Ia a particle 'real?'

[abashed]

@Francis_Vaughan

Nobody ever suggested that these models are the phenomena. Mapping is exactly what is being done. However, when it comes to a deep set of questions about the nature of quantum mechanics, there is a very real notion that we have a set if descriptive tools that cover the entire information content of the phenomena. We would have to posit that there is some form of structure of the universe that was intrinsically unknowable by any form of experiment that we could ever devise to believe that we could never know about that part of its nature. This is a self defeating argument.

Yes, we are able to derive aspects of phenomena via our measurements but it could be likened to standing on a sea-shore and discovering one or two interesting pebbles while the vast expanse of ocean lay ahead of us, undiscovered. Obviously there is structure to the universe but what I am saying is that what we codify as information is based on our mental predispositions and it is this that is knowable to us. We filter incoming information much as a radio receiver filters different radio frequencies that it is attuned to. It doesn’t mean what we ‘pick out’ as meaningful is a full representation of reality. We are very ‘picky’ in what we choose to call scientific data because it has to conform to something that is going to prove useful to our species. The universe doesn’t care about us so it won’t provide information automatically for our benefit; we have to do this for ourselves.

The axioms we use to base our understanding are axioms we believe are as open as possible. There are some parts to those axioms we do take on trust. We discount the idea that we live in The Matrix, or some other simulated reality. We don’t invoke higher beings or deities as the underling causes of our results. We believe that a parsimonious approach is the only reasonable one. We add the minimal amount of information to our models as we possibly can. Our mathematics is built upon a set of axioms that allows us to feel highly confident that there are no edge cases in our manipulations that lets a grasp of the model we generate fail. (Sometimes these may be slightly controversial. But science is a work in progress.)

But, again, axioms based on what? On our natural predispositions which have been formed by natural processes.

Again, no. Gödel deals with the ability of mathematical systems to be self describing. This is at the set theory end of mathematics, and is firmly in the province of pure mathematics and the theory of computability. It relates to questions such as - can I construct a computer program that can tell if any computer program it is given will stop in finite time or not. (Answer no.) Black hole physics has nothing to do with shortcomings in mathematics. It is well accepted that it has everything to do with our lack of a fully worked theory of quantum gravity, or a fully unified theory of all the forces. The breakdown of the current theories are not a break down of mathematics - they are basically a more messy version of dividing by zero, when zero is all we currently have. There are plenty of ways to not divide by zero, but what we are lacking is an understanding of which one to use, from a choice of known ideas or new ideas.

The problem Russell and Whiteheadfaced when attempting a pure synthesis of mathematics from formal logic was that they could not resolve some questions and paradoxes starting with things like “does the set of all sets contain itself?”. “The set of all sets that do not contain themselves”. Eventually Gödel showed that that no formal system extending basic arithmetic can be used to prove its own consistency. None of what Gödel did has any bearing on the mathematical tools used to create models of reality, such as QM. What he did show has deep bearings on computability theory and philosophy. Sadly there is a popular idea that runs about that claims that he showed that all mathematics is broken, when he did no such thing.

Our intuition is based upon how we interact with the universe on our own scale. It is what our brains learn from the cradle based upon what we experience. Our intuition doesn’t allow us to expect many macroscopic effects that have little to nothing to do with QM. We have to learn most of the simple conservation laws (there is a common psychological question about when children manage conservation of volume of liquids.) Try such simple things as the Magnus effect.* As I wrote, Galileo understood the problems with intuition (probably the most famous example of intuition versus reality being the equivalence principle, and ordinary folks “intuitive” belief that heavier objects fall faster. You don’t need to go to QM levels, or cosmological scales to find ordinary experiences that counter our intuitive understanding of how the universe works. Drop a magnet down a conductive tube and see what your intuition thinks.

If you regress back to ability to sense phenomena as the only truth, and all else a model, you will know exactly nothing. **

• I highly recommend the Veritassium YouTube channel. Go wild and watch as much as you can.

** Doesn’t end well.

Okay maybe I’ll leave it then. Thank you.

The problem here is that you are assuming the universe can be totally described by using mathematics. You can get so far with mathematics but it seems to me quite presumptuous to suggest that something as rigid as mathematics can fully provide an understanding of all aspects of reality. This should not be surprising given that we base mathematic on a relatively few set of rules. What our species has achieved is providing schemas of reality that conform to mathematics but that does not mean most of reality does. We have managed to forge a clear path through a dense jungle of confusing incoming sensations and called it reality but, actually, it is our reality, not necessarily someone else’s. The problem with mathematics is that it is a closed system and, therefore, self-referential so that the only way we can know about stuff is the way it is represented by the formulas we use. In this sense, it is too parsimonious to really* be* reality and again, we are back to relying on something that provides a model and serves us in our cause.

[Francis_Vaughan]

@abashed

We are very ‘picky’ in what we choose to call scientific data because it has to conform to something that is going to prove useful to our species. The universe doesn’t care about us so it won’t provide information automatically for our benefit; we have to do this for ourselves.

But, again, axioms based on what? On our natural predispositions which have been formed by natural processes.

You seems to be demanding that there is s deeper universe that actively wants to keep itself secret. The core axioms we use are the philosophical tenets of science. You would prefer axioms developed by unnatural processes?

The problem with mathematics is that it is a closed system and, therefore, self-referential so that the only way we can know about stuff is the way it is represented by the formulas we use. In this sense, it is too parsimonious to really* be* reality and again, we are back to relying on something that provides a model and serves us in our cause.

Actually the mathematics we are worried about here isn’t self referential. Being closed does not imply self referential. That was the whole point of Gödel. Very loosely - that mathematics that is self referential is incomplete. But that is not all mathematics. Until you try to develop a formal mathematics of mathematics that describes itself you are not incomplete. All the tools we use to describe physics are not part of this. They are neither known to be incomplete nor self referential.

The point about using mathematics is that we can develop any formalisms to describe phenomena we observe. We are not limited by the tools we already have. But we require our tools not to be shoddy, and to not be internally inconsistent. If they are internally inconsistent we know that we can prove nothing, or rather, can prove anything. We assume (as a scientific axiom if you will) that the universe is consistent in its behaviour. It is not capricious. The cosmological principle demands that we don’t assume we have a special vantage point. We demand that scientific theories (and thus the mathematics that describes them, if appropriate) be falsifiable, and we demand that they be parsimonious. You don’t get to keep adding special cases and dispensations to your theories every time you get a conflicting experiment. It took a long time to get to these ideas about the nature of science. Indeed a lot of famous science was done without them, and in places suffered because of it.

Mathematics is remarkable in that so far as we have any evidence, it is a universal truth. Moving to another part of the universe doesn’t change the way mathematics works. Further, it contains internal things that maintain consistencies that border on jaw dropping. Even better, it has managed to allow the development of internally consistent and predictive system that exceed anything our brains can grok. Like QM. Mathematicians delight in throwing around concepts that have absolutely no basis in the experience of our puny wetware brains.

You seem to be demanding a special kind of universe. One that contains intrinsically unknowable facts. That somehow humankind can never observe even a puzzling anomaly in our experience that somehow contradicts established knowledge and theories. So we spend our entire lives living in some sort of deluded state where every possible experiment we can conduct, and every experience we can possibly have, whilst completely consistent with our mathematics and physics, cannot uncover any of these hidden truths.

Further you demand that these hidden truths are not amenable to any formal description that involves such niceties as internal consistency. That makes them little short of a claim for magic.

We are certainly resigned to the reality that there will be things we will never be able to reach, some parts of the universe are intrinsically hidden to us - if only due to the size of the universe relative to the time we have, and the time we have had.

But why we should be unable ever have any evidence at all of some hidden reality seems a remarkable notion. After all, there is exactly zero evidence that this is true, and the claim is that there can never be any such evidence. You may as well believe in faeries that vanish whenever you try to look at them.

[abashed]

@Francis_Vaughan

Sadly, the reality is that a lot of people will never have the mental ability or the desire to put the work in to get the mathematics. But they still have an genuine interest in the science. Managing the gap is really hard. And because it runs against the macro scale intuition people’s brains learn, it is even harder. Worse, a lot of people have done a very poor job of bridging the gap in popular media. There are more books than I care to think about that spend more time on mysticism and really rotten analogues when more care could be applied.

Sadly, many people who could bridge the gap to the next level of the descriptions are put off because maths is so poorly taught in general. So they get put off very early, and forever regard anything mathematical as “too hard” or “not for me”. And don’t get me started on the generations of women denied even the basics.

A great deal of life requires one to put the time in to get to a level of capability where the target subject becomes something they can converse sensibly at. Indeed it is almost impossible to come up with an are where this is not true. From following a sport to politics to religious dogma to philosophy. You can the the lite version, or you can put the effort in. No different to getting to the point where you won’t make an idiot of yourself if you walk into a sports bar and try to engage a fan in conversation.

I see what you mean but I can understand the need to gain some kind of intuitive understanding because that is how we normally think about things. Perhaps it is a bit of a cop-out to simply present the mathematics without attempting any interpretation. I don’t know. After all, we have a number of well known proposed interpretations for QM so maybe we cannot resist doing it.

[Leo_Bloom]

@Grey

…
Consider it this way, there exists an object that when interacted in a variety of ways behaves in a consistent manner. We can now call that [real] object [del]an electron[/del] my wife… [strike through and underlined words added]

So this explains it.

Creed Bratton also understands.

[Ornery_Bob]

You can’t prove that reality is independant of you. It’s simply not possible to “prove” in any way that reality or any aspect of it exists in an objective way, because every “proof” winds up back at you.

But our experience of life clearly demonstrates that while we cannot prove that anything exists outside of ourselves, assuming that it does is the only way to get anything done. Just because you can’t prove that the sun doesn’t exist independently of you, doesn’t mean that you can do anything about it.

So you can either throw yourself down the well of a subjective reality, or you can accept that reality is objective, even though your experience of it is purely subjective. If you accept that anything exists outside of yourself, then accepting things like measurements makes sense. If not, then you’re down the well. Enjoy the view.

[abashed]

@Leo_Bloom

So this explains it.

Creed Bratton also understands.

That’s not an unreasonable definition. And I think it is the methods with which we interact with such objects, whether this be mathematically or descriptive or observational, that we define as reality.

[abashed]

@Ornery_Bob

You can’t prove that reality is independant of you. It’s simply not possible to “prove” in any way that reality or any aspect of it exists in an objective way, because every “proof” winds up back at you.

But our experience of life clearly demonstrates that while we cannot prove that anything exists outside of ourselves, assuming that it does is the only way to get anything done. Just because you can’t prove that the sun doesn’t exist independently of you, doesn’t mean that you can do anything about it.

So you can either throw yourself down the well of a subjective reality, or you can accept that reality is objective, even though your experience of it is purely subjective. If you accept that anything exists outside of yourself, then accepting things like measurements makes sense. If not, then you’re down the well. Enjoy the view.

I like this definition. It sums up my basic position too.

[abashed]

@Francis_Vaughan

You seems to be demanding that there is s deeper universe that actively wants to keep itself secret. The core axioms we use are the philosophical tenets of science. You would prefer axioms developed by unnatural processes?

Actually the mathematics we are worried about here isn’t self referential. Being closed does not imply self referential. That was the whole point of Gödel. Very loosely - that mathematics that is self referential is incomplete. But that is not all mathematics. Until you try to develop a formal mathematics of mathematics that describes itself you are not incomplete. All the tools we use to describe physics are not part of this. They are neither known to be incomplete nor self referential.

The point about using mathematics is that we can develop any formalisms to describe phenomena we observe. We are not limited by the tools we already have. But we require our tools not to be shoddy, and to not be internally inconsistent. If they are internally inconsistent we know that we can prove nothing, or rather, can prove anything. We assume (as a scientific axiom if you will) that the universe is consistent in its behaviour. It is not capricious. The cosmological principle demands that we don’t assume we have a special vantage point. We demand that scientific theories (and thus the mathematics that describes them, if appropriate) be falsifiable, and we demand that they be parsimonious. You don’t get to keep adding special cases and dispensations to your theories every time you get a conflicting experiment. It took a long time to get to these ideas about the nature of science. Indeed a lot of famous science was done without them, and in places suffered because of it.

Mathematics is remarkable in that so far as we have any evidence, it is a universal truth. Moving to another part of the universe doesn’t change the way mathematics works. Further, it contains internal things that maintain consistencies that border on jaw dropping. Even better, it has managed to allow the development of internally consistent and predictive system that exceed anything our brains can grok. Like QM. Mathematicians delight in throwing around concepts that have absolutely no basis in the experience of our puny wetware brains.

You seem to be demanding a special kind of universe. One that contains intrinsically unknowable facts. That somehow humankind can never observe even a puzzling anomaly in our experience that somehow contradicts established knowledge and theories. So we spend our entire lives living in some sort of deluded state where every possible experiment we can conduct, and every experience we can possibly have, whilst completely consistent with our mathematics and physics, cannot uncover any of these hidden truths.

Further you demand that these hidden truths are not amenable to any formal description that involves such niceties as internal consistency. That makes them little short of a claim for magic.

We are certainly resigned to the reality that there will be things we will never be able to reach, some parts of the universe are intrinsically hidden to us - if only due to the size of the universe relative to the time we have, and the time we have had.

But why we should be unable ever have any evidence at all of some hidden reality seems a remarkable notion. After all, there is exactly zero evidence that this is true, and the claim is that there can never be any such evidence. You may as well believe in faeries that vanish whenever you try to look at them.

Ultimately, mathematics is a tool and like any tool will shape and modify that which it is applied to. So whatever was present prior to being ‘shaped’ by mathematics will become a ‘creation.’ You can only operate within the methods that mathematics is designed to use and its internal logic; that’s what I meant by ‘self-referential.’

To take an analogy: If you have a rough piece of flint you could argue that within the body of this stone is a tool which can be used for cutting, say. However, this new form isn’t immediately apparent because you have to somehow ‘create’ it and you achieve that by shaping it until the required end-product is made. The same with mathematics. You apply mathematics to some phenomenon and by stringently observing its rules produce a new form that was not apparent in the phenomenon before. So what you have done is extracted those aspects of a phenomenon that represent a consistent model of some of its behaviour. You have brought to light that which was once hidden, which is great. But that does not mean we have totally defined the phenomenon in every possible way, only insofar as we can now manipulate it. There will still be ‘secrets’ we may never know about the phenomenon but we don’t care about that because we have accomplished what we want for the purposes of utilitarianism.

[abashed]

@abashed

Ultimately, mathematics is a tool and like any tool will shape and modify that which it is applied to. So whatever was present prior to being ‘shaped’ by mathematics will become a ‘creation.’ You can only operate within the methods that mathematics is designed to use and its internal logic; that’s what I meant by ‘self-referential.’

To take an analogy: If you have a rough piece of flint you could argue that within the body of this stone is a tool which can be used for cutting, say. However, this new form isn’t immediately apparent because you have to somehow ‘create’ it and you achieve that by shaping it until the required end-product is made. The same with mathematics. You apply mathematics to some phenomenon and by stringently observing its rules produce a new form that was not apparent in the phenomenon before. So what you have done is extracted those aspects of a phenomenon that represent a consistent model of some of its behaviour. You have brought to light that which was once hidden, which is great. But that does not mean we have totally defined the phenomenon in every possible way, only insofar as we can now manipulate it. There will still be ‘secrets’ we may never know about the phenomenon but we don’t care about that because we have accomplished what we want for the purposes of utilitarianism.

Maybe the answer to my original question is; yes, a particle is real to us.

[Francis_Vaughan]

@abashed

Ultimately, mathematics is a tool and like any tool will shape and modify that which it is applied to. So whatever was present prior to being ‘shaped’ by mathematics will become a ‘creation.’ You can only operate within the methods that mathematics is designed to use and its internal logic; that’s what I meant by ‘self-referential’.

OK, it is however not what is understood by the term self referential. You really mean internally consistent. Self referential means the system is capable of letting you define and reason about the system as part of that systems capabilities, and not requiring an external logic. That means your particular system includes formal logic in addition to the arithmetic components, as an intrinsic manipulatable element. The vast majority of mathematical systems and tools do not. You can in some forms of set theory.

I think you still don’t really get what the underlying capabilities of what we term mathematics as. Mathematics is in the end a way of building tools to represent things, where often those tools and those things is a totally abstract thing. It isn’t a just a study of say calculus or analysis. Those are highly useful areas that have been developed over the history of mathematics. Formal logic is a component of mathematics. This means the rules of argument and rhetoric as well. What is really really important is that there are elements to mathematics that allow us to reason about the way new ideas, new ways of representing things, and new tools for manipulating those things will behave. This is extraordinarily powerful. And the applicability of some of these new ideas can be zero except as a form of navel gazing about a wildly abstract idea. Sometimes what were considered little more than the musing of a few closeted academics becomes a front line component of new understandings about the real world. Sometimes our attempts to understand the real world delivers a puzzling set of constraints that demand a totally new form of mathematics to begin to understand them. What “mathematics” gives us as a basic thing is a large body of experience about how we might go about building new tools, and a very valuable set of meta-tools that allow us to know that if we craft our new ideas to meet some core demands, that they will suddenly become amenable to an existing body of work that allows us to reason about, and to extend their capabilities with ease and speed.

At the dawn of the quantum age, nobody would have guessed that Group Theory could be pressed into service to provide a way of taming the particle zoo. When Einstein was puzzling over how to make his ideas for GR converge and show they aligned with reality, it was a pre-exisiting bit of abstract geometry that allowed him to do so. The idea that complex analysis could describe in a useful way a lot of how physics works is also a surprise if you were only schooled in Newtonian physics.

[abashed]

@Francis_Vaughan

OK, it is however not what is understood by the term self referential. You really mean internally consistent. Self referential means the system is capable of letting you define and reason about the system as part of that systems capabilities, and not requiring an external logic. That means your particular system includes formal logic in addition to the arithmetic components, as an intrinsic manipulatable element. The vast majority of mathematical systems and tools do not. You can in some forms of set theory.

I think you still don’t really get what the underlying capabilities of what we term mathematics as. Mathematics is in the end a way of building tools to represent things, where often those tools and those things is a totally abstract thing. It isn’t a just a study of say calculus or analysis. Those are highly useful areas that have been developed over the history of mathematics. Formal logic is a component of mathematics. This means the rules of argument and rhetoric as well. What is really really important is that there are elements to mathematics that allow us to reason about the way new ideas, new ways of representing things, and new tools for manipulating those things will behave. This is extraordinarily powerful. And the applicability of some of these new ideas can be zero except as a form of navel gazing about a wildly abstract idea. Sometimes what were considered little more than the musing of a few closeted academics becomes a front line component of new understandings about the real world. Sometimes our attempts to understand the real world delivers a puzzling set of constraints that demand a totally new form of mathematics to begin to understand them. What “mathematics” gives us as a basic thing is a large body of experience about how we might go about building new tools, and a very valuable set of meta-tools that allow us to know that if we craft our new ideas to meet some core demands, that they will suddenly become amenable to an existing body of work that allows us to reason about, and to extend their capabilities with ease and speed.

At the dawn of the quantum age, nobody would have guessed that Group Theory could be pressed into service to provide a way of taming the particle zoo. When Einstein was puzzling over how to make his ideas for GR converge and show they aligned with reality, it was a pre-exisiting bit of abstract geometry that allowed him to do so. The idea that complex analysis could describe in a useful way a lot of how physics works is also a surprise if you were only schooled in Newtonian physics.

I appreciate you can extend mathematics, and I’m no mathematician, but you can’t just invent a new system of mathematics independent of what has gone before. There still has to be a basic level of integration with the rules that form the foundation of maths. There still has to exist parameters within which new mathematical ideas operate.

[Whack-a-Mole]

@Derleth

Do electrons exist?

Interestingly there is a notion that there is only one electron that exists and it moves backwards and forwards in time so it appears to us lots of them exist. But really there is only one (if it travels backwards in time we see it as a positron).

Before you think this is completely ridiculous it was a notion noted physicist John Wheeler proposed to Nobel Prize winning physicist Richard Feynman (and Feynman used the idea in part to consider anti-matter as time reversed matter).

This recent PBS Spacetime Video explains it all much better than I ever could.

[Francis_Vaughan]

@abashed

I appreciate you can extend mathematics, and I’m no mathematician, but you can’t just invent a new system of mathematics independent of what has gone before. There still has to be a basic level of integration with the rules that form the foundation of maths. There still has to exist parameters within which new mathematical ideas operate.

There are, but I think you are assuming much more complex sets of rules and ideas than are actually required. The fundamentals are really little more than the usual rules of formal logic (and even these are not set in stone, there are entire areas where we can play with using different rules of logic). After that the inputs are imagination, and a general desire that the result is interesting. It is trivial to come up with ideas that lead to systems that are just plain boring - as in they just don’t do anything. Also we like the systems to be self consistent, as without that we find the systems become boring again.

But that is about it. I think you might find looking at a little formal logic, some set theory, and maybe some group theory a useful thing before you dismiss the nature of mathematics. You seem to be beset with a view that is rooted in prescriptive and naive classroom instruction, probably from teachers who actually had no idea about the deeper elements of what they were teaching. This is an all too common problem. There are also deep philosophical questions about the nature of mathematics. A book I quite like, one that is gentle and very human is “What is Mathematics Really?” by Reuben Hersch. I personally don’t ascribe to some of his viewpoints, but the book itself is a valuable guide to the ideas.

[abashed]

@Francis_Vaughan

There are, but I think you are assuming much more complex sets of rules and ideas than are actually required. The fundamentals are really little more than the usual rules of formal logic (and even these are not set in stone, there are entire areas where we can play with using different rules of logic). After that the inputs are imagination, and a general desire that the result is interesting. It is trivial to come up with ideas that lead to systems that are just plain boring - as in they just don’t do anything. Also we like the systems to be self consistent, as without that we find the systems become boring again.

But that is about it. I think you might find looking at a little formal logic, some set theory, and maybe some group theory a useful thing before you dismiss the nature of mathematics. You seem to be beset with a view that is rooted in prescriptive and naive classroom instruction, probably from teachers who actually had no idea about the deeper elements of what they were teaching. This is an all too common problem. There are also deep philosophical questions about the nature of mathematics. A book I quite like, one that is gentle and very human is “What is Mathematics Really?” by Reuben Hersch. I personally don’t ascribe to some of his viewpoints, but the book itself is a valuable guide to the ideas.

Well, fine, I appreciate people have worked out ways to think about the world and codified systems that seem to stand up to rigour, however, all this stuff comes from the human mind so, by implication, arises from the action of neurons, synapses and so on. The former has been developed over great areas of time via evolution and it has been the interaction of organisms with their environment that has been the great shaker and mover. Now, to apply this to weird stuff like QM is going to cause a problem since it is attempting to use a ‘tool’ that is designed to be worked with something else, a wonderful, adaptive tool I grant you, but nevertheless, not really designed to deal with things outside of human experience. And so we have to use this incredible tool as best we can by using it to its limits but such limits will always be a constraint on what we can really know. That’s all I’m saying.