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How to envision quantum fields in physics?

Thunderballs September 17, 2021 at 17:08 8700 views 66 comments
I'm surprised to see here many comments and questions about science but virtually none about science itself.

For example, about physics. In the old days philosophy and physics were still married. Unlike nowadays. IMO this resulted in a deeper understanding of nature.

For example, quantum field theory is nowadays mainly concentrated on the math and less on that what the math describes. Virtual particles are considered no more than that: virtual, only a math expression leading to correct observations. But what describes this math expressiin? What is the math of the whole field of QFT describing? Shut up and calculate diesn't sattisfy! The pop-view of particles expanded?

Comments (66)

TheMadFool September 17, 2021 at 18:55 #596510
Reply to Thunderballs Thanks for reminding me of what I read, actually skimmed through, a coupla days ago. Unfortunately, I'm unable to recall the source. The "shut up and calculate" remark, made by David Mermin, was meant to discourage people from trying to make sense of or comprehend quantum physics in the same way as one sussed out Newtonian mechanics for example. It was simply not possible for reasons which include the difficulty/impossibility of visualizing what the equations of QM were saying.

I guess this is the point where you say, like Wolfgang Pauli did after he went through a paper of a young physicist, "it is not even wrong!"
Thunderballs September 17, 2021 at 19:03 #596512
Quoting TheMadFool
It was simply not possible for reasons which include the difficulty/impossibility of visualizing what the equations of QM were saying.


What are these reasons? Why writing difficulty/impossibility? Is it both? If it's difficult it's not impossible. Difficult but possible. Giving two possibilities always makes it right. Possible or not...Of course! I'm not asking about QM, I'm asking about QFT. QM can be induced from QFT. Which means QFT is the base.
PoeticUniverse September 17, 2021 at 19:46 #596537
Quoting Thunderballs
quantum field theory


And more, even the answer to Existence:

On the One and Only Existence
Prolog

In this lost haunt on the Orion arm
Of the galaxy, safe from the core’s harm,
The philosophers meet in the forum,
As sleuth-hounds unweaving the Cosmic yarn.

We search for the Start of the Universe,
The End, the Before, the After, the Kinds,
The Measures, and All That Lies Between:
The Music of the Spheres’ Magnificat.

We follow every single avenue,
Whether it’s brightly lit or a dark alley,
Exploring one-ways, no-ways, and dead-ends,
Until cornered where the Truth is hiding.

Since we all became of this universe,
Should we not ask who we are, whence we came?
Insight clefts night’s skirt with its radiance—
The Theory of Everything shines through!

We are ever in touch with the unknown,
For that’s ever the reach of science shown.
Reality is grasped by focusing
On what interacts with what and the means.

There is a realm of happenings, not things,
For ‘things’ don’t remain the same on time’s wings.
What remains through time are processes—
Relations between different systems.

An Eternal Basis has to be so,
For a lack of anything cannot sow,
Forcing there to be something permanent,
As partless, from which the particles grow.

Consider quantum fields of waves atop
One another: waves are continuous,
And so qualify as Fundamental;
Quantized lumps are particles, then more.

Note that there is no other absolute:
Newton’s fixed space and time got Einstein’s boot;
Particle spigots making fields are mute;
Classic fields have no fundamental loot.

There’s a lightness of elemental being
Since any more would have to be of parts,
And thus go beyond the fundamental arts.
The puffs of vacuum energy are small.


On the Forced Defaults for the Only Existence

There can only be the one Existence,
Forced, with no option for it not to be,
Which is no mystery because the ‘Nil’
Cannot be, even as spacers within.

There is neither ‘Full’ nor ‘Null’,
But a lightness of being near ‘Zero’,
As that’s what the universe amounts to,
Nor ‘Nil’s kin as ‘Still’, since there’s constant change.

This must-be partless Existence Eterne
Can’t end, so it must remain as itself,
Transmuting into multiplicity
Of the temporary as ‘elementaries’.

Since Existence has to be, of not ‘null’,
‘Supernatural Magic’ isn’t required;
So, there’s only the natural as the base;
One degree of freedom is its forced default.

Motion is a must, or naught could happen;
It can’t have parts, so it’s continuous;
Since no end, it can return to itself.
There can’t be anything else but it.

It is everywhere, with no gaps of ‘zilch’,
Waving, as that’s ubiquitous in nature;
Rearranging to the elementary
Particles at stable rungs of quanta.

Only quantum fields fit the criteria;
‘Particles as spigots’ failed to flow,
Newton’s ‘Space’ and ‘Time’ disappeared via
Einstein’s relativity special and general.

Quantum field points that just spring up and down
Form the field’s waves by dragging on others.
These sums of harmonic oscillations
Force the fixed quanta energy levels.

So the wave estimate proved to be right;
An electron/photon goes through both slits
Because it is a spread out field quantum.
Quantum jumps are due no wave fractionals.

The universe is a large quantum field,
For the 24 quantum fields interact,
This containing the whole of physics.
There’s no ‘God’s’ eye view; anything happens.

The anything in the massive universe
Is a lot of needed ‘extravagant’ stuff,
Since on Earth the right conditions obtained,
Our planet being where and what it has to be.

Cosmic and biological evolution were forced,
Stars collecting the elementaries,
Producing all the atomic elements
That went on to molecules, cells, and more.

All this took 13.75 billion years,
Since, again, there were no hoodoo shortcuts.
Life and consciousness emerged, no ‘Mojo’—
Since before that time on Earth there was none!

We, too, are forced to exist.

‘Magic’ has fallen by the wayside, it
As trancendence an intangible writ,
Unable to be distinct from matter,
Having to talk/walk the talk/walk of it.

An extra distinct realm isn’t needed,
As ‘intangible’, ‘ineffable’, etc.,
For it only begs the question—a shock!—
And as separate couldn’t have effect.

The ‘nonmaterial’ and ‘nonphysical’
Haven’t shown anything at all to date,
Plus, all the more they’d have to be explained;
The ‘metaphysical’ search has to fail.

The ‘God’ idea has fallen from its throne;
Forever quantum fields’ excitations’
Elementary quanta roll on those fields
That are everywhere and remain themselves.


Epilog

The quantum fields’ unity is the Whole,
Being ever, exhausting Reality,
Unbreakable and Unmakeable,
As partless and continuous monads.

All that emerges is still the fields at heart,
Though secondary and temporary,
Arising and at some time returning;
The quantum fields are Indivisible.

Quantum fields are the fundamental strokes
Whose excitations at harmonics cloak
The quanta with the stability
To persist and thus obtain mobility.

The elementary particles beget,
As letters of the Cosmic alphabet,
And combine in words to write the story
Of the stars, atoms, cells, and life’s glory.

Why Something?

Quantum states melt via uncertainty,
And this means that no quantum property
Can e’er be zero—a precise amount,
And so it is that motion can ne’er cease.

The Something

The quantum field is the bridge between ‘Nil’
And basic matter, and can ne’er be still;
Thus the ‘vacuum’ is the quietest field—
The closest approach to ‘Nothing’ that can be.

No ‘Null’ nor Matter Full

‘Nothing’ had no chance to be the hero,
Plus QM scrubs the idea of zero
Out of the physical world of being;
‘Zilch’ ne’er sleeps, but is e’er up to something.

A Mere Blip

But for the small quantum uncertainty,
The Cosmos sums to naught, its lunch being free:
No net electric charge; a weightless brick;
Minus-potential = plus-kinetic.

Oh, those imaginings of what can’t be!
Such as Nought, Stillness, and the Block’s decree,
As well as Apart, Beginning, and End,
The Unfixed Will, Blame, Fame, and Theity.
Thunderballs September 17, 2021 at 19:57 #596542
Quoting PoeticUniverse
The Music of the Spheres


You got a higher power (Coldplay). Nice poem!
Thunderballs September 17, 2021 at 20:01 #596543
Reply to PoeticUniverse

Jesus! You had an epiphany? Wow!

Ah yes! The poetic universe!
PoeticUniverse September 17, 2021 at 20:38 #596564
Quoting Thunderballs
Jesus! You had an epiphany? Wow!


Quantum Field Theory is the most accurate and succcesful in the history of science. The model of the sums of harmonic oscillators and its math matches the experimental results and gives rise to the standard model from which all kind of devices can be made that work.

I don't know why QFT doesn't get explored all that much on this forum.
Thunderballs September 17, 2021 at 20:42 #596567
Quoting PoeticUniverse
I don't know why QFT doesn't get explored all that much on this forum.


I do. It's considered difficukt while in fact there ain't nothing to it. Maybe we should start a lecture! For starters. The math terrifies a lot of people. Challenging their intelligence.
PoeticUniverse September 17, 2021 at 20:48 #596572
Quoting Thunderballs
I do. It's considered difficukt while in fact there ain't nothing to it.


We always knew the TOE had to be simple and thus almost boring technically but still very exciting as the answer to the most often asked question.
Thunderballs September 17, 2021 at 20:54 #596578
Quoting PoeticUniverse
the answer to the most often asked question.


What question?
PoeticUniverse September 17, 2021 at 21:14 #596589
Quoting Thunderballs
What question?


Of those like "Why anything?" or "What's it's all about?"
Thunderballs September 17, 2021 at 21:16 #596591
Quoting PoeticUniverse
Of those like "Why anything?" or "What's it's all about?"


Only God(s) knows that.
PoeticUniverse September 17, 2021 at 21:19 #596593
Quoting Thunderballs
Only God(s) knows that.


Well, He's not needed any more since Existence has no alternative. No need to move up a level.
Thunderballs September 17, 2021 at 21:24 #596599
Quoting PoeticUniverse
Well, He's not needed any more since Existence has no alternative. No need to move up a level.


It's not moving up a level. You can of course ask "but where did gids came frim". But that's a different question. I can't imagine the universe to be there without a creation by god(s). Even when it's eternal. There has to be someone behind it.
PoeticUniverse September 17, 2021 at 21:31 #596604
Quoting Thunderballs
It's not moving up a level. You can of course ask "but where did gids came frim". But that's a different question. I can't imagine the universe to be there without a creation by god(s). Even when it's eternal. There has to be someone behind it.


Can't have a complexity as First and Fundamental, not even a proton, much less some ultimate System of Mind.

Quantum Fields are the Ground of Determination (G.O.D.).
jgill September 17, 2021 at 21:33 #596606
Quoting TheMadFool
The "shut up and calculate" remark, made by David Mermin, was meant to discourage people from . . .


Like others, I attributed this wonderful line to Feynman. Mistakenly it would appear. Thanks.

Quoting PoeticUniverse
I don't know why QFT doesn't get explored all that much on this forum.


Oh oh. Awakening a slumbering giant! :gasp:
Thunderballs September 17, 2021 at 22:01 #596619
Quoting PoeticUniverse
Quantum Fields are the Ground of Determination


But from where came the quantum fields, these simultananeity of all paths in phasespace (or Markov chains)? These fields in a spacetime. From where came spacetime in its eternity?
PoeticUniverse September 17, 2021 at 22:06 #596622
Quoting Thunderballs
But from where came the quantum fields, these simultananeity of all paths in phasespace (or Markov chains)? These fields in a spacetime. From where came spacetime in its eternity?


The quantum fields exhaust Reality. There's no "coming from" for the Eternal Fundamental that has no beginning or end.
Thunderballs September 17, 2021 at 22:07 #596624
Quoting PoeticUniverse
The quantum fields exhaust Reality. There's no "coming from" for the Eternal Fundamental that has no beginning or end.


That' s the question!
PoeticUniverse September 17, 2021 at 22:09 #596625
Quoting Thunderballs
That' s the question!


There's no question about the ever and always of the Fundamental.
Thunderballs September 17, 2021 at 22:12 #596629
Quoting PoeticUniverse
There's no question about the ever and always of the Fundamental.


That's the question! Why shouldnt there be a question? Is the question. Because it is like you think?
PoeticUniverse September 17, 2021 at 22:20 #596633
Quoting Thunderballs
That's the question!


Existence is the mandatory default, given that 'Nothing' cannot be, much less be productive.

Do you want 'Nothing' to have some capability to 'it'? Then it's not a 'Nothing' but a something.
jgill September 18, 2021 at 03:41 #596718
Quoting Thunderballs
What is the math of the whole field of QFT describing?


The first step is to visualize a vector field:

User image

Thunderballs September 18, 2021 at 06:15 #596745
Quoting jgill
The first step is to visualize a vector field:


Visual poetry! Tthanks for your contribution. Now it's going somewhere! Do you think we can speak of fields of particle trajectories? I know that a quantum field is formally, mathematically, a distribution of operators. Of creation or destruction operators (what expressions...). These create particles (or states in Fock space, excuse the language).
Wayfarer September 18, 2021 at 08:32 #596775
Check out this article https://aurocafe.substack.com/p/the-shapes-of-things?r=l7mv0&utm_campaign=post&utm_medium=web&utm_source=copy

Mornhoff is a qualified physicist and educator. (Incidentally the Greek word given in the opening paragraph is, I presume, ‘atomos’, although I don’t read Greek.)
Thunderballs September 18, 2021 at 08:50 #596778
Reply to Wayfarer

I know this article! Nice. In it:

"Why formless? According to the current (so-called) standard model of particles and forces, certain quantum objects, such as electrons and quarks, are fundamental in the sense that they are not composed of other quantum objects. While such objects are often described as pointlike (and many physicists take this to be the literal truth), this can only mean that they lack internal structure, which is another way of saying that they lack component parts and therefore are formless."

Points have no form indeed. Their relation wrt each other does though. Quarks and leptons might be composed and thus have a very small fuzzy form. The fuzziness relates to the strange property of particles (the image of a particle moving in spacetime is a popular view) that everypossible classical path is present, each one with its own probability amplitude. Particles can even be created. In the popular view, a gauge particle, like a photon, emerges (or is absorbed) from a a particle that's electrically charged. Pairs of particles can be excited from the fluctuating vacuum fields.
Thunderballs September 18, 2021 at 09:25 #596784
Quoting jgill
The first step is to visualize a vector field:


What's the purple line in your picture above? What's the green dot? A particle? Is it a trajectory (purple) of a particle (green) in a vector field? What do the vectors represent? What creates them?
Wayfarer September 18, 2021 at 09:43 #596792
Quoting Thunderballs
I know this article!


So you must be on Ulrich’s mailing list. It was only published yesterday.
Thunderballs September 18, 2021 at 09:51 #596795
Quoting Wayfarer
So you must be on Ulrich’s mailing list. It was only published yesterday.


I know what he thinks. He is a "well-known" figurre!

He says:

"A quantum object has no way of being something in itself, independently of the experimental context in which it is observed"

Here I disagree.
magritte September 18, 2021 at 10:46 #596807
Quoting jgill
The first step is to visualize a vector field:


:up: and over time ?
magritte September 18, 2021 at 10:48 #596808
Quoting Thunderballs
"A quantum object has no way of being something in itself, independently of the experimental context in which it is observed"

Here I disagree.


Then you're lost
Thunderballs September 18, 2021 at 11:04 #596811
Quoting magritte
Then you're lost


Magritte would disagree. Once lost you can only be refound by the truth. Experimental habitats exist only a few hundred years. If objective existence needs conscious observers to exist the n how could conscious beings develop in the first place. Quantum reality doesn't care about us nor our experiments. The latter can be discussed though.
Pop September 19, 2021 at 23:52 #597699
Quoting jgill
The first step is to visualize a vector field:


The way I am starting to understand this from an information theoretic is: The particle is a body of information being acted upon by an informational field that is forming and determining the particle, in shape and direction.

Consciousness is a similar such body of information that is formed from and determined entirely by information acting upon it.
jgill September 20, 2021 at 03:27 #597760
Quoting Thunderballs
The first step is to visualize a vector field: — jgill

What's the purple line in your picture above? What's the green dot? A particle? Is it a trajectory (purple) of a particle (green) in a vector field? What do the vectors represent? What creates them?


This is a relatively simple vector field in the complex plane based upon the function f(z)=-cos(z). The contour is a streamline describing the path of a point moving under the impetus of f(z). I suspect quantum fields are far more complicated and elaborate than this one. Kenosha Kid might chime in if he is around for an expert opinion.

Physical field theory seems quite different, involving tensors,etc.
Wayfarer September 20, 2021 at 03:39 #597762
Quoting Thunderballs
If objective existence needs conscious observers to exist then how could conscious beings develop in the first place?


A quantum experiment suggests there’s no such thing as objective reality.
TheMadFool September 20, 2021 at 07:46 #597811
Quoting Wayfarer
I know this article!
— Thunderballs

So you must be on Ulrich’s mailing list. It was only published yesterday


:lol: Speaking for myself, I don't want to be on any mailing list - yes, I might miss out on some good offers but I definitely won't be scammed! :grin:
Wayfarer September 20, 2021 at 08:13 #597821
Reply to TheMadFool Ulrich Mornhoff is definitely not going to scam anyone. You can click the link I provided with confidence.

The reason I said that is because when I posted the link to that article, Thunderballs said he knew the article. So I pointed out it had only been published a day previously.
TheMadFool September 20, 2021 at 09:39 #597840
Quoting Wayfarer
Ulrich Mornhoff is definitely not going to scam anyone. You can click the link I provided with confidence.

The reason I said that is because when I posted the link to that article, Thunderballs said he knew the article. So I pointed out it had only been published a day previously.


:ok: I just found it funny and also very inspiring that there are people on this forum who take knowledge seriously - keeping up to speed is not my cup of tea, as it is I have difficulty with what's already known.

You might find the following to be an interesting conversation (transcribed from an interview) between Hannah Fry (mathematician) and Prof. Ivette Fuentes (quantum physicist).

[i]Hannah Fry: It seems that there's quite a lot of uncertainty in quantum physics. Does that bother you?

Prof. Ivette Fuentes: No, when I heard that things were, you know, uncertain and also against our common sense in quantum physics then I thought, oh wow!, that sounds interesting, I want to know more about that.

Hannah Fry: Ok, alright, I'll tell you what then, quantum physics lesson 101, where do we start?

Prof. Ivette Fuentes: Ok, I would say we have to start with superposition. So, let's talk about electrons. So, they're very small particles and they can be in two states, spin, and the spin can be pointing up or down. So, if we were in the classical world, the spin could only be either up or down but in the quantum world, the spin is in a superposition which it means it can be up and down at the same time.

Hannah Fry: In the quantum world you can have your cake and eat it too. Alright, tell me about entanglement then.

Prof. Ivette Fuentes: Ok, so take two electrons. If the electrons are entangled, and if I do something to one of the electrons, for example change the direction of the spin, that will instantaneously affect the state of the other electron even if they're separated (by) long distances.

Hannah Fry: How far are they from each other?

Prof. Ivette Fuentes: Well they can be a few centimeters but now the latest experiments, using satellites, show entanglement across 1,200 km.

Hannah Fry: What? You've got something over here and something 1,200 km away. You do something to one and the other one instantly knows what's happened?

Prof. Ivette Fuentes: Yes, you affect the state of the other one instantly.

Hannah Fry: Apparently, there is no causal link. The only thing we can say is that the two particles are synchronized. How does one know what the other one is doing?

Prof. Ivette Fuentes: Well, that we're still trying to understand because that's what mathematics tells us and then we can show it in the experiment but we're still struggling to understand what that means. And one of the reason why we don't understand it in, you know, like you're asking is because we don't see it in our everyday lives. So, let's say it's not part of our experience and common sense but that doesn't mean it doesn't happen.[/i]

PoeticUniverse September 20, 2021 at 17:06 #597941
How to envision quantum fields in physics?

A field has a value at every point. Picture each point being on a spring going up and down; this is the harmonic oscillator! These points moving affect other points moving, dragging on them. The sums of the harmonic oscillators are the wavering waving fields. There are fields for boson and fermions. They can affect one another.

At rest, the fields still fluctuate (since there can be no stillness), about the zero-point energy, which isn't zero but to a physicist. The Higgs field at rest is of an even higher energy! All the fields overlap and merge into the one quantum field of the universe. They exhaust reality; there isn't anything else. They provide the entirety of physics. They are here now and were there before the Big Bang and are ever and always.

As fundamental, a field must ever remain as itself, thus but rearranging itself to form the elementaries of the Standard Model, which occur at stable rungs of energy and sometimes charge, as quantum excitations of the field being at certain stable unit levels.
bert1 September 20, 2021 at 18:08 #597954
Reply to PoeticUniverse

As it famously says in Acts 17:28 "For in the quantum field we live, and move, and have our being"

PoeticUniverse September 20, 2021 at 20:24 #597996
Quoting bert1
"For in the quantum field we live, and move, and have our being"


"The Quantum Field that made the Universe is the Ground of Determination and does not live in Colliders built by human hands. It made everything from the field excitations that are the stable elementaries."
ArisTootelEs September 20, 2021 at 23:32 #598059
Reply to PoeticUniverse

Quantumfields also live in colliders.
ArisTootelEs September 20, 2021 at 23:34 #598063
Reply to Wayfarer

There are two objective realities for a black hole too. What is meant by two objective realities is that two observers see different parts of the same objective reality.
ArisTootelEs September 20, 2021 at 23:51 #598076
Quoting Pop


The particle is a body of information being acted upon by an informational field that is forming and determining the particle, in shape and direction.


The particle is just an almost point-like structure which moves on ALL trajectories through spacetime (also backwards in time!) simultaneously. As such it contains no information. The only information is contained in their respective probability amplitudes. The wavefunction is inferred from these paths (path integral formalism(. The only usefull information to people lies in the collective forms of interacting particles (through gauge fields). We see these. They can be usefull to us. A quantum field can be pictured:

For one particle as all paths in spacetime of an almost pointlike classical particle interacing with fluctuations of the vacuum fields of ALL elementary particles (quarks, leptons, or even more fundamenta ones. and vacuum gauge fields, like the photon, gluons and gravitons).

For more particles the situation is the same but the particles interact on top with one another and excitations (creation and destruction operators) of fields can cause more or less particle to fly around.

A field can be seen as an operator valued distribution. The operators are creation and destruction operators. With, say, that one particle such a distribution is associated. Corresponding to all these trajectories and probability amplitudes.
Pop September 20, 2021 at 23:58 #598082
Reply to ArisTootelEs Thanks for that. What is meant by an operator valued distribution?
ArisTootelEs September 21, 2021 at 00:04 #598086
Reply to Pop

A distribution (a function-like structure) of operators. Around and at (not only AT) each point in spacetime an operator is assigned. Creation or destruction operator.
Pop September 21, 2021 at 00:08 #598089
Reply to ArisTootelEs Do you mean the operator in this case would be the forces of the vector field - Operating on the particle?
ArisTootelEs September 21, 2021 at 00:11 #598093
Reply to Pop

I mean creation or destruction operators creating or destroying elementary partcles. They act on vacuum fields of elementary particles (matter and gauge).
Pop September 21, 2021 at 00:12 #598096
Reply to ArisTootelEs Thanks - I have quite a bit of catching up to do! :smile:
ArisTootelEs September 21, 2021 at 00:14 #598098
Reply to Pop

You're welcome! :smile:
ArisTootelEs September 21, 2021 at 00:57 #598121
Quoting PoeticUniverse
A field has a value at every point. Picture each point being on a spring going up and down; this is the harmonic oscillator! These points moving affect other points moving, dragging on them. The sums of the harmonic oscillators are the wavering waving fields. There are fields for boson and fermions. They can affect one another.


This is the wrong nature of fields. Imaginative and helpfull though. Reminds me of "Quantum field theory in a nutshell", where a comparison with a spring matrass is made.
PoeticUniverse September 21, 2021 at 01:10 #598130
Quoting ArisTootelEs
nutshell


Acts 29 “Therefore since we are the field's box spring's offspring, we should not think that the field's being is like gold or silver or stone—but like a mattress."

Manuel September 21, 2021 at 01:15 #598134
Reply to jgill

In some of the pop-physics books I've read, people like Sean Carroll, Carlo Rovelli, Art Hobson and the like, they tend to say that a field is kind of like a space, not unlike when we think of a field ordinarily, but we abstract away all the phenomenal qualities we tend to associate with them (greenness, grass, sand, whatever).

What that image presents is a kind of curved loop area. Or am I misinterpreting the image?

Tom Storm September 21, 2021 at 01:33 #598144
Reply to Manuel Kind of. There's a pretty good discussion of this by David Tong @ the Royal Institution on YouTube. It's calledQuantum Fields The Real Building Blocks of The Universe
Ozymandy September 21, 2021 at 01:36 #598147
Quoting Manuel
In some of the pop-physics books I've read, people like Sean Carroll, Carlo Rovelli, Art Hobson and the like, they tend to say that a field is kind of like a space


More or less. Take just one particle (spin 1/2) in empty space. This particle, if prepared firstly by an interaction, also called a measurement, is essential for spinor fields (quarks and leptons and maybe even more deep) to localise. This particle moves on ALL possible trajectories at once. If it had not interacted all probability amplitudes for these paths (and these are litterally ALL paths) are equal. All these particle paths and interactions later constitute space. Space is that what allows all these particle trajectories. But these paths don't constitute space.
Manuel September 21, 2021 at 01:47 #598160
Reply to Tom Storm

Ah cool. I will take a look. Thanks. :up:

Quoting Ozymandy
All these particle paths and interactions later constitute space. Space is that what allows all these particle trajectories. But these paths don't constitute space.


Very interesting.

For my benefit, permit me to re-formulate this: So the particles move in all trajectories in these paths, these paths later constitute space, at the end of a process.

Space is what allows or permits these processes happening. So would the fields be space itself or would they be what is involved in the paths particles take?

In other words, are fields the process by which particles move in all directions, or are fields more fundamental than that?



Ozymandy September 21, 2021 at 01:54 #598164
Quoting Manuel
Space is what allows or permits these processes happening. So would the fields would be space itself or would they be what is involved in the paths particles take?


Good thought! I answered it in my last sentence. These paths dont constitute space though its tempting to think. Would we finally know what spac actually is. MAYBE... they constitute spacetime... Must think about that! Thanks! :grin:
Manuel September 21, 2021 at 02:03 #598173
Reply to Ozymandy

:chin:

Looking forward to your eventual reply, once your done cogitating for a while. :)
Ozymandy September 21, 2021 at 02:04 #598175
Quoting Manuel
Looking forward to your eventual reply, once your done cogitating for a while. :)


:smile:
jgill September 21, 2021 at 04:07 #598231
Vector space does not mean vectors in space.
jgill September 21, 2021 at 21:37 #598512
Entanglement frequently arises in these discussions, and it's tempting to wander into quantum mysticism. Here is a fairly clear-eyed perspective of it, from Quora by Mark John Fernee:

It's the quantum version of a correlation. That means that two or more parts of a quantum system have correlated properties. What's strange about it is that the correlation is indeterminate until a measurement is made, after which the correlation is revealed.

A reasonable example is that of a pattern. A pattern represents collective information that isn't apparent unless the entire pattern is observed. That's a classical pattern! Such a pattern can be said to always exist, regardless of whether it's measured. For the quantum version, there may be two or more possible patterns, which all exist in an abstract space. However, just a single local measurement will select the entire pattern that will be observed. That means a local measurement seems to have a nonlocal effect. However, that nonlocal effect is not apparent at the local level. You need to see the entire pattern, which entails making lots of local measurements and comparing them.
DMcpearson September 21, 2021 at 22:12 #598525
It's the quantum version of a correlation. That means that two or more parts of a quantum system have correlated properties. What's strange about it is that the correlation is indeterminate until a measurement is made, after which the correlation is revealed.


The hidden variable approach says no indeterminacy exists. Pure chance is unreal. Chance is deterministic. Like quantum fields are.
DMcpearson September 21, 2021 at 22:13 #598526
Reply to jgill

By the way. I see youre a math guy. Whats the difference between a function and a distribution?
jgill September 21, 2021 at 22:46 #598544
The second paragraph here is a good description: Generalized functions. I've never worked with these things. Continuous linear functionals are called distributions, also. A linear functional takes a function in a function space and produces a number (real or complex). For example, in the space of complex contours the length of a contour is one such functional.
Jeunesocrate September 21, 2021 at 23:53 #598566
I aske because of fields being operator valued distributions. Defined at and around points. Like a dirac delta.
jgill September 21, 2021 at 23:57 #598568
From lecture notes by Sourav Chatterjee, Stanford:

Although quantum mechanics has been successful in
explaining many microscopic phenomena which appear to be genuinely ran-
dom (i.e., the randomness does not stem from the lack of information about
initial condition, but it is inherent in the behavior of the particles), it is not
a good theory for elementary particles, mainly for two reasons:

• It does not fit well with special relativity, in that the Schr ?odinger
equation is not invariant under Lorentz transformations.
• It does not allow creation or annihilation of particles.

Since in lots of interesting phenomena (e.g., in colliders) particles travel at
speeds comparable to the speed of light, and new particles appear after they
collide, these aspects have to be taken into account.

Quantum field theory (QFT) is supposed to describe these phenomena
well, yet its mathematical foundations are shaky or non-existent. The fun-
damental objects in quantum field theory are operator-valued distributions.
An operator-valued distribution is an abstract object, which when integrated
against a test function, yields a linear operator on a Hilbert space instead
of a number.
Jeunesocrate September 22, 2021 at 00:00 #598569
Quoting jgill
The fun-
damental objects in quantum field theory are operator-valued distributions.
An operator-valued distribution is an abstract object, which when integrated
against a test function, yields a linear operator on a Hilbert space instead
of a number.


That's what I mean.