What about elementary particles? Does an electron have depth? — ucarr

Yes, but it's not shaped like a little sphere or even spheroid. It's an irregular excitation within a field which propagates in spacetime.

What about quarks and gluons, mere fractional parts of elementary particles, with fractional charges? — ucarr

What about them? What are you asking? proton's and neutrons are not fundamentals, Electrons are, as are quarks and gluons.

At the sub-atomic scale it’s probably hard to talk about the three spatial dimensions of the human-scale of experience, given the unusual and startling attributes of quantum mechanical physics. — ucarr

Why? In what way does such as quantum entanglement, superposition or tunnelling, clash with 3d?

If we imagine an authentically 1D or 2D object in our 3D world, can it have any workable reality? — ucarr

No (Imo) but it's very useful in mathematical modelling.

How could you move a 1D or 2D object absent the third dimension of depth? — ucarr

In flat land (2D) you cannot move up or down.
In line land (1D) You cannot move up or down or overtake.

Likewise, how could you bend or reconfigure such a physical object without the third dimension of depth? — ucarr

You couldn't, (EDIT: apart from squishing it, ultimately into a pointlike configuration,) just like we cant project a 3D object into a 4th dimension, regardless of whether or not a 4th dimension is macro, or is wrapped around every set of 3D spacetime coordinates.
It's mathematically easy to refer to 4th dimensional spacetime as (x,y,z, a, t) but you cant show the 'a' coordinate geometrically.

Given our apparent human entrapment within an empirical experience of 3D, does that entrapment render the first two spatial dimensions of our real world as metaphysical objects? — ucarr

You could use the very overburdened label 'metaphysical,' for such, imo, if you want to, but you invite the supernatural woo woo, associated with the term, if you do.

Have you read "Flatland." It deals with some of these intricacies.

https://www.amazon.com/Flatland-Romance-Dimensions-Edwin-Abbott/dp/B0875SRH84/ref=sr_1_1?crid=3TGN15CI0WCZS&keywords=flatland+edwin+abbott&qid=1674664998&sprefix=flatland%2Caps%2C124&sr=8-1

:up: You've answered my questions with useful info. Thank-you.

What about quarks and gluons, mere fractional parts of elementary particles, with fractional charges? — ucarr

What about them? What are you asking? proton's and neutrons are not fundamentals, Electrons are, as are quarks and gluons. — universeness

I'm asking whether these existentially -- right? -- fractional quarks and gluons are expanded into three spatial dimensions. Is the answer similar to your answer re: the 3D shape of the electron?

Given our apparent human entrapment within an empirical experience of 3D, does that entrapment render the first two spatial dimensions of our real world as metaphysical objects? — ucarr

You could use the very overburdened label 'metaphysical,' for such, imo, if you want to, but you invite the supernatural woo woo, associated with the term, if you do. — universeness

I'm not married to "metaphysical" as a modifier in this conversation. What do you say to the following reformulation: Given our apparent human entrapment within an empirical experience of 3D, does that entrapment render the first two spatial dimensions of our real world as abstract objects known solely a priori?

:up: Thanks for the citation. I'll check it out.

You've answered my questions with useful info. Thank-you. — ucarr

:up:

I'm asking whether these existentially -- right? — ucarr

I don't know what you mean by these words.

fractional quarks and gluons are expanded into three spatial dimensions. Is the answer similar to your answer re: the 3D shape of the electron? — ucarr

I don't know what you mean by 'fractional quarks,' a quark is not 'fractional' unless you simply mean that they combine to make a proton or a neutron an in that sense they are 'part' of a hadron structure.
Yes, quarks are 3D field excitations. A proton is made of 3 quarks, 2 'up' quarks and 1 down quark. Held together by gluons. There are no free quarks, all quarks are 'bound up.' Neutrons are also made of 3 quarks but 2 are down quarks and 1 is an up quark. There are other types of quark, bound up in other types of matter, such as neutrino's. See https://en.wikipedia.org/wiki/Quark

What do you say to the following reformulation: Given our apparent human entrapment within an empirical experience of 3D, does that entrapment render the first two spatial dimensions of our real world as abstract objects known solely a priori? — ucarr

Well, I would ask, why you are differentiating is any sense between the 3 dimensions we 'empirically experience?' Why would 'two' spatial dimensions be abstract and another real? All three have equal 'significance of presence' and all three are experienced equally by humans (although up/down could be considered a different experience to forwards/backwards and side to side, I suppose).
I don't see how you can connect a dimension of space with the concept of an 'object'. An object can have dimensions but I don't see how it can be posited AS a dimension. Perhaps I am missing your main 'philosophical' point here. Can you exemplify further?

I'm asking whether these existentially -- right? — ucarr

I don't know what you mean by these words. — universeness

For clarity, let me extend the quote just a bit,

I'm asking whether these existentially -- right? -- fractional quarks... — ucarr

Above I'm trying to ask whether quarks are ontically fractional and, if so, how does a fractional or incomplete object express itself as a spatially dimensional entity.. This, however, is a distortion of the facts by me. After revisiting the Murray Gell-Mann story, I see that,

...in 1964, Gell-Mann and George Zweig (PhD '64) independently flew in the face of all that was known by proposing that the fundamental triplet had one member with a +2/3 charge and two members with charges of –1/3.

Gell-Mann called the members of his triplet "quarks..." Everything found in the old SU(2) symmetry group could be fashioned from +2/3 "up" quarks and –1/3 "down" quarks...

Quarks are not themselves fractional, but rather their charges are fractional. I don't suppose electric charge, an energy field, also possesses a particle configuration, so I won't be particular about asking whether electric charge has spatial expansion in three dimensions (unless you happen to know that it does).

Yes, quarks are 3D field excitations. A proton is made of 3 quarks, 2 'up' quarks and 1 down quark. Held together by gluons. There are no free quarks, all quarks are 'bound up.' — universeness

Do the fractional charges of quarks play an essential role in the outer boundary of a quark's field excitations?

Gell-Mann presented quarks as no more than an expedient accounting system, writing, "It is fun to speculate about the way quarks would behave if they were physical particles of finite mass (instead of purely mathematical entities . . . )."

Does Gell-Mann answer my question by identifying quarks as purely mathematical entities?

Well, I would ask, why you are differentiating is any sense between the 3 dimensions we 'empirically experience?' Why would 'two' spatial dimensions be abstract and another real? All three have equal 'significance of presence' and all three are experienced equally by humans (although up/down could be considered a different experience to forwards/backwards and side to side, I suppose).
I don't see how you can connect a dimension of space with the concept of an 'object'. An object can have dimensions but I don't see how it can be posited AS a dimension. Perhaps I am missing your main 'philosophical' point here. Can you exemplify further? — universeness

The above block of questions are important. They are clarifying and they address the philosophical point I'm trying to examine.

With respect to the central focus of my philosophical inquiry, the critical question is,

Why would 'two' spatial dimensions be abstract and another real? — universeness

Does the material universe have a one-dimensional realm? Does it have a two-dimensional realm? For three-dimensional humans, are these realms, if extant, inaccessible?

Your block of above questions present a picture of empirical reality a bit more complex than Gell-Mann's expedient accounting system of purely mathematical entities in that it posits two (presumably) purely mathematical dimensions as essential to the empirical experience of 3D humans.

If quarks, like you say of 1D and 2D within the human empirical experience, somehow play as essential to our empirical experience -- fractional charges included -- then do we have reason to see that Gell-Mann, by characterizing quarks as purely mathematical entities, creates some distortion of truth via simplification for the sake of clarity?

The only way to escape our 3D world is using mathematics - we can probe higher dimensions with it and we already have, haven't we? Math is like periscope peering over our 3D walls - at what fantastic objects/beings might exist in higher dimensions. Even if we can't liberate ourselves from our 3D prison, we can at least appreciate the freedom of higher dimensional prisons. :lol:

Your statement is clarifying. Math takes us on cerebral journeys to higher dimensions. If, as I read your statement, these higher dimensions we peer at from afar might exist up there as real material objects, then my question comes into a sharper focus. What is the ontological status of these theoretical objects represented by math entities within our 3D world?

Murray Gell-Mann characterized quarks as purely mathematical entities. As I understand him, unlike you, he's not claiming his mathematical entities might describe real material objects at higher dimensions. Or is he? Quarks are supposed to be telling us real things about protons. Last time I checked, protons exist as material objects.

When he develops mathematical proofs is he discovering what pure math can do independent of material objects? If these theoretical math representations run parallel to our material universe, what is theoretical physics doing beyond playing mind games?

Higher dimensions are mathematically consistent (I hope) and in philosophy that means possible. I'm afraid that's as far as we can go down this road mon ami.

Do the fractional charges of quarks play an essential role in the outer boundary of a quark's field excitations? — ucarr

Sorry, ucarr, you have just went past my current physics. I am not sure who are the most qualified physics folks on this forum. From my personal previous exchanges, perhaps @noAxioms could offer a more accurate, detailed physics response to your above question, than I could.

Does Gell-Mann answer my question by identifying quarks as purely mathematical entities? — ucarr

No, because I think Gell-Mann is wrong.

From phys.org:

Quarks have an astonishingly wide range of masses. The lightest is the up quark, which is 470 times lighter than a proton. The heaviest, the t quark, is 180 times heavier than a proton -- or almost as heavy as an entire atom of lead.
"So why these huge ratios between masses? This is one of the big mysteries in theoretical physics right now," Lepage said. "Indeed it is unclear why quarks have mass at all." He added that the new Large Hadron Collider in Geneva was built to address this question.

Does the material universe have a one-dimensional realm? Does it have a two-dimensional realm? — ucarr

Only imaginary realms or mathematical realms not 'real' ones, imo. Such realms can be modelled but not realised within our universe. If string theory is correct and we have more that 3 dimensions in THIS universe then none of those extra dimensions are macro (or extended dimensions.) They are all posited are dimensions which are all wrapped around every 3D coordinate in our universe. The calibi-yau manifolds are an attempt to display a 2D representation of a multi-dimensional space. The following is a 2D representation of a 6D space (that I admit, means nothing to me, as it just looks like an interesting shape, that I don't understand, at all!)



This image is on wiki, here.
Does this mean that it can be suggested that in our 3D extended space, each dimension is 'wrapped' around an original single dimension? I think the answer is no and I know of no currently plausible scientific hypothesis that suggests otherwise.

For three-dimensional humans, are these realms, if extant, inaccessible? — ucarr

Carl Sagan in one of his episodes of Cosmos, models a 3D object landing in 'flat land.' I think he used an apple on a piece of 2D card with little square lifeforms moving around on the card. He explains that the flat land lifeforms would just see some strange geometric, disjointed 'slices,' appear from nowhere.
It offered a 'little' understanding of a 3D object trying to manifest in a 2D space.
NO! this does not make 'crop circles,' 4D lifeforms trying to manifest in 3D space :lol: I doubt you were making any such connections!

then do we have reason to see that Gell-Mann, by characterizing quarks as purely mathematical entities, creates some distortion of truth via simplification for the sake of clarity? — ucarr

Yes, I think so. It's similar to the current debate on exactly what 'virtual particles' are. Some very learned people say they are 'real' (kinda makes the word 'virtual' confusing) and others say they are only mathematical (I would agree). I think vp's really help in explaining what is going on at a quantum level.
From wiki: https://en.wikipedia.org/wiki/Virtual_particle
The concept of virtual particles arises in the perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles.

mere fractional parts of elementary particles — ucarr

By definition, elementary particles cannot have parts.

fractional quarks and gluons are expanded into three spatial dimensions — ucarr

I don't know in what way you might consider a quark to be fractional (or worse, 'ontically fractional;) other than it being a part of something non-fundamental like a proton. I also don't know what you're trying to convey with the phrase "expanding into .. dimensions". You seem to be trying to apply classic properties to quantum entities, which doesn't make sense. A quark doesn't have meaningful size, but a pair of them might have a meaningful separation.

Do the fractional charges of quarks play an essential role in the outer boundary of a quark's field excitations? — ucarr

It is meaningful to talk about fractional charge, like a helium nucleus has 2/3 the charge of a lithium nucleus. Again, I don't know what you mean by boundaries of a field excitation. A field is arguably 4D, so the title of this topic might be about being trapped in a 4D world. I don't think an excitation has anything that can meaningfully be considered a boundary. An electron for instance might be measured anywhere with finite probability.

mere fractional parts of elementary particles — ucarr

By definition, elementary particles cannot have parts. — noAxioms

Yes. I posted mis-information that claims ontically fractional quarks. Universeness
set me straight about that. It's fractional charges attached to quarks, not fractional quarks.

fractional quarks and gluons are expanded into three spatial dimensions — ucarr

I don't know in what way you might consider a quark to be fractional (or worse, 'ontically fractional;) other than it being a part of something non-fundamental like a proton. — noAxioms

I stand corrected on this info also. I see that what you say is true.

Do the fractional charges of quarks play an essential role in the outer boundary of a quark's field excitations? — ucarr

It is meaningful to talk about fractional charge, like a helium nucleus has 2/3 the charge of a lithium nucleus. — noAxioms

Does this tell me that a charge can be considered fractional in a ratio with another charge but not ontically fractional in of itself?

...I don't know what you mean by boundaries of a field excitation. A field is arguably 4D, so the title of this topic might be about being trapped in a 4D world. I don't think an excitation has anything that can meaningfully be considered a boundary. An electron for instance might be measured anywhere with finite probability. — noAxioms

In the above block you make important observations of some curious details of elementary particle physics and the theoretical math measuring them. At bottom, I'm trying to look at the elementary particles as physically real material objects. Looking through this lens I'm assuming a field excitation of an electron is a material object with some type of boundary. I understand that energetic fields require nuanced measurements unlike the more simple measurements of what we call solid objects. Since, however, energetic fields dissipate their volume of energy over distance, as in the case of the inverse-square law describing how visible light energy dissipates as it travels through space, I've been assuming energy fields have some type of physically real boundary. Am I wrong about this?

A field is arguably 4D, so the title of this topic might be about being trapped in a 4D world. I don't think an excitation has anything that can meaningfully be considered a boundary. An electron for instance might be measured anywhere with finite probability. — noAxioms

We humans have reason to believe our world includes a fourth spatial dimension? I've heard a claim the fourth spatial dimension is perpendicular to the other three spatial dimensions. The claim goes on to say that, given this configuration, the 3D level of spatial expansion in no way closes itself off from the fourth spatial dimension. Does this openness of 3D to the fourth spatial dimension explain to some extent your statement that,

An electron for instance might be measured anywhere with finite probability. — noAxioms

I can now explain that the root of my inquiry pertains to the whereness -- I hope you can tolerate the neo-logism -- of material objects and how the perception of whereness is being modified by evolving theories.

What entrapment? And "metaphysical objects" is an oxymoron

What entrapment? — Zettel

From your question above I surmise you reject my supposition -- elaborated above in the OP -- that 1D, 2D, 4D and all dimensional expansions not the seamless 3D expansion of our empirical experience are only mental apprehensions known solely a priori. As this supposition claims, while I have some understanding of it, I can't actually pick up and hold in my hand an authentically 1D line. Any physical line within my empirical experience may appear to my senses to be flat, but no. It actually has depth, albeit in small volume.

Universness talked about compressing a 1D line into a dimensionless point and I thought, maybe that's an example of moving a 1D object in our 3D world. Wait a minute! In order for compression to happen, even along a straight line, don't we have to assume the presence of the third dimension of depth?

..."metaphysical objects" is an oxymoron — Zettel

Firstly, your comment suggests to me you hold that metaphysical implies abstract entity known solely a priori.. My interpretation here supposes that object in this context denotes a material thing that can be seen and touched.. If it is your supposition that metaphysics has no material members in its set, then I make brief mention of a notion of mine.*

Secondly, language posits another type of object as with "I hit the ball." wherein the verb hit takes ball for its object. This type of object is conceptual, not physical. Following this line of reasoning, I can claim the members of the metaphysical set are conceptual objects of my perceiving mind.

*As we have complex numbers with one part real and one part imaginary, might we have complex objects with one part real and one part imaginary? Meta holds here according to the ordinal scheme that posits first-order, second-order, etc.

Does this tell me that a charge can be considered fractional in a ratio with another charge but not ontically fractional in of itself? — ucarr

You still haven't defined what you mean by 'ontically fractional', so the question is unanswerable. The numbers assigned to the charges of various things are just conventions. They could just as easily have assigned charges of -7, +14 +21 and -21 to down and up quarks, protons and electrons respectively. There's nothing special about where they assigned '1'.

I've been assuming energy fields have some type of physically real boundary. Am I wrong about this?

Fields are 'the value of something at various points in space (or spacetime)'. Since a field by definition covers all of space, it would not seem to have a boundary. The EM field for instance cannot just stop somewhere, beyond which there are no EM effects. I think you're talking about not the field, but a given quantum excitation of one, but then the word 'boundary' only has classical meaning and I cannot figure out how to apply it to a quantum entity.

We humans have reason to believe our world includes a fourth spatial dimension

Spacetime has a time dimension, not a 4th spatial one. Certain higher theories like string theory posit more spatial dimensions, but they're not macroscopic like the three we know.

I've heard a claim the fourth spatial dimension is perpendicular to the other three spatial dimensions.

Doesn't have to be just like the 3 you know don't need to be orthogonal. Making them so just makes the mathematics far simpler. The time dimension is perpendicular to the spatial axes, but the specific direction it goes is an abstract choice. Once 3 dimensions are defined, the 4th no- longer has any choice if they're all to be orthogonal.
All that said, I've not heard any suggestion of a 4th macroscopic spatial dimension. It only takes 3 coordinates to define any point in space, so you'd have to demonstrate that to be incorrect.

I can now explain that the root of my inquiry pertains to the whereness -- I hope you can tolerate the neo-logism -- of material objects and how the perception of whereness is being modified by evolving theories.

Didn't understand any of that. Work from the back: what theories, how are they evolving, and in what way is that relevant to the rest of this?

Does this tell me that a charge can be considered fractional in a ratio with another charge but not ontically fractional in of itself? — ucarr

You still haven't defined what you mean by 'ontically fractional', so the question is unanswerable. — noAxioms

An ontically fractional electric charge is my attempt to describe an energy field that can only be accurately mathematically modeled to experimental observation by assignment of a fraction, and not by an integer.

The numbers assigned to the charges of various things are just conventions. — noAxioms

Given this convention, could someone, by convention alone, assign -1/2, -1/3, -1/4... as numbers assigned to the charges of various elementary particles?

Since a field by definition covers all of space, it would not seem to have a boundary. — noAxioms

Does it follow from this that what we call the gravitational field of the earth and the gravitational field of its moon are really one gravitational field?

I've not heard any suggestion of a 4th macroscopic spatial dimension. It only takes 3 coordinates to define any point in space, so you'd have to demonstrate that to be incorrect. — noAxioms

Does this tell me the hypercube is not a real entity, just an imaginary object of science fiction?

The holographic theory of the universe -- along with the event horizon surrounding a black hole -- adds complexity to the facts about the location of a material object in proximity to extreme gravitation.

Susskind's debate with Hawking re: the conservation of energy of material objects consumed by a black hole and the claims black holes are animate and eventually evaporate add complexity to the facts about where things are ultimately within spacetime.

An ontically fractional electric charge is my attempt to describe an energy field that can only be accurately mathematically modeled to experimental observation by assignment of a fraction, and not by an integer. — ucarr

But I did it with integers, so I guess it's not 'ontically fractional'.

Given this convention, could someone, by convention alone, assign -1/2, -1/3, -1/4... as numbers assigned to the charges of various elementary particles?

I don't see elementary particles with charges with those ratios, so no.

Does it follow from this that what we call the gravitational field of the earth and the gravitational field of its moon are really one gravitational field?

Yes, they are. Both moon and Earth contribute to the gravitational field, and their influence is not bounded, just like a = GM/r² never falls to zero regardless of how distant (r) you get from it.

Does this tell me the hypercube is not a real entity, just an imaginary object of science fiction?

Depends on your definition of being real. I certainly don't see any hypercubes in this universe, but it indeed would take 4 coordinates to define a point within one.

The holographic theory of the universe -- along with the event horizon surrounding a black hole -- adds complexity to the facts about the location of a material object in proximity to extreme gravitation.

Susskind's debate with Hawking re: the conservation of energy of material objects consumed by a black hole and the claims black holes are animate and eventually evaporate add complexity to the facts about where things are ultimately within spacetime.

Evaporation of a black hole doesn't contradict energy conservation. It all comes back as radiation.