## A mathematical proof of physics, obtained by formalizing the scientific method (attempt 3)

• 157
I believe to have discovered a methodology to prove the laws of physics from first principle. This is my third and hopefully final attempt (with some changes based on the comments in a previous conversation on this site). The abstract reads as follows:

It is normally expected that the laws of physics are the general end-product of the scientific process. In this paper, consistently with said expectation, I produce a model of science using mathematics, then I use it to derive the laws of physics by applying the (formalized) scientific method to the model. Specifically, the laws of physics are derived as the probability measure that maximizes the quantity of information produced by the scientific method as the observer traces a path in the space of all possible experiments. In this space said probability measure describes a general linear ensemble of programs which is a foundation sufficient to express all known physics. Since the definitions are purely mathematical and contain no physical baggage of any kind, yet are nonetheless able to derive the laws of physics from first principles, then it follows that the present derivation of said laws, as it is ultimately the product of the (formalized) scientific method, is the minimal mathematical foundation of physics as well as its philosophical less controversial formulation. We end with applications of the model to open problems of physics and produce testable predictions.

https://philpapers.org/archive/HARTAO-72.pdf

Looking for feedback and discussion.
• 2.6k
Since the definitions are purely mathematical and contain no physical baggage of any kind, yet are nonetheless able to derive the laws of physics from first principles,

This cannot be. Both Euclidean and non-Euclidean geometry are logically consistent, and mathematics can't say which is true about the universe. Without physical axioms or principles, you could not use math alone to determine physical truths.

There are many other such examples of mutually inconsistent mathematical theories that are logically consistent by themselves. ZF set theory with the axiom of choice and without, for example. There's no end of such examples.

How can you use math by itself, without any physical principles, to know anything about the world? Math doesn't tell you the charge of an electron or the mass of a proton or the binding energy of a pair of quarks. It doesn't even define concepts like charge, mass, or energy. You need physical principles to apply math to.

Surely you must start from some basic physical principles. Perhaps I'm misunderstanding what you mean by baggage.

The work looks impressive, but by your own description, it cannot be right.

ps -- Random quibble. Was just scanning around, noted that in 4.3.2 you prove something's a Hilbert space by assuming it's finite dimensional. I didn't see you handle infinite dimensional Hilbert space anywhere, but I was under the impression that QM uses the infinite dimensional case.

pps -- Another random quibble. In section 5.4 you take one short paragraph to "solve" wave function collapse. This is a problem that's vexed the smartest minds in the world for a century. I'm going to go out on a limb and say that one paragraph won't do, and you probably didn't solve the problem.

ppps -- In 5.6.1 you "solve" quantum gravity? Another limb for me to go out on. You didn't do that.

I am not qualified to read your paper in terms of the physics. But grandiose claims evoke suspicion.
• 1.5k
In (2) of 3.1.1, are you defining the expression |p| with a bar over the top on the right side?
• 157
In (2) of 3.1.1, are you defining the expression |p| with a bar over the top on the right side?

Bar on top, by convention indicates the average of a value. Will add a note under the equation to specify.
• 157
Without physical axioms or principles, you could not use math alone to determine physical truths.

What is your definition of physical truth?
• 157
How can you use math by itself, without any physical principles, to know anything about the world?

Both Euclidean and non-Euclidean geometry are logically consistent, and mathematics can't say which is true about the universe.

I advise that you utilize my definition of universal facts in your mathematical work and this will negate you ability to create irreconcilable splits in the logical domain.

Instead of defining a theory via a finitely axiomatic system (then wondering which of many incompatible finitely axiomatic system corresponds to the universe) rather define a theory via a manifest: a collection of universal facts. Under this definition, all finitely axiomatic systems whose theorems enumerates the element of the same manifest are said to be de-factor-isomorphic.

Then, define the state of affairs of reality as a manifest --- a state of facts that are 'known'. It then follows that any finitely axiomatic system de-facto-isomorphic with said manifest are correct logical representations of reality.

Finally, the rules that govern the transformations of manifests are the laws of physics --- the reason is of course that any change in the physical state of a system must change the facts that are 'known' (otherwise nothing has changed).
• 7.9k
"Many philosophies discuss facts, but it appears they all missed the mark on what
a fact actually is (in terms of a precise exploit-free mathematical definition).
The archetypal example of a fact is given in many philosophical textbooks:
”1 + 1 = 2”, is in fact not a fact."

Your use of "exploit" is new to me. Either it is a term of art you need to define, or you need an editor. And can you cite any philosophy textbook that represents 1+1=2 is a fact? Because it isn't, and I very much doubt that any textbook worthy of the name claims that. As to the rest, as nearly every other respectable scientist of whatever repute labors mightily to make his or her work accessible, your attitude guarantees your work, in terms of your claims, is nonsense.

"A manifest theory M is defined as a set of
universal facts:
M := {(TM1, p1),(TM2, p2), . . . } (2)
The set can be either finite or infinite, and it can be either decidable or
non-decidable."

It's time for you to lay out just how a UTM works, because I do not see how one stops on an undecidable proposition.

All facts are historical. What I suspect you mean by "fact" is "true." But that presents a whole other set of problems, true being hard to define except in abstract terms, and that at best a partial listing of the conditions under which something may be called true.

You appear to seek incomprehensibility thinking it a virtue. It isn't. And incomprehensibility is ultimately incomprehensible. If you want critical response, then make it comprehensible.

"The wave-function collapse has been a tough
pill to swallow because, before these results, we did not know that the origin of the wave-function was in entropy under geometric constraint — we, at
best, believed it was a measure over a postulated unitary sample space, and
any geometric properties it may have (space-time normalization/Lorentz invariance) were strapped on as a secondary set of axioms tied in to a normalization
condition in space-time, then we noticed to our surprise that such geometric
properties ought to be represented in the same unitary space as the rest of the
theory."

Just for the heck of it, I can almost make sense of the above sentence. Care to try for English?

And do not complain about your viewers: you chose them, not they you.

I'll give credit for this. Many TPFers "prove" their claims fallaciously from an incomplete modus ponens. But you use definitions. And that leaves the definitions themselves. Which is a problem in itself. If the world is how you define it, and is the world - do you see the problem?
• 157

Not sure of how an 'attitude' can have a bearing of the truth of a mathematical statement, nonetheless I will take your advice and tone it done. If there are any other passages you think I should tone down, please let me know.

It's time for you to lay out just how a UTM works, because I do not see how one stops on an undecidable proposition.

The statement is: The *SET* can be either finite or infinite, and it can be either decidable or
non-decidable
. One can define a un-decidable set. For instance the set of all theorems of arithmetic is un-decidable. No need to cheat the non-halting problem to define that.

All facts are historical. What I suspect you mean by "fact" is "true." But that presents a whole other set of problems, true being hard to define except in abstract terms, and that at best a partial listing of the conditions under which something may be called true.

Understood. Since universal facts equates the two via a state of affairs, I was over focusing on one aspect of the definition and not enough on the other. I'll adjust.

Just for the heck of it, I can almost make sense of the above sentence. Care to try for English?

In 'standard' physics the collapse of the wave-function to a point in space-time upon a measurement is postulated because it is not derivable from the formalism of complex Hilbert spaces.

In my work, I derive Hilbert spaces from an entropy maximization procedure on an ensemble constrained to linear transformations. Thus, the Hilbert space is derived, not postulated. Then, the collapse of the wave-function trivially follows from a sampling the underlaying ensemble without needing to be postulated. A sampling of the ensemble induces a projective measurement on the derived Hilbert space.
• 2.6k
Without physical axioms or principles, you could not use math alone to determine physical truths.
— fishfry

What is your definition of physical truth?

Whatever is true, at least to the limits of our ability to experiment and observe, about the world. Bowling balls fall down. That's a physical truth.

There's no physics in math. You can use math to model real physics, as in the physics of the universe; or fake physics, as in the physics governing a video game. Math doesn't distinguish. How do you determine what's true about the world we live in, without any physical principles or empirical evidence?

You could, for example, use math to code up a video game in which bowling balls fall up. All that's needed is to change the sign of the value of gravitational acceleration. Math is agnostic on the issue.

Instead of defining a theory via a finitely axiomatic system

You have been misinformed. The standard axioms of set theory are infinite in number. That's because the axiom schema of specification and the axiom schema of replacement are templates that instantiate a new axiom for each predicate. What is true, if it helps your ideas, is that the axioms are recursively enumerable. That's what makes Gödel's incompleteness theorems work.

https://en.wikipedia.org/wiki/Axiom_schema_of_specification

https://en.wikipedia.org/wiki/Axiom_schema_of_replacement
• 157
I didn't use the phrase, and I included my own words that you quoted in my quote, so that you can see that.

I am sorry. I am not sure I follow your point - you are saying you did not write the words in your quote? (I must be misunderstanding).
• 2.6k
I am sorry. I am not sure I follow your point - you are saying you did not write the words in your quote? (I must be misunderstanding).

• 157
You have been misinformed. The standard axioms of set theory are infinite in number. That's because the axiom schema of specification and the axiom schema of replacement are templates that instantiate a new axiom for each predicate. What is true, if it helps your ideas, is that the axioms are recursively enumerable.

I meant finite in the sense that the number of bits required to specify the axioms is finite, thus schemas are fine. The correct therm I should have used is formal instead of finite... thus I will correct this to formal axiomatic system to avoid future confusion. Sorry for the trouble and thanks for pointing it out.

There's no physics in math. You can use math to model real physics, as in the physics of the universe; or fake physics, as in the physics governing a video game. Math doesn't distinguish. How do you determine what's true about the world we live in, without any physical principles or empirical evidence?

• Do you believe one can define a computer (such as Alan Turing did) purely mathematically? I assume you say yes.
• Do you believe computers exists in nature? I assume you say yes.
• Thus, you have one example of a theory that is purely mathematically derived, which nonetheless corresponds to the rules of computations which are found in nature.
• I have therefore produced a counter example to your claim that "There's no physics in math.".

Would you like to respond or revise your claim?

Why do you think my paper is purely about Turing machines and computation?
• 2.6k
I meant finite in the sense that the number of bits required to specify the axioms is finite, thus schemas are fine. The correct therm I should have used is formal instead of finite... thus I will correct this to formal axiomatic system to avoid future confusion. Sorry for the trouble and thanks for pointing it out.

Glad I could be of help.

Do you believe one can define a computer (such as Alan Turing did) purely mathematically? I assume you say yes.

Of course, but note that there are no Turing machines in nature, since a TM has an unbounded tape and my local computer store doesn't have that much RAM in stock.

Do you believe computers exists in nature? I assume you say yes.

Haha you didn't think you'd sneak that one by me, did you? Of course computers exist in nature, I'm typing on one as we speak. But we are now using the word computer in two distinct ways: A TM, which is a purely conceptual object with an unbounded tape; and my laptop, with a fixed, finite amount of memory. That's two distinct and inconsistent usages of the word computer.

So yes, there are TMs in the world of abstract ideas; and yes there are computers down at the electronic gadget store; but these are not the same thing.

Thus, you have one example of a theory that is purely mathematically derived, which nonetheless corresponds to the rules of computations which are found in nature.

"Thus" has been refuted, since you equivocated the word computer. Your argument failed. There is no unbounded tape in nature as far as we know. There are only $10^{78}$ atoms in the observable universe, and that's a hard upper limit on how how big your tape could be.

An analogy would be that I can have 1 apple, 2 oranges, 3 visually challenged mice, 4 calling birds and so forth, each appearing in nature. But the set of all natural numbers {1, 2, 3, 4, ...} is only an abstract conceptual fiction appearing in pure mathematics in the form of the axiom of infinity. There aren't infinitely many of anything in nature. Whatever point you are making is wrong and muddled, because you are conflating the physical with the abstract.

I have therefore produced a counter example to your claim that "There's no physics in math.".

Would you like to respond or revise your claim?

You haven't got an argument at all. There are no Turing machines in nature. Of course there are abstract conceptual objects inspired by nature; just as the infinite set of natural numbers is inspired by the familiar everyday counting numbers 1, 2, 3, ... But the former is purely conceptual; while many (but not all) of the latter can be physically instantiated as apples and atoms.

Why do you think my paper is purely about Turing machines and computation?

I don't know. That was another question I had. You seem to be confusing physics with computation. After all, a TM can't solve the Halting problem, but we don't know whether or not the universe can.

But answer me this. What principle of mathematics says that bowling balls fall down, instead of up? After all if I implement Newtonian physics in a computer simulation but I reverse the sign of gravitational acceleration, bowling balls will fall up. The math doesn't care.
• 157
But the set of all natural numbers {1, 2, 3, 4, ...} is only an abstract conceptual fiction appearing in pure mathematics in the form of the axiom of infinity. There aren't infinitely many of anything in nature.

Thank good I am not using Peano's axioms then - if I did I would be in real trouble because indeed as you say there are more facts in PA than there are in nature. Glad I spent 15 years coming up with the definition of a manifest theory (theories of finitely many theorems) specifically to negate this problem! I'd be in a real pickle otherwise.

Haha you didn't think you'd sneak that one by me, did you? Of course computers exist in nature, I'm typing on one as we speak. But we are now using the word computer in two distinct ways: A TM, which is a purely conceptual object with an unbounded tape; and my laptop, with a fixed, finite amount of memory. That's two distinct and inconsistent usages of the word computer.

Right, but if the tape is not infinite, then it is just an automata and these were also described by Alan Turing purely mathematically along with universal Turing machines (perhaps even earlier than that). I strongly recommend that you check my definition of manifest (as a tuple of experiments), then read the subsequent paragraphs regarding repetitions of experiments for how one can naturally deduce whether one's reality is universally Turing complete or not. My definition grabs and correctly deals with all edge cases similar to the one you have raised. I will copy paste the paragraph which discussed it here:

Allowing repetitions within the manifest is necessary because it allows one to build evidence, and thus increase one's confidence, that nature allows for the construction of a reliable universal Turing machine. Thus, a valuable use for repetitions is as a quality check on the UTM. Indeed, if one randomly or pseudo-randomly repeats many different experiments across the logical spectrum, and are indeed correctly reproduced, then one knows with a high degree of confidence that one uses a reliable computational system. Whereas for a manifest theory as a set, which includes no repetitions, the existence of a reliable UTM is merely assumed and in fact conditional to the framework, and as such cannot be inferred or proven. To prove with absolute certainty that the world allows for a universal Turing machine, one has to repeat every pair infinitely many times. Consequently, in any practical case one only infers, to a finite degree of certainty, that one has access to such a machine. Knowing that nature allows for the construction of a UTM, or if it does not then what are the specific limits to its construction --- is essential knowledge about reality. Using a tuple of experiments grants us this knowledge, whereas using a set of universal facts does not. This difference defines a classification between a mathematical and a scientific theories --- and any enumeration strategy which involves maximizing the entropy will differ in the scientific case from the mathematical case as a result.

But answer me this. What principle of mathematics says that bowling balls fall down, instead of up? After all if I implement Newtonian physics in a computer simulation but I reverse the sign of gravitational acceleration, bowling balls will fall up. The math doesn't care.

Your phrasing comes from a series of assumption as to what the laws of physics are, and the problems that you create follow from these assumptions. The laws of physics are simply not what you think they are. First of all, in even in modern physics (and in my framework as well) the laws of physics are a probability measure on the possible states of nature. Of course, physics is full of 'older' theory which have yet been integrated as such; for instance general relativity (or in your example classical gravity), the idea that a particle is a 'body of matter' in spacetime is another, etc. Of course if you pick these as your examples then you will have a bad time understanding that the laws of physics depend only on the 'bit' and the 'it' is derived.

In my framework, gravity, and anything else for that matter, are simply the consequence of invariant transformations associated with the general linear probability amplitude. I'll let you lead with your follow up questions and comments.
• 2.6k
The laws of physics are simply not what you think they are.

If your theory can't prove that bowling balls fall down, it's not a good theory.

Of course I'm not sufficiently versed in modern physics to know whether even it can prove that bowling balls fall down. Maybe in some other universe they fall up. Which would be consistent with your idea of a probability measure. Who knows, maybe bowling balls do fall up. I'd call that an argument against modern physics. Or your physics. Or anyone's physics; since gravity is an attractive force and not a repulsive one. If your theory can't prove that, then you haven't got a theory of physics. But I'll admit that I'm in over my head on the physics, so I can't really comment.
• 157
If your theory can't prove that bowling balls fall down, it's not a good theory.

Of course it does - I told you how in the previous post. In my framework, gravity, and anything else for that matter, are simply the consequence of invariant transformations associated with the general linear probability amplitude. I don't necessarily expect one (you or anyone else) to just understand what a general linear probability amplitude is without additional comments, but I am stating how it does (vaguely) to at least show there is an answer.
• 2.6k
Of course it does - I told you how in the previous post. In my framework, gravity, and anything else for that matter, are simply the consequence of invariant transformations associated with the general linear probability amplitude.

In simple words for my simple little mind, explain how you can prove that bowling balls fall down without using physical principles. Because you could certainly simulate Newtonian physics by reversing the sign of G and thereby make it a repulsive force. Math does not distinguish these two conditions. You have to look up at the sky and work from Tycho Brahe's data as Kepler and Newton did.

Right, but if the tape is not infinite, then it is just an automata and these were also described by Alan Turing purely mathematically along with universal Turing machines (perhaps even earlier than that).

Ok so you've backed down from TMs and you're now using finite state machines. Fair enough. But now your argument is:

P: There exists a mathematical theory of FSMs.
P: This theory describes actual real life computers.
C: Therefore pure math can tell whether bowling balls fall up or down.

The conclusion simply does not follow from the premises.

Thank good I am not using Peano's axioms then - if I did I would be in real trouble because indeed as you say there are more facts in PA than there are in nature.

FWIW you need Peano to have an unbounded tape. You can always have one more cell. That's Peano.

To prove with absolute certainty that the world allows for a universal Turing machine, one has to repeat every pair infinitely many times.

It's perfectly obvious that the world does NOT allow for any TMs, universal or not, since a TM has an unbounded tape. A TM is a purely conceptual object that does not exist in the real world and is in fact based on the existence of infinitely many natural numbers arranged in a well-ordered sequence. That is, you do believe in the Peano axioms after all; and you use them (implicitly) to be able to talk about TMs; BUT you occasionally forget that TMs do NOT exist in the world.

But I don't want to argue about TMs. I just want to point out that if you have two mathematical models of gravity, one that says bowling balls fall down and another that says they fall up, the ONLY way to tell which one is right is to interrogate the data. That is, drop a bowling ball and see which way it goes. That's physics, not mathematics.
• 157
Because you could certainly simulate Newtonian physics by reversing the sign of G and thereby make it a repulsive force. Math does not distinguish these two conditions.

Yes, but I am not running a simulation here. I am describing the state of affairs indubitably and infallibly (exclusively by using universal facts), and show that the rules of general computation which governs the transitions between manifests (infallible descriptions of reality) are a unifying statistical framework that happens (I believe by necessity, but your mileage may vary) to be the 'correct' framework to express and understand the laws of physics.

With this framework, I obtain a general linear probability amplitude, which supports quantum gravity. Specifically, the metric-affine gravity is obtained by gauging the affine group (there is a lot of literature on the subject). I assume that the valid solutions of this gauge theory admit universes in which objects falls down, but I have not verified if this is true or not of all possible solutions of the metric-affine gravity.

You have to understand that facts such 'the apple I am looking at falls down', and 'the fridge in my home has milk in it' are facts that may be found in a given manifest, but the laws of physics are statements about transformations of states between manifests. To deduce from 'the apple I am looking at falls down' that 'all apples falls down' is not a legit deduction. You are not allowed to use induction to derive the laws of physics because your induction will not be infallible. You have to use the structure of universal fact I propose or your argument will always be weaker. There is a way to do it, but one has to 'reset' his or her intuition about how to do things and how things work.

Imagine a universe that does not move (frozen in time / no transformations) --- does it obey any laws of physics? Seriously, think about this. If the universe were frozen, all the facts and all the information about it is still in there... but since it does not transform how can you possibly deduce any laws of physics from this information! You then simply define the laws of physics with respect to transformations between manifests.
• 2.6k
You have to understand that facts such 'the apple I am looking at falls down', and 'the fridge in my home has milk in it' are facts that may be found in a given manifest, but the laws of physics are statements about transformations of states between manifests.

I just want to point out that if you have two mathematical models of gravity, one that says bowling balls fall down and another that says they fall up, the ONLY way to tell which one is right is to interrogate the data. That is, drop a bowling ball and see which way it goes. That's physics, not mathematics.

Every time I ask you if your theory proves that bowling balls fall down, you throw out a lot of buzzwords. I submit that if your theory can't tell whether gravity is an attractive or a repulsive force, you may be doing mathematics, but you are not doing physics.

To know whether bowling balls fall down, you have to drop a bowling ball. That's the only point I'm making. I am not qualified to judge the rest of your paper.
• 157
To know whether bowling balls fall down, you have to drop a bowling ball. That's the only point I'm making.

I am sorry, but you are making errors at the most fundamental level, but it really isn't obvious and I can see why one would be making it. The problem is that you do not know what a law of physics is and assume that because, historically, gravity (as objects which falls down) was presented as a law then it must be a law of physics. As hard to believe as that may be, I guaranteed you it is not.

Let me try to explain. The only restriction that the laws of physics imposes on you is that you cannot leave experimental space no matter what you try. But other than that you are granted the computation freedom to 'transform' the probability measure of reality into any other state of experimental space. Thus, if it is conceivable that a given manifest in the space of all possible manifests admits a behaviour such that gravity points differently (maybe its just impossible, I'd have to know all the solutions of metric-affine gravity) then by necessity of it being possible then it follows that the laws of physics cannot render that state impossible... lest they would negative a state which is possible.

This does not give you infinite freedom however --- your life and existence is strongly limited in practice by the computational costs to 'reverse' the direction of gravity within your manifest. The flexibility is a necessary consequence of Turing completeness of experimental space. The restriction of not leaving experimental space is the only restriction of the laws of physics that can never be falsified, and thus constitute the 'true' eternal laws of physics.

Any other wishes that you place on the laws of physics is called, in the framework, a scientific law and is the result of producing a formal axiomatic representation of a finite manifest. This is allowed, but bear in mind that such is likely to be falsified at the some future transformation of your manifest. In all scientific theory are eventually falsified, except for the laws of physics.

Now if you had taken an example of what the laws of physics sets such as "will the universe ever violated the general linear probability amplitude" then I would confidently answer with no, as this is indeed set by the theory of everything. Do any universe not contain a collapse of the wave-function - again I would confidently say they all do. You picked a specific example for your law of physics that is NOT a law of physics.
• 2.6k
As hard to believe as that may be, I guaranteed you it is not.

Yes I believe you. My sense is that a professor of modern physics could not tell me whether bowling balls fall down either. Beyond that, I'm afraid I'm not qualified to judge your work any further.
• 1.5k
Bar on top, by convention indicates the average of a value. Will add a note under the equation to specify.

No need to, Alexandre. As a complex variable person I immediately thought of a conjugate, not having used the bar notation in many years for the mean. :yikes:
• 157
My sense is that a professor of modern physics could not tell me whether bowling balls fall down either.

If he is any good he will tell you that wether the balls falls down, up or side ways, is dependant on the reference frame of the observer.
• 2.6k
If he is any good he will tell you that wether the balls falls down, up or side ways, is dependant on the reference frame of the observer.

I have used the terms attractive and repulsive specifically to avoid being subject to such a rejoinder.

If your theory can't tell if gravity is attractive or repulsive, then it's a bad theory. I can't state for sure whether the modern notion of a physical theory passes my test.
• 157
If your theory can't tell if gravity is attractive or repulsive, then it's a bad theory. I can't state for sure whether the modern notion of a physical theory passes my test.

My theory supports quantum gravity. You can ask me if quantum gravity is always attractive. The answer is yes, if all solutions of quantum gravity are attractive, and no if they are not. I personally have not investigated the question.
• 2.6k
I personally have not investigated the question.

Well you should go out and get a bowling ball. Let me know when you've got one and I'll tell you the next step! LOL.

I understand the point you're making, that modern physical theory is at a deeper level than mere facts about bowling balls. So is there any fact about the world that I I can go out and verify with my own eyes, that your theory predicts?

I'm not really arguing with you about your theory, I didn't follow it in detail and don't know enough physics to comment. I'm just poking around the edges.

I was also wondering about your focus on TMs. After all as I noted, a TM can not solve the Halting problem, but for all we know, the universe can. Or maybe it can't. The question is at least open. The computability of the universe is an open question. So how can the study of TMs help us to understand the world? At best it can only help us to understand computer simulations of the world.
• 157
Well you should go out and get a bowling ball. Let me know when you've got one and I'll tell you the next step! LOL.

I get that, but it doesn't mean you account for all possible experimental scenarios by looking out the window and playing with one ball. If one uses induction one gets an empirical theory and such theories can be falsified (fundamental theorem of science).

So is there any fact about the world that I I can go out and verify with my own eyes, that your theory predicts?

Glad you asked. If you look at the last section of the paper you can see the experiment I propose. It involves the observation of geometric interference exceeding that which is possible with complex interference of QM. I think it is very interesting and ought to be fairly easy to test (no need to build a bigger particle accelerator for instance).

I was also wondering about your focus on TMs, After all, as I noted, a TM can not solve the Halting problem, but for all we know, the universe can. Or maybe it can't. The question is at least open.

Well that would be one way to falsify my claims. However, such a thing would violate a lot of things... the fundamental assumption science (a definition in my paper) would be violated, and would further make it impossible to formulate a scientific theory around those parts with exceed Turing computation. My probability measure 'travels' from manifest to manifest using a cumulation of computing steps. It would be unable to 'travel' to regions which cannot be reached by computation.
• 2.6k
I get that, but it doesn't mean you account for all possible experimental scenarios by looking out the window and playing with one ball. If one uses induction one gets an empirical theory and such theories can be falsified (fundamental theorem of science).

Hmmm. By that logic Newton shouldn't have based his theory of gravity based on studying just one solar system.

I'm just giving you a hard time, as I've said, I haven't followed your paper in detail and I'm not in a position to offer any more substantive points than I already have.

Glad you asked. If you look at the last section of the paper you can see the experiment I propose. It involves the observation of geometric interference exceeding that which is possible with complex interference of QM. I think it is very interesting and ought to be fairly easy to test (no need to build a bigger particle accelerator for instance).

Interesting.

Well that would be one way to falsify my claims. However, such a thing would violate a lot of things... the fundamental assumption science (a definition in my paper) would be violated, and would further make it impossible to formulate a scientific theory around those parts with exceed Turing computation. My probability measure 'travels' from manifest to manifest using a cumulation of computing steps. It would be unable to 'travel' to regions which cannot be reached by computation.

I think you're making a good point distinguishing between a scientific theory, on the one hand, and how the world works, on the other. I would tend to agree with you that all scientific theories are computable in the sense of Turing, even if the universe itself isn't.
• 157
Hmmm. By that logic Newton shouldn't have based his theory of gravity based on studying just one solar system.

It was beneficial no doubt not only for his career and reputation but also for the history of science as a whole, but Newton got an empirically derived theory which was eventually falsified, because he looked at a subset of experimental space. Whereas, my framework allows one to look at all of experimental space at once, thus allowing for an "absolute" definition of the laws of physics.

I'm just giving you a hard time, as I've said, I haven't followed your paper in detail and I'm not in a position to offer any more substantive points than I already have.

I appreciate your feedback greatly, and I would not be engaging if I didn't.
• 2.6k
It was beneficial no doubt not only for his career and reputation but also for the history of science as a whole, but Newton got an empirically derived theory which was eventually falsified, because he looked at a subset of experimental space. Whereas, my framework allows one to look at all of experimental space at once, thus allowing for an "absolute" definition of the laws of physics.

If only Newton had understood the errors of inductive reasoning, he'd have given up science and devoted more time to his religious studies. :-)

My understanding is that a lot of modern physics is sadly divorced from empirical reality. Your theory is in that same spirit, I gather. Physical laws are contingent and could be some other way in some other universe. People take this kind of reasoning seriously. Maybe they're right. I think the problem is that we've gotten to the point where experiments are just too expensive, so physicists go looking for mathematical trouble. A point that @Metaphysician Undercover and I agree on, even though he blames it on math. But it's not math's fault. A hammer can build a house or be used by a vandal to break your car window. The tool isn't responsible for the user's bad behavior.

I appreciate your feedback greatly, and I would not be engaging if I didn't.

Glad I could be of some help even if I don't understand the details.
• 9.1k
There's no physics in math.

This is probably not true. The circle has 360 degrees, very similar to the number of days in the year. Coincidence? The right angle was apparently developed as a means for creating parallel lines for measuring plots of land. Can we say that numbers were created for the purpose of counting things? It appears to me like principles of physics are firmly embedded into the fundamentals of mathematics. The divorce which you want to believe in, which would separate mathematics from its pragmatic inspiration, is not at all real.

A point that Metaphysician Undercover and I agree on, even though he blames it on math. But it's not math's fault. A hammer can build a house or be used by a vandal to break your car window. The tool isn't responsible for the user's bad behavior.

You forget, a tool is designed for a purpose,. And the purpose for which the tool is designed may be judged as good or bad as well.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal