What Is a Particle? (2020)

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

Woke: “electrons aren’t 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.

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.

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

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.

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

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.

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.

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).

I think we’re failing miserably precisely because we don’t.

Or at least, I'm interpreting "the friends you make along the way" as the sum total of the effects of a particle on the surrounding world. Saying "the particle doesn't exist, but it has effects X, Y, and Z" is the same as "the particle exists and has effects X, Y, and Z". If a distinction is not observable, then it's meaningless to quibble over whether it's "real" or not.

(Which all just proves that my interpretation isn't the one you were using....)

What I am sayings is that there are many useful interpretations of what a particle "is" that allows science to progress. The theoreticians and the experimentalists use, sometimes even form, those interpretations to help them along in their work. I'm saying that they yet remain interpretations, even analogies; and it really doesn't matter whether those folks believe in an objective reality or not, good work still gets done. Maybe it's subjective in that sense, but a particle is whatever they say it is; and nothing more can be said with certainty unless you dive into philosophy.

You can measure a perturbation in a field, or a track in a bubble chamber, and call it a particle. Then you can work backwards to an "objective" representation, and a particle still becomes whatever you say it is. It's still scientific, consistent, mathematically rigorous, and in line with theory and observation, but it remains a human construct. You can't escape that. Ultimately, one is free to believe that there is some fundamental thing; and, maybe there is and maybe there isn't.

> literally everything we know of is whatever we say it is

Of course "literally everything we know of is whatever we say it is". That, precisely, is my point. It most certainly does not mean that we can just state anything as true unless it is sensible, consistent, observable and verifiable; and expect not to be challenged.

It's at 3:17 in this video of an interview with him https://www.youtube.com/watch?v=hV41QEKiMlM

It's representative of a view that there's a thing (a particle) that explains another thing (a force) that was consistent with both theory and experiment. Thus, a quark could be a particle, and it was whatever the experimentalists and theorists said it was, however it was measured or contemplated.

For a deeper meaning it becomes an exercise in hermeneutics i.e what does it mean when we say "particle"? That was the point of the original piece - there is no uncontested view of a particle's form, should one even exist. Each field, in order to advance, finds it useful to interpret it, or think about it, in different ways.