[AlbertCory]

I'm reading "The Big Picture" (Sean Carroll) right now.

I'd love to have a real physicist explain this, but:

When we think of what a particle IS, we often think as though it were dirt, or a billiard ball, or something. As though there were some other substance of which it's made. At least I do.

But the definition is as low as you can go. It's hard to wrap your head around that. Unless you're trained to do so, I guess.

[ziofill]

Physicist here. You are right that the mental picture we get when we use the term “particle” is a little ball or something like that. It is unfortunately a confusing name… You need to begin with a field, like the electromagnetic field for instance. When you look at its properties like energy, polarization and so on, in order to write down a state of the field you need to specify all of them in a way or another. In quantum mechanics you can associate a vector space to each property, and then (here is the important bit) you need to pick a basis for your vector space in order to write down its vectors. Obviously there is an infinite number of possible choices, and we usually end up choosing what makes things simple, so in the case of energy we pick the basis of eigenvectors of the Hamiltonian, because to evolve them in time you just need to multiply them by a complex number and that’s it. Well, those basis vectors are the “particles“ because when taken individually they share some properties with macroscopic particles, but the analogy really only goes so far. And the thing is that usually the state of the field is not in a single one of these basis vectors unless the conditions are very special, so even saying that the field is “made of particles” is misleading because it’s like saying that the wind is made of air going vertically, horizontally and across, which sure it’s “correct” because you can combine those directions and get any other direction but it’s also not really that…

[evanb]

Also a physicist.

It's not quite right to call basis vectors particles, even in a free field theory. The particles correspond better to the creation / ladder operators that take you from one Hamiltonian eigenstate to another.

In a perturbative interacting case, people still think of particles as these same ladder operators, but they don't connect eigenstates so simply (the interactions generically mix all the states with the same quantum numbers).

In a strongly interacting case the story is even more subtle, because composite operators may be closer to the ladder operators between the asymptotic states, even though they're built of other... particles? Language isn't great in this instance.

[ziofill]

Yeah it’s hard to use everyday language to exactly describe these things… And even more difficult to decide where to draw the line where some hand waving is acceptable.

[tel]

As an amateur, I think I follow most of this, at least at some level, but I don't follow why you'd unify the basis elements and particles. Thinking of a quantum harmonic oscillator, the eigenstates have some kind of localization that feels particle-like, but the oscillating pattern of a coherent solution seems "more particle-like" and arises out of the interference between those eigenstates. In particle-speak, I might try on a sentence like "this classical particle is generated by the interaction between... other... particles" but I'm clearly at a loss there.

On basis of that, I'd be more likely to say "QM needs to describe everything as a wave, and sometimes certain kinds of localized 'wave-packets' move around coherently, and that's what we'd call 'particles'". That also seems to gel with less coherent states where it feels like there's not really a particle to be found.

So, I'm curious why you'd prefer to relate the eigenstates themselves as particles. Again in the oscillator case, the eigenstates themselves seem less coherent and seem to behave less classically than I'd hope.

My best guess is that the property those states have that is not as well replicated by the "particle as a coherent wave packet phenomenon" is that they have well-defined energy quanta. But that's just a bit of a stab in the dark here. It perhaps makes more sense from the perspective of "particles are the things that we're able to measure in detectors" POV, though.

[ziofill]

You are exactly right at the end when you say that particles are what makes a detector go click. Let me try to clarify further. The "particleness" is not about localization, but about energy quantization. In fact, a single photon can be very non-localized, because spatial position is a different Hilbert space and it can be entirely independent of the energy. So the packets you are referring to are particles only if in their energy Hilbert space they correspond to a well-defined photon numbers, and that's why the analogy with classical particles only goes so far. To add to the confusion, one can speak of packets localized in phase space (e.g. coherent states, like the light produced by a laser) and packets localized in physical space like a short pulse, and these refer to different Hilbert spaces.

[divs1210]

Particle spin explained:

Imagine a ball that’s rotating,

Except it’s not a ball, and

It’s not rotating.

(popular particle physics meme)

From what I understand of QFT, the Universe is made of fields of different types, and a “fundamental particle” is just an excitation (wave) in the corresponding field.

For example, a photon is a wave in the universal electromagnetic field, A charm quark is a wave in the universal charm quark field, etc.

I’m not a trained physicist, so I might be wildly wrong.

[binary132]

I get it but I still think these sorts of concepts are also just another level of mathematical abstraction that isn’t necessarily “really what it is” any more than a rotating ball or a math equation or any of the other ideas are “really what it is”

[lottin]

It's very frustrating. The idea that the universe is made of fields is nonsensical. I don't understand why so many physicists keep saying that.

[antonvs]

If you don’t invest the statement “the universe is made of fields” with more meaning than necessary, then it makes more sense.

A quantum field is just a mathematical construct that models an aspect of what can happen at every point in spacetime. The fields follow rules for how they interact, and fluctuations in the fields and interactions between them, according to their respective rules, provide a good model for the universe we observe.

If you consider this purely mathematically, it’s hard to argue with. The models in question make very accurate predictions, can correctly model the vast majority of observations we know how to make, and don’t predict many things that we don’t observe. In other words, all the evidence is that it’s a very good model - a very good fit for the universe we observe.

From this perspective, one way to interpret the statement that “the universe is made of fields” is simply that the universe conforms to the quantum field model. Again, this claim is hard to argue with - it seems to me like a true statement, and there’s a lot of evidence for it.

Hawking & Mlodinow explored this in their description of what they called “model-dependent realism” - see: https://en.wikipedia.org/wiki/Model-dependent_realism

If perspectives like these don’t satisfy you, and you want to try to develop an understanding beyond mathematical models, then you have a tough problem to solve: how to go beyond the models that we know how to construct, to something that somehow gives you some sort of more fundamental insight. But what would that even look like? How would you test it? What would make this approach more true than existing theories?

In short, an answer that satisfies the criteria that you want it to satisfy may simply not be possible.

[jerf]

The Universe May Do As It Damned Well Pleases.

Maybe it is "made of fields", maybe it isn't, but "I think that's nonsense", which is just a gussied up way of saying "my intuition rejects that", is not a valid judgment method. The universe does not check with our intuition before doing what it Damned Well Pleases.

[lottin]

So you think the universe might be made of, say, subordinate clauses?

[jerf]

Whether or is or it isn't, it does it without consulting you or me or our intuitions.

I assume you meant that as an obvious absurdity, but if you were going for that you probably should have avoided the concept of "language", which can be Turing Complete. Still, the main point is, whatever it is, it is, and it isn't asking us for permission to be what it is.

[binary132]

One of the ultimately epistemological puzzles to me is the question of what math really is. Like, obviously, it is fundamentally descriptive. “Two and two makes four” is pretty straightforwardly talking about something “out there”. And when we’re talking about fields, we are clearly also describing something that is really happening, that is really “out there”; it’s not the math itself that is the real thing, but rather it is a language for accurately describing and analyzing real things. But at some level, the real things it’s describing become so abstract and immaterial that they might as well be magic, or spirit. And it seems to me like our minds also contain and experience such things, too. Very advanced math and physics necessarily start to border on philosophy or theology.

[travisjungroth]

One way of viewing it is that math is games. Not in the winner sense, but in the activities with rules sense. Addition is a game.

Some games make you better at other activities. Like, playing chess could make you better at logistics because you’re practicing planning and managing losses.

Some games match some real world situations so tightly that we can go through them step by step and solve the real world situation in the game. You can play addition to figure out two apples and two more makes four apples.

Whether the game is “real” or not is immaterial. It just needs to be internally consistent and matched to the right thing.

There’s also the idea that math is another world that we can visit, similar to the dream world. But that’s a whole other thing.

[fasa99]

The idea that it's an abstraction is 100% accurate. That physics is a discrete set of fields with field rules and interaction rules, and what we observe is a scaffold on top of that. It's like okay, let's say the math is right and we have a set of fields, what are they and where are they from, how do we manipulate them. Then the physicists, often driven by ego, is want for an explanation and points to vibrating strings and such, and finally they knock on the door of the empiric physicist and say "can you do an experiment to show that I'm right" "sure, build a machine the size of the universe and I could test that" and that's the state of physics the last gorillion years

https://www.youtube.com/watch?v=FYJ1dbyDcrI

[itishappy]

The magnetic field is one which you've probably had a chance to experience for yourself. Wave a magnet around a magnetic field and you can feel it has a different effect at different points in space. Fields are just time and space varying values for physical properties. Is the universe being composed of magnetism and a few related fields really so nonsensical?

[binary132]

Not really, until you go “well, what’s magnetism made of?” and the answer is “a field!” That’s pretty nonsensical.

[itishappy]

I disagree! I think fields are very intuitive and it's everything else that's nonsensical!

Magnetism isn't made of anything. It is a field, and it's one your can interact with directly.

Compare that with, say, table salt. "What's table salt made of?" Uh. It's made of atoms entirely unrelated to salt, like sodium and chlorine. "What are atoms made of?" Uh. They're made of tiny electric particles zipping around at relativistic speeds but bound together by forces like magnetism.

Richard Feynman does a better job than me of describing this exact problem in one of my favorite physics videos of all time:

https://www.youtube.com/watch?v=Q1lL-hXO27Q

[blahblahblah10]

A great lesson one learns as a physicist is that one must develop a new intuition mainly through years of practice. So when you say "It's very frustrating", I interpret it as "this doesn't seem reasonable to me". But it doesn't have to be reasonable - none of us have any intuition for what happens at scales far different from our everyday lives.

The real question you raise is a very good one - how seriously should physicists take mathematical theories. If we were building a statistical model of, say, house prices and construct a reasonable linear regression model, we certainly don't believe that the market plugs the parameters of a house into the model to decide the price. The model is an approximation of the real dynamics of the market and this approximation might not hold in the future.

On the physics front, I would argue no one would consider a quadratic in speed air resistance term in Newton's second law, a fundamental feature of the universe. One can build a reasonable model that results in that term and it might even be a good approximation for some fluids in some speed/density range.

But, when it comes to more fundamental (as of today) theories like quantum electrodynamics, electroweak theory, quantum chromodynamics (all quantum field theories), or even general relativity (modulo discussions of quantum gravity) - both the predictive power and accuracy of these theories is so stunning (matching all the data generated at colliders like the LHC), that one starts wondering if we are no longer dealing with models but a true description of nature. The mathematical descriptions are also so constrained unlike the house price example above, that one can't just make modifications to the theories without violating core principles (and experimental data) like unitarity, causality, locality, Lorentz invariance etc. This only reinforces this view that perhaps this is close to a true description of what we see.

Now it is entirely possible (but IMO not probable) that this whole view will be upended and replaced by a very different physical picture. In a sense, string theory (which is now discredited heavily in the public's eye but that's a story for another day) was an attempt at a different physical picture that resulted in very rich structures that had nothing to do with physical reality.

So, physicists say that because the more time you spent understanding and studying quantum field theory and as more experiments are done (all the collisions at the LHC verify the standard model's predictions including the Higgs once its mass was known), it only reinforces that there's something deep about the current theories even though we have several unsolved problems (dark matter, dark energy, quantum gravity, fine-tuning problems).

Addendum 1: I'll add a book that is not accessible to non-physicists but gives a glimpse into the actual struggle of research and building intuition for something very abstract:

https://www.amazon.com/Feynman-Lectures-Gravitation-Richard-...

Feynman, like many others, spent considerable time applying all his powers to understand general relativity from a QFT perspective but eventually it didn't pan out (for anyone).

[Koshkin]

"It's very frustrating. The idea that Earth revolves around the Sun is nonsensical. I don't understand why so many astronomers keep saying that."

[binary132]

“It just is how it is, no we don’t know why, just accept it”

[jiggawatts]

Spin is easy as long as you avoid trying to draw a direct analogy with ordinary rotation.

It’s just the statement that the object spinning is attached to its surroundings in a smooth and continuous fashion. Less rigid object, more a patch of space-time fabric spinning.

There’s a video here: https://youtu.be/LLw3BaliDUQ?feature=shared

[im3w1l]

It's worth keeping in mind that we don't yet have the sought-after Theory of Everything. We have a bunch of theories that mostly work in their domain of validity. These field theories are supposedly very accurate we don't actually know if they are the final word.

[elashri]

> we often think as though it were dirt, or a billiard ball, or something

The problem lies that it is hard to imagine something that does have zero dimensions. You can get the example of ant walking into 2D and it is unaware of third dimension to explain we are have something similar for space-time 4D (although not the same picture exactly as time is different from spatial dimensions). But we don't have an idea how to approximate a mental picture of what a zero dimension could be. So you have something that does not occupy a volume in space (Talking strictly about elementary particles here) in the classical sense.

This does not mean they are abstract concept. According to QFT -Quantum field theory- you would think (by training) of particles are excitations or quanta of their respective fields. Fields are there always (vacuum is just filled with fields) and particle appears when they are excited (more complex processes occurs). So you would think of each particle as a manifestation of a quantum field that permeates the universe. What is interesting (and probably confusing to most people) is that these fields are not zero-dimensional, instead, they exist everywhere in space and time. But the quanta (particles themselves) are considered point-like with no spatial extension.

In practice physicists will think about particles properties (i.e charge, mass, interactions, spin) ..etc instead of what this particle actually is from that point of view. This is often for practical reasons. You are a working physicist and you learned from your training that you shut up and calculate (or implement if you are doing experimental particle physics as you spend most of your time coding) by this stage.

[hughesjj]

I just think of a zero dimensial object as a ghost.

Topological defect. The unpictured thing the contour lines are swirling around. It's influence is only felt by seeing the effects on higher dimensional space, but you can never see the ghost itself.

[mock-possum]

So more like a poltergeist really

Or a magnet

[Traubenfuchs]

So we have the three spatial dimensions, + time as 4. dimensions and at any of those 4-part coordinates there are additional properties like mass/spin/etc., some of much always come together or at least strongely correlate, and those values not being zero means there is a particle there and every value corresponds to a certain „field“ and it not being zero means the field is excited?

[xanderlewis]

> The problem lies that it is hard to imagine something that does have zero dimensions.

Do you really think so? It’s not hard to picture the real number line, with the point zero (or any other single point) distinguished. Sure — if you draw it in the standard schematic way you have to give it some area, but it still seems quite intuitive that it’s ‘zero-dimensional’. Especially if you play around with converging sequences and open sets and stuff; you quickly develop intuition for what it means to be a point rather than something higher dimensional.

[mock-possum]

I do - specifically, it’s hard to imagine a group of things which collectively constitute mass, but individually constitute no mass.

How can something come from nothing?

[xanderlewis]

I thought you were just speaking geometrically.

What particles are you talking about exactly? I was under the impression that most particles that constitute things with mass do themselves have mass.

[lisper]

Richard Feynman gave what I consider to be the best possible answer to questions like this:

https://www.youtube.com/watch?v=Q1lL-hXO27Q

[aaa_aaa]

At first I was impressed with that video. Then I felt he does not have an answer and unnecessarily gets edgy with it, because question is valid.

[AlbertCory]

I just watched it. I don't think he's edgy.

You can't explain it in terms of anything else, which was sorta my original point. Maybe he could have been more touchy-feely in his answer, but that wasn't his nature.

[johndhi]

Hmm I think he's merely explaining what physics is and is not. Physics isn't really answering "why" questions, at least not ones with infinite scope.

[vertnerd]

Feynman grapples with the question the same way we would grapple with a question from a child: "why is the sky blue?" If you drill down into the explanation, you ultimately reach a statement that everyone just accepts as true, or you simply end with, "no one knows".

[mewpmewp2]

The way Feynman answered it looked extremely condescending and anti curiousity. Being pedantic for no reason. When answering you should try to guesstimate what the asker who is not an expert in your field is looking for and then start explanation relative from there.

At certain point, yes, you do have to say that either you don't know or humans haven't figured it out yet.

[hnuser123456]

I took it very differently. I took it as him encouraging curiosity, because his point was, if you are curious, and nobody's explanation is satisfying you, then you should go research it yourself and be the first one to be able to explain it to the level you were looking for.

It's Richard Feynmann. He wasn't gonna be like "Magnets attract and repel because the spins of the electrons in atoms in the magnet are preferentially aligned which causes a macroscopic dipole in the magnetic field", and just leave it at that, like he just shared de-facto science gospel, because he doesn't want to assume that you won't ask something like "why do aligned electron spins create a macroscopic magnetic field?" or "Why do electrons spin?" or "is a magnetic monopole possible?"

He is teaching the core of curiosity itself. You can ask as many questions you can think of, but if you're not happy with the answers, then there's no other option than to go out there and do your own science. He is one of the smartest physicists of the last century and he is telling you that you don't have to take his word for it, he will not be able to answer everything for you and nobody will. And hopefully you are still curious after that.

[kstrauser]

Having read some of his lectures, and his autobiography, he was anything but anti-curiosity in him or in others. Watch that through the lens of someone who valued nothing more than asking questions and it might come across differently.

[lisper]

> he does not have an answer

Well, yeah. That's the whole point.

[alok-g]

The additional important point, of course, is that there are many more 'Why' questions to be asked (often more interesting, and more important than corner cases like human-scale magnetism) that do not get asked just because of familiarity. Familiarity however is not understanding, and it is the same as simplicity.

[aaa_aaa]

He could simply say so.

[hydrogen7800]

He does repeatedly. And continues to explain why there is no satisfying answer, because we normally stop asking "why" once we reach a level of familiarity. That level of familiarity to the layperson is different between electromagnetism and slippery ice.

[datavirtue]

I see what you did there.

[passion__desire]

In similar vein, the following question is very apt. Please read the question because it captures all of our intuition when we try to understand something.

https://physics.stackexchange.com/questions/46573/what-are-t...

What are strings made of?

One answer is that it is only meaningful to answer this question if the answer has physical consequences. Popularly speaking, string theory is supposed to be the innermost Russian doll of modern physics, and there are no more dolls inside that we can explain it in terms. However, we may be able to find equivalent formulations.

[mock-possum]

I knew it would be that video.

His attitude really bugs me, and it’s on full display in this clip - everything about this to me says “I am so smart and you have asked me a question so dumb that I don’t know how to dumb down my answer for you, now I will show how smart I am in the course of explaining how dumb your question is in excruciating detail, so next time you’ll know not to waste my smart time with dumb questions.”

Instead of playing games and being evasive and ‘owning’ the interviewer, he could have just worked with the guy to clarify the question and to talk through the guy’s understanding - he didn’t try to do that, though, and you can tell how delighted he is for this chance to show the guy up. His autobiography is written the same way, it’s a series of anecdotes about times where he was smart and other people were dumb. Really rubs me the wrong way.

[lisper]

> you have asked me a question so dumb

You must have missed the part where he says that it's an excellent question.

> he was smart and other people were dumb

But he was smart. A lot smarter than you and me and the vast majority of people. He was also pretty humble about it, once famously saying that if he couldn't explain something to a freshman it's because he himself didn't understand it.

[__MatrixMan__]

I've only got a physics minor, so hardly an expert, but I felt like quantum mechanics got a lot easier once I started thinking of a particle as merely a situation which has some probability of causing a state change in a detector of some kind.

[elbasti]

This might sound tautological but a particle is, well, a thing that behaves like a particle.

Those behaviors are something like:

- it has momentum - it's state is uniquely defined by a position in space and a velocity

What's not a particle? A wave (well, until 1900 or so ...).

Sort of like asking "what is a number?"

A number is a thing that obeys certain rules. (You can add them; there's an `identity `, for every number there's a number which if you add together gives zero, etc).

That allows things like `(3 + 5i)` to be a number, for example.

[mr_toad]

> a particle is, well, a thing that behaves like a particle

Except when they don’t

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

[deanCommie]

The same is true about the terms "waves" and "fields" when it comes to quantum mechanics.

They're analogies. The concepts need names, but I think they do more harm than good because people then start with a mental model of a membrane or a surface - something they have experience seeing waves in. And then after 1 or 2 steps where the analogy helps, it breaks down, and people start being confused.

Of course the alternative isn't any better. If they had named it a "Wazoo function" and a "Quantum Flarg" everyone would've just kept asking "OK but what IS a Wazoo? What IS a Flarg" and not been satisfied with a "Yeah, it's a fundamental own thing".

Feynman, of course, has a pretty definitive response on the difficulty of this problem: https://www.youtube.com/watch?v=Dp4dpeJVDxs

[danbruc]

I mean I can not speak for you, but I do not think that the problem necessarily is that people think of them as made from some stuff, I think what causes the most trouble is the desire to visualize particles.

The trouble is that an electron is an electron and it is nothing like anything you have ever seen in your macroscopic classical world. It shares some aspects with billiard balls and some with water waves but it is not like either. And it does not switch between being a billiard ball and a water wave, it always is the same thing, it always is an electron.

It just happens that in certain situations the billiard ball properties are more apparent and in others the water wave properties and in yet other situations neither of the two analogies will help. I think that is what trips people really up, they want to visualize their electron as one thing they know, as something they have an intuition for, but no such thing exists.

And electrons being electrons also means that they are not excitations in quantum fields. Those fields are mathematical models that describe the behaviour of electrons, they are not the electrons. Certainly not in the very direct sense of nature is just mathematics because I can differentiate, integrate, and square fields at will but I can not do this to electrons. And even the less direct interpretation, there are real entities in the universe that behave exactly like our mathematical fields, does not seem likely, what would the gauge symmetries mean?

[criddell]

> And electrons being electrons also means that they are not excitations in quantum fields

You’re going against the dominant interpretation of QFT here, aren’t you?

[danbruc]

I have no idea whether or not most physicist think that there are actually quantum fields in the universe. The Navier–Stokes equations provide a good description of milk mixing into my coffee, but should I therefore conclude that my coffee mug is filled with density and velocity fields and that what coffee really is, is a region in spacetime with a nonzero value of the coffee density field?

Quantum fields have gauge symmetries which means that they are a redundant description, i.e. any given physical situation is represented by an entire equivalence class of field configurations which makes me highly suspicious of there being real quantum fields. Quantum fields are a nice mathematical tool but I do not think we have any good reasons to think they are real, but I am not a physicist and I am certainly in dangerous half-knowledge territory here.

I have been wondering for years whether this might actually be a non-issue, could the universe secretly have fixed a gauge and just ran with it? Or would this somehow be inconsistent?

[pgotibojgg]

Do you think photons are real?

Because according to QFT they only exist because of the gauge symmetries. Photons are the solution to the redundant symmetries. Remove those redundant symmetries and you also need to remove the photons.

Universe "fixing a gauge" means no photons and no electromagnetic field, because the electromagnetic field IS the gauge symmetry.

[raattgift]

> I am not a physicist and I am certainly in dangerous half-knowledge territory here.

Gauging is just dealing with the fact that there is no absolute universal fixed value against which can compare a value at some point in a field; but we still want to consider values at one or more points in the field.

Let's do a really simple static model of the atmosphere, with a single scalar value: air pressure at each point. Let's use a simple device: an air pressure gauge which reports some fraction of a pressure measured when we push a "calibrate now" button. We'll call this a calibrated barometer. We can then recover the full air pressure field by measuring at every point in space (not space-time, the staticity means there is no time-dependence to the measurements; we can do them in any order and not have to worry about time of day or season).

Where do we push the "calibrate now" button? At some point on the surface? At mean sea level? At the top of the atmosphere? The choice of any of these will provide different readings on our gauge (i.e., it reports some fraction of the calibrated pressure, will differ when the calibration point is 101 kPa vs some fraction of the value actually measured at a specific point on the surface). But with a bit of care in choices of units, whatever we use as the calibration point, the difference between two different points in space will be the same.

A good choice of gauge lets use our calibrated barometer as an altimeter. In aviation, aircraft pressure altimeters have a calibration knob, which is used to recalibrate during different stages of a flight. Common calibration points are: QFE, field elevation, which lets one know how far above an airfield one is if separated only vertically from it, at the cost of being unable to simply compare the vertical separation between two aircraft above two different airfields; SPS (the pressure of the standard atmospheric pressure, 1013.25 hPa) is a global setting useful for quickly determining the vertical separation between two reasonably nearby aircraft, at the cost of not being able to quickly determine height above terrain, or even the height above mean sea level; QNH is another local setting which lets one compare how high above mean sea level the aircraft is, at the cost of needing to know the height above mean sea level of local terrain, and not being able to easily compare vertical distances with aircraft using one of the other two calibrations.

All three settings are "redundant descriptions" of the aviator's atmosphere. They describe the same column of air, but each makes it easier to pinpoint different hazards scattered through that column (the ground, other aircraft in level flight, the aircraft's operating ceiling).

We could complicate the atmosphere by introducing time dependency (at night in cold dry winter a QNH altitude will be fewer RADAR-measured metres above the same patch of ground), and atmospheric interactions (atmospheric waves, Bernouilli effects from winds). Each complication can be made to vanish via a careful choice of gauge, although it gets harder and harder to write down such a gauge as complications increase. (As a result, in aviation they allow for a certain amount of measurement error and safety margin, and comparisons with different means of measuring altitude like radio altimeters and satellite multilateration.)

In a quantum field theory (QFT), one might choose a gauge in which some particles vanish. A sibling comment pointed out that very commonly one wants to choose a gauge in which gauge bosons like photons don't need to be counted, rather than a gauge in which there is a sea of an enormous number of low-energy gauge bosons. Choosing the gauge does not eliminate the low-energy gauge bosons; in general QFT field values are time-dependent (and usually gauged to admit only "relevant" fluctuations). Low-energy fluctuations can be boosted into "real particles" by relativistic observers, and strongly accelerated observers can count more particles than a weakly accelerated one. Therefore the choice of a gauge for one observer might make calculations for another observer more difficult.

In QED there are several well-known and frequently-used gauges roughly analogous to SPS/QFE/QNH, and one often chooses one of them for convenience. Each of tehse gauges breaks the gauge freedom.

Gauge freedom means simply an uncalibrated system waiting to be calibrated. A common illustration of this is to choose a non-rotating sphere and setting down latitude/longitude. A less-gauge-symmetrical rotating sphere naturally picks out latitudes (the poles and the equator, notably), but there's still gauge freedom in longitude that we can fix by choosing a prime meridian, and gauge freedom in picking out one of the primary compass directions. These choices do not change the sphere or its rotation (or non-rotation), and of course one can choose any other set of coordinates one wants.

Once one has fixed the gauge on the sphere, though, one can more easily compare positions on the surface: is point A in the northern hemisphere, is point B in the eastern hemisphere? Just asking if point B is North-East of point A requires us to at least choose a north pole -- that can be one of two places on a rotating sphere, and it can be anywhere at all on a non-rotating one. The "right hand rule" is the conventional "gauge" for rotating astronomical bodies: anticlockwise rotation around the north pole (right hand: thumb up, fingers curled). But we don't have to use that convention as our "gauge". (We also have a problem for a truly non-rotating spherical object: where's the north pole? We might solve that by using an imagnariy axis parallel to the axis of a relevant body like the local star or the parent galaxy).

Finally, in many gauge theories there are gauge invariant quantities. On our spheres the geodesic intervals between two points are gauge invariant. The gauge tells us something about direction. In practice, fixing a gauge also usually involves choosing (and scaling) units: on our geodesic which might run south-east to north-west (gauge problem), the length might be measured in metres or light seconds (units problem) or kilometres and light-years (scaling problem). We might want to label different points along the geodesic in latitude/longitude (coordinate problem) rather than adapted Cartesian sphere-centred/sphere-fixed ("ECEF" on Earth) or tangential ("Local East-North[-Up]", "LENU") ones.

[binary132]

I think this is why “shut up and calculate” is popular

[User23]

Or as Newton more eloquently put it hypothesis non fingo.

[auntienomen]

Yep. Also, ignoring all the ways in which an electron isn't an electron. Electrons can be created and destroyed, and they are both indistinguishable and exchangeable. We can't assign identity to them, thanks to their Fermi statistics. They're just methods of explaining clicks in a detector.

I worked in particle physics for years and never once saw an electron. :-)

[binary132]

Joke: “birds aren’t real”

Woke: “electrons aren’t real”

[bbor]

I’m not a physicist, but as an arrogant philosopher of science: isn’t it just field excitation? Like, every particle looks like a circle bouncing around a 2D piece of paper, but if you look reeaaaaally closely it’s just a localized 3D spike of energy in a usually 2D field of energy? So it’s made of the field/paper itself.

I must be under-thinking this, but that’s what’s worked pretty convincingly for me.

[griffzhowl]

So what is a field?

[im3w1l]

A function that takes a point in space as input. The output can be various things, e.g. a scalar field gives a (possibly complex) number as output.

[contravariant]

That's a bit too simple, not all functions work well as fields (differentiability is quite desirable) and you have no way to interact with the fields that way.

I think principal bundles come closest to what physicists call fields. Though I'm holding open the option that really the things in most equations are more like elements of the corresponding Lie-algebra.

[bbor]

It’s everything! Idk, I don’t think the universe owes us an answer there. What is a human? Well, it’s a human. You can think of all sorts of mental tools for understanding humans (eg “species”), but ultimately they just are.

[lottin]

No... a field is mathematical representation. The universe is most definitely NOT made of fields.

[bbor]

Ok fair: they're things that right now are best understood using the term Field. I don't understand what kind of answer you're hoping for that would be better than this -- what kind of answer to "what is a particle" wouldn't be describable by mathematics?

By saying "the universe is fields", I'm saying "it's distributions of energy across spacetime". That's seemingly a consensus. Why demand that that energy must also form into strings or even tinier spheres or spheres in an alternate dimension or something? We have described fields in detail, I say Mission Accomplished

[lottin]

Let's say we describe a particle as being an excitation of a field. Can't we describe any physical phenomenon in the same way? For example, describe a football as an excitation of the football field. I think we all agree that this description does a terrible job of actually describing a football. In fact, I don't think it can be called a description at all. Likewise, I find describing a particle as an excitation of a field to be equally unsatisfactory.

[dgoodell]

Are you saying that the universe cannot be represented by mathematics?

I imagine you could use that argument to shoot down pretty much any explanation.

[lottin]

I'm saying that a mathematical representation of a physical phenomenon isn't the physical phenomenon.

[librasteve]

a thing that can have particle-like excitations

[im3w1l]

Historically, electrical and magnetic fields were discovered first. Then em-waves. Then photons.

This should tell us that fields are useful in their own right, without referencing particles.

[FollowingTheDao]

A probability.

[scotty79]

Particle is a cloudy, fuzzy thing that can fly and wobble through space. It can be more sharp or more fuzzy and when it overlaps with another fuzzy particle object they might exchange a neat portion of momentum, angular momentum and energy and violently reshape becoming sharper or fuzzier (that's the wave function collapse and expansion) then they go again on their separate merry ways.

Sometimes when particles meet or even spontaneously they can split or merge altering other parts of their nature (unrelated momentum, energy and angular momentum). This happens for example when neutron decays into proton and electron.

Sometimes they get stuck together because of electromagnetic force and they resonate in interesting harmonies and travel together. That's atoms. Interestingly when they are resonating in those harmonies they become quite fussy about amounts of energy they prefer to exchange and they do it only in a very specific quanta.

And there's a class of particles called quarks that travel together all the time as they are always tightly bound with each other and can never get free despite possessing incredible amounts of energy they continuously exchange. That's nucelus.

We really don't like this image because fuzziness is actually two dimensional in every point of our already 4 dimensional space-time and described by complex numbers so we prefer to focus on those brief moments when particles interact since if we have a lot of particles that are bound together to form measurement apparatus they are so sharp that the interaction they participate in squash other particles nearly to a point and we can declare that the measure particle collapsed to have some momentum, or location, or spin described by a single vector instead of a cloud. It neatly turns out that the square of complex number fuzziness describes the probability that a fuzzy particle will interact with a sharp one (one of those bound together in measurement apparatus) with a specific outcome.

[darby_nine]

A metaphor with another physical object will always fall short. Why not just state the number of bits a particle represents? It's much easier to describe going through each dimension (colloqiual, I hate string theory for the same reason of unnecessarily using a physical analogy) and describing how it interacts with other particles. Sure you'll lose a lot of your audience but those that remain will have a much clearer picture than via a comparison to a billiard ball. This also makes the more advanced topics like singularities, entanglement, teleportation, the lack of true vacuum, etc much easier to manage.

(I'm aware we don't have an understanding of how quantum physics interacts with singularities, but the whole billiard ball metaphor certainly is incoherent with it)

[at_a_remove]

It's a useful fiction, but the map is not the territory. This sounds blithe but ... it is as close as you will get to the truth.

I only got the bachelors' version of physics, though I did take some grad classes, so here is what I will tell you:

The human mind learns from experience and it thinks of things in terms of the past experiences it has had. We are big assemblages which exist in a narrow range of temperatures (think in terms of Kelvin). Our experience is classical, in the Newtonian sense: we move at not a particularly notable fraction of c, we are too warm to note the strangenesses which happen below, say, twenty or four or a thousandth of a Kelvin (superfluids and BECs are out), we are too cold to have a great internal experience of plasma, leaving us to be creatures of solid and liquid, with a sort of inferred understanding of gas. We are too large to feel the quantum realm, in the sense that the uncertainty principle is not obvious to us from what we have felt.

So, we must make do with abstractions, with fictions, with approximations. Conscious that we are the epitome of the six blind men trying to understand the elephant through touch alone, we try to break our understanding, to search for flaws in our inferences. Yet this does not grant us true experience when we run across, say, the electron. We try to think of it like a billiard ball, but we can say that a billiard ball is this wide, yet we are fairly sure at this time that the electron has no radius, no diameter, that it might as well be a geometric point. Every time we try to measure, we can only establish a smaller and smaller upper bound for the confounded thing's radius. That's not like our lives at all!

The reality of this electron is that if we get it going fast enough, it stops getting much faster no matter how hard we smack it. That's not like our reality. If we try to pin down where it is, the more we do it, the harder it is to figure out how fast and in what direction it moves. And as we work to ascertain the velocity (and therefore momentum), we lose sense of this bit of weirdness' position.

You eventually have to develop an understanding based not on experience at all.

Perhaps this was unique to me, but the first time I understood integration in calculus, I had a brief moment of dizziness as I apprehended this new thing. You know how you are working a math problem and you have a good idea of what the answer is already, a sense of what the magnitude and direction might be? I had ground my way through vector and tensor calculus, and had been working a problem in gravitation and relativity class when I sensed what the resulting tensor would look like, the shape of it, in the sense that I would know if my figures were way off. I nearly fell off the chair, my head spun so.

If you care to, you can do this for a particle.

[heresie-dabord]

Thank you for this post. Given the limitations of human understanding and experience, one could safely use one metaphor or another for casual description. But at a deeper level of understanding, we do understand that our common experience does not apply, and that human language is too imprecise.

[librasteve]

this

[mensetmanusman]

https://youtu.be/j2oSyAfPzWg?si=bwM2NAsORzkqLQLk

Fun fields discussion on what particles are…

[yahalo]

What a trip, the guest speaker was clearly a pseudoscientist, talking about "evolution fields" and "mind fields" and equating fields to souls.

[mensetmanusman]

If anyone that attempts to explain the nature of consciousness in a non-falsifiable is a pseudo-scientist, then yes. I thought it was fun to hear perspectives like this.

Also, the soul discussion was pointing more at the history of language and concepts versus a crude equation of the two :)

[throwaway314155]

I truly appreciate the discussion your comment has brought about. Some really great sibling comments.

There's also a lot of overlap with the article itself however. From the sibling comments too. At risk of breaking the rules, it's very much worth the read if you haven't read it!

[csomar]

This is essentially the Bohr take on the matter. There is no physicality in the sense that we interact with the world in. There are also no real dimensions as they are just our understanding of what we consider the physical world.

If that gets around your head, you’ll throw the physicality and real world away and you’ll come to see everything as information interaction.