[HN Gopher] How the Higgs field gives mass to elementary particles
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       How the Higgs field gives mass to elementary particles
        
       Author : bigeatie
       Score  : 133 points
       Date   : 2024-09-03 16:11 UTC (6 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | bloopernova wrote:
       | Layman trying to wrap my head around this: the Higgs field causes
       | other fields to stiffen by giving them a resonant frequency, with
       | higher frequencies meaning more mass.
        
         | fredgrott wrote:
         | keep in mind that its against the other whole mass of universe
         | thing doing that same thing that also contributes to a mass
         | reading.
        
         | seiferteric wrote:
         | Hmm, now this is making me think, does the Higgs field act like
         | an additional degree of freedom for energy to be dumped into? I
         | mean like a photon is massless, so any amount of energy, it
         | will already be going the speed of light so the only place
         | where additional energy to go into is the frequency. Perhaps
         | with massive particles, a portion of this additional energy now
         | gets dumped into this resonant frequency rather than
         | translating into motion? So the energy stored in this resonant
         | frequency would be like the kinetic energy...? or maybe totally
         | wrong :)
        
           | cryptonector wrote:
           | It's potential energy (m_0 c^2), but in a way it's also
           | kinetic because it is a moving wave, it's just that it's a
           | standing wave so it's as though it's reflecting, but being a
           | standing wave causes that part of the particle's bundle of
           | energy to manifest as potential energy.
        
       | wyager wrote:
       | I studied wave mechanics in college, but the origin of mass
       | didn't click for me until several years later (and in fact I
       | don't believe it was every brought up in the context of wave
       | mechanics, which seems like a problem in retrospect). The
       | conceptualization that worked for me is this:
       | 
       | The normal wave equation is (ignoring constant factors like mass
       | and propagation velocity):
       | 
       | d^2/dt^2 f(x,t) = d^2/dx^2 f(x,t)
       | 
       | <acceleration> = <pulled towards neighbors>
       | 
       | This says "if a point in the field is lower than its neighbors,
       | it will be accelerated upwards. If a point in the field is higher
       | than its neighbors, it will be accelerated downwards." This
       | equation is the lowest-order description of most wave phenomena
       | like sound waves, water surface waves, EM waves, etc. and it's
       | usually pretty accurate.
       | 
       | If you look for solutions to this differential equation, you can
       | get
       | 
       | f(x,t) = exp(i * w * (x+-t))
       | 
       | w is the frequency of the wave
       | 
       | This tells you that the frequency and wavenumber of waves is
       | determined by the same parameter (w), so they are proportional to
       | each other
       | 
       | Now, what if we add a restoring force to this equation? This is a
       | force that pulls the value of the field towards zero.
       | 
       | d^2/dt^2 f(x,t) = d^2/dx^2 f(x,t) - M^2 f(x,t)
       | 
       | M is just a parameter that tells you the strength of the
       | restoring force. The force increases as the field gets farther
       | from zero, like a spring.
       | 
       | Now, solutions to the equation look instead like
       | 
       | f(x,t) = exp(i*k*x +- i*w*t)
       | 
       | Where w^2 = k^2 + M^2
       | 
       | (or something like that, I need to re-derive this on paper, just
       | going off memory, but I think if you plug it in it should work)
       | 
       | Notice that now, if you have a spacial frequency k, your temporal
       | frequency is actually higher. In fact, if your spacial frequency
       | k is 0 (corresponding to a stationary wave), your temporal
       | frequency is still M!
       | 
       | This is what mass is. Having a non-zero frequency even if the
       | wave is the same everywhere in space (which corresponds to no
       | movement)
       | 
       | A field with no restoring force is e.g. the EM field, so photons
       | are massless. The rate at which they oscillate in time is the
       | same rate at which they oscillate in space. A massive particle
       | has a restoring force, so its temporal frequency is higher than
       | its spacial frequency.
       | 
       | In physics, this equation is often reordered like this:
       | 
       | d^2/dt^2 f(x,t) - d^2/dx^2 f(x,t) = - M^2 f(x,t)
       | 
       | (d^2/dt^2 - d^2/dx^2) f(x,t) = - M^2 f(x,t)
       | 
       | (d^2/dt^2 - d^2/dx^2) f(x,t) + M^2 f(x,t) = 0
       | 
       | [?] f(x,t) + M^2 f(x,t) = 0
       | 
       | (the d'alembert operator)
       | 
       | ([?] + M^2) f(x,t) = 0
       | 
       | Again, this is ignoring constant factors like c, h, etc.
       | 
       | The above equation is nice because it's relativistically
       | invariant. The d'alembert operator is the contraction of the
       | 4-momentup operator with itself, p^u p_u. This is a concept worth
       | studying - tells you a lot about what mass, energy, velocity, and
       | momentum actually are in a general sense
        
         | tines wrote:
         | > The rate at which they oscillate in time is the same rate at
         | which they oscillate in space.
         | 
         | Wouldn't it be the opposite, that they do not oscillate in time
         | at all so that they oscillate in space as rapidly as possible
         | (since, as we know, time doesn't pass for photons)? And
         | stationary particles don't oscillate in space, so they
         | oscillate in time as rapidly as possible. Or are you using
         | "oscillate" in a different sense here?
        
           | wyager wrote:
           | Photons have their spacial frequency directly locked to their
           | temporal frequency.
           | 
           | Temporal frequency f
           | 
           | Spacial frequency k
           | 
           | f = k * c
           | 
           | Dimensional analysis: t^-1 = l^-1 * l t^-1
        
         | oytuntez wrote:
         | chatgpt convo to understand "temporal frequency" better:
         | https://chatgpt.com/share/f8601523-2d3f-4497-a9b4-071d6a8778...
        
         | cryptonector wrote:
         | This is beautiful. Thanks for this. Is the choice of `M` for
         | "the strength of the restoring force" intended to resemble `m`
         | for mass?
        
       | tines wrote:
       | So to conceptualize the difference between fields with and
       | without restoring forces, I imagine that, for a field that
       | doesn't have a restoring force, the medium itself can move
       | permanently. For example if you have just a bunch of ball
       | bearings lying on the surface of a table, you can cause a wave to
       | go through the balls by hitting one. One bumps into the next,
       | which bumps into the next, etc. There's no restoring force, so
       | the wave is moving through the balls, and the balls are actually
       | moving into a new position and they stay there.
       | 
       | Compare that to a water wave, where gravity is trying to restore
       | the particles to a "flat" position in space. If you cause a wave
       | in water, the medium will return to the space it occupied before
       | through the restoring force, even as the wave travels through it.
       | 
       | Is this really how it works, so that e.g. the EM field itself can
       | move in space, whereas e.g. the electron field cannot move in
       | space, it's "pinned" in some sense by the Higgs field?
        
         | wyager wrote:
         | First, worth noting that "the EM field" (the thing that shows
         | up in the wave equation) in this case is specifically the EM
         | 4-potential. This doesn't work if you try to treat "the EM
         | field" as the strength of the E and B fields or something - it
         | has to be the 4-potential. I got tripped up by this at one
         | point
         | 
         | Second, this isn't pinning the field _in space_ , it's pinning
         | the _magnitude of the field to be close to some value_
         | (probably you can call that value 0)
         | 
         | So if the field locally gets "too high" or "too low", there's a
         | restoring force accelerating it back towards the "normal"
         | value, like a spring attached to the normal value.
         | 
         | It's not pinning it in the sense of stopping translation
         | through space or time
         | 
         | In the water wave analogy, we're using the vertical dimension
         | to represent the magnitude of the water wave, but translating
         | that to other contexts, we're not literally talking about a
         | physical height, just the magnitude of the field. (Which, for
         | all I know, maybe you can formulate that as a position in some
         | higher-dimensional space or something)
        
           | tines wrote:
           | What trips me up is that we don't think of the field being a
           | real physical thing. But isn't the field really the _true_
           | physical thing, and the wave is just a concept we overlay on
           | it? Like, water is the real physical thing, and the wave is
           | just an arrangement of the water that we recognize as humans.
           | Isn't it the same with the EM and electron fields etc?
        
             | layer8 wrote:
             | For fields, it's rather that the wave is the only
             | physical/real thing, and there is no separate "substance"
             | that is waving. "Substance" is a concept that disappears in
             | fundamental physics.
        
             | wyager wrote:
             | At some point this all kind of drifts apart from ontic
             | science and starts to become a matter of narrative or
             | interpretation, but I would generally agree with that.
             | 
             | Waves are mathematically-friendly possible configurations
             | of the underlying system.
             | 
             | It's mathematically valid to choose the most convenient
             | configurations for analysis because the systems are
             | (pretty) linear, so we can just project any actual state
             | into a sum of wave states, apply our mathematical model,
             | and add it all back to get the new real state.
             | 
             | A lot of physical phenomena are composed of pretty
             | predictable distributions of wave states, so projecting
             | from a realistic state to a sum of wave states is usually
             | straightforward enough.
             | 
             | For example, a moving particle looks like the sum of a
             | bunch of waves all closely grouped around a particular
             | wavelength.
        
             | cryptonector wrote:
             | Think of a field as a set of scalar field strength values,
             | one value at every point in space. It's not a "thing" you
             | can grab or see. The field strength values are based on the
             | distances to and the magnitudes of the "particles" have
             | have {charge, mass, color, whatever} (with the complexity
             | that the particles themselves are really just standing
             | waves, thus the scare quotes).
        
       | Angostura wrote:
       | As a lay person, I found that a clear and understandable
       | explanation, which in my experience suggests it is a wild wild
       | over simplification - but enjoyable nonetheless
       | 
       | A question for the more expert amongst you. Is the Higgs field
       | unique in its interaction with other fields, or are there other
       | similar fields which similarly change the way that other fields
       | (and associated particles) behave?
        
         | itishappy wrote:
         | I believe it's both. All fields can stiffen their fellows like
         | this, but only the Higgs is stably non-zero.
        
           | thrtythreeforty wrote:
           | What's another example of cross-field interaction? Where
           | (say) the EM field changes the restoring force of the
           | gravitational field?
        
             | dataflow wrote:
             | Total layman here, but doesn't an EM field carry energy,
             | and thus have similar effects as mass - thus warping
             | spacetime?
        
             | itishappy wrote:
             | My mental model is that of the EM field coupling with the
             | internal EM fields of a material to give rise to the
             | phenomenon of index of refraction where light appears to
             | move slower than the speed of light in a vacuum in said
             | material.
             | 
             | As I understand, a more advanced version of this occurs in
             | superconductors which serves as a much better model of the
             | phenomenon. At least I'm told it would if I could claim to
             | understand it!
             | 
             | https://physics.stackexchange.com/questions/33240/how-
             | come-a...
             | 
             | https://physics.stackexchange.com/questions/47791/what-do-
             | ma...
        
         | emblaegh wrote:
         | I'm not a qft-ist, but from the top my head the Higgs field
         | wouldn't explain the (likely positive) mass of neutrinos. So
         | there could potentially be another mass creation mechanism. But
         | someone else more informed could clarify.
        
           | eigenket wrote:
           | There are essentially two "easy" ways to add neutrino mass to
           | the standard model without breaking things too much.
           | 
           | One is to use the Higgs to give neutrinos mass. For technical
           | reasons this only works if there are both right and left
           | handed neutrinos. We have only ever detected left handed
           | neutrinos, so you'd have to also add right handed neutrinos,
           | and just say that they don't really interact with anything
           | else.
           | 
           | The second way you can do it is add a very heavy Majorana
           | particle to your theory for each of the 3 neutrinos we know
           | about. These Majorana particles are their own anti-particle
           | (just like the photon is) and as a result are able to have a
           | non-zero mass without the Higg's mechanism. The three types
           | of neutrinos we already know about would then get their
           | masses as a result of some slightly complicated maths
           | involving the masses of the three new Majorana neutrinos.
        
       | OgsyedIE wrote:
       | How does this idea mesh with the other model given to laymen that
       | the Higgs field causes charged particles to flip helicity
       | extremely rapidly?
        
       | immibis wrote:
       | And "the Higgs field suddenly switched on" is analogous to the
       | pendulum's random vibrations slowing down enough that they no
       | longer overwhelm its pendulum behaviour?
        
       | prof-dr-ir wrote:
       | Very nice explanation by Matt Strassler. I am not sure it is
       | possible to do better without getting into the details of quantum
       | field theory.
       | 
       | For those who know quantum mechanics I would add that the
       | oscillations mentioned in the article are just the familiar exp(
       | i E t ) of any wave function that is an eigenfunction of the
       | Hamiltonian. For a particle at rest in a relativistic theory (and
       | in units where c=1), we of course have E = m.
        
       | throw0101d wrote:
       | > _Quantum field theory, the powerful framework of modern
       | particle physics, says the universe is filled with fields.
       | Examples include the electromagnetic field, the gravitational
       | field and the Higgs field itself. For each field, there's a
       | corresponding type of particle, best understood as a little
       | ripple in that field. The electromagnetic field's ripples are
       | light waves, and its gentlest ripples are the particles of light,
       | which we call photons._
       | 
       | What are these fields made of? Are all fields made of the same
       | thing(s), or is each field made differently?
        
         | layer8 wrote:
         | They aren't made of anything (other than numbers). Fields are
         | currently the fundamental ontology. They are mathematical
         | objects.
        
         | cosignal wrote:
         | I think that's a tricky question. In one sense, they aren't
         | made of anything since they are elementary fields. Meaning they
         | don't have constituent parts. But one could still argue that
         | it's relevant to say that they are of some kind of substance in
         | a sense. The nature of that substance is the domain of Theories
         | of Everything and some argue that the discussion becomes either
         | purely mathematical or somewhat philosophical in nature, more
         | so than a matter of physics anymore. For example, some argue
         | that the fields are all made of math, so to speak, or likewise
         | that their differences are like geometric variations on the
         | same substrate.
        
         | akomtu wrote:
         | Afaik, the official answer is that they are made of nothing
         | because they are fundamental. That's how scientists say "we
         | don't know". But when a fridge magnet sticks to a fridge,
         | something holds it there and it's not nothing. It's not photons
         | either. It's the magnetic field itself, the one that's made of
         | "nothing". Photons are like waves in the magnetic field
         | "water", but water isn't made of waves. Equations of magnetic
         | field have a curious similarity with the flow of something in 4
         | dimensions (I mean that kaluza-klein theory), but nobody has
         | managed to make that theory work yet, so there must be
         | something else. Iirc, Einstein himself spent half of his life
         | on this idea, but didn't succeed.
        
         | jmcclell wrote:
         | The book Waves in an Impossible Sea really goes into some depth
         | on this (for a layman -- which I am) and tries to drive home
         | the point that there are two perspectives one might take.
         | There's the perspective of the medium and the perspective of
         | the field.
         | 
         | Using wind, as an example, we can measure the wind
         | speed/direction at various points in a given space. We don't
         | need to know what wind _is_ to feel its effects. Instead, we
         | might view it as a force wave that propagates through space and
         | interacts with everyday objects. The measurements of this force
         | that we take at various points in space across a given area
         | form what we might call the Wind Field. We don 't need to know
         | the nature of the medium these wind waves propagate through in
         | order to study wind and how it interacts with other objects.
         | This is the field perspective.
         | 
         | Of course, we know that wind is _really_ an effect of air
         | molecules moving through space. That is, the medium for wind is
         | the atmosphere. This gives us deeper insight into what wind is
         | and how it works. This is the medium perspective.
         | 
         | According to the book, we don't know what the media for the
         | elementary particles are or if there even are any. Our
         | intuition based on waves that we see in everyday life tell us
         | that there must be some medium through which the wave can
         | propagate, but thus far we have found no such medium for waves
         | such as light.
         | 
         | We just know there are measurable properties that we can
         | measure across points in space and we have created mathematical
         | objects (fields) to represent this. From there, we can
         | construct theories and make predictions based on these models.
        
         | oezi wrote:
         | I always thought the fields are just the mathematical
         | representation of the respective force carrier particles
         | travelling through space. Such particles (the photon is
         | certainly the most relevant for us) are having such a big size
         | due to their statistical nature that the fill space even though
         | their own size when probed is tiny.
        
           | halyconWays wrote:
           | Particles don't actually exist, however. They're excitations
           | in various fields. A proton, for example, is actually a sea
           | of three quarks of different "colors" that continually
           | exchange energy (and only have potential positions) via
           | gluons, and those quarks and gluons themselves aren't
           | particles, but excitations in fields
        
             | oezi wrote:
             | So we have a duality of fields and particles. Likely it
             | doesn't make sense to give one representation precedence
             | over the other.
        
               | calf wrote:
               | Yeah did everything forget about the double slit
               | experiment? Why are fields any more real than particles?
               | Is the updated science now resolved on wave particle
               | duality then?
        
               | halyconWays wrote:
               | It's more like, particles are how we experience collapsed
               | wave functions, and both are manifestations of
               | excitations in the underlying quantum field.
        
               | halyconWays wrote:
               | QFT doesn't have a duality of particles and waves, it
               | explains both as excitations in underlying fields. So
               | even the particle in a double slit experiment is just the
               | collapsed wave function, but we experience it as a
               | particle. So precedence in this case is that QFT is the
               | underlying explanation.
        
         | cryptonector wrote:
         | Fields aren't made of anything. When you feel static
         | electricity, like when you rub a balloon against your hair, and
         | your hair then stands up, that electric charge on the balloon
         | and your hair is somehow being made evident across the space
         | between the hair and the balloon. That communication of force
         | electric charge happens over the electric (really,
         | electromagnetic) field. It happens across air and vacuum alike.
         | Nothing need be between the charged objects and yet the charge
         | will be "felt" by them. That "field" is just the numeric
         | electric charge felt at each point in space, for all points in
         | space. It's just field _strength_ -- a bunch of scalar values,
         | one for every point in in space. We call that a field, but it
         | 's not an object made of stuff, just a mathematical object.
        
       | throw0101d wrote:
       | > _Once upon a time, there came into being a universe. Searingly
       | hot, it swarmed with elementary particles. Among its fields was a
       | Higgs field, initially switched off. But as the universe expanded
       | and cooled, the Higgs field suddenly switched on, developing a
       | nonzero strength._
       | 
       | Any particular reason/mechanism why the Higgs field suddenly
       | (gradually?) switched on?
        
         | LegitShady wrote:
         | If the higgs field did not exist, particles would not have
         | enough mass to attract each other, and the universe as we know
         | it would not exist.
         | 
         | So while I do not know if there is some particular cause of the
         | higgs field, no reality like ours would exist without it, and
         | realities without it would not look like anything we recognize
         | (although maybe scientists could simulate it).
        
           | emblaegh wrote:
           | Beware when mixing quantum field theory (Higgs) with gravity
           | (attraction). We don't have any idea how these two relate to
           | each other.
        
             | LegitShady wrote:
             | the entire theory of the higgs field and its discovery came
             | from understanding that the model without it lacked
             | sufficient gravity to match the world around us.
             | 
             | So I understand what you're saying, I disagree that we
             | don't know how these to relate to each other. The reason
             | Peter Higgs theorized the higgs field is because we have
             | some idea of it.Maybe it gets more complicated than we
             | understand currently, but we understood it enough to guess
             | some properties of the higgs boson and discover it
             | experimentally.
        
               | pdonis wrote:
               | _> the entire theory of the higgs field and its discovery
               | came from understanding that the model without it lacked
               | sufficient gravity to match the world around us._
               | 
               | No, it didn't. Mass is not required for gravity; only
               | energy is. The energy was there before the electroweak
               | phase transition; it just wasn't in the form of rest
               | mass. It still produced gravity.
        
               | LegitShady wrote:
               | The end of the electroweak epoch is estimated at 10^-12
               | seconds after the big bang. So while I understand that
               | something existed prior to the universe as we understand
               | it now, for the overwhelming majority of the existence of
               | reality we have lived in a reality after the electroweak
               | phase transition, and the universe we live in today and
               | the features we recognize of it are a result of forces
               | including the effect of the higgs field on mass and thus
               | gravity.
               | 
               | So you're right technically, but it has nothing to do
               | with what I said in my first comment - without the higgs
               | field the universe as we know it today would be
               | unrecognizable, and a universe without a higgs field
               | would not look like ours.
        
               | leptons wrote:
               | >Mass is not required for gravity; only energy is.
               | 
               | E = MC^2
               | 
               | Can't have energy without mass, and mass leads to
               | gravity.
        
           | pdonis wrote:
           | _> If the higgs field did not exist, particles would not have
           | enough mass to attract each other, and the universe as we
           | know it would not exist._
           | 
           | This is not correct. Rest mass is not required for gravity.
           | The source of gravity in GR is the stress-energy tensor,
           | which was nonzero in the early universe even though all of
           | the Standard Model fields were massless. Indeed, a vacuum
           | electromagnetic field today has a nonzero stress-energy
           | tensor even though, at the QFT level, it is a massless field
           | (the photon).
        
         | svachalek wrote:
         | It is believed to be the cooling of the universe. At
         | ridiculously high temperatures, such that have not existed
         | since the first fraction of a second of the universe, the
         | electroweak symmetry was broken and most physics we are
         | familiar with didn't work. Unfortunately the math behind it is
         | way over my head so that's about all I can say on it.
        
           | benreesman wrote:
           | Not a physicist, just a fan. As far as I understand it, we
           | believe that it was in the early universe that the symmetry
           | was unbroken [1].
           | 
           | [1] https://en.wikipedia.org/wiki/Electroweak_interaction#Aft
           | er_...
        
         | pdonis wrote:
         | _> Any particular reason /mechanism why the Higgs field
         | suddenly (gradually?) switched on?_
         | 
         | "Switched on" is not really a good description. According to my
         | understanding of our best current model, the Higgs field was
         | _not_ in its vacuum state in the very early universe--there
         | were lots of Higgs particles around--so it was not  "switched
         | off" any more than any of the other Standard Model fields were.
         | But in the very early universe, the electroweak interaction
         | worked differently than it does now. As the universe cooled,
         | there was a phase transition that changed how the electroweak
         | interaction worked, and after that phase transition, the Higgs
         | field acquired what is called a nonzero "vacuum expectation
         | value", meaning that even though there were no longer any Higgs
         | particles around-- the Higgs field was in its vacuum state--
         | that vacuum state now corresponded to a nonzero value of the
         | Higgs field, meaning that the field can interact with other
         | fields, and that interaction is what we observe as mass for
         | those other fields.
        
         | Sniffnoy wrote:
         | My understanding: The Higgs field, uniquely, has a nonzero
         | vacuum expectation value -- so, when it's in its ground state,
         | it's "switched on", it has an effect. In the early universe, it
         | was in a higher energy state; for most fields, that would cause
         | them to _have_ an effect, but for the Higgs field that instead
         | allowed it to take on a _zero_ vacuum expectation value and to
         | be  "switched off". The Higgs takes on nonzero values at low
         | energies instead of at high energies like other fields, so it
         | "switched on" as the universe cooled.
        
           | antihipocrat wrote:
           | Is it possible for there to be other undiscovered fields with
           | a similar mechanic - turning on when the universe hits a
           | future heat threshold?
        
         | pb1729 wrote:
         | tldr is that it happened because the universe cooled down from
         | a stupendously insanely high temperature to a merely insanely
         | high temperature shortly after the big bang.
         | 
         | First look at this picture [0]:
         | https://en.wikipedia.org/wiki/Higgs_mechanism#/media/File:Me...
         | 
         | The Higgs field is a complex number Ph (this number can vary at
         | different points in space, we'll come back to this, so don't
         | worry about it for now). You can imagine it as a ball bouncing
         | around on the landscape shown in the image. The higher the
         | altitude of the ball, the more energy it has (just like a ball
         | in real life). Ph = 0 corresponds to the center of the image,
         | the point right at the top of the little hill.
         | 
         | At a high temperature, the ball is jostling and moving around
         | like crazy. You can imagine constantly pelting the ball with
         | marbles from all directions, causing it to dance eratically
         | around the landscape. (Further, the ball doesn't experience any
         | friction. It slows down when it happens to get hit by a marble
         | that's heading in the opposite direction to it.) In reality,
         | there are no marbles, of course, the jostling comes from the
         | interactions of the Higgs field with other fields, all of which
         | are also stupendously insanely hot.
         | 
         | The landscape in the picture has a rotational symmetry. You can
         | rotate it by any angle, and it will still look the same. When
         | the temperature is very high, the ball dances across the whole
         | landscape. It slows down as it climbs up a slope, so it does
         | spend less time at the bits that are at a higher altitude. But
         | if we consider a thin ring around the center that's all at
         | about the same altitude, the ball is equally likely to be
         | anywhere along the ring. The average value of Ph is 0.
         | 
         | As the temperature decreases, the ball's motion calms down, and
         | it spends more and more of its time in the deepest valley of
         | the landscape. It rarely has the energy to climb high up the
         | slopes anymore. Eventually, the ball will start to live on just
         | the narrow ring around the center where the altitude is lowest.
         | 
         | Now we come back to the fact that the Higgs field is a field,
         | which means it has a value at every point in space, and these
         | values can differ from each other. It turns out that all fields
         | in physics "prefer" to have similar values at nearby points in
         | space. There is an energy penalty for fields that change
         | rapidly in space. At high temperature, this didn't matter too
         | much. The Higgs field had lots of energy to pay this penalty,
         | just like it had lots of energy to climb up the slopes of the
         | landscape. So the field here and the field 1nm to the left
         | could have wildly different values. At cold temperatures, it
         | matters a lot. So the Higgs field has the lowest energy if it
         | has the same value everywhere in space. Anything else comes
         | with an energy penalty. If we pick a point in space, and try to
         | move the field clockwise or counterclockwise around the center,
         | the neighbouring points in space pull the field back towards
         | the average of the surrounding values.
         | 
         | So at any point in space, Ph is just equal it its average
         | value, which is not 0. It's not zero because we have to
         | randomly pick a point somewhere along the ring of lowest
         | altitude, which is some distance from the central 0. The
         | universe has randomly selected a direction in this landscape to
         | be "special".
         | 
         | This is the situation from when the universe was insanely hot
         | all the way up until the present. Incidentally, if you vibrate
         | the ball radially, towards and away from the center of the
         | landscape, this vibration corresponds to the Higgs boson.
         | 
         | If we could somehow heat the universe up to a stupendously
         | insanely high temperature again, then the special direction
         | would disappear, and the average of Ph would be 0 again. This
         | is kind of similar to how magnets lose their magnetization if
         | heated past a certain critical temperature, the Curie point.
         | [1] If we let it cool down again, it would choose a different
         | random special direction.
         | 
         | [0] https://en.wikipedia.org/wiki/Higgs_mechanism [1]
         | https://en.wikipedia.org/wiki/Curie_temperature
        
           | lainga wrote:
           | Very nice explanation! Is it possible that Ph could vary
           | smoothly and subtly over space, such that it's a few degrees
           | or so away from our value in the Andromeda galaxy?
        
       | idontwantthis wrote:
       | Does anyone know the genesis of the Higg's field as mud
       | explanation?
       | 
       | I remember reading that since I first heard about the "God
       | Particle" in the Science Times maybe 20 years ago.
       | 
       | Have journalists been using that deeply flawed analogy since
       | Higg's hypothesis was first published?
        
       | hinkley wrote:
       | Imagine some preindustrial scientist being awakened in the modern
       | era to find that the aether has been first debunked for more than
       | a century and then rediscovered, but with different rules.
        
         | emrah wrote:
         | Aether has a specific definition and it still does not exist.
         | It was not rediscovered. QFT is not aether-like.
         | 
         | Aether was a substance filling all space, while QFT fields like
         | higgs are not physical at all (but rather give rise to physical
         | properties)
        
           | wyager wrote:
           | > QFT fields like higgs are not physical at all (but rather
           | give rise to physical properties)
           | 
           | I think this is a nonsense cop-out and bad ontology. What
           | does it mean to "be physical" if not to be causally
           | downstream of other physical effects?
        
           | Maxatar wrote:
           | What was the "specific" definition of the aether? It looks
           | from reviewing the history that there was no consensus on
           | what the aether was or what its properties were.
           | 
           | Interestingly enough what I did manage to find is a lecture
           | given by Einstein in 1920 where he argues that the ether is
           | in fact essential towards the understanding of general
           | relativity, and that it could be through the ether that
           | gravity and electromagnetism are unified:
           | 
           | https://www.researchgate.net/publication/358617464_Ether_and.
           | ..
        
             | simpaticoder wrote:
             | The aether (or just ether) was assumed to be the substance
             | in which light waves waved, just as air is the substance
             | that sound waves. If this substance existed it was likely
             | that the Earth was moving through it at some velocity, and
             | the Michelson-Morley experiment famously showed that this
             | is not so. There were also observations of Jupiter's moons.
             | These null results led to Lorentz' quantification of what
             | would become Einstein's definition of special relativity in
             | 1905.
             | 
             | Our confidence in SR is so strong now that c is _defined_
             | and length unit defined as the distance light travels
             | during a set time.
        
               | Maxatar wrote:
               | That hardly constitutes a precise definition, but at any
               | rate the lecture I linked to goes over the history and I
               | quote, once again from Einstein himself:
               | 
               | >The next position which it was possible to take up in
               | face of this state of things appeared to be the
               | following. The ether does not exist at all...
               | 
               | >More careful reflection teaches us however, that the
               | special theory of relativity does not compel us to deny
               | ether. We may assume the existence of an ether; only we
               | must give up ascribing a definite state of motion to it
               | 
               | This is about half way through the lecture before
               | Einstein touches on general relativity. Towards the end
               | he is quite adamant that a theory of the ether is
               | necessary to fully appreciate general relativity.
               | 
               | With that said I do not want to fall into an argument
               | from authority, certainly much of what we understand
               | about relativity today along with its implications
               | differs from its original formulation, but I present the
               | lecture because I think a lot of people don't quite have
               | the appreciation or historical understanding of what the
               | ether was or wasn't, they just read about how the
               | Michelson-Morley experiment proved that it can't exist
               | along with sensational views that the experiment
               | represented some kind of embarrassment or catastrophe in
               | physics and the ether became a fall-guy of sorts that we
               | must entirely rid ourselves of.
               | 
               | But if you read through the actual primary sources you
               | get a very different picture of how physics progressed
               | bit by bit.
        
               | simpaticoder wrote:
               | _That hardly constitutes a precise definition_
               | 
               | It is precise enough for our purpose: ether is a
               | hypothetical medium for light waves to propagate.
               | Moreover it would need to have no interaction with
               | ordinary matter, or else it would cause planets' orbits
               | to decay.
               | 
               |  _only we must give up ascribing a definite state of
               | motion to it - Einstein_
               | 
               | This is a "No True Scotsman" fallacy wherein one
               | redefines the assertion to deal with specific objections.
               | I hesitate to criticize Einstein, of course, but in this
               | case it's not clear that "ether" minus motion means
               | anything. One can be generous and say he had an intuition
               | about fields, however fields aren't ether, either.
        
               | Maxatar wrote:
               | > ether is a hypothetical medium for light waves to
               | propagate.
               | 
               | If that's the extent of your definition then it is not at
               | all inconsistent with Einstein's definition of the ether
               | in the lecture I linked to.
               | 
               | >This is a "No True Scotsman" fallacy wherein one
               | redefines the assertion to deal with specific objections.
               | 
               | Imagine using your argument to claim that atoms don't
               | exist because atoms were by definition indivisible
               | structures, and so anyone who argues that atoms are made
               | up of protons, neutrons and electrons is just engaged in
               | a "No true Scotsman" fallacy.
               | 
               | This might be how people on the Internet argue, but it's
               | not how curious people make genuine advances in science.
               | 
               | Note that your definition of ether never said anything
               | about having a definite state of motion so it's not at
               | all clear what exactly you're looking to criticize to
               | begin with. Einstein isn't claiming that the ether has no
               | motion, just that it's motion adheres to Lorenz
               | invariance.
               | 
               | >One can be generous and say he had an intuition about
               | fields
               | 
               | Claiming that it's generous that Einstein had some kind
               | of intuition about fields is so absurdly laughable that
               | I'm not sure there is much more to even discuss on this
               | matter. How generous you must be to recognize that Albert
               | Einstein had some kind of intuition about fields.
               | 
               | It certainly makes me wonder if people read what they
               | write sometimes before hitting the reply button.
        
               | simpaticoder wrote:
               | I think you need to review the site guidelines about tone
               | and purpose. Moreover, I'd suggest you review the history
               | of quantum mechanics, because Einstein did not invent
               | field theory, just as Newton did not invent or understand
               | the Lagrange or Hamiltonian formulations, nor statistical
               | mechanics, even though his theory provided the foundation
               | of them all. I'm not a historian of physics, or a
               | psychologist, so I will bow out of the conversation. May
               | your clear passion for science continue without making
               | you hostile.
        
               | Maxatar wrote:
               | You're bringing in a bunch of entirely irrelevant topics
               | into this instead of actually addressing the points.
               | 
               | My apologies if pointing that out in clear language goes
               | against site guidelines, it might be rude to point it out
               | but this site does have a problem with people who think
               | they know it all and blurting out something as laughable
               | as it's "generous to say Einstein had an intuition about
               | fields" is in my opinion a prime example of it.
               | 
               | All the best to you.
        
             | eigenket wrote:
             | > What was the "specific" definition of the aether?
             | 
             | TL:DR the aether has a reference frame. This is exactly
             | what it's inventors wanted and exactly what modern things
             | don't have.
             | 
             | Here is the long version:
             | 
             | When you put together a couple of the constants of
             | classical electromagnetic theory (specifically the
             | quantities called the permitivity and permeability of free
             | space) you get out a quantity which has the units of a
             | speed. You get this thing which is measured in metres per
             | second.
             | 
             | Now if you're a Victorian era scientist, and you have fully
             | internalised Gallilean relativity and Newtonian mechanics
             | then this is absolutely, completely, insane. There is no
             | way in their worldview for a speed to exist in isolation,
             | without a reference frame for it to be measured with
             | respect to.
             | 
             | If I measure a guy on a bike going at 10 miles per hour,
             | and a guy in a car going at 30 miles per hour past him then
             | the guy on the bike sees the car going at 20 miles per hour
             | relative to him. If I sit opposite you on a train I measure
             | your speed to be 0, even though we're both moving at 100+
             | km/hour. Speeds are (for Victorian scientists) completely
             | relative.
             | 
             | So they have the theory of electromagnetism, which seems to
             | be giving amazingly accurate predictions, except that it
             | also gives you this apparently absolute speed, which makes
             | no sense. Someone realises pretty fast that it's about the
             | speed that light goes. So what do they do? They propose the
             | existence of this "aether" stuff which is everywhere at all
             | times and critically _which has a reference frame_. The
             | aether provides a reference frame for the speed of light
             | and the crazy meaningless absolute speed they didn 't know
             | what to do with now makes sense, it's relative like any
             | other speed, but the magic quantity they got is the speed
             | in the aether's reference frame.
             | 
             | Of course a few decades later Michelson and Morley show
             | that this idea doesn't work, in an incredibly beautiful
             | experiment, and the aether theory starts to look shaky. A
             | few years after that Einstein (with input from people like
             | Lorentz) cooks up special relativity which is _almost_ like
             | Gallilean relativity in that _almost_ all speeds are
             | relative, except specifically the speed of light is not.
             | The speed of light is absolute, just as it has to be
             | because of the way it pops out of electromagnetism.
        
           | halyconWays wrote:
           | > while QFT fields like higgs are not physical at all
           | 
           | Phew, I feel better now. Non-physical scalar and tensor
           | fields permeating all of expanding spacetime in a non-
           | physical manner give rise to physical behavior via local
           | nonphysical wavefunction collapse that we call excitations.
        
             | criddell wrote:
             | That's why the mathematical universe hypothesis (everything
             | is built from mathematical structures) seems likely to me.
        
               | halyconWays wrote:
               | It's sort of unsatisfying to say that math has the
               | ability to experience itself, though
        
           | calf wrote:
           | How does something not physical give rise to physical
           | properties? Saying that way makes it sounds like a logical
           | conceit is being used.
        
         | Zondartul wrote:
         | Rule #1 of talking about the aether is "don't call it aether".
         | Nowadays it's "spacetime this" and "mass-energy tensor that"
         | and "properties of vacuum something else".... and we still end
         | up with empty space behaving like a funky fluid.
        
           | ISL wrote:
           | The aether originally suggested a preferred reference frame
           | -- something thoroughly debunked by tests of special
           | relativity.
           | 
           | The universe could still have various preferred/interesting
           | frames (the CMB's rest-frame sure is interesting), but it
           | won't have much, if anything, to do with the movement of
           | particles or light.
        
           | BlarfMcFlarf wrote:
           | Notably, though, unlike an aether, none of those things have
           | a measurable rest frame.
        
         | cryptonector wrote:
         | It's not an aether... I mean, aether was a crutch, but the
         | mathematics that Lorentz developed simplified and you just
         | don't need aether -- it's enough to assume that there's a
         | maximum speed of light and the relativity principle.
         | 
         | (Well, that's only true if you assume there's no as-yet
         | undiscovered fields and particles with FTL that we could
         | eventually interact with -- then we would be able to get
         | something like measurements of speeds of everyday particles and
         | photons relative to such fields, and if they were much faster
         | than light then those measurements would look like "absolute
         | speed" to us. But that's sci-fi fantasy.)
         | 
         | Higgs is not aether for electromagnetic waves. It's only a wee
         | bit like aether for matter if you squint real hard, but still,
         | it's not a medium of travel for matter, so it's not an aether.
        
       | mfworks wrote:
       | PBS Spacetime has a fantastic video on the Higgs Field that
       | explains it about one level deeper that typical pop science, and
       | answers some of the questions I'm seeing in this thread, include
       | "why did the field switch on suddenly?" and "Why is the Higgs
       | Field different from other fields"
       | 
       | link: https://www.youtube.com/watch?v=G0Q4UAiKacw
        
         | programd wrote:
         | I can also add this set of articles from Matt Strassler which
         | explains it all with surprisingly simple math. It really is
         | quite understandable and I wish more pop-sci discussions of the
         | subject threw in a few equations now and then to explain such
         | stuff.
         | 
         | https://profmattstrassler.com/articles-and-posts/particle-ph...
        
       | sieste wrote:
       | > A common approach has been to tell a tall tale. Here's one
       | version: There's this substance, like a soup, that fills the
       | universe; that's the Higgs field. As particles move through it,
       | the soup slows them down, and that's how particles get mass.
       | 
       | Is that really so? I've never heard this analogy, so the whole
       | premise seems a bit of a straw man...
        
         | pdonis wrote:
         | _> Is that really so?_
         | 
         | As the article notes, no, this is not a correct description.
        
           | sieste wrote:
           | sorry for the confusion, I meant is it really the case that
           | this is a commonly used description of the higgs field.
        
         | Sniffnoy wrote:
         | I've seen it a bunch, FWIW.
        
         | pests wrote:
         | A "tall tale" is one that is likely false.
        
       | tsimionescu wrote:
       | If anyone wants to dig deeper, there is an excellent lecture on
       | YouTube by Leonard Susskind. This goes into some details on how
       | fields in general give mass to (composite) particles, and how the
       | Higgs field has certain properties that allow it to give mass to
       | elementary particles. It goes only into a tiny bit of math,
       | absolutely intelligible at the high-school or at least
       | undergraduate level.
       | 
       | https://youtube.com/watch?v=JqNg819PiZY
        
       | simpaticoder wrote:
       | This article is suspect as it mentions a "stationary electron".
       | Such an electron would have precisely known momentum, and so
       | exist throughout all of spacetime. This is a common starting
       | point for solving the (e.g. Dirac) equations, but it's not
       | physical.
        
       | russellbeattie wrote:
       | > _By suggesting that the Higgs field creates mass by exerting
       | drag, they violate both Newton's first and second laws of
       | motion._
       | 
       | Personally, I've wondered why theoretical physicists don't dive
       | into Newton's laws more. Ever since I was a kid and first learned
       | about the Voyager probes continuing to move through space
       | forever, my question was _why_??
       | 
       | All matter is energy, and energy is vibrations in quantum fields,
       | and that vibration never stops (you can never reach absolute
       | zero). From the smallest gluon bouncing between quarks to
       | galaxies to the expansion of the universe itself, matter never
       | stops moving. Where does this infinite source of energy come
       | from?
       | 
       | I understand that physics simply describes _how_ reality works,
       | not _why_ , but I think it'd be valuable to know the reason
       | fields continue to vibrate forever.
        
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