Roadfood, the Higgs boson really is, by itself, nothing special. We are so excited about it because it proves the existence of the Higgs field. The Higgs field is a big deal. But just like any other field, it has excitations (particles), in this case the Higgs boson. This is very useful for proving that the field exists, but otherwise it plays no important role. It decays immediately after having been produced. It’s as though we have a trampoline, and it just so happens that there is a very short-lived vibration we can make in the trampoline, and it just so happens that observing this vibrations is the only way to prove the trampoline exists. But the vibration itself is, well, just a vibration. That’s not to say that measuring the properties of the Higgs boson is unimportant. Knowing its mass, spin, etc, and decay modes, we can be sure it is consistent with the Higgs field of the Standard model, and allows us to theoretically predict more accurately how other particles decay, although only as a tiny, tiny correction to our current predictions. The Higgs may also have played a role in the very early universe, although I’m not an expert on that.
I know this is probably an unanswerable question, but do these fields “exist” or are they the equivalent of defining “Alan Smithee” as a perturbation of an “Alan Smithee field” extending throughout the universe that just happens to have a strength of 0 at every point except those I am occupying, which have a field strength of 1?
ETA: My sense from reading the parts of this thread I don’t really understand is that it depends on the field, and that the Higgs field is and the gravitational field (and the electromagnetic field? can’t remember) are the only ones that really extend measurably throughout the universe, while the neutron field, for example, is more like the Alan Smithee field, but that treating them all as fields makes everything consistant. Is that right?
Ontology is tricky at the boundaries of knowledge – and really anywhere if you let it. Do we have a mathematical framework for describing particles and their interactions in which the fundamental beast is a “field”, a real thing posited to exist and posited to provide us with our observed particles and interactions? Yes. Are those fields actually real? Well, it’s pretty handy linguistically to call them real. But, they are no more or no less real than any other construct we use to describe nature.
If someone were to come up with a completely new description of nature that worked just as well but didn’t involve fields, that would be perfectly fine. And the fact that it would be perfectly fine is proof enough that we can never say that fields are real. But this holds for whether anything is real – it’s not limited to forefront fundamental physics – and it’s a matter of philosophical taste where you choose to draw the line.
Yeah, I know all that, so I should have known better than to ask the question. Hopefully my edit made it a little clearer what I was getting at. I suppose what I really want to know is what it means to say that " we have a mathematical framework for describing particles and their interactions in which the fundamental beast is a ‘field’."
Only, you know, not what it really means, because that would involve math beyond my comprehension, but instead the made-up baby version of what it means that I can actually (pretend to) understand. 
ETA: For starters, is the “Alan Smithee field” a good analogy? Would quantum field theory actually say that there is (trivially) an Alan Smithee field like the one I described?
Depending on the interpretation, I think Quantum Mechanics would actually say Alan Smithee is a probability wave existing in all the other known fields.. (since the aggregation of all the things that go into Alan Smithee is just a human construct)
This is what I was feeling, particularly if the field exists and permeates the Universe regardless of particles. I’m not sure, when saying that electrons are excitations of the electromagnetic field, if that’s the same field set up by charges, or a field that just exists.
First, note that “field” is an overloaded word. Its most general definition is “a thing that has a value everywhere in some space”. So, the temperature throughout the earth could be called a field. We might label it T, hiding the fact that it is a function of 3D position, T(x,y,z). For gravity near a planet, it can be convenient to define a function G(x,y,z) such that the force on an object due to the gravity of that planet can be calculated as F=mG. Since G is a function that has a value everywhere, we call it a field – the gravitational field. (Technical note: G is a vector fields, meaning that every point in space has a magnitude and a direction. Contrast T, which has only a magnitude.)
For the Higgs discussion, we are still talking about a mathematical object that has a definable value everywhere, but it is a very different thing. It’s a “quantum field”. The temperature and gravitational fields described above (and also the electric and magnetic fields discussed in classical electromagnetism) are not quantum fields. The concepts of excitations, particles, wiggles, … are not applicable. These fields are just functions that depend on position. In particular, gravity (the “gravitational field”) should be set aside entirely in this thread as we do not know how to write down a working quantum field theory for gravity, and there isn’t any hay to make by comparing the apples and oranges that are the classical gravitational field and a quantum field.
In the case of quantum fields, they indeed extend throughout all of space. One can ask various questions about them. One can ask of the positron field “how many positrons of momentum p are there?” and the answer might be zero if there are no positrons. This is a question relating to the quantum excitations of the field. One could also ask the field what its magnitude is. Since things are quantum in nature, you’d actually ask “what would I measure, on average, your magnitude to be?” If there are no positrons around, then the answer to this question is zero.
One can ask the same questions of the Higgs field. “How many Higgs particles of momentum p are there?” (probing the excitations of the field). “What would I measure, on average, your magnitude to be if there are no Higgs particles present?” Here’s where the magic happens. For the Higgs field, the answer is 246 GeV, not zero, even when there are no particles around.
Both fields exist throughout all of space. Both can support multiple particles (specific sets of excitations) being created or destroyed. One happens to have a non-zero “vacuum expectation value” of 246 GeV, but that’s neither here nor there existentially. If Alan Smithee were a field, it would extend throughout all of space, and I could create an Alan Smithee particle by appropriately exciting the field.
To borrow iamnotbatman’s trampoline metaphor from above: the trampoline exists everywhere whether or not there is a detectable excitation of the trampoline currently in existence.
(Apologies if I’ve repeated anything from upthread. I haven’t read through everything.)
This jumped out at me, yet I haven’t seen any comments on it.
Everything said about modern physics falls out of the math. Everything. The confirmed theories, the speculative theories, the alternate speculative theories, the really far-out theories, the theories that try to define time, the stuff that New Scientist hypes every issue as “going to change everything” or “what if Einstein was wrong” theories. Everything.
Few if any of these theories will be confirmed. That’s irrelevant to their claims. What’s crucial is that every wild claim falls out of the math. If it didn’t physicists would ignore it. (Which is also why they can instantly and without serious study reject the claims made by posters that sometimes come here to peddle their theories: the claims are written in words and those are by definition wrong.) Trying to explain what falls out of the math in ordinary English words is often an almost impossible feat of translation. Many of these concepts have no everyday equivalents, so even attempts at analogies and approximations leave people with the wrong ideas.
You experts in this thread are doing a terrific job of explanations. The only gap that I see is a universal problem. As experts you sometimes fail to see where laypeople misunderstand because they fail to grasp a necessary underlying principle that is so central to your thinking that you can’t conceive that it’s missing. That happens in every expert thread on every subject and I don’t have any suggestions for how to address it. (If I had an answer for it, I would deserve much more than a mere Nobel Prize because that would alter all human communications.) Just take comfort that if you’re sometimes frustrated by not being able to get a point across, it’s not you: it’s us.
@Exapno Mapcase (great name!)
I’m not sure everything falls out of the math. Take the “many worlds” interpretation of probability waves. While it seeks to explain / interpret a mathematical result, it does so in such a science fiction-y way, and it has other aspects which make it feel just not like science (makes no testable predictions, offers no real explanatory power, etc.) And it’s just so incomplete (where are these other worlds?)
So something like that, while taking off from a real mathematical result, goes so far from any substance, it’s functionally equivalent to theorizing the universe is a soap bubble on the back of big green giant. I can’t help suspect some other wild claims and interpretations are similarly ungrounded…
(P.s., I’d also add the at-one-time popular notion that human consciousness is critical to collapsing a wave function. That always felt like a solipsistic interpretation of QM.)
These last two posts are priceless. Talk about interpreting the same information in two diametrically opposed ways - - and by well-informed thinkers, too.
In the same way that you expressed surprise that the smallness of extra dimensions falls out of the math, you might be surprised that some of the more sci-fi-like theoretical concepts are better-founded than their corresponding popular science articles would suggest. In the particular case of the many-worlds theory, it is a good example of casting the same mathematics into different intuition-helping backdrops.
For a more everyday example, consider throwing a ball across the room. One could say the following about what happens to the ball: First, a hand imparts momentum to the ball. Then, in each tiny interval of time, the ball does two things. (1) It moves in a straight line parallel to its momentum, and (2) it changes its momentum based on the forces acting on it (say, gravity) according to a simple rule (Newton’s 2nd Law). After a series of many such updates, the ball will have followed a trajectory through space.
This mathematical description gives predictions that match what we observe, so we use it. It isn’t the only description possible, though. One could also say this: First, a hand imparts momentum to the ball. Then, the ball stops and considers all possible trajectories it might take. It could go in a zig zag. It could go down and then back up. It could go to the moon and back very fast or very slow. For each trajectory considered, the ball calculates a specific integral related to the velocity it has along the hypothetical path and the forces (gravity) it feels along the way. (This integral is called the “action”.) The ball looks at all the infinite possible trajectories and finds the one with the smallest value for this integral. That’s the one it choose, and it proceeds to move along that trajectory.
The second description gives the same predictions as the first. Which is right? Neither. One isn’t trying to be more right than the other. They are simply two usefully different mathematical approaches to getting predictions for the ball’s behavior.
So too with the various interpretations of quantum mechanics. As much as the occasional pop-sci headline would like you to think there is a Battle Royale among them, there is not, at least to the extent that they give identical predictions about the world. It isn’t that the many-worlds interpretation has no testable predictions. It has all the same testable predictions as a collapsing-wavefunction-based interpretation. It’s just a different descriptive framework.
A great many historical breakthroughs have come about by switching to a novel way of describing something and finding that the new description makes extensions or modifications more obvious. Until those extensions are found, one can use whichever description is most convenient. But it is still important to develop new descriptions.
So, does the “Many Worlds” framework offer any unique math or method of solving a wave equation?
(Now that you mention it, I seem to remember an “In Our Time” podcast with a physicist who implied there actually was some substantive work in this area. I’d be interested to learn what that might be. I still think the “human consciousness collapses the wave form” was a silly, sensationalist idea
Actually, the “many worlds” interpretation (MWI) is a very good example of something that “falls out of the math”! Despite common misconception, the MWI is simpler than the other interpretations, and its central idea is to trust the math even though it may seem counterintuitive at first.
You see, in quantum mechanics, the evolution of wave functions are described by schrodingers equation. But many interpretations attempt to add some mechanism by which the wave function is said to collapse. This is some non-linear process that is not understood, explained, or motivated. Nobody has any dynamic description of it. It is extraordinarily ugly, and people still argue over the precise mechanism that causes this mysterious collapse. The MWI, on the other hand, is simply the idea to trust in the math: the schrodinger equation is correct, waves evolve, and that’s that! The rest, the unintuitive interpretation of “many worlds” falls out of that. But note that it is not some ad-hoc fanciful “let’s make it so our universe keeps splitting into multiple universes all the time”. It is a mathematical equivalency of discovered after to simply decide to trust the math.
Nope. But applying Occam’s razor, I think it should be the default interpretation. Mirroring the two String Theory camps I described earlier, stances on the MWI are like follows (even among some physicists):
- What are you smoking? That’s unnecessarily outlandish don’t you think?
- We’re not idiots over here. You just don’t get it.
Keep in mind that (I’d say) the majority of the theoretical physicists are MWI-believers. In my experience a significantly smaller fraction of experimental physicists are MWI-believers. I think that comes from the fact that they are never taught the MWI in school; they just accrue the same vague 1) attitude from hearing popular (and terrible) attempts to popularize physics by inaccurately dramatizing the “many worlds” in MWI.
This particle doesn’t have a cool name, and I think it needs one. Cases in point:
Neutron? Neat!
Electron? Excellent!
Proton? Prosaic!
Quark? Quaint!
Neutrino? Natty!
Dark matter? Dope!
Higgs Boson particle? HISS!
Higgs? Hugs!
Just to add on a bit: everything falls out of the math. That you consider the results science-fiction-y is backwards. Science fiction has always based even its wilder notions on actual science. Parallel universes were written about earlier - usually credited to Murrary Leinster’s 1934 “Sideways in Time” - but Everett’s math found something that was new and unthought of. And while it might be simpler in math, it’s vastly more complicated for fiction and I don’t think any major stories have been based squarely on it.
I keep hearing that many-worlds is becoming the preferred interpretation among physicists, because of the way the math works. Whether that’s true of not, remember that it is exactly mathematically equivalent to every other interpretation of QM. If it’s correct math it doesn’t matter in the least whether you or even any physicist approves of what falls out.
Moreover, the multiverse concept in various forms seems to fall out of everything these days. Brain Greene in The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos talks about nine separate and distinct forms of multiverse that are generated by nine separate mathematical approaches. Whether they are ever proven by observation (or ever can be) is moot today but that doesn’t negate the point you are getting wrong. Everything falls out of the math. The words used to express the math may sound out of your everyday experience as a mid-sized massive object living on spherical geometry but that everyday experience has little or nothing to do with the way the universe and the sub-atomic world works.
Re: Many Worlds…
This seems like an interesting point of disagreement (I clearly am on the side of “what are you smoking”). I understand that it may be intellectually pleasing to work with an interpretation that simply corresponds to what the math is telling you, but underneath, it seems to have the same ugliness as “collapsing a wave form.” How does it fit with the rest of what we know of the universe (i.e., where are these other worlds, once an event is observed?) How does it fit in any way with what we observe? In other words, how is different than interpreting Newton’s equations as being driven by invisible dragons being the ones creating force?
And perhaps more importantly, MWI has been around longer than String Theory and you’re saying it hasn’t resulted in any testable predictions or unique methods. At some point you have to see that others might see this as sterile intellectualizing, no matter how beautiful…
And also I’m not sure I agree that this is a case of boldly “trusting the math.” My understanding is that Einstein trusted the math when it said speed of light is constant, and doing so resulted in special relativity. Then he trusted the math that said gravity was like angular acceleration and out came general relativity. So, Einstein trusted math that corresponded to phenomenon people could observe and measure. In contrast, some subset of theoretical physicists are “trusting” (I would say interpreting) the wave equation to say there are many potential outcomes (of which we somehow only observe one), and that results in…(?)
I’m not sure that’s what Greene means. Basically, and someone straighten me out, there are multiple approaches to achieving the same results depending on what mathematical approach you take in M theory. Similar to how matrix and wave mechanics can be used to reach the same result in quantum mechanics and so we wind up with transformation theory and Hilbert space. But just because 2 different mathematical formulations gives you the same answer doesn’t mean you get 2 universes.
Note though, I may have misunderstood Greene’s point.
Maybe his point is that there is more than one theory (as well as physical processes that happen) that seems to indicate the universe is a much weirder place than it looks from our everyday human perspective. One little theory or one thing you might be able to brush off. A handful and you have to start thinking there might be something to it?
Haven’t read the book.