A distinction I read somewhere, that I think is useful, is that people tend to be either primarily conceptualist in their thinking, or they are empiricists who learn from experience. Conceptualists have their big breakthroughs before the age of 35, and empiricists have their big breakthroughs after 35.
In conceptual fields, such as math and physics, the big breakthroughs happen young. Werner Heisenberg was 27 when he came up with the Uncertainty Principle, and Einstein was 26 when he discovered relativity.
In fields where progress is primarily empirical, such as biology, the big breakthroughs tend to happen later. Alexander Fleming was 42 when he discovered penicillin and Jonas Salk was 40 when he invented the vaccine for polio.
This distinction can be extended to artists. To write a great empirical novel, one rich in observed life experience, one must live a long time, and therefore Tolstoy was 41 when he wrote War and Peace. But to write a novel where one demonstrates new techniques for grammar and structure and pacing (a novel noteworthy for conceptual innovation) then one will be young, and therefore Hemmingway was only 26 when he wrote The Sun Also Rises.
Einstein, in particular, is an interesting case. He was 26 when he had his annus mirabilis (1905) in which he published 5 ground-breaking papers in physics, including the Special Theory of Relativity.
However it took another 11 years until he was able to grasp enough of the mathematics to finally formulate the General Theory of Relativity in 1916, at age 37. Of course, if you're going to use statistics from Nobel Prize winners' works, you have to keep in mind that Einstein won not for the General Theory nor the Special Theory of relativity with which we usually associate him. He won for his paper on the photoelectric effect, one of the other papers he published in 1905...at age 26.
Edit: It's probably also worth pointing out that, someday in the future, it's not inconceivable that we may eventually place the Einstein-Podolsky-Rosen Paradox in the same league as Relativity. That paper was published in 1935, when Einstein was already 56 years old. If it is not currently considered of the same merit as Relativity, that is only because we still don't have a good handle on the full implications of that work. (And, yes, I realize that ultimately EPR will likely prove to be wrong, but a great scientist teaches as much by being wrong as by being right.)
So Einstein, Podolsky, and Rosen were sitting around (presumably) looking over the mathematical foundations of Quantum Mechanics, when they noticed something. In certain situations, you could end up with one wave function describing two physically separated particles in a mutual superposition of states. The consequence is that altering the state of one particle would instantaneously cause the state of the other to become resolved. Effectively they "discovered" quantum entanglement (which has since been verified as a real phenomenon, not just a mathematical curiosity).
What really makes the EPR paradox important, though, is what it implies about reality. Einstein, et al. realized that there were only two ways to explain quantum entanglement. One possibility is that the entangled particles contain extra information, inaccessible to normal observation, about their respective states and which way the superposition will resolve. This is the so-called "hidden variables" solution. The other possibility is that an action on one particle is, in fact, instantaneously causing an effect on the other particle. While this is not, strictly speaking, a violation of General Relativity as no information is exchanged, Einstein found this possibility so unsettling that he famously coined it "spooky action at a distance". The conclusion from the EPR paper was that the "hidden variables" solution was more likely, implying that Quantum Mechanics was an as-yet incomplete theory.
Fast-forward a couple of decades, and we're just beginning to appreciate that "spooky action at a distance" is actually more likely to be the correct explanation. As I mentioned before, what this implies about reality itself is pretty mind blowing. To go even further, we've since learned that entanglement can not only occur between particles separated in space, but also between particles separated in time. Quite literally, the future and the past may be linked by this "spooky action at a distance".
We still don't fully grasp what, exactly, this means. One possible implication of this is that our existence as sentient beings may simultaneously be a consequence and the cause of a universe that can give rise to sentient beings. Needless to say, even though it's likely that Einstein was wrong about "hidden variables", the course of investigation that the EPR paper set the physics community down is at least as important as Relativity.
Not to be "that guy", but a lot of this is terribly incorrect:
* General relativity did not come from "grasping the mathematics" of special relativity. SR can be completely understood by an undergraduate and is an internally consistent description of mechanics and electromagnetic phenomena. Like Newtonian mechanics before it, it doesn't need anything more to be consistent.
* Local hidden variables are not "likely wrong", they are provably impossible. It is impossible to have hidden variables without breaking the principle of causality.
* Entanglement does not break the principle of causality. "Spooky action at a distance" is not an "effect" in a well-defined physical sense. It cannot be used to send information or cause things to happen.
* All of this could be--and was--understood without the EPR paper. Relativity was the most important thing since Newton. EPR was minor in comparison.
* I have no idea what connection you're trying to draw between sentient life and QM.
> * General relativity did not come from "grasping the mathematics" of special relativity.
I wrote that he had to "grasp enough of the mathematics to finally formulate the General Theory of Relativity". Human language is neat in the way it allows for ambiguities, but if you understood "the mathematics" in that sentence to be a reference to SR, then that is because it is what you read into it. I was referring to the time it took for Einstein to fully understand/appreciate the work of Minkowski.
> * Local hidden variables are not "likely wrong", they are provably impossible
> * Entanglement does not break the principle of causality. "Spooky action at a distance" is not an "effect" in a well-defined physical sense. It cannot be used to send information or cause things to happen.
Funny, I thought I wrote: "While this is not, strictly speaking, a violation of General Relativity as no information is exchanged." Oh wait, I did.
> * All of this could be--and was--understood without the EPR paper. Relativity was the most important thing since Newton. EPR was minor in comparison.
Yes, and Einstein also wasn't the only physicist to come across the field equations in GR. He just happened to be the only one to appreciate their full impact. No scientific discovery stands in isolation, so it's really not worth debating this point much. I have noticed, however, that many in the QM community seem to look down on EPR and much of Einstein's other work in QM, probably (not entirely without justification) because of the rather dim view Einstein held on much of their work.
> * I have no idea what connection you're trying to draw between sentient life and QM.
Not me. You should go talk to John Archibald Wheeler about the Participatory Anthropic Principle.
Note local hidden variables is impossible. The pilot wave theory is the theory of "hidden variables" that led Bell to his theorem. Basically, EPR shows that either nature is nonlocal or there were hidden variables. Bell showed that hidden variables had to have something nonlocal about them. So Einstein created relativity and helped to highlight how nature has an aspect that seems incompatible with it (basically, there is a "now" which, however, may be undetectable and is not our "now").
For those curious, the nonlocal hidden variables are the positions of the particles. Very hidden. So hidden, they are the only thing we see in experiments!
The particles are guided by the wave function. This resolves all the weird paradoxes such as Schrodinger's cat. It provides a great way to understand and investigate nonlocality, spin, identical particles, etc. in a very precise theory that even has broadly applying existence and uniqueness of solution theorems, unlike classical mechanics.
Hi! I'm a mathematician, I've always been curious about physics, but I've never understood some of the concepts of QM, such as what is "observation" in the Schrodinger's cat paradox, why QM means the universe is not deterministic, why hidden variables cannot exist, ... mostly because every physicist that I was able to talk to has been unable to properly explain these concepts. Do you know any books/articles/sources about QM that could understand these concepts, without going in unnecessary mathematical and physical details (i.e. using the least physics and mathematics necessary to explain the paradoxes of QM)?
Tough question. The reason you probably did not understand them is that there are reasons are faulty.
The textbook QM says that when experiments happen, the continuous wave function evolution stops and a new wave function is used in its place, chosen randomly based on a prescription using probabilities coming from the original wave function's decomposition in terms of an operator's (matrix) eigenvalues. This is a postulate in their view and that's that.
It makes no sense since what is an observation? They don't explain. They just know it. They use it when doing their experiments and it works well enough. Attempting to formalize it leads to wrong conclusions.
Bohmian mechanics/pilot wave theory is a deterministic, hidden variable theory that works. Within that context, you can understand the rise of operators as observables and the entire collapse rule which turns out to be a convenient approximation to reality in this theory; no actual collapse occurs. There is just one wave function on configuration space (3n dimensional space, n being the number of particles in the universe) evolving continuously via Schrodinger's equation and the particles themselves being guided by the wave function. It is the configuration space for the wave function where nonlocality arises from. Understanding its role in relation to relativity is the key question to understand.
The wave function evolves with lots of its branches being irrelevant which is why we can effectively get rid of them, i.e., collapse the wave function.
I have read it and I must have missed the part you refer to. He was a strong proponent of pilot-wave theory though towards the end he also started to like GRW which itself consists of two distinct ontological possibilities.
In as much as QM makes predictions, pilot wave theory makes the same predictions. But pilot wave theory has the advantage of being an honest theory that actually does make predictions. QM suffers from needing an external agent to collapse the system, an agent that is never specified, particularly on the universal level. Bell puts it very eloquently about whether one needed to wait for the first form of life to do it or perhaps one with a PhD to collapse the universe. He concludes it must be happening more or less all the time and that the mechanism needs to be explained in the theory. We can either change Schrodinger's equation as in GRW or we can add additional variables such as positions of particles as in pilot wave theory. Or we need to accept that most of reality is unlike our actual experience of a single reality such as in many worlds.
The EPR paradox was resolved a while ago, strongly in favour of Einstein's "spooky action at a distance". The first experiments were done in the 70's. See:
Yes, but as with most things in physics, the first signs that an idea is dead usually come decades before the ghost is truly given up. Take, for example, this work from 2012 that was still dealing with a variation on the "hidden variables" formulation: http://arstechnica.com/science/2012/10/quantum-entanglement-...
A theory is (as Heisenberg explained in his book "Physics and Philosophy") an interpretation of data based upon unscientific, non-falsifiable, a priori assumptions on the part of the theorist. You can't really disprove something as nebulous as "hidden variables." That's not a falsifiable statement. What you can do is disprove some theory based on hidden variables. Such evidence does not apply to the possibility of other theories of hidden variables that are yet unformulated.
"What's more, people who excel in abstract fields, like art or physics, tend to be younger than those who win prizes in fields that require more context, like history or medicine. Another 1977 study found that physics Nobel winners were 36 on average when they did their prize-winning work, while chemists were 39 and medical doctors were 41."
This is the thesis of David Galenson's "Old Masters and Young Geniuses", which is a good read. He also talks about how trying to find a single average age of peak creativity hides other possibilities, such as the one he suggests, where there are clusters among the young (conceptual innovations) and old (experimental innovations).
A distinction I read somewhere, that I think is useful, is that people tend to be either primarily conceptualist in their thinking, or they are empiricists who learn from experience.
Galenson's book Old Masters and Young Geniuses: The Two Life Cycles of Artistic Creativity discusses this point extensively, in addition to being a pleasure to read on its own.
>What's more, people who excel in abstract fields, like art or physics, tend to be younger than those who win prizes in fields that require more context, like history or medicine.
Precisely the ideas discussed by S. Chandrasekhar (White dwarfs; Chandra X-ray telescope) in his book "Truth and Beauty: Aesthetics and Motivation in Science"[0]. The book draws a large number of examples from (astro)physicists, but he also expands into Beethoven and Shakespeare among others.
A must read if such ideas interest you. And even if they don't, it is an awesomely well written book, well worth a read!
The conceptualist // empiricists seems to apply heavily to me as well, in my entrepreneurial career. Despite thinking I have good business concepts down, I've learned far more through practice than I have through books. For me, I have to apply something to truly learn it.
In conceptual fields, such as math and physics, the big breakthroughs happen young. Werner Heisenberg was 27 when he came up with the Uncertainty Principle, and Einstein was 26 when he discovered relativity.
In fields where progress is primarily empirical, such as biology, the big breakthroughs tend to happen later. Alexander Fleming was 42 when he discovered penicillin and Jonas Salk was 40 when he invented the vaccine for polio.
This distinction can be extended to artists. To write a great empirical novel, one rich in observed life experience, one must live a long time, and therefore Tolstoy was 41 when he wrote War and Peace. But to write a novel where one demonstrates new techniques for grammar and structure and pacing (a novel noteworthy for conceptual innovation) then one will be young, and therefore Hemmingway was only 26 when he wrote The Sun Also Rises.