How the Higgs field gives mass to elementary particles(quantamagazine.org)
quantamagazine.org
How the Higgs field gives mass to elementary particles
https://www.quantamagazine.org/how-the-higgs-field-actually-gives-mass-to-elementary-particles-20240903/
110 comments
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...
https://profmattstrassler.com/articles-and-posts/particle-ph...
Sean Carroll produces a great deal of content for people that want a bit more rigorous explanation rather than the leaky metaphors of most popsci. He often delves into equations and technical details, but keeps it at a level mostly understandable for someone who has basic scientific understanding, but isn't a professional/academic. I spend many hours every month listening to him and recommend his content every chance I get.
Carroll's latest book "Quanta and Fields: The Biggest Ideas in the Universe" is about all this quantum field theory, and I think it perfectly covers the gap between pop-sci and academic material for people with some math exposure.
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")
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")
Just to go off these great works, there's a wonderful academic piece on the interaction between cosmology, quantum particles, and the higgs field here:
https://www.youtube.com/watch?v=FYJ1dbyDcrI
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
https://youtube.com/watch?v=JqNg819PiZY
> 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?
Any particular reason/mechanism why the Higgs field suddenly (gradually?) switched on?
> 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.
"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.
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.
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#After_...
[1] https://en.wikipedia.org/wiki/Electroweak_interaction#After_...
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.
Is it possible for there to be other undiscovered fields with a similar mechanic - turning on when the universe hits a future heat threshold?
What you are trying to describe is what we call phase transition. So just to make it clear the reason higgs field working like that is that after the big bang and cooling of universe to about 10^5 kelvins (don't try to convert this to this strange unit of Fahrenheit) the field transitioned from high energy state to lower energy state. This is what gave rise to the higgs mechanism (what the article talks about).
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]
[1] https://en.m.wikipedia.org/wiki/False_vacuum
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]
[1] https://en.m.wikipedia.org/wiki/False_vacuum
> about 10^5 kelvins (don't try to convert this to this strange unit of Fahrenheit)
Challenge accepted... it's about 10^5 Fahrenheit.
Challenge accepted... it's about 10^5 Fahrenheit.
[deleted]
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).
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).
Beware when mixing quantum field theory (Higgs) with gravity (attraction). We don’t have any idea how these two relate to each other.
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.
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.
> the model without it lacked sufficient gravity to match the world around us
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...
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...
> 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.
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.
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.
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.
> and thus gravity.
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.
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.
>Mass is not required for gravity; only energy is.
E = MC^2
Can't have energy without mass, and mass leads to gravity.
E = MC^2
Can't have energy without mass, and mass leads to gravity.
Actually it is
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.
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.
The full equation is: E^2 = (p*c)^2 + (m0*c^2)^2.
https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...
https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...
This ignores Planck's energy-frequency relation. Things like photons are affected by gravity as well.
> E = MC^2
Is only an approximation for particular cases, not a general law.
Is only an approximation for particular cases, not a general law.
> 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).
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).
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 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
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
Very nice explanation! Is it possible that Φ could vary smoothly and subtly over space, such that it's a few degrees or so away from our value in the Andromeda galaxy?
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.
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.
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.
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.
> The aether originally suggested a preferred reference frame -- something thoroughly debunked by tests of special relativity.
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.
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.
Notably, though, unlike an aether, none of those things have a measurable rest frame.
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)
Aether was a substance filling all space, while QFT fields like higgs are not physical at all (but rather give rise to physical properties)
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...
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...
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.
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.
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.
>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.
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.
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.
> 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.
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.
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.
> 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.
First of all, physical fields were a concept far before QFT came in the picture, and they are the same concept as QFT's fields. Einstein was definitely familiar with classical field theories, which were prevalent ways of looking at gravitation and electromagnetism far before even quantum mechanics was discovered.
Secondly, Einstein died some time after QFT had become a real theory, so it is very likely that later in life he could have been at least passingly familiar even with some concepts of quantum fields (though of course, not at the time he wrote his GR papers).
First of all, physical fields were a concept far before QFT came in the picture, and they are the same concept as QFT's fields. Einstein was definitely familiar with classical field theories, which were prevalent ways of looking at gravitation and electromagnetism far before even quantum mechanics was discovered.
Secondly, Einstein died some time after QFT had become a real theory, so it is very likely that later in life he could have been at least passingly familiar even with some concepts of quantum fields (though of course, not at the time he wrote his GR papers).
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.
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.
> 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.
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.
> 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.
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.
That's why the mathematical universe hypothesis (everything is built from mathematical structures) seems likely to me.
It seems incredibly unlikely to me.
It's more likely all physics is argument by analogy from limited human experiences, and math is just a culturally consistent subset of that.
What look like genius predictions are mostly (Einstein aside...) generations of post docs throwing equations at their whiteboards to see what sticks.
A few happen to be confirmed by experiment. Most are quietly forgotten.
I strongly suspect we literally can't begin to imagine what's really going on.
It's more likely all physics is argument by analogy from limited human experiences, and math is just a culturally consistent subset of that.
What look like genius predictions are mostly (Einstein aside...) generations of post docs throwing equations at their whiteboards to see what sticks.
A few happen to be confirmed by experiment. Most are quietly forgotten.
I strongly suspect we literally can't begin to imagine what's really going on.
> I strongly suspect we literally can’t begin to imagine what’s really going on.
I also happen to believe that might be true. In the same way a dog will never understand single variable calculus, there probably are concepts that are out of reach for us.
I also happen to believe that might be true. In the same way a dog will never understand single variable calculus, there probably are concepts that are out of reach for us.
It's sort of unsatisfying to say that math has the ability to experience itself, though
Is it? That’s basically what a conscious AI would be and I have a hard time coming up with reasons why a software brain couldn’t replace a biological brain.
> 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?
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?
How does something not physical give rise to physical properties? Saying that way makes it sounds like a logical conceit is being used.
It organises stuff instead of being stuff.
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.
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.
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.
(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.
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?
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?
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.
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.
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.
I believe it's both. All fields can stiffen their fellows like this, but only the Higgs is stably non-zero.
What's another example of cross-field interaction? Where (say) the EM field changes the restoring force of the gravitational field?
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...
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...
Total layman here, but doesn't an EM field carry energy, and thus have similar effects as mass - thus warping spacetime?
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?
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?
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)
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)
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?
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.
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.
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.
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).
> 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...
Is that really so? I've never heard this analogy, so the whole premise seems a bit of a straw man...
I've seen it a bunch, FWIW.
> Is that really so?
As the article notes, no, this is not a correct description.
As the article notes, no, this is not a correct description.
sorry for the confusion, I meant is it really the case that this is a commonly used description of the higgs field.
> is it really the case that this is a commonly used description of the higgs field.
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.
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.
A "tall tale" is one that is likely false.
> 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.
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.
> 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?
What are these fields made of? Are all fields made of the same thing(s), or is each field made differently?
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.
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.
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.
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.
They aren’t made of anything (other than numbers). Fields are currently the fundamental ontology. They are mathematical objects.
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.
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.
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
So we have a duality of fields and particles. Likely it doesn't make sense to give one representation precedence over the other.
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.
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?
It's more like, particles are how we experience collapsed wave functions, and both are manifestations of excitations in the underlying quantum field.
Last I checked the theory of wave function collapse is still unresolved, with competing explanations. We don't know the answer and should not talk like we pretend we do. Unless you are personally one of those scientists or researchers endorsing one such theory, and even then you have to be clean and transparent and admit the matter is not settled by consensus yet.
What I'm describing is physics 102 and non-controversial. No one is pretending anything.
What you're referring to are competing interpretations for what it means when the superposition of eigenstates collapses into a single state, which we call wave function collapse. The most popular interpretation is the Copenhagen interpretation (observation causes collapse), and the second most probably the many worlds hypothesis (we only observe collapse due to being in one path among all real paths).
Quantum uncertainty doesn't mean you have to approach every topic going "ohh we just don't know! No one can be certain about anything! Leave this to the experts!" These are surface-level descriptions of basic quantum phenomena.
What you're referring to are competing interpretations for what it means when the superposition of eigenstates collapses into a single state, which we call wave function collapse. The most popular interpretation is the Copenhagen interpretation (observation causes collapse), and the second most probably the many worlds hypothesis (we only observe collapse due to being in one path among all real paths).
Quantum uncertainty doesn't mean you have to approach every topic going "ohh we just don't know! No one can be certain about anything! Leave this to the experts!" These are surface-level descriptions of basic quantum phenomena.
[deleted]
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?
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.
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.
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?
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?
How does this idea mesh with the other model given to laymen that the Higgs field causes charged particles to flip helicity extremely rapidly?
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.
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.
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 :)
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.
keep in mind that its against the other whole mass of universe thing doing that same thing that also contributes to a mass reading.
[deleted]
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
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
> 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?
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?
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
Temporal frequency f
Spacial frequency k
f = k * c
Dimensional analysis: t^-1 = l^-1 * l t^-1
This is beautiful. Thanks for this. Is the choice of `M` for "the strength of the restoring force" intended to resemble `m` for mass?
Exactly. Didn't want to confuse it with the normal lowercase `m` that might show up in a wave equation derivation for masses-on-a-string or whatever
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
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
chatgpt convo to understand "temporal frequency" better: https://chatgpt.com/share/f8601523-2d3f-4497-a9b4-071d6a8778...
Looks correct to me, and I like that it pointed out that my final equation I wrote is the klein-gordon eqn. Forgot to mention that in the original post
link: https://www.youtube.com/watch?v=G0Q4UAiKacw