In particles physics, they have a different explanation of electromagnetism that is also very natural, almost inevitable. https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathem... The explanation in particle physics is compatible with Quantum Mechanics and Special Relativity, but no one is sure about how to extend it to General Relativity. I'm not sure how compatible is it with the proposal in the article discussed here.
Non technical version (ELI25):
In quantum mechanics the wavefunction Ψ is has complex values. If you multiply everything in the universe by -1, nothing changes because all the physical results use ΨΨ* (where * is the complex conjugation). You can also multiply everything by i or -i. Moreover by any other complex number of modulo 1 because ΨΨ* does not change. (The technical term for this is U(1) global gauge symmetry.)
But you can be more ambitious and want to multiply each point of the universe by a different complex number of modulo 1. ΨΨ* does not change but the derivatives of Ψ change and they are also important. (When you use the same complex number everywhere, the derivatives is just a multiple of the original derivative. When you use a different number in each point, it changes.)
The only way to fix the problem with the derivative is to add a new field A. When you and multiply each point of the universe by a different complex number of modulo 1, then A changes in a simple to calculate but not obvious way. The change in A fix the problem with the derivatives of Ψ.
So now the equations of the universe with Ψ and A don't change when you make this change. (The technical term for this is U(1) local gauge symmetry.) When you write carefully how a universe like this look like, the new field A is electromagnetism. (Actually, you can get the electric field and magnetic field using the derivatives of A.)
This explanation looks more complicated than the explanation of the article, but the article is full of technical terms that you really don't want to know, like:
> Riemann curvature tensor is more than just Ricci curvature—electromagnetic fields stretch and bend the spacetime
Thanks for the explanation. If you have the time, can you also explain _why_ would we be multiplying "each point of the universe with a different complex number of modulo 1?" What does it mean in physical reality; why multiply points with any number at all?
The simple answer is "because we can". In general, physicists have found that we should write down the most general mathematical theory compatible with what's observed. A famous example of this is Einstein's cosmological constant -- I'll leave that one to wikipedia [1] since I'm a particle physicist and not an expert on GR.
In the case of gauge theory, the idea that we should consider the most general case has been well proven. As GP pointed out, all observable phenomena ultimately depend only on the absolute modulus of the field Ψ, so a theoretical physicist naturally wonders, what happens if you allow its complex phase to vary. Turns out nothing interesting happens if you apply a global phase, but if you allow the phase to vary at every point in spacetime, it ends up breaking the theory. That is, unless you include an additional field at every point in spacetime that precisely cancels out the change induced by the gauge freedom.
In other words, the motivation is that we can't simply look and "see" whether or not there is a locally varying phase on the wavefunction Ψ, since we only can measure |Ψ|^2. So we have to assume there is, until proven otherwise. Since a local phase would imply the existence of an extra field to cancel it out, we can indirectly check for this scenario by looking for the corresponding field. As pointed out by GP, in the case of a U(1) gauge, it turns out there is such a field, and electromagnetism (and all of its laws) exactly fit the bill.
There are other "unmeasurable" symmetries you could apply to the wave function as well, beyond just a complex phase. SU(2) is a Lie group symmetry which would mean that the measurable properties of certain tuples of fields (Ψ, ϕ) are indistinguishable under a sort of complex-valued rotation of Ψ->ϕ and ϕ->Ψ. Again, if you assume a such symmetry is locally varied at every point in spacetime, you end up requiring not one but three new fields to cancel out the effects on the SM Lagrangian. It turns out that the vector bosons W+, W-, and Z, which mediate weak nuclear forces exactly fit the bill.
I don't know about quantum mechanics, but when we talk about space we should be free to add a quantity to the whole universe (like adding 1 to the x coordinate of everything) because this just shifts the whole universe, or accordingly, shifts the origin - the (0, 0, 0) point - in the opposite direction.
The origin is set at an arbitrary point so this "space shift invariance" is saying that it doesn't matter what point we set for the origin (and mathematically this corresponds to the conservation of momentum - see Noether's theorem[0])
Hmm maybe the "zero" for the quantum states is arbitrary, so you should be able to add anything to it for the whole universe, and this merely changes the zero state in the opposite direction.. and since this should be a conversation law, pretty sure this is equivalent to the conservation of electric charge
Not GP, or a physicist, but my understanding is that the different number at each point you multiply with represents a degree of freedom at each point of spacetime, and in this degree of freedom is where the electromagnetic field lives.
Based on my reading, the particle physics explanation/theory is precisely the current consensus. And, given my research into electrodynamics in order to understand the propagation of EM wave fronts in antenna design, I also think the article has some merit (which is, at its core, a call for some experiments).
Given that "light" is fundamentally a electromagnetic wave and its propagation in spacetime is constant, and this results in time slowing down when you go faster to maintain this property, it isn't unreasonable to hypothesize a more fundamental basis here.
Personally, I think adding in the time component will be essential to completing this puzzle but all in all it makes for an avenue of investigation which is interesting.
Note that light isn't particularly special in this context, what is special (very special) is the speed of light. Other things travel at the speed of light, indeed everything massless is forced to travel at the speed of light. Other things that travel at the speed of light include gravitational waves and gluons*.
Basically "the speed of light" should be called "the speed of massless things" or possibly "the speed of causality" or something. We just call it "the speed of light" because light is the first thing we discovered that travels at this special speed.
*the star is because everything about quantum-chromodynamics is terrible so gluons don't really ever exist as particles themselves. If they did they would travel at the speed of light.
>Personally, I think adding in the time component will be essential to completing this puzzle but all in all it makes for an avenue of investigation which is interesting.
Not a physicist, but I've often wondered if the basis of QFT got off on the wrong foot by making time a privileged coordinate instead of a quantum operator like it does for position.
This is absolutely an amazing explanation of local gauge symmetry I've ever seen. Thank you for writing this up. Gems like this is the reason I love HN!
> but the article is full of technical terms that you really don't want to know
The article looks a lot like word salad... too many specific technical terms for the average person to manage, yet lacking in the specifics that would be needed by someone capable of understanding their theory.
If it's written for their audience, then the only audience they seem to be targeting is average people who won't understand their assertions may be a load of crap.
Or is there someone here with a deep understanding of these topics that would care to chime in?
I have been really interested in general relativity and watching youtube videos for the past few months. I understood all the words (I would not have a year ago.) I think it does have enough detail to understand what they're saying. There's a lot missing, but I assume you'd go to the paper for that.
But I think the article is well written. It essentially says, "We think this interesting thing is true. It has these nice properties, and should be provable/falsifiable. Please help us prove it!"
I'm not the person you're replying to, but yes A definitely is the electromagnetic vector potential (from classical electrodynamics). In gauge theory A tells you how to relate the phase of Ψ at nearby points in space/time.
Now that may purely a choice of convention for Ψ at different points in space/time (a choice of "gauge" in the jargon), but where it gets interesting is if your successive nearby points in space/time trace out a closed loop. If your A is such that the phase of Ψ ends up different as a result of going round the loop, you have an electromagnetic field!
If I understand you correctly, you claim that electromagnetism follows immediately from quantum mechanics because Born's rule exhibits a U(1) symmetry? That doesn't seem right to me.
It's not only the Born's rule. All the equations have a similar symmetry. (You may have ∂Ψ=VΨ, or Ψ∂Ψ*+∂ΨΨ*+ΨΨ*. See the real examples in the link in Wikipedia. But you never have something like ΨΨ+Ψ*Ψ* that mix the number of times that the linear and the conjugate version appears.)
Also, it's not so immediate, because you must be stubborn enough to think that a global obvious symmetry "must" be extended to a local symmetry. And in any case, it took like 40 years a few brilliant persons to discover it.
So A/electromagnetism is a natural consequence of the universe having a free (complex modulo 1) parameter/field in addition to just the wavefunction Ψ. ?
"I'm not sure how compatible is it with the proposal in the article discussed here."
Right. It seems to me that both approaches make sense. Perhaps with some cleaver yet-to-be-determined math both ideas can finally be mated.
I've never been convinced that the æther doesn't exist. Sure, it's been long debunked in the luminiferous æther sense but as the article points out "...the aether hypothesis was abandoned, and to this day, the classical theory of electromagnetism does not provide us with a clear answer to the question in which medium electric and magnetic fields propagate in vacuum." It is this aspect of the abolition of the æther that has always worried me.
For starters, any new model of the æther would have to exhibit Lorentz-invariant properties. Then there's the matter of vacuum permittivity ε0 and vacuum permeability μ0 to consider as the speed of light/aka 'electromagnetism' is directly linked to these physical constants via the expression c = 1/(μ0 ε0)^0.5. If one constant were to change then so too would the others including α Sommerfeld's fine structure constant, RK the von Klitzing constant, and Z0 the vacuum (free space) impedance, etc., etc. (Anyway, one would expect them to change—not that we'd ever know as we'd likely not exist if they did). ;-)
But I digress a little. We know that ε0 and μ0 have actual non-zero values and cannot be equated out (as we sort of tried to do in the days when we expressed electromagnetism in cgs units). In essence, physical constants ε0 and μ0 are absolutely intrinsic to electromagnetism, and whilst I cannot prove the fact, it seems to me they would be just as intrinsic to any new definition of the æther. Moreover, similar reasoning makes me think that QFT, ZPE/Zero-point energy/quantum vacuum state, ε0 and μ0 are all inextricably linked to GR.
It seems to me that whilst matters such as whether the spacetime manifold is Ricci-flat, etc. are extremely important principally from the perspective that when properly dovetailed into any new theory they'll provide proof thereof—are secondary to the proposition (note, I'm not saying they're secondary aspects of physics, only that they're secondary to the initial proposition).
Moreover, an equally important question to ask is why the constants ε0 and μ0 have the values they do given the quantum vacuum state, etc. Of course, the same logic applies to both α and c. Finally, we base just about everything on c it being the fundamental immutable constant (despite the the perennial emphasis/importance of α ≈ 1/137). The question is, is it in fact so, or is it that underlying physics first determines ε0 and μ0 and thus these constants could be considered more fundamental to any new formulation of the æther than that of c, it being the consequential resultant of the properties of those constants. (Heresy I know, but it would seem to make sense to view c in this context if or when we end up with new definition for the æther.)
My personal take on the question of space is that because of Lorentz contraction there is always an observer that sees the universe as a flat pancake. There is no true "distance" between any particles, and therefore no space. Every interaction between particles is because these particles actually collided for some specific hypothetical observer.
It's very hard! I tried to simplify as much as possible and use as many small lies as possible, but keep the explanation faithful to the central idea.
For example, I used that if k is a complex number with modulus 1, and k* is the conjugate, then kk*=1. It's a subject from a course of the first years of the university of a technical degree and perhaps a high school. Adding a detailed explanation in the middle makes the explanation too long. Also, it's a very important part of the correct technical complete version of the explanation, it's not a side comment or a metaphor.
I think it could be explained better, or with different tradeoff to make it easier to understand. Anyway, it's my best effort with my personal taste.
If you tell me the part that confused you, I can try to explain that part more. (And if you provide some personal background, like age range and what you studied, I can try to tailor it more.)
Er, I'm not sure that things like dressed particles [1] and off-shell matter [2] violating E=mc^2 [3] could be described as even remotely "natural".
Perhaps they are valid theories, but "natural" certainly isn't an appropriate description of most of what unavoidably follows from particle assumptions.
Virtual particles are basically just a mathematical trick to make doing calculations easier in perturbative quantum field theory. You shouldn't take them too seriously.
If you do the calculations in another way (e.g. by discretizing stuff on a lattice) no virtual particles appear but your calculations become a lot harder.
I'm not an expert in GR, but the linked paper seems nonsensical[0]. It postulates a highly degenerate decomposition of the metric tensor, for which they postulate a contrived action which then seems to correspond to the Einstein-Hilbert, through mathematically unsound manipulations (how can you raise indices with the metric being nowhere even close to invertible?).
Besides, how can you talk about unifying general relativity and electromagnetism without mentioning Kaluza-Klein theory[1]? And what about one of the most beautiful principles in physics, gauge invariance[2]?
I don't want to be rude, but I'm very curious as to how this got through peer review.
> Besides, how can you talk about unifying general relativity and electromagnetism without mentioning Kaluza-Klein theory[1]?
No offense but the very first paragraph of the article's introduction mentions Kaluza's work:
> The earliest attempts can be reasonably traced back to the German physicist Gustav Mie (1868-1957) and the Finnish physicist Gunnar Nordström (1881-1923). Fruitful efforts came, for example, from David Hilbert (1862-1943), Hermann Weyl (1885-1955), Theodor Kaluza (1885-1954), Arthur Eddington (1882-1944) and of course also from Albert Einstein (1879-1955). It is less well-known that, for example, Erwin Schrödinger (1887-1961) had such inclinations as well, see [1]. For a thorough historical review, see [2].
Kaluza's work is mentioned in the first paragraph of the paper. How can you write such an inflammatory critique without having actually read the paper?
Kaluza's name is mentioned, but not Klein's, and there's no mention of their theory whatsoever.
Kaluza-Klein theory is the archetype of expressing electromagnetism purely through curvature, and I'd expect any paper doing the same to refer to it, as well as explain how the work in the paper differs from or expands on it.
The fact that the metric proposed in the paper corresponds to the term added to the 4D spacetime part of the Kaluza-Klein metric is already suspicious. It makes me think they're either repeating Kaluza and Klein's work, or aren't properly citing it when they should have.
Yeah, I think so too. While the authors might attempt to counter that they are only describing EM in vacuum, the fact is that GR is nonlinear. You can’t just add an EM sector by a rank-1 metric component and expect linearity to apply.
At some level, this feels like a vacuous result. If you start with a rank-2 massless field theory, and constrain it to act on rank-1 fields, is it surprising that you get a rank-1 massless field theory? Is this not just an elaborate form of completing the square?
Yeah first thought that popped into my head was Kaluza-Klein theory, and I'm far from an expert enough to dissect the paper but it has that smell of junk science.
This article is not really coherent. It seems like a bunch of random statements about physics, strung together without explanation. This paragraph for instance is a bunch of true-ish sentences but overall is gibberish:
> The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.
> This paragraph for instance is a bunch of true-ish sentences but overall is gibberish:
>> The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.
Could you elaborate on why you think this is gibberish? I mean, I agree that the article is giving off a pseudo science vibe and the authors should work on their style. (Instead of presenting their results in a matter-of-fact manner, they should rather dedicate more time to explaining their assumptions and their reasoning in a step-by-step manner.) But the paragraph you quoted seems perfectly fine.
All of the sentences in the paragraph are real sentences from physics but they're strong together like they were generated by GPT-3 or something. For instance what does "how lengths determine in spacetime" mean? Why is it saying that curvature is what we feel as force? Why is it suddenly talking about test particles without introducing the term? Why does it jump to talking about geodesics in the last sentence? etc. it just feels like it was strung together by an algorithm.
There’s a paper with equations linked at the bottom. I suspect it sounds like gibberish because its describing a mathematical proof with common language. The paper assumes you have a lot of knowledge as well.
“metric tensor of spacetime”… When I hear a series of words that I feel sound like bullshit I Google them. And, like you I felt this paragraph felt like a healthy bit of BS but was surprised that this paragraph is pretty much the Wiki definition of the phrase “metric tensor of spacetime”. I still dont understand it however.
Oh, yes, that's a real phrase that's ubiquitous in physics. It's the weird progression of sentences, wandering through ideas with no explanation or implication, that makes it sound like gibberish.
This is interesting and if the experimental evidence confirms this hypothesis, it bodes well for our future. A universe where we can interact with spacetime via engineering is one that allows for a lot of creative freedom. They also have another interesting article claiming that the imaginary structure of QM is the result of stochastic optimization on spacetimes: https://www.nature.com/articles/s41598-019-56357-3
Maybe the UAPs really are just secret warp drive tech we made 20 or 30 years ago.
IIUC the authors are saying that if we associate the metric with the four-potential via an outer product, they get a picture coherent with the current understanding of how electromagnetism "works" in GR under certain circumstances.
I can somewhat see how to interpret the mathematics in free space. But what about when there are massive bodies in the picture? They will result in a non-flat metric... does that imply they create their own electromagnetism?
It’s really interesting to see other fields trying to explain research.
Here, I feel the authors are not entirely clear who the audience is supposed to be. At first, they seem to target people who need the difference between Einstein and Maxwell explained. The section is titled:“ Maxwell's equations and general relativity—what are these all about?“
Then when they reveal the missing link, the uninformed reader is presented with a logical progression that is obviously written towards somehow for whom the statement:“the Lagrangian of electrodynamics is just the Einstein-Hilbert action“ is self explanatory.
You know, people who say, yes of course, if you say:“ keep the spacetime manifold Ricci-flat.“
That reminds me of Roger Penrose's 1100pp The Road to Reality: A Complete Guide to the Laws of the Universe, which I was very excited about reading when I bought it years ago. Lots of lovely diagrams.
Turns out I could learn almost nothing from it, although I really tried: The first half of the book was basic stuff I already knew, but I could understand nothing of the second half, it passed so quickly from the elementary to the super-advanced. I ended up wondering who it was written for—I imagined everyone would have a similar experience, whatever their level—it's stuff you already know until suddenly it's stuff you can't understand, and no way of passing beyond. It covers so much ground so quickly, with no time for enough explanation—if you didn't already understand the current topic. Maybe that was just me! But it was extremely surprising putting so much (money,) time and effort into a book with rave reviews by a leading physicist, and learning virtually nothing.
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yesenadam 1 day ago | parent [–] | on: Electromagnetism is a property of spacetime itself...
That reminds me of Roger Penrose's 1100pp The Road to Reality: A Complete Guide to the Laws of the Universe, which I was very excited about reading when I bought it years ago. Lots of lovely diagrams.
Turns out I could learn almost nothing from it, although I really tried: The first half of the book was basic stuff I already knew, but I could understand nothing of the second half, it passed so quickly from the elementary to the super-advanced. I ended up wondering who it was written for—I imagined everyone would have a similar experience, whatever their level—it's stuff you already know until suddenly it's stuff you can't understand, and no way of passing beyond."
This is nearly universally an answer to the request" tell me you don't understand something you think you understand without telling me that you don't understand something that you think you understand"
The ramp isn't steep. It's just that if you think you're on it but aren't, then the second floor looks like a wall
Reading the article, this appears to be a speculative rehash of past theories claiming to unify electromagnetism and general relativity. The article ends on the note that empirical research is needed.
I did not see anything novel that would warrant further attention - did I miss something?
mass/energy conversion (in particular to/from photons, i.e. EM waves) is a kind of huge hint that there is really only energy and spacetime (and with energy being just a configuration of spacetime we're left with the spacetime only really). The only issue is the nature of electric charge - what is it really, i.e. can it be reduced to gravity? can it be just an emergent property of energy/spacetime? And in particular the repelling property of the charge which at first seems to not exist for gravity - then where it comes from? I think it is some spin based effect along the lines of the [non-charged] black holes spin-spin interaction based repelling effect, something like this https://arxiv.org/abs/1901.02894
Another commenter https://news.ycombinator.com/item?id=27943428 talks what basically looks to me as an emergence of EM field from rotation - "to multiply each point of the universe by a different complex number of modulo 1" - ie. as an artefact emerging by changing the frame to the one where the system is rotating (ie. gets a spin). Kind of similar how magnetic field is just emergent artefact in the frame where charge is linearly moving.
Readit News
Non technical version (ELI25):
In quantum mechanics the wavefunction Ψ is has complex values. If you multiply everything in the universe by -1, nothing changes because all the physical results use ΨΨ* (where * is the complex conjugation). You can also multiply everything by i or -i. Moreover by any other complex number of modulo 1 because ΨΨ* does not change. (The technical term for this is U(1) global gauge symmetry.)
But you can be more ambitious and want to multiply each point of the universe by a different complex number of modulo 1. ΨΨ* does not change but the derivatives of Ψ change and they are also important. (When you use the same complex number everywhere, the derivatives is just a multiple of the original derivative. When you use a different number in each point, it changes.)
The only way to fix the problem with the derivative is to add a new field A. When you and multiply each point of the universe by a different complex number of modulo 1, then A changes in a simple to calculate but not obvious way. The change in A fix the problem with the derivatives of Ψ.
So now the equations of the universe with Ψ and A don't change when you make this change. (The technical term for this is U(1) local gauge symmetry.) When you write carefully how a universe like this look like, the new field A is electromagnetism. (Actually, you can get the electric field and magnetic field using the derivatives of A.)
This explanation looks more complicated than the explanation of the article, but the article is full of technical terms that you really don't want to know, like:
> Riemann curvature tensor is more than just Ricci curvature—electromagnetic fields stretch and bend the spacetime
In the case of gauge theory, the idea that we should consider the most general case has been well proven. As GP pointed out, all observable phenomena ultimately depend only on the absolute modulus of the field Ψ, so a theoretical physicist naturally wonders, what happens if you allow its complex phase to vary. Turns out nothing interesting happens if you apply a global phase, but if you allow the phase to vary at every point in spacetime, it ends up breaking the theory. That is, unless you include an additional field at every point in spacetime that precisely cancels out the change induced by the gauge freedom.
In other words, the motivation is that we can't simply look and "see" whether or not there is a locally varying phase on the wavefunction Ψ, since we only can measure |Ψ|^2. So we have to assume there is, until proven otherwise. Since a local phase would imply the existence of an extra field to cancel it out, we can indirectly check for this scenario by looking for the corresponding field. As pointed out by GP, in the case of a U(1) gauge, it turns out there is such a field, and electromagnetism (and all of its laws) exactly fit the bill.
There are other "unmeasurable" symmetries you could apply to the wave function as well, beyond just a complex phase. SU(2) is a Lie group symmetry which would mean that the measurable properties of certain tuples of fields (Ψ, ϕ) are indistinguishable under a sort of complex-valued rotation of Ψ->ϕ and ϕ->Ψ. Again, if you assume a such symmetry is locally varied at every point in spacetime, you end up requiring not one but three new fields to cancel out the effects on the SM Lagrangian. It turns out that the vector bosons W+, W-, and Z, which mediate weak nuclear forces exactly fit the bill.
[1] - https://en.wikipedia.org/wiki/Cosmological_constant
The origin is set at an arbitrary point so this "space shift invariance" is saying that it doesn't matter what point we set for the origin (and mathematically this corresponds to the conservation of momentum - see Noether's theorem[0])
Hmm maybe the "zero" for the quantum states is arbitrary, so you should be able to add anything to it for the whole universe, and this merely changes the zero state in the opposite direction.. and since this should be a conversation law, pretty sure this is equivalent to the conservation of electric charge
https://en.wikipedia.org/wiki/Noether's_theorem
It's a complex number for QED but in general, it's a unitary matrix: a rotation which preserves the magnitude of a wavefunction (a complex vector).
In physics, symmetries play a fundamental role.
Given that "light" is fundamentally a electromagnetic wave and its propagation in spacetime is constant, and this results in time slowing down when you go faster to maintain this property, it isn't unreasonable to hypothesize a more fundamental basis here.
Personally, I think adding in the time component will be essential to completing this puzzle but all in all it makes for an avenue of investigation which is interesting.
Basically "the speed of light" should be called "the speed of massless things" or possibly "the speed of causality" or something. We just call it "the speed of light" because light is the first thing we discovered that travels at this special speed.
*the star is because everything about quantum-chromodynamics is terrible so gluons don't really ever exist as particles themselves. If they did they would travel at the speed of light.
Not a physicist, but I've often wondered if the basis of QFT got off on the wrong foot by making time a privileged coordinate instead of a quantum operator like it does for position.
The article looks a lot like word salad... too many specific technical terms for the average person to manage, yet lacking in the specifics that would be needed by someone capable of understanding their theory.
If it's written for their audience, then the only audience they seem to be targeting is average people who won't understand their assertions may be a load of crap.
Or is there someone here with a deep understanding of these topics that would care to chime in?
But I think the article is well written. It essentially says, "We think this interesting thing is true. It has these nice properties, and should be provable/falsifiable. Please help us prove it!"
https://news.ycombinator.com/item?id=27944642
(Warning: Rather technical and full of math)
Now that may purely a choice of convention for Ψ at different points in space/time (a choice of "gauge" in the jargon), but where it gets interesting is if your successive nearby points in space/time trace out a closed loop. If your A is such that the phase of Ψ ends up different as a result of going round the loop, you have an electromagnetic field!
https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#P...
A is quantum, the electromagnetic potential is classical, so they are not really the same thing.
Also, it's not so immediate, because you must be stubborn enough to think that a global obvious symmetry "must" be extended to a local symmetry. And in any case, it took like 40 years a few brilliant persons to discover it.
Right. It seems to me that both approaches make sense. Perhaps with some cleaver yet-to-be-determined math both ideas can finally be mated.
I've never been convinced that the æther doesn't exist. Sure, it's been long debunked in the luminiferous æther sense but as the article points out "...the aether hypothesis was abandoned, and to this day, the classical theory of electromagnetism does not provide us with a clear answer to the question in which medium electric and magnetic fields propagate in vacuum." It is this aspect of the abolition of the æther that has always worried me.
For starters, any new model of the æther would have to exhibit Lorentz-invariant properties. Then there's the matter of vacuum permittivity ε0 and vacuum permeability μ0 to consider as the speed of light/aka 'electromagnetism' is directly linked to these physical constants via the expression c = 1/(μ0 ε0)^0.5. If one constant were to change then so too would the others including α Sommerfeld's fine structure constant, RK the von Klitzing constant, and Z0 the vacuum (free space) impedance, etc., etc. (Anyway, one would expect them to change—not that we'd ever know as we'd likely not exist if they did). ;-)
But I digress a little. We know that ε0 and μ0 have actual non-zero values and cannot be equated out (as we sort of tried to do in the days when we expressed electromagnetism in cgs units). In essence, physical constants ε0 and μ0 are absolutely intrinsic to electromagnetism, and whilst I cannot prove the fact, it seems to me they would be just as intrinsic to any new definition of the æther. Moreover, similar reasoning makes me think that QFT, ZPE/Zero-point energy/quantum vacuum state, ε0 and μ0 are all inextricably linked to GR.
It seems to me that whilst matters such as whether the spacetime manifold is Ricci-flat, etc. are extremely important principally from the perspective that when properly dovetailed into any new theory they'll provide proof thereof—are secondary to the proposition (note, I'm not saying they're secondary aspects of physics, only that they're secondary to the initial proposition).
Moreover, an equally important question to ask is why the constants ε0 and μ0 have the values they do given the quantum vacuum state, etc. Of course, the same logic applies to both α and c. Finally, we base just about everything on c it being the fundamental immutable constant (despite the the perennial emphasis/importance of α ≈ 1/137). The question is, is it in fact so, or is it that underlying physics first determines ε0 and μ0 and thus these constants could be considered more fundamental to any new formulation of the æther than that of c, it being the consequential resultant of the properties of those constants. (Heresy I know, but it would seem to make sense to view c in this context if or when we end up with new definition for the æther.)
For example, I used that if k is a complex number with modulus 1, and k* is the conjugate, then kk*=1. It's a subject from a course of the first years of the university of a technical degree and perhaps a high school. Adding a detailed explanation in the middle makes the explanation too long. Also, it's a very important part of the correct technical complete version of the explanation, it's not a side comment or a metaphor.
I think it could be explained better, or with different tradeoff to make it easier to understand. Anyway, it's my best effort with my personal taste.
If you tell me the part that confused you, I can try to explain that part more. (And if you provide some personal background, like age range and what you studied, I can try to tailor it more.)
Er, I'm not sure that things like dressed particles [1] and off-shell matter [2] violating E=mc^2 [3] could be described as even remotely "natural".
Perhaps they are valid theories, but "natural" certainly isn't an appropriate description of most of what unavoidably follows from particle assumptions.
[1] https://en.m.wikipedia.org/wiki/Dressed_particle
[2] https://en.m.wikipedia.org/wiki/On_shell_and_off_shell
[3] https://en.m.wikipedia.org/wiki/Virtual_particle#Properties
If you do the calculations in another way (e.g. by discretizing stuff on a lattice) no virtual particles appear but your calculations become a lot harder.
Besides, how can you talk about unifying general relativity and electromagnetism without mentioning Kaluza-Klein theory[1]? And what about one of the most beautiful principles in physics, gauge invariance[2]?
I don't want to be rude, but I'm very curious as to how this got through peer review.
0: https://iopscience.iop.org/article/10.1088/1742-6596/1956/1/... 1: https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory 2: https://en.wikipedia.org/wiki/Gauge_theory
No offense but the very first paragraph of the article's introduction mentions Kaluza's work:
> The earliest attempts can be reasonably traced back to the German physicist Gustav Mie (1868-1957) and the Finnish physicist Gunnar Nordström (1881-1923). Fruitful efforts came, for example, from David Hilbert (1862-1943), Hermann Weyl (1885-1955), Theodor Kaluza (1885-1954), Arthur Eddington (1882-1944) and of course also from Albert Einstein (1879-1955). It is less well-known that, for example, Erwin Schrödinger (1887-1961) had such inclinations as well, see [1]. For a thorough historical review, see [2].
Kaluza-Klein theory is the archetype of expressing electromagnetism purely through curvature, and I'd expect any paper doing the same to refer to it, as well as explain how the work in the paper differs from or expands on it.
The fact that the metric proposed in the paper corresponds to the term added to the 4D spacetime part of the Kaluza-Klein metric is already suspicious. It makes me think they're either repeating Kaluza and Klein's work, or aren't properly citing it when they should have.
At some level, this feels like a vacuous result. If you start with a rank-2 massless field theory, and constrain it to act on rank-1 fields, is it surprising that you get a rank-1 massless field theory? Is this not just an elaborate form of completing the square?
> The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.
>> The metric tensor of spacetime tells us how lengths determine in spacetime. The metric tensor also thus determines the curvature properties of spacetime. Curvature is what we feel as "force." In addition, energy and curvature relate to each other through the Einstein field equations. Test particles follow what are called geodesics—the shortest paths in the spacetime.
Could you elaborate on why you think this is gibberish? I mean, I agree that the article is giving off a pseudo science vibe and the authors should work on their style. (Instead of presenting their results in a matter-of-fact manner, they should rather dedicate more time to explaining their assumptions and their reasoning in a step-by-step manner.) But the paragraph you quoted seems perfectly fine.
https://en.m.wikipedia.org/wiki/Metric_tensor_(general_relat...
Maybe the UAPs really are just secret warp drive tech we made 20 or 30 years ago.
I can somewhat see how to interpret the mathematics in free space. But what about when there are massive bodies in the picture? They will result in a non-flat metric... does that imply they create their own electromagnetism?
Here, I feel the authors are not entirely clear who the audience is supposed to be. At first, they seem to target people who need the difference between Einstein and Maxwell explained. The section is titled:“ Maxwell's equations and general relativity—what are these all about?“
Then when they reveal the missing link, the uninformed reader is presented with a logical progression that is obviously written towards somehow for whom the statement:“the Lagrangian of electrodynamics is just the Einstein-Hilbert action“ is self explanatory. You know, people who say, yes of course, if you say:“ keep the spacetime manifold Ricci-flat.“
Writing about science is hard
Turns out I could learn almost nothing from it, although I really tried: The first half of the book was basic stuff I already knew, but I could understand nothing of the second half, it passed so quickly from the elementary to the super-advanced. I ended up wondering who it was written for—I imagined everyone would have a similar experience, whatever their level—it's stuff you already know until suddenly it's stuff you can't understand, and no way of passing beyond. It covers so much ground so quickly, with no time for enough explanation—if you didn't already understand the current topic. Maybe that was just me! But it was extremely surprising putting so much (money,) time and effort into a book with rave reviews by a leading physicist, and learning virtually nothing.
That reminds me of Roger Penrose's 1100pp The Road to Reality: A Complete Guide to the Laws of the Universe, which I was very excited about reading when I bought it years ago. Lots of lovely diagrams. Turns out I could learn almost nothing from it, although I really tried: The first half of the book was basic stuff I already knew, but I could understand nothing of the second half, it passed so quickly from the elementary to the super-advanced. I ended up wondering who it was written for—I imagined everyone would have a similar experience, whatever their level—it's stuff you already know until suddenly it's stuff you can't understand, and no way of passing beyond."
This is nearly universally an answer to the request" tell me you don't understand something you think you understand without telling me that you don't understand something that you think you understand"
The ramp isn't steep. It's just that if you think you're on it but aren't, then the second floor looks like a wall
I did not see anything novel that would warrant further attention - did I miss something?
Another commenter https://news.ycombinator.com/item?id=27943428 talks what basically looks to me as an emergence of EM field from rotation - "to multiply each point of the universe by a different complex number of modulo 1" - ie. as an artefact emerging by changing the frame to the one where the system is rotating (ie. gets a spin). Kind of similar how magnetic field is just emergent artefact in the frame where charge is linearly moving.