Information as the key underlying physical principle

[Digitalism]

I feel as though "information" is just the keyword or buzzword within the physics community currently that allows for multidisciplinary problems to be formalized rigorously. You can see similar ideas within other disciplines such as mathematics

 

[atyy]

The assumption that N is some function of K treats K as a variable. The interpretation is that there is a (single) function F such that any population of physical systems that has degrees of freedom K has dimension N = F(K). It is a statement that considers varying the population of physical systems that are used as inputs to experiments. (I find this a surprising assumption.)

Is this like saying that as systems get bigger or smaller, one doesn't get a transition from a classical to a quantum system?

 

[naima]

In this paper
the author writes:
As we have dealt with characterization of quantum informati
on it is natural to ask about its role and status in
quantum physics. In particular, our motivation to discuss q
uantum information in the context of philosophy of
physics follows in part from the fact that its impact on inter
pretative problems is rather little. For instance, in a
recent interesting review article on interpretations of Qu
antum Mechanics the term ”quantum information” does not
occur even once

I think that you will get no definition of "quantum information" Maybe information is not encoded in the wave function but is the wave function itself.

 

[Feeble Wonk]

I feel as though "information" is just the keyword or buzzword within the physics community currently that allows for multidisciplinary problems to be formalized rigorously. You can see similar ideas within other disciplines such as mathematics

I think that this misses the initial conjecture of the thread... that the "information" contained in the quantum state vector doesn't simply describe physical existence, but at a fundamental level, it "is" physical existence.

 

[Feeble Wonk]

But perhaps one should also remember that "information is physical" :)

I'd appreciate it if atyy could expound on this idea. I'm intrigued.

 

[naima]

it from bit

 

[Feeble Wonk]

Thanks Naima... Yes, that's the general idea that the thread began with. As suggested by John Wheeler, ". . . one enormous difference separates the computer and the universe--chance. In principle, the output of a computer is precisely determined by the input . . . . Chance plays no role.In the universe, by contrast, chance plays a dominant role. The laws of physics tell us only what may happen. Actual measurement tells us what is happening (or what did happen). Despite this difference, it is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer."
Yet, while this implication seems to be indicated by quantum physics, I still struggle with the conceptualization of physical existence consisting of only information. That's why I was hoping atyy would clarify his statement earlier.

 

[Digitalism]

I think that this misses the initial conjecture of the thread... that the "information" contained in the quantum state vector doesn't simply describe physical existence, but at a fundamental level, it "is" physical existence.

I did not miss the point, I was specifically guarding against that conjecture which I view to be an error. Perhaps I am incorrect.

 

[Feeble Wonk]

Sorry Digitalism. I meant no offense. I was simply trying to return to the initial line of inquiry. But, on second thought, perhaps your statement is not off the mark at all... because the crux of the debate is precisely the question of whether the "information" contained in the state vector (and/or quantum state) is merely mathematical formalism or the fundamental essence of physical existence.

 

[naima]

It is interesting to see that information (as energy) cannot be destroyed.
look at fig 1
When you try to hide information, it skips somewhere else in the environment.
We can say that all the information which was in particle 1 skipped to particle 3.
But we can say that particle 3 was replaced by particle 1.

 

[Digitalism]

Sorry Digitalism. I meant no offense. I was simply trying to return to the initial line of inquiry. But, on second thought, perhaps your statement is not off the mark at all... because the crux of the debate is precisely the question of whether the "information" contained in the state vector (and/or quantum state) is merely mathematical formalism or the fundamental essence of physical existence.

You are overkind. By no means did I mean to stifle inquiry. It is an interesting question, I was simply advising caution. Thank you for listening.

 

[Feeble Wonk]

It is interesting to see that information (as energy) cannot be destroyed.
look at fig 1
When you try to hide information, it skips somewhere else in the environment.
We can say that all the information which was in particle 1 skipped to particle 3.
But we can say that particle 3 was replaced by particle 1.

Sorry Naima, but I'm not sure I understand what you are saying. Did you mean to ask whether we can say that your hypothetical particle 1 was replaced by particle 3? If so, I think that's a very pertinent question.

I have heard of speculative descriptions of quantized space-time, such as with loop quantum gravity, where the Hilbert space is thought of as interconnected yet discrete nodes across which particles "hop". So, if we think of a unitary translation from one quantum state to the next... as you asked (if you meant to)... if the "information" of particle 1 skips to particle 3, is it meaningful to say that particle 3 "replaced" particle 1. I'm not sure about that. Yet, the information content describing particle 1 would be maintained in the subsequent quantum state (now referred to as particle 3?).

 

[naima]

We see that when you have a perfect knowledge about a particle if you try to erase all this information (with a maximum entropy) all this information skip elsewhere (here on another particle in the environment). Here particle and its state are the same.
Things become more difficult when only a part of the information is hidden. In the case of a Bell pair where each particle has a maximun entropy we often read that the whole information is in the correlation. Pati writes that information cannot be created nor destroyed but i never saw something like an energy balance: at the beginning we had a total information of 10 bits here and here and here and at the end we have 3,5 here in the correlations between a and b an c and ... and 6,5 in particle p an q and ...

 

[Stephen Tashi]

A pure state is an extreme point in a convex set of states. Hardy gives examples of pure states in Eq 2.

I don't know if this is true in general, but in both classical physics and in quantum mechanics, it means that within the theory, a pure state can be taken to be the complete state of a single object. Then an ensemble in which 50% of the objects are in pure state A and 50% are in pure state B is said to be in a mixed state.

In classical physics, relying on classical probability, the convex set of states is a simplex. In quantum mechanics, the convex set of states is not a simplex (usually drawn as a circle).

OK, but can a person interpret Hardy's words as stand-alone document? Does his paper really describe a precise model? (I wonder if people who claim to interpret his paper actually interpret what he wrote or do they have the usual approach to quantum mechanics so much in the back of their minds that they just make a "free association" on the phases that appear in it. Do they think "Oh, he's really talking about ..." and substitute-in a different model? Do other papers in the Parade Of Links for this thread have similar problems?)

(Hardy's lecture "Reconstructing quantum theory from reasonable postulates" and other lectures are available at http://pirsa.org/index.php?p=speaker&name=Lucien_Hardy. )Hardy writes about the "N distinguishable states" and later in the paper says these are the "pure" states. That conflicts with my interpretation in previous post that the N distinguishable states are those with distinguishable state vectors. We we take the state vectors of the N distinguishable states by my definition and form their convex hull then the corners are the "pure states". But would it follow that these mathematically defined corners represent states that can actually be output by the Preparation device?

Hardy says in a lecture that the Preparation device may emit "composite" systems (on some knob settings). As far as I can see, the Preparation device might also emit some mixed states - just as long as running over all possible knob settings on it only produces a finite number N of distinguishable states - however those are to be defined.

 

[Ilja]

If there is information, it is information about something. Else, I would not name it information. So, information IMHO presupposes the existence of something, else it would be meaningless. Thus, it is something derived from real existence. So, "bit is about it", which makes "it from bit" circular.
Moreover, information is always stored in something which really exists. This storage is, of course, something completely different than what the information is about. The nice pictures on the stick are usually not pictures of the stick. But, nonetheless, this is a second direction where the bit is impossible without a preexisting it.

So I would clearly reject any attempts to consider information as fundamental.

On the other hand, I think we should learn the lessons of the interpretation of statistical physics. Here, we have the frequency interpretation, where probability theory looks physical, with frequencies as defined by reality, by physical law, and entropy being something which can be measured. On the other hand, we have the Bayesian interpretation of it, which derives entropy and frequencies and all the statistical physics from the available information. The second approach seems to me much more justified (ergodicity, even if it could be proven, usually it isn't, fails to justify statistics because of the astronomic time which would be necessary to obtain it), and has a much wider domain of applicability (it is much more natural to apply it in non-equilibrium situations). Here, the error was to interpret something as real, physical, which is in fact not about reality but about our information about reality.

To correct this, we have to make a shift in the interpretation of, in particular, entropy: From something real to information about something real. Means, from it to bit. After this, entropy is no more something real, but information. And I think a similar shift it necessary also in the interpretation of quantum theory.

But, note: Entropy in the Bayesian approach does not become some "pure information". It remains information about something, namely, information about the real configuration of the system. Which exists, and is even well-defined by the equations, it is simply unknown, with only a very restricted information available about it.

And this reality is what I miss in the "it from bit" concept.

 

[Feeble Wonk]

If there is information, it is information about something. Else, I would not name it information. So, information IMHO presupposes the existence of something, else it would be meaningless. Thus, it is something derived from real existence. So, "bit is about it", which makes "it from bit" circular.
Moreover, information is always stored in something which really exists. This storage is, of course, something completely different than what the information is about. The nice pictures on the stick are usually not pictures of the stick. But, nonetheless, this is a second direction where the bit is impossible without a preexisting it.And this reality is what I miss in the "it from bit" concept.

Precisely IIja! This is exactly the discussion I was hoping for. This seems to be the intuitively obvious position that I've always believed myself.
Yet, I struggle with being able to conceptualize an objective, substantive "it" that is consistent with the physical action described by quantum physics (at least to the feeble degree that I understand it).

So, again, I was hoping for atyy to clarify what he meant by his statement that "information" is "physical".

 

[Feeble Wonk]

But perhaps one should also remember that "information is physical" :)

I don't mean to press, but I know that your posting on multiple threads which take your attention. So I just wanted to bump this thread in hopes that you would take a little time to explain what you meant.

The definition of *physical* (other than the biological meanings) according to dictionary.reference.com is..."of or relating to that which is material:
the physical universe; the physical sciences."

The freedictionary.com is slightly more inclusive, offering two (nonbiological) definitions that might apply... "3. Of or relating to material things: a wall that formed a physical barrier; the physical environment.
4. Of or relating to matter and energy or the sciences dealing with them, especially physics."

All of these refer to "material" existence with respect to being something *physical*. In what manner do you view information as being physical.

 

[Paulibus]

I suspect that there is an elephant in this particular room, namely the distinction between what we are and what we do.

Just as an elephant is an animal, so are we. And, although elephants do communicate well enough for elephant purposes, we excel in this respect -- as in this interesting thread --- having invented various languages to serve the human purpose of exchanging 'information'. But a language, even quantitative mathematics, is only a mental construct; not something as physical as say, a brick, despite the way we physically represent it as 'squiggles on paper' or binary bits.

That's why I also

... struggle with the conceptualization of physical existence (as) consisting of only information.

. Could this concept be just a bit of human foolishness?

 

[friend]

If there is information, it is information about something. ...
Moreover, information is always stored in something which really exists.

But the basis of matter is the quantum mechanical wave function, which seems to be a probabilistic creature by nature. So it seems the basis of reality is probabilistic. What is the wavefunction a distribution of, if not pure possibility from which we get information?

 

[Feeble Wonk]

Just as an elephant is an animal, so are we. And, although elephants do communicate well enough for elephant purposes, we excel in this respect -- as in this interesting thread --- having invented various languages to serve the human purpose of exchanging 'information'. But a language, even quantitative mathematics, is only a mental construct; not something as physical as say, a brick, despite the way we physically represent it as 'squiggles on paper' or binary bits.

Very well written Paulibus. I would agree that, intuitively, the assertion that information (and only information) is the fundamental essence of *physical* existence would appear on its face to be utter "human foolishness".
Yet, having said that, I'd also suggest that there is a fundamental difference between human spoken/written language, which is a human creation, and quantitative mathematics, which is not. I've often heard it said that Newton and/or Leibniz created "The Calculus". But that's sheer silliness. It's like claiming that some ancient pebble pusher created "The Addition"... as if 2+2 had not equaled 4 prior to that. At best, Newton and/or Leibniz "discovered" calculus. Or you could say that they developed the mathematical "language" to manipulate the formulas that represent the underlying mathematics itself. However, the logical and quantitative relationships expressed by the mathematical "language" simply are what the are because they are what they are. That self referential consistency, which appears to be reflected in nature, gives me sufficient pause to not reflexively give into my intuitive inclinations.

 

[Paulibus]

I'm afraid I agree with the ancient pebble pusher. Even at the risk of being thought silly , I resist the proposition that two and two make four can be characterised as some sort of eternal truth, and prefer to think of calculus as an evolved and heroic human invention; certainly not as a complex of discoveries. When I walk in the woods I don't expect an abstract descriptive label like a number to jump out of a bush and bite my leg, as it were. I maintain that abstractions are invented, however cleverly, and not discovered; and that it's only long familiarity that tempts us to confuse abstract concepts with real things. Perhaps a matrix is more easily recognised as an abstraction than a counting number formula? I see mathematical language not as compendium of relationships that 'simply are what they are because they are what they are', but as a human construct that wonderfully serves to usefully describe the physical situation we find ourselves in. Viva mathematics, viva!

 

[Feeble Wonk]

I see mathematical language not as compendium of relationships that 'simply are what they are because they are what they are', but as a human construct that wonderfully serves to usefully describe the physical situation we find ourselves in. Viva mathematics, viva!

I certainly didn't mean to belittle the accomplishments of mathematicians throughout history. On the contrary, advanced mathematics, particularly its application in the physical sciences, would have to be considered one of the pinnacles of human intellectual achievement.
Yet, as miraculous as that achievement is, it still seems to me that what they have done is to recognize, decipher and manipulate the extant mathematical patterns, not create them. Can you tell me that the ancient brute, before our pebble pusher, when holding two rocks in one hand and two in the other was not holding four rocks?

 

[Paulibus]

Again, what we actually are (walking, talking, and now writing primates) is key here. We describe what matters to us because we can. In your example the ancient brute created a four-rock pattern which you so described with the help of the extant language of arithmetic; an ancient abstract , human construct, not an eternal truth that always existed to be recognised. Mathematics is revered because it has a predictive and therefore verifiable character, which helps amazingly with living, prospering and surviving in this physically complex universe, so strangely equipped with past, present and future. But I think that mathematical patterns are 'only' intangible constructs of our minds, rather than tangible realities. As they say in France, à chacun son goût .

 

[marcus]

I suspect that there is an elephant in this particular room, namely the distinction between what we are and what we do.

Just as an elephant is an animal, so are we. And, although elephants do communicate well enough for elephant purposes, we excel in this respect -- as in this interesting thread --- having invented various languages to serve the human purpose of exchanging 'information'. But a language, even quantitative mathematics, is only a mental construct; not something as physical as say, a brick, despite the way we physically represent it as 'squiggles on paper' or binary bits.

That's why I also .
[as Feeble Wonk # 42 said:]
"... struggle with the conceptualization of physical existence (as) consisting of only information."
Could this concept be just a bit of human foolishness?

I think its fair to be skeptical of ideas about what existence IS or CONSISTS of. But I wouldn't object to the idea that "physics is ABOUT information".
Physics is about measurement and interaction, which are exchanges of information. Time is about changing from one quantum state to another and this is a change of information. Entropy is unavailable or irrelevant information to the observer. The idea of "observer" is an information theoretical idea. Rovelli channeled Bohr when he said "we are not concerned with what Nature IS but with how she responds to measurement" or something like that. Theories do not say what Nature IS, they predict, again information.
So maybe we can throw this idea of nature "consisting" of information into the garbage.

OK Physics is ABOUT information---we all know that, and it is not a new idea, but that is not the same thing as "Nature consists".

Excuse me if I am talking vaguely and haven't studied the thread enough. Just saw a couple of posts that I liked, and wanted to say something.

 

[marcus]

... prefer to think of calculus as an evolved and heroic human invention; certainly not as a complex of discoveries.
... viva!

I think that is right. And the idea of numbers as mental constructs agrees verbatim with how numbers appear in the foundations of mathematics. Based on axiomatic set theory, the cardinal number 3 is the set of all sets with three elements. there is a one-to-one mapping between a set of three tigers to a set of three lions and so both those sets are elements of the cardinal number 3.
and the ordinal number 3 is {∅, {∅, {∅}}}
If S is an ordinal number you take the NEXT ordinal by forming the set consisting of the empty set ∅ and S, so the next ordinal is {∅, S}. You can see how I formed the ordinal number 3, by taking the number 2 and forming the next ordinal after that. One can also represent the ordinals as a sequence of tree graphs.

Clearly the numbers, in mathematics, are not "discovered" :w They did not jump from behind a bush and bite Pythagoras on the leg as he was ambling through the woods in Magna Graecia, as per Paulibus example.

However it is just possible that some aliens orbiting a nearby star, perhaps only 1000 lightyears from here, who were busy developing their civilization, could ALSO have thought up numbers. If they have thought of axiomatic set theory, all the better! It could be a bond between us, so that love or at least toleration, could grow up between intelligent (to use a flattering term) species.

 

[marcus]

..., which helps amazingly with living, prospering and surviving in this physically complex universe, so strangely equipped with past, present and future. But I think that mathematical patterns are 'only' intangible constructs of our minds, rather than tangible realities.

D'accord.

 

[Stephen Tashi]

I suggest that the participants in this thread return to technical issues and avoid the vague philosophical discussions because Philosophical threads on the forum get closed as a matter of policy.

I'd like to hear from anyone who can discuss the mathematical details of an information theoretic approach to a physical theory.

 

[marcus]

I suggest that the participants in this thread return to technical issues and avoid the vague philosophical discussions because Philosophical threads on the forum get closed as a matter of policy.

I'd like to hear from anyone who can discuss the mathematical details of an information theoretic approach to a physical theory.

Why sure, Stephen :) Let's take a look at these and see if we want to discuss them. I am especially interested in the frontier physics questions where there is no other explanation besides the information theoretical one.
For example in the context of GR there is no concept of thermal equilibrium! Because two systems can be in contact and nevertheless be at a different temperature. In GR, temperature is affected by position in gravitational potential. (Tolman effect). To arrive at a workable concept of thermal equilibrium you must actually introduce the concept of information flow between the systems. Temperature alone is not enough.

http://arxiv.org/abs/1309.0777
Coupling and thermal equilibrium in general-covariant systems
Goffredo Chirco, Hal M. Haggard, Carlo Rovelli
(Submitted on 3 Sep 2013)
A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.
8 pages, 3 figures Physical Review D 88, 084027 (2013)

A paper for wide audience that is related to the Chirco Haggard Rovelli one mentioned above.
http://arxiv.org/abs/1311.0054
Relative information at the foundation of physics
Carlo Rovelli
(Submitted on 31 Oct 2013)
Shannon's notion of relative information between two physical systems can function as foundation for statistical mechanics and quantum mechanics, without referring to subjectivism or idealism. It can also represent a key missing element in the foundation of the naturalistic picture of the world, providing the conceptual tool for dealing with its apparent limitations. I comment on the relation between these ideas and Democritus.
3 pages. Second prize in the 2013 FQXi context "It From Bit or Bit From It?"

Another interesting question: why are gauge theories so prevalent in physics? A clue to this riddle is provided by considering how systems couple, so that information can flow between them. Gauge quantities can be mathematically redundant if the system is described in isolation, but essential (not redundant at all!) with the system coupled to the outside world. The very reason we have gauge theories could be information theoretical.
http://arxiv.org/abs/1308.5599
Why Gauge?
Carlo Rovelli
(Submitted on 26 Aug 2013)
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe "handles" though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it is a consequence of a relational structure of physical quantities.
8 pages published in Foundations of Physics 44 (2014) 91-104

 

[Paulibus]

However it is just possible that some aliens orbiting a nearby star, perhaps only 1000 light years from here, who were busy developing their civilization, could ALSO have thought up numbers.

I vaguely remember that NASA folk have already acted on this possibility. The human artefact that is now remotest from planet Earth is, I think, an early space probe (Pioneer?) that is now traveling away, far beyond the solar system. It carries a plaque with an engraved message to any alien folk 'out there' that may encounter it. This message consists of mathematical truths about geometry and/or numbers. The hope was that mathematics, as a universal language, could be understood by intelligent aliens who would then recognise that the plaque was evidence that another intelligent species existed.

I still hope that if this happened, the aliens would be benign folk who don't come looking for us as food!

Enough philosophic musings. Apologies.

 

[Stephen Tashi]

Let's take a look at these and see if we want to discuss them.
http://arxiv.org/abs/1311.0054

That philosophical paper would send us back to Philosophy.

It puts the burden of specifics on a reference to:
"Relational Quantum Mechanics" (1996) http://arxiv.org/pdf/quantph/9609002.pdf.

We could discuss that paper, although, just from scanning it, I'm not sure it establishes a formal structure for dealing with information in a quantitative way.

 

[marcus]

Stephen and Paulibus,
the one I would prefer is the one published in Physical Review D about inventing a concept of equilibrium that works in general covariant settings.
It quantifies information flow between two systems. And also relates that to the passage of time. Remember that TIME proceeds at different rates for things at different gravitational potential. So you see it is quite an intriguing problem. In ordinary statistical physics when two systems are placed in contact they implicitly experience the same time. One is not time-dilated relative to the other. But in the real world (GR) this is not true. If one is upstairs and one is down they have different time.
As well as (by the Tolman effect) different temperature even though they be closely coupled.

The only way to solve the contradictions is to introduce the idea of information. So I would vote for reading and discussing this one by Chirco Haggard Rovelli (CHR)

==excerpt from previous post==
For example in the context of GR there is no concept of thermal equilibrium! Because two systems can be in contact and nevertheless be at a different temperature. In GR, temperature is affected by position in gravitational potential. (Tolman effect). To arrive at a workable concept of thermal equilibrium you must actually introduce the concept of information flow between the systems. Temperature alone is not enough.

http://arxiv.org/abs/1309.0777
Coupling and thermal equilibrium in general-covariant systems
Goffredo Chirco, Hal M. Haggard, Carlo Rovelli
(Submitted on 3 Sep 2013)
A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.
8 pages, 3 figures Physical Review D 88, 084027 (2013)

 

[Stephen Tashi]

http://arxiv.org/abs/1309.0777

Related to that paper we can add http://www.theorie.physik.uni-goettingen.de/forschung/qft/theses/dipl/Paetz.pdf to the Parade of Links. It might be an easier read.

I'm not particular about what papers are discussed. Discussing several at once will probably be no more or no less confusing to me that discussing one paper. I prefer to go through them step by step, starting to where the technicalities begin. I won't understand them if the discussion begins in the middle - but if there are forum members who can jump to the middle, don't let me hold you back.

 

[naima]

I am reading "Black Hole: a war of savants". In this very good book, Susskind writes that there is a limit in the quantity of bits that can be stored in a given region or on a given surface. Wheeler thinks in his "it from bit" point of view that space IS a set of elementary grains which contain 0/1 bits. Is LQG very far from this quest?

 

[Feeble Wonk]

I am not being argumentative just for the sake of the debate, but I believe this is a critical point in our discussion... perhaps THE critical point. I will concede that the "language" of mathematics is a human creation of abstract thought. Further, I will concede that through sheer human ingenuity we have progressively mastered the ability to manipulate the abstract mathematical concepts described by that language. As Paulibus has suggested, the "predictive" and "verifiable" nature of these abstract concepts has enabled us to use them as a mental tool, in combination with carefully designed and controlled experimentation, to learn about the world we live in.

Yes, yes and yes. And yet... In any physical system, "quantities" are an observable of sorts, either as a multitude or magnitude. The ancient brute holding 2 stones in each hand IS holding 4 stones, whether he can count them or not, let alone have the cognitive ability to perform the mental operation of addition. 2 such brutes, each holding 4 stones, WOULD have 8 stones in total, whether the abstract concept of multiplication had ever been conceived or not. Regardless of the language one uses to "represent" the quantities of 2,4 and 8, the quantities exist and, in that sense anyway, they are "real". The quantitative relationships exist in a spatial relation as well, and those relationships are similarly real, even in the absence of the abstract mathematical and/or geometric "representation" of the relationships.

Several millennia before the birth of Newton, if our ancient brute had thrown his stone up in the air, it would still have followed the classical parabolic trajectory described by Newton's calculus. Given, the calculus does not just describe an existing quantitative/geometric relationship, but a change in that relationship over time as a factor of gravity and momentum. Change implies action, which is just a fuzzy philosophical step away from causation. This is admittedly a slippery slope I think we should shy away from.
I would like to make it clear that I am not suggesting the quantity of stones ARE the stones themselves, or that the calculus describing the stone's trajectory IS the actual stone flying through the air. I am simply trying to establish that quantitative and spatial relationships exist in nature, as described by the increasingly abstract mathematical language created by humans, even in the absence of that language... indeed, even if humans had never evolved to begin with.
Furthermore, as we all know, the very human ingenuity that we've discussed, with the use of abstract mathematical concepts and carefully controlled experiment, has demonstrated with as much scientific certainty as can reasonably be expected that the stone, the brute that throws it, and even the beast that jumps from the bush to bite the leg of our clever primate, are all "course grained" human perceptions of physical processes that are quantitative ("quantumtative" if you will >_<) at a more fundamental level.

And lastly, as our Friend has reminded us, physical action at that fundamental level appears to be probabilistic by its very nature.

But the basis of matter is the quantum mechanical wave function, which seems to be a probabilistic creature by nature. So it seems the basis of reality is probabilistic. What is the wavefunction a distribution of, if not pure possibility from which we get information?

So, I am compelled to suggest that what we are questioning in this thread is not just "what physics is about", but what physical existence is about.

 

[Feeble Wonk]

Apologies about the philosophical tone of my last entry. I couldn't help myself. I'll drop the matter at this point.