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]
Challenge accepted... it's about 10^5 Fahrenheit.
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.
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.
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.
No. The electroweak phase transition had no effect on gravity whatever; the stress-energy that was governing the expansion was the same before and after. Again, the source of gravity in GR is the stress-energy tensor, not rest mass.
E = MC^2
Can't have energy without mass, and mass leads to gravity.
https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...
E^2 = (MC)^2 + (PC^2)^2
The first term is describing the rest mass. You can redefine the mass term to make it E=mc^2 but now this mass does not correspond to the rest mass. And for sure you can have energy without having a rest mass. Actually for the early universe all you had was a form of radiation and energy.
Is only an approximation for particular cases, not a general law.
True, but 99% of the rest mass of a Proton comes from the gluon field, not the Higgs mechanism. The universe wouldn’t fly apart without the Higgs field.
https://en.wikipedia.org/wiki/Quantum_chromodynamics_binding...
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