that there’s a certain expectation of directed and iterative progress, and when that doesn’t seem to happen, it casts doubt on the whole process.
A good time to link to a favourite comic.
PhD Comics, Science News Cycle.
It is not the assumptions and definitions that makes mathematical proof problematic since the assumptions and definitions are also included in the statement of the theorems. What is problematic is the basic axioms that underlie it all. What Godel showed was that any axioms for mathematics strong enough to allow basic arithmetic cannot be proved consistent.
But I wanted to bring up another example. For a couple decades Katalin Kariko worked on studying mRNA despite a strong consensus that what she was doing was pointless. She was denied funding, eventually demoted from laboratory scientist to a more menial position. Until she won that Nobel prize and now Penn celebrates (in their alumni magazine) that this Nobel quality work was done at Penn. And of course the covid vaccine was based entirely on her work (and that of her eventual collaborator and co-Nobelist Drew Weissman).
Also, mathematicians do sometimes make mistakes in their proofs. You can double-check the proofs, but maybe the checkers made mistakes, too. There are automatic proof-checking programs, too, but how sure are you that you programmed them correctly? Now you’re back to checking and rechecking, but for the proof-checker instead of the proof itself.
This is relevant, for instance, for the primality tests that “almost always” work (but are quick) versus the ones that “always” work (but are slow). Because the probability that the “almost always” tests are wrong (assuming they’re working right) is much less than the probability that all of the mathematicians who have ever worked with those tests all made the same mistakes and the test doesn’t actually work after all
True, but his point was not just that. At some point, the axioms cease to help you. Is every Abelian group A with Ext¹(A, ℤ) = 0 free? Is 2ℵ0 = ℵ1 ?
Perhaps, but I still trust the formal proof-checker any day of the week and twice on Sundays before any human.