https://profmattstrassler.com/articles-and-posts/particle-ph...
While other authors just keep shy of equations and thus need to resort to simplified analogies, Carroll is not afraid of throwing a good share of math stuff and explaining the rationale from one equation to the other, while avoiding the really hard parts ("solving this equation tortures undergrad physics students for a year, but we won't be doing that")
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.
[1] https://en.wikipedia.org/wiki/Electroweak_interaction#After_...
Now this mechanism is responsible for the electroweak symmetry breaking, could it be others? Yes many think so. A lot of grand unification theories (GUTs) predict existence of some. The most famous one is Supersymmetry. There is a term called GUT phase transition that describes these fields.
Well another particular similar field would be what cosmology people call the inflaton. It is hypothesized that it has driven the expansion of the universe during the inflation event. But that cannot be repeated because it needs much higher energy state that it cannot be happening again.
But some theories of dark matter involve fields that could still be in a symmetric state (like higgs before phase transition) and that these fields would undergo a phase transition that we can see some observation like changes in dark matter distribution.
There is the concept of late dark matter symmetry and false vaccum decay (an idea that we are actually in a local minimum and that the true absolute point is not reached yet. If this is true it would be interested as if we reached this point then laws of physics will change (not our understanding but literally the laws will change). This could lead to a changes in particles properties, masses and forces. This could even change the structure of the space-time itself. This transition will be interesting because it could propagate as a bubble through the universe at speed of light. It seems more on a verge of science fiction but there is a theory behind that [1]
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).
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.
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).
First look at this picture [0]: https://en.wikipedia.org/wiki/Higgs_mechanism#/media/File:Me...
The Higgs field is a complex number Φ (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). Φ = 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 Φ 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, Φ 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 Φ 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
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.
AFAIK, lightspeed could differ based on which direction you go without breakung relativity. And we haven't measured the single direction lightspeed.
Not that I actually think it differs based on direction.
Aether was a substance filling all space, while QFT fields like higgs are not physical at all (but rather give rise to physical properties)
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...
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.
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.
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.
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?
Which is less of a logical conceit, and more metaphysics.
No one knows what quantum fields are made of. There are various ideas (loop quantum gravity, causal dynamical triangulation, others...) but QFT defines what quantum fields do, not what their component parts are at a more fundamental level.
(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.
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?
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.
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...
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?
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)
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.
Is that really so? I've never heard this analogy, so the whole premise seems a bit of a straw man...
As the article notes, no, this is not a correct description.
For whatever it's worth, it's not a description I had seen before I read the article. It's certainly not one you're going to find in actual textbooks or physics papers.
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.
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
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?
Temporal frequency f
Spacial frequency k
f = k * c
Dimensional analysis: t^-1 = l^-1 * l t^-1
Should probably have mentioned - the final equation in my derivation is the Klein-Gordon equation, which is a relativistic equation for the behavior of spinless particles (and maybe bosons in general? I forget)
To get an equation that describes fermion behavior, you need to do another step, which I believe Dirac was the first to do; try very hard to take the square root of both sides of this equation, so you only have first-order derivatives. Dirac really dislike the idea of having a second-order equation, because it leaves an extra initial condition you have to specify. If you expand the p^u p_u term, you can see that it's impossible to take the square root of both sides using normal algebra, because you're trying to take the square root of the sum of multiple terms (d^2/dt^2 - d^2/dx^2 - d^2/dy^2 - d^2/dz^2) . You have to introduce gamma matrices or clifford algebras (IMO the better option) to do it, which seems like a weird and non-physically-motivated approach, but if you do it, spin up and spin down states miraculously fall out of the equation. Eigenchris on youtube has a video that helped me to figure out what was going on there
What are these fields made of? Are all fields made of the same thing(s), or is each field made differently?
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.
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.
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?
