Mathematics and the Universe

[CoxRox]

I also think it is significant that the "fundamental" physics that is elegantly expressed arose from theory instead of experimentation,

This is very interesting. I think I alluded to this in another thread. Is this the same as some mathematics being 'discovered' before they were applied to the real world? This seems to suggest these 'rules' are already out there.

I like this quote of Feynman's, when asked if he thought mathematics and hence the laws of physics had an independent existence:

"The problem of existence is a very interesting and difficult one. if you do mathematics, which is simply working out the consequences of assumptions, you'll discover for instance a curious thing if you add the cubes of integers. One cubed is one, two cubed is two times two times two, that's eight, and three cubed is three times three times three, that's twenty-seven. If you add the cubes of these, one plus eight plus twenty-seven- let's stop there - that would be thirty-six. And that's the square of of another number, six, and that number is the sum of those same integers. one plus two plus three...Now, that fact which I've just told you about might not have been known to you before. You might say "Where is it, what is it, where is it located, what kind of reality does it have?' And yet you came upon it. When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere, but there's nowhere for such things. It's just a feeling...Well, in the case of physics we have double trouble. We come upon these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing...Those are philosophical questions that I don't know how to answer." (The Mind of God- Paul Davies)

[Purple Rabbit]

Purple Rabbit, these 'laws' are explained in our book we have chosen:
'God: The Failed Hypothesis'. No doubt what you have said, will be covered in detail by Stenger. We can discuss this once we've read the book. Thanks again.

May the force be with you.

---

I also think it is significant that the "fundamental" physics that is elegantly expressed arose from theory instead of experimentation, and is elegant because our minds seek symmetry. Some of that theory, such as relativity, has been taken as confirmed by certain observable phenomenon at the macroscopic level. But more advanced physics, and here I am speaking of quantum mechanics in particular, arose purely from experimental observance of extremely surprising, baffling phenomenon that cannot be described elegantly in mathematics. The theoretical school of physics cried foul as the experimental physicists presented their findings. But that theoretical school has been discredited to a large degree.

I don't agree that fundamental physics arose from theory instead of experimentation. The starting point for Einstein's Special Relativity was to take the results from the Michelson-Morley experiment (MME) as an elementary result and starting point for his theorizing. In MME the speed of light was measured in two perpendicular directions. It was designed to measure differences that would be attributed to a hypothetical aether in which light was supposed to travel much in the sense that waves on water need water to exist. The existence of this mythical 'aether' (still found as a word used in the world of radio broadcast) that supposedly permeated all of space, certainly permeated almost all of the scientific community in Einstein's days. It was Einstein's genius and also an important feat for empiricism to take the results of MME seriously.

There are some theories in physics however that not yet have been tested experimentally. The most obvious one is M-brane theory (aka superstring theory), but to all scientists in the field it is clear that M-brane theory is in desperate need for experimental proof to shake off it's current hypothetical status. In the scientific community some debate on this is going on. The debate is nicely covered by Lee Smolin in his "The Trouble With Physics".

[infidel666]

I don't agree that fundamental physics arose from theory instead of experimentation. The starting point for Einstein's Special Relativity was to take the results from the Michelson-Morley experiment (MME) as an elementary result and starting point for his theorizing. In MME the speed of light was measured in two perpendicular directions. It was designed to measure differences that would be attributed to a hypothetical aether in which light was supposed to travel much in the sense that waves on water need water to exist. The existence of this mythical 'aether' (still found as a word used in the world of radio broadcast) that supposedly permeated all of space, certainly permeated almost all of the scientific community in Einstein's days. It was Einstein's genius and also an important feat for empiricism to take the results of MME seriously.

There are some theories in physics however that not yet have been tested experimentally. The most obvious one is M-brane theory (aka superstring theory), but to all scientists in the field it is clear that M-brane theory is in desperate need for experimental proof to shake off it's current hypothetical status. In the scientific community some debate on this is going on. The debate is nicely covered by Lee Smolin in his "The Trouble With Physics".

For fundamental physics, I'm talking about the theory of gravity, for example. The greeks initially thought and took as given that objects of different masses, dropped from the same height, would hit the ground at different times. They thought that the rate of falling was proportional to the mass of the object, so the heavier object would fall faster. Eventually, someone discovered it was not true, and the mass of the object is irrelevant. Eventually, the theory of gravity was developed. Later, that theory was found to be incomplete, and so on. But the problem is that people have continuously attempted to theorize something elegant to reconcile a foregone conclusion with a contradiction.

In contrast, quantum mechanics has developed from pure experimentation. Attempts to make predictions based on it have largely failed. Attempts to reconcile general relataivity with quantum mechanics have failed. And it is because we keep trying to reconcile this beloved, elegant, foregone conclusion with inconvenient evidence that it is wrong. Past attempts were successful, but quantum mechanics is an insurmountable hurdle. You have to give up the elegant math. The elegant stuff is wrong.

[CoxRox]

''The elegant stuff is wrong.''

I don't know about that........

[Edwardo Piet]

In contrast, quantum mechanics has developed from pure experimentation. Attempts to make predictions based on it have largely failed.

That's funny! Because I swear I've heard on more than one occasion that Dawkins say that Richard Feynman says how Quantum Theory's predictions are extremely accurate.

Found a clip here. Its only 1:20 long:
[youtube]NQYGkuHFNuU[/youtube]

I think its relevant to what you said. And I am understanding that videos go in the video thread when they are a video thread. And they are a video thread when the first post contains a video.

Right? That's what I heard anyway. This video clip seems relevant to what you said. At least to me.
evf

[infidel666]

But ... but ... but ...

OK, "predictions" are made, but the predictions are not things like E=mC^2. People don't come up with a theory based on quantum mechanics and then go look for a way to verify it. The "predictions" of quantum mechanics are about probability fields of particle position and momentum.

Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement.

The way to make those predictions flows entirely from a methodology developed directly from observables that defy a different kind of "prediction" (and here I mean INTUITION) by humans hypothesizing a law and seeking to test it. In fact, the only attempt I know of to hypothesize off of quantum mechanics in the theoretical school sense of the word is M theory, which is really just an attempt to reconcile general relativity (the beloved lie) with quantum mechanics (the inconvenient truth). How convenient that M theory is practically untestable.

Not hard to tell I took my physics degree at a University that adheres to the tradition of the experimental school, as opposed to the theoretical school. The rivalry lives!

[Purple Rabbit]

For fundamental physics, I'm talking about the theory of gravity, for example. The greeks initially thought and took as given that objects of different masses, dropped from the same height, would hit the ground at different times. They thought that the rate of falling was proportional to the mass of the object, so the heavier object would fall faster. Eventually, someone discovered it was not true, and the mass of the object is irrelevant.

The relevant point is that it was found to be a wrong hypothesis empirically. The actual testing of hypothesis was a very significant break with traditional thinking. By it Aristotelean intuïtion was proven wrong. Also it should be made clear that at the time of the falling body experiment (for the first time in 1544, the historian Benedetto Varchi referred to tests which refuted Aristotle's assertion) the empirical scientific approach was in it's infancy. There was no distinction between philosophy and science. Because of this it doesn't serve as an example that fundamental physics arose from theory instead of experimentation.

Eventually, the theory of gravity was developed. Later, that theory was found to be incomplete, and so on.

Again it was found to be incomplete empirically. Also Einstein's original paper on Special Relativity emphasizes the empirical basis of the postulates he used.

But the problem is that people have continuously attempted to theorize something elegant to reconcile a foregone conclusion with a contradiction.

Do you mean contradiction with empirical facts?

In contrast, quantum mechanics has developed from pure experimentation.

I think theoretical consideration may guide empirical investigation and vice versa. The emphasis may vary from theory to theory, but there is never a strict division between the two. In case of the Pauli Exclusion Principle (PEP) I think it is clear that empirical facts (certain spectroscopic phenomena) are generalized to a prescriptive rule. In January 1925 Pauli wrote:

In an atom there cannot be two or more equivalent electrons for which the values of all four quantum numbers coincide. If an electron exists in an atom for which all of these numebers have definite values, then this state is occupied.

As you can see, it's first application was confined to the atom. A year later in 1926 Fermi and Dirac independently from each other reformulated the rule in a mathematical form that suggested a more general domain of application outside the atom but still for electrons only. Later in 1940 it became clear that the rule could be extended to any half spin particle. Eventually it became a building block for QCD. In this case you clearly can see that empirical facts are formulated as rules triggering the theoretical investigation into a broader domain of validity than from the empirical facts at hand could be deduced, in turn triggering empirical reasearch. In the case of the PEP this bouncing from empirical investigation to theoretical investigation happened more then once. It's almost a case of stress testing a principle. Pauli had struck gold without knowing it's broad application. Empirical testing was guided by theorizing about the genericity of the principle. Imo this shows that in QM also theoretical argument and empirical results go hand in hand.

Attempts to make predictions based on it have largely failed. Attempts to reconcile general relataivity with quantum mechanics have failed. And it is because we keep trying to reconcile this beloved, elegant, foregone conclusion with inconvenient evidence that it is wrong. Past attempts were successful, but quantum mechanics is an insurmountable hurdle. You have to give up the elegant math. The elegant stuff is wrong.

The history of PEP, I think, tells another story.

[DD_8630]

But ... but ... but ...

OK, "predictions" are made, but the predictions are not things like E=mC^2. People don't come up with a theory based on quantum mechanics and then go look for a way to verify it.

What? Yes, we do! I myself have used quantum mechanics to predict the tunnelling current through a Scanning Tunnelling Microscope at a given distance from a sample.

The "predictions" of quantum mechanics are about probability fields of particle position and momentum.

That, and everything predicted by classical mechanics (above atomic-scale physics, that is; quantum mechanics refines classical predictions at the atomic scale and below).

Not hard to tell I took my physics degree at a University that adheres to the tradition of the experimental school, as opposed to the theoretical school. The rivalry lives!

[infidel666]

But ... but ... but ...

OK, "predictions" are made, but the predictions are not things like E=mC^2. People don't come up with a theory based on quantum mechanics and then go look for a way to verify it.

What? Yes, we do! I myself have used quantum mechanics to predict the tunnelling current through a Scanning Tunnelling Microscope at a given distance from a sample.

The "predictions" of quantum mechanics are about probability fields of particle position and momentum.

That, and everything predicted by classical mechanics (above atomic-scale physics, that is; quantum mechanics refines classical predictions at the atomic scale and below).

Not hard to tell I took my physics degree at a University that adheres to the tradition of the experimental school, as opposed to the theoretical school. The rivalry lives!

Fair enough. I should have said that quantum mechanics is used to predict values of measurements of characteristics of observable quanta. But I don't think predicting the current in a microscope is quite the same thing as coming up with a paradigm shifting relationship like E=mC^2.

Just the way I view it anyway. Plus, I know I'm right because a bunch of esteemed physics profs told me so and I paid them lots of money to do it. So there!

Please, God, don't let it have been all for nothing. Oooops. I think I just prayed.

---

For fundamental physics, I'm talking about the theory of gravity, for example. The greeks initially thought and took as given that objects of different masses, dropped from the same height, would hit the ground at different times. They thought that the rate of falling was proportional to the mass of the object, so the heavier object would fall faster. Eventually, someone discovered it was not true, and the mass of the object is irrelevant.

The relevant point is that it was found to be a wrong hypothesis empirically. The actual testing of hypothesis was a very significant break with traditional thinking. By it Aristotelean intuïtion was proven wrong. Also it should be made clear that at the time of the falling body experiment (for the first time in 1544, the historian Benedetto Varchi referred to tests which refuted Aristotle's assertion) the empirical scientific approach was in it's infancy. There was no distinction between philosophy and science. Because of this it doesn't serve as an example that fundamental physics arose from theory instead of experimentation.

Eventually, the theory of gravity was developed. Later, that theory was found to be incomplete, and so on.

Again it was found to be incomplete empirically. Also Einstein's original paper on Special Relativity emphasizes the empirical basis of the postulates he used.

But the problem is that people have continuously attempted to theorize something elegant to reconcile a foregone conclusion with a contradiction.

Do you mean contradiction with empirical facts?

In contrast, quantum mechanics has developed from pure experimentation.

I think theoretical consideration may guide empirical investigation and vice versa. The emphasis may vary from theory to theory, but there is never a strict division between the two. In case of the Pauli Exclusion Principle (PEP) I think it is clear that empirical facts (certain spectroscopic phenomena) are generalized to a prescriptive rule. In January 1925 Pauli wrote:

In an atom there cannot be two or more equivalent electrons for which the values of all four quantum numbers coincide. If an electron exists in an atom for which all of these numebers have definite values, then this state is occupied.

As you can see, it's first application was confined to the atom. A year later in 1926 Fermi and Dirac independently from each other reformulated the rule in a mathematical form that suggested a more general domain of application outside the atom but still for electrons only. Later in 1940 it became clear that the rule could be extended to any half spin particle. Eventually it became a building block for QCD. In this case you clearly can see that empirical facts are formulated as rules triggering the theoretical investigation into a broader domain of validity than from the empirical facts at hand could be deduced, in turn triggering empirical reasearch. In the case of the PEP this bouncing from empirical investigation to theoretical investigation happened more then once. It's almost a case of stress testing a principle. Pauli had struck gold without knowing it's broad application. Empirical testing was guided by theorizing about the genericity of the principle. Imo this shows that in QM also theoretical argument and empirical results go hand in hand.

Attempts to make predictions based on it have largely failed. Attempts to reconcile general relataivity with quantum mechanics have failed. And it is because we keep trying to reconcile this beloved, elegant, foregone conclusion with inconvenient evidence that it is wrong. Past attempts were successful, but quantum mechanics is an insurmountable hurdle. You have to give up the elegant math. The elegant stuff is wrong.

The history of PEP, I think, tells another story.

Well, I didn't mean to imply that no theoretical consideration has guided the development of Quantum Mechanics, or that no empirical evidence has guided Relativity or Classical Physics. I don't think I said that. What I did say, I think, or what I meant to say, was that Classical Physics and Relativity started out as pure conjecture/philosophy and was then guided by empiral evidence, while Quantum Mechanics started out as empirical evidence (non-intuitive evidence at that) that has been developed into a theory. And sure, predictions have been made from quantum mechanics, such as Hawking radiation, and later found (exception proves rule?). And sure, it is possible to view Relativity and Quantum Mechanics as two bracnhes of science that developed from classical physics in response to new observable phenomenon. But there is a philosophical difference in the type of rigor that led to these two branches of science (experiment as starting point vs. conjecture), perhaps simply because quantum mechanics is so non-intuitive.

[DD_8630]

Fair enough. I should have said that quantum mechanics is used to predict values of measurements of characteristics of observable quanta. But I don't think predicting the current in a microscope is quite the same thing as coming up with a paradigm shifting relationship like E=mC^2.

On the contrary, physics went from classical blocks to quantum fuzz with an audible clunk. The paradigm shift was as significant as Einstein's theories of relativity, or Darwin's theory of common descent.

Perhaps the greatest implication of quantum mechanics is that it subverts our intuitive understanding of causality and discreteness.

Just the way I view it anyway. Plus, I know I'm right because a bunch of esteemed physics profs told me so and I paid them lots of money to do it. So there!

They were probably just experimental physicists, so what do they know