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.
And at the risk of muddying the original point, it turns out that strictly speaking the neither the neutral Z boson nor the electromagnetic photon can be said to come from SU(2) or U(1). Instead, each field is a linear combination of some abstract fields (namely the neutral W0 and the weak hypercharge B bosons) from the unitary gauge induced by the compound symmetry SU(2)xU(1). This is because when both symmetries SU(2) and U(1) are present, there are different ways you can "mix" the two into the Lagrangian. The mixing that gives us the photon and the Z0 boson is known because of the experimental confirmation of these particles. This is what is meant when it is said that electromagnetism and weak neuclear forces are united in a higher-energy theory as a single "electroweak" force.
This is great, you perfectly bridged the gap between having been 25 once and vaguely remembering the math terms mentioned and bringing it back to reality. Really epic how this (at least to me) abstract and arcane math not only explains the behaviors of the subatomic particles, but even predicts the existence of more and their related forces.
The work of theoretical physicists always seemed like the other side of an ocean of math away, but thanks to this explanation it feels like I can at least make out a lighthouse in the distance.
> That is, unless you include an additional field at every point in spacetime that precisely cancels out the change induced by the gauge freedom.
Could you elaborate on this a bit? To a layperson this sounds like a hack. "Things get screwy when you screw with them, UNLESSSSS we add a magic thing that undoes our work". Well yeah.
It's just a mathematical tool of curiosity that we have found very useful.
Here's an analogy: You find a box, and you can't see inside it. You have no reason to think there's something inside it. But also, boxes have stuff in them sometimes. So, you shake the box, and hear something clinking around. Therefore, you infer there's something in the box.
Somebody next to you says "This sounds like a hack. There was a box and you had to go shake it until it started making sounds that it wasn't making before. UNLESSSSS we now magically have to agree that there's something in the box."
It's a perfectly reasonable question, and I'm just turning your words on you in good faith :)
To take the technical discussion a bit further, it's exactly this kind of reasoning that led to the discovery of the Higgs boson. Strictly speaking, it's impossible for gauge bosons (that's what the particles are called that show up when you add these locally-varying symmetries) to have nonzero mass.
The photon and gluons (from the SU(3) strong force) are massless, but the W and Z bosons are VERY massive.
This was a big problem with the Standard Model; the vector gauge bosons had every property expected from the gauge theory, except for this one point about their mass, which was experimentally incontrovertible.
That is, until Brout/Englert/Higgs came along.
They said "Yeah the vector bosons must be massless UNLESSSSSSSS you assume there's this magic additional field that couples to every particle's mass, in which case it perfectly cancels out all the problems and allows the W and Z bosons to be heavy".
It took 50 years but we found that particle eventually.
You're a really great writer on this topic. If you're not already, and you have the time, you should seek out ways to do this in a way that has more reach. Thank you!
You know I tend to agree with the previous poster, not that it's a hack, but that I've always felt its a bit backward reasoning. You say the physics should be invariant under curvature of the field, but it isn't unless you add another field to cancel it. But you might as well have said from the start that the field is curved by another field and we need to consider that in our derivatives that describe our local physics, making them covariant. The explanation that "it makes sense that the fields are locally gauge invariant" always seemed a bit constructed after the fact so to speak.
The argument isn't against physicists inventing new fields or interactions to fit data. The argument is about why you can motivate it as "something that has to be added out of pure logic" :)
I don't think it's backwards. We started out with this big sweeping and simple statement that (seems to) holds true for physical reality, but it doesn't account for everything. The statement allows for two realities, one where there is one single global phase, and another where each point has its own local phase.
The first option might be true, no real way to measure it and that's sort of it, no explanation for all the other stuff going on. The second option is a little more complex, it requires an extra construct to make it work. And apparently when we do the math and work out this construct, it exactly maps to things we can measure in reality, that were not explained by the other simpler option.
So it's not backwards because it's simply the first full match in a depth first search through the possible realities that follow from this wave function theory.
It makes a lot more sense if you have the historical context though. When this is taught the context is left out and then it feels more like mathemagics to me and probably others as well. Maybe there are good books that explain this from a historical point of view, while still teaching the theory, but they must be pretty rare.
My comment (the GG..GGP) was an (over)reaction to the posted article. The article presents the new approach like a very "natural" explanation, but there are already some other "natural" explanations.
In a Physics degree, the order is quite historical. Like one full course for the three first next items, and all the other together. I'm not sure if there is a book with all of them, you probably need 4 or 5 books.
1) Non-Quantum Non-Relativistic Electromagnetism
2) Quantum Non-Relativistic Electromagnetism
3) Non-Quantum Relativistic Electromagnetism
4) Quantum Relativistic Electromagnetism
5) By the way, you can interpret the Quantum Relativistic Electromagnetism as a U(1) symmetry. (my comment)
6) It looks like a good idea. Let's use other groups to explain other known forces: the weak and strong force. (The G...GP comment about SU(2) and SU(3).)
7) ???
[See note 1]
For some reason, popular science articles love to show something almost magical and prefer to present something like the "5)". It makes it easier to hide the math and use hand waving.
Also, Physicist working in physic particle also believe that "5)" and "6)" are the correct approach, and the other are just useful for teaching and for historical reasons. But to discover "7)" it's better to think about some weird new symmetry group [2].
For examples, a few years ago, it was popular to think the next step "7)" was using a new group SU(5) that combines SU(2) and SU(3). The problems is that the experiments gave different results than then new proposed theory, not too bad but like 1% off. I still remember my professor talking about how great was SU(5) and how the experiment disagree, and he looked heartbroken because he really liked SU(5).
[1] You should add some material about the historical discovery of the weak and strong forces between "5)" and "6)".
[2] Other's prefer superstrings for "7)", there are other approach, but all are weird.
>To a layperson this sounds like a hack. "Things get screwy when you screw with them, UNLESSSSS we add a magic thing that undoes our work". Well yeah.
What you describe as a "hack" is actually the empirical (look/probe and see what happens) nature of physics as a science.
It seems like a hack because there's no a priori theoritical reason to do it. But physics is not based on verifying empirically a set of a priori rules (who would give them?), but by building theories and rules by empirically looking at things at seeing what model fits, and if a changed model fits better - we then verify those empirically with more experiments.
And this is not "Things get screwy when you screw with them, UNLESSSSS we add a magic thing that undoes our work", but more like a reverse engineering session:
"Behavior X appears to be described by this formula with parameter p. What if we changed the parameter to -p? Hmm, the results would still be consistent with X, if only there was an additional factor v in the formula.
Would this (-p,v) combo buy us anything over our previous (p)?
Wow, yeah, v would then perfectly match the behavior we see for this other thing Y too. So (-p, v) seems to describe both X and Y, whereas before with p we could only describe X.
A really simple example is voltage. What does it even mean if one cable is on a potential of 5 V? It's always compared with the Ground voltage since the voltage is always a difference between 2 electric potentials. That means you could add a constant to each potential and nothing would change. So in this case not gauging would be quite hacky... (This example has nothing to do with the phase though, but just to illustrate. Almost always when you measure something, some gauging is at least implicitly involved.)
So it turns out this happens quite often that there is some kind of constant that can be divided out. In case of particle physics a whole framework has been developed out of it that has really close relations to Lie group theory. (The experimentally confirmed parallels are just astonishing with group generators and elements corresponding to interaction particles and the normal particles.)
But there is an important distinction between global and local symmetries. Global symmetries, when you apply the same change to the field at every point, are physically meaningful, not so local symmetries, when you apply [potentially] different changes at different points.
For example the laws of physics are time translation invariant, i.e. it does not matter what point in time you call t equals zero which essentially means that the equations do not contain time but only time differences so that you can add the same constant to all your times and nothing changes as the constant cancels out when calculating a difference between two times.
Its the same with voltage, where you put your reference potential does not matter but this is again a global symmetry and you have to use the same reference potential everywhere, you will obviously get nonsense if you use different reference potentials at different points.
Local symmetries on the other hand are kind of defects in the mathematics of physical theories, they are the expression of redundancies in the mathematical description. Say you want to describe the orientation - but not the strength - of the magnetic field on earth and for simplicity lets assume the earth is flat and the magnetic field parallel to the surface, then you could do this by associating a two dimensional vector with each point on earth that describes the tip of a compass needle placed at that point.
But there is a problem, there are longer and shorter compass needles but that is irrelevant for the orientation of the magnetic field, the length of the vector does not actually matter. You could multiply this vector field with a different constant at every point, i.e. independently change the length of all the compass needles and you would still describe the same magnetic field orientation across earth. What you do to fix this is to declare that all fields are physically equivalent if they only differ by a constant factor - which may depend on the point - at each point.
The other solution is to use a better mathematical representation without the redundancy, instead of compass needle tip vectors you use the bearing angle and take the compass needle length out of the equation to begin with. Problem solved. Now you can no longer change the field value, i.e. the angle, at every point independently and still describe the same physical situation. Also note that there is still a global symmetry, you can still change all the angles by the same constant, you are free to pick which direction you label with angle zero, which is again physically meaningful and expresses that space is isotropic, i.e. there is no preferred direction and the equation therefore do not depend on the direction but only on the angle between directions.
And you can do the same thing with the known physical laws, you can for example get rid of the U(1) symmetry - which should better be called a redundancy - in quantum electro dynamics. The price you have to pay is that the resulting equations lack some other properties often considered desirable, for example they are no longer obviously local.
Nitpicking: IIRC Adding 5V everywhere is like multiplying Ψ by expt(i 5V t cte), where t is the time and cte is a constant that may involve c, ℏ, e, and perhaps a number, but I'm too lazy to lookup.
Looking at my comment, it says "multiply each point of the universe by a different complex" it's actually a "event" like in relativity, i.e. (ct, x, y z). This is an easy case where the function you use to multiply does not depend on x, y, z, but only on t.
It turns out that the magic thing we have to add, exactly fits the observations we have of electromagnetism. That's an indication that we screw with the theory in the same way that nature does, and in the end that's the goal of physics: understand the way nature behaves.
You are excellent at explaining this stuff. You're bringing some clarity to things that typically sound like abstract gobbledygook to me. We need more people who can bridge that gap.
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
I may be starting to get it. The magic numbers we add to everything or multiply everything with really represents just a change in the viewpoint, origin of the observer. And because it should be possible to change the "location" of the observer (say the voltage we take to be 0 volts) and still get the same theory to hold up, we can discover that it can only hold up if we assume the existence of some new field. Something like this?
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.
While I sympathize with your unease about making time a privileged coordinate, even in conventional quantum mechanics an operator for time seems difficult. What would that operator measure? The time at which a given object "is"? The whole point of physics is to describe the dynamic nature of reality, parametrized by time.
Speaking of which, time(-of-arrival) measurements in quantum mechanics have recently attracted quite some interest: The classic Copenhagen formalism doesn't seem to give an answer here (or at least not a unique one – it depends on how you perform the calculation). Meanwhile, Bohmian mechanics does seem to make a precise prediction. It will be interesting to see what experiments will yield.
You just get into a twist of not being able to renormalize if you create a dependency chain like that. The same reason quantum gravity is such a problem - gravitons emit gravitons..
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.
They don't just become harder, they become open problems -- open problems with a million dollar bounty on them! There is no known non-perturbative quantization of the Yang-Mills theory.
They are still a trick because they are used to propagate a particle exactly where it needs to go in order to exert the force of the field. So the field is everywhere, but is pretty much invisible except for when virtual particles mediate it.. No efficient simulation on a computer could operate in such a manner. It's explanatory but not a constructive proof. I can't build an efficient simulation of our universe based on the virtual particle paradigm.
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.
> 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.
But they do:
> The strength of the present approach is simplicity, there
is no need for higher dimensions, torsion tensors, asymmetric metrics or the like.
(emphasis mine)
> 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.
Why? There aren't many ways to write down a symmetric 2-tensor starting with a vector field.
> It makes me think they're either repeating Kaluza and Klein's work, or aren't properly citing it when they should have.
They're doing neither. Sure, they might have mentioned Kaluza's work more explicitly (AFAIK Klein's contribution was the suggestion to compatify the 5th dimension) but I suppose 1) they assumed that readers are familiar with it and 2) they wanted to mention several approaches to marry GR and ED and Kaluza's approach was just one of them.
I have never been in academia and this is the first time it clicked to me that citing a paper is not just an act of mentioning it as a networking artefact, and should be critical to the substance. Thanks for the explanation.
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.
> they're strong together like they were generated by GPT-3 or something
I agree, the article is not very coherent. However, neither of the authors is an English native speaker, so maybe that is playing a role here?
OTOH, the website where the article is being hosted does look somewhat sketchy, so maybe you're right and the article was not written by the paper's authors but indeed strung together by an algorithm.
It should be "how lengths are determined in spacetime" which I assume is just a mundane english second language issue.
In the view of GR, all objects follow straight lines absent acceleration, and the force of gravity is actually a result of curvature of spacetime. That and the rest of your points that follow are more an issue of not being familiar with GR. I agree the article could have done a better job of elaborating these to a wider audience, but if you've read about GR a bit these concepts will be quite familiar.
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
> 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"
I have no idea what this means, sorry.
> 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'm not sure what this is meant to mean. Could you be less cryptic? Thanks.
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.
Maxwell's equations and general relativity—what are these all about?
Maxwell's equations are the key linear partial differential equations that describe classical electromagnetism. The equations relate the electromagnetic field to currents and charges. On the other hand, in general relativity, the Einstein field equation is a set of nonlinear partial differential equations describing how the metric of spacetime evolves, given some conditions, such as mass density in the spacetime. Both equations are ultimately of second order, if seen properly.
Therefore, we thought that perhaps we are talking about the same governing equation, which could describe both electromagnetism and gravitation. Indeed, it becomes clear that Maxwell's equations hide inside the Einstein field equations of general relativity. 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.
> it makes me think they are not being the most objective evaluators of reality.
Generally in physics and in maths researchers tend to spend time evaluating solutions that are symmetrical or otherwise elegant. I suppose that does make us biased but we’re searching for answers in a very large space of possible answers. Beaming towards elegant solutions seems like a reasonable heuristic.
Aesthetics, harmony, and simplicity are the guiding principles of mathematical conjecture. This piece is simply hypothesizing about a link while calling for further empirical research.
Aesthetics should have nothing to do with science. Aesthetics is the reason we thought the Earth was at the center of the universe and everything outside the orbit of the moon was made of perfect spheres. It's why the Soviet Union pushed Lamarckian biology instead of Darwinism.
There are copious amounts of examples showing how Nature is attracted to symmetry(a form of beauty). Why wouldn't we use this is evidence as a heuristic?
You just gave a non-aesthetic reason to explore symmetry. I'm not saying we should only look at theories that are not beautiful, but instead we should not use that to evaluate if a theory is worth exploring.
To scholastic thinking it was the heliocentric view that was hubris, since it didn't place the Earth at the lowest level of creation where it belonged.
Don't neglect the fact that aesthetic sense is evolved. To the degree that our perception has connection with reality we'll probably find spheres beautiful because they manifest an elemental mathematical relation that is ubiquitous in nature.
Copernican theory made worse predictions than Ptolemaic theory, but it was simpler. Both explained the same facts.
The acceptance of heliocentricity was an aesthetic judgement, one which favored simplicity, and predated the work on elliptical orbits which gave the Copernican theory, thusly modified, equivalent predictive power.
This is not true. Copernican theory allowed the existences of moons around other planets and explained the phases of Venus when seen through a telescope. The Copernican model allowed things that the Aristotlean model did not and those things exist in the universe. The Aesthetics of having an Earth centered Universe prevented these truths from being quickly and easily accepted.
Also in the Tycho Brahe system Earth is at the center of the solar system but it is equivalent to the Copernican one, you can just change the coordinates.
And that was a complete mess if a system when you start considering moons orbiting around planets orbiting around the sun orbiting around the Earth. Not to mention anything outside our solar system.
For one, it's going to produce a metric where all the diagonal elements are positive (or zero) - different from the -+++ or +--- signature of "normal" spacetime.
The paper's calculation reminds me of Kaluza-Klein theory, which uses a similar construction as part of extending the metric from four dimensions to five:
I was thinking about the signature issue as well. In flat space (i.e. Minkowski metric), this would imply a constant four-potential with an imaginary 0'th component, which I can not make sense of.
A gauge field is tensor-valued; what's wrong with that?
Although it does seems strange for other reasons. Primarily because it seems very unlikely that everyone else who developed this field wouldn't have considered the possibility and then discarded it.
Although a gauge field has multiple components, it transforms differently from tensors under a change of coordinates:
A -> O A O^{-1} - dO O^{-1} (O is the Jacobian matrix)
The second term is absent for tensors (such as the left side of their equation 4). It also vanishes on a flat spacetime where one only considers linear (Lorentz) coordinate transformations, but based on my cursory reading they don't seem to be making that assumption.
I'm not sure I'm following. In General Relativity, the 4-electromagnetic potential A^μ is simply a vector field on spacetime, so what's wrong with taking the (symmetrization of) the tensor product of A_μ with itself to obtain a symmetric 2-tensor? (Whether or not that 2-tensor satisfies the requirements for a semi-Riemannian metric is another question.)
Why is A_\mu a vector field on spacetime? In the standard treatment A is the (pullback to the base of the) connection 1-form of a connection on a principal U(1)-bundle on spacetime. Technically it's valued in the Lie algebra of U(1), but as that can be identified with i times the real numbers, we can ignore that here. Does the product A_\mu A_\nu happen to transform tensorially? Because as the parent pointed out, the transformation rule for A involves an extra term, so it's not obvious.
You're right – maybe I should have been more precise with my wording.
Let me address curt15's (and your) question in two ways:
####### The physicist's argument #######
In classic electrodynamics it doesn't make much sense to talk about a U(1) gauge symmetry (whether global or local) – because there's no electron field exhibiting such a symmetry in the first place. Gauge symmetries really only become important when talking about quantum mechanics, Dirac's equation and, more generally, coupling particle fields to force-carrying boson fields in a QFT. There it turns out that imposing local gauge invariance would guarantee you a way to accomplish the coupling while preserving the conservation of the Noether current associated with the global gauge symmetry.
But in classical electrodynamics, none of that is needed and the vector potential is simply a vector field on Minkowski space. In fact, the value of the vector field and the choice of gauge are not even important because there's no classic analogue of the Aharonov-Bohm effect.
Now pretty much the same applies to Einstein-Maxwell theory: There is no electron field and no U(1) gauge symmetry. It's all classical. Indeed, in my experience relativists just view the vector potential as a vector field on spacetime and ignore the QFT-inspired classical gauge theory stuff (principal bundles, associated vector bundles, etc.) altogether. You might disagree with this approach but given that no one has yet managed to write down any 4-dimensional, coupled quantum field theory in a mathematically coherent fashion (let alone on a curved background), I wouldn't say there's too much pressure to incorporate results from QED into GR.
Back to the paper: The authors basically start from the same perspective, i.e. the foundations of Special Relativity and classic electrodynamics where A was simply viewed as a vector field. They then propose an alternative to General Relativity and, in fact, electrodynamics(!) Like true physicists, they first worry about the functorial nature of their objects (what do they do & how do they relate to one another), not about the category the objects live in. If that means redefining[2] what A is in a mathematical sense, so be it. At the end of the day, experiments are what matters.
####### The mathematician's argument #######
Could it be that you and curt15 are thinking of the transformation behavior of A under local gauge transformations[0], not coordinate transformations? Because, unless I'm mistaken[1], the transformation of A under coordinate transformations is the same as for a vector fields, see definition 5.4.1 on p. 270 of [3]. The relevant portion reads:
Let p: P -> M be a principal G-bundle on the manifold M and A a connection 1-form on P, let s: U -> P be a local gauge of the principal bundle on an open subset U of M. Then we define the *local connection 1-form* (or *local gauge field*) A_s on U by
A_s := A ○ Ds = s* A
If we have a manifold chart on U and {∂_μ} (μ=1,…,n) are the local basis vector fields on U, we set
A_μ := A_s(∂_μ)
Now since the basis vector fields ∂_μ transform in the usual way and A_s is linear, the components A_μ should transform just like those of a section of the cotangent bundle T*M. Am I missing something?
I'm not too familiar with the physics side of things, so maybe I'm misunderstanding the notion of gauge symmetry, but even in the absence of matter I think there is a U(1) gauge symmetry present. The homogeneous Maxwell's equations are expressed purely in terms of the curvature F of the connection, if I remember correctly. So you might add a flat U(1)-connection to A without changing the equations of motion.
As for the math: the key point is that the metric is globally defined on the spacetime manifold M. I agree that the A_\mu transform as the coefficients of a differential form (A is a connection after all), but the notation elides the fact that the A_\mu are defined only on U. They depend, in particular, on the choice of local gauge s:U \to P. So the question about covariance (or globalization or coordinate-independence or whatever you want to call it) of both sides of the equation g_{\mu\nu}=A_\mu A\nu very much involves the question of local gauge transformations.
Either the principal bundle is assumed to be trivial, in which case there exists a global gauge and the connection A can be identified with a global 1-form on M (connections form an affine space modeled on such 1-forms; a gauge effectively converts this affine space to a vector space by choosing an origin), or we need to check that the right-hand side A_\mu A_\nu is indeed a symmetric two-tensor on M. The latter is not clear to me.
I admit I haven't looked at the paper carefully, and physicists typically don't approach things in such an explicitly mathematical way. So perhaps there's some (physical?) justification for why that equation typechecks. I don't quite see it though.
> but even in the absence of matter I think there is a U(1) gauge symmetry present
I don't think there is. The local U(1) gauge symmetry really comes from the (complex-valued) Dirac field and its coupling to the photon field (i.e. A). In classic electrodynamics you can add the 4-gradient of any function to the 4-potential A without changing the equations of motion, so the space of valid gauge transformations is infinite-dimensional. (Which is not that interesting – given that you can't measure the potential A –, so all those degrees of freedom are non-physical.)
> I agree that the A_\mu transform as the coefficients of a differential form (A is a connection after all), but the notation elides the fact that the A_\mu are defined only on U.
That's a very good point indeed! Though I think the authors simply interpreted A as a regular vector field on the manifold, meaning that it is defined everywhere. But following your train of thought for a moment: Could you solve this issue through a partition-of-unity argument? I.e. cover the manifold with neighborhoods where you have local gauges and then construct the metric locally as a finite sum of those A_{\mu,s} (s being the gauge).
The issue of a metric constructed this way not necessarily being a Lorentz metric (let alone non-degenerate) of course nonwithstanding. Then again, the authors didn't worry too much about this, either… :)
Electromagnetism is already understood to be a special case of the electroweak interaction, which is itself a component of the standard model. The paper mentions Maxwell's equations, but not these more general models.
So what? The very first step to unifying GR with quantum mechanics and the standard model might actually be to realize that part of the standard model can be embedded in GR (at least when EM is considered as a classical field theory). I don't think it's a deficiency of the paper that it doesn't present a solution to everything.
> In a way, spacetime itself is therefore the aether.
This somehow reminds me of C.S. Lewis’s “Out of the Silent Planet”, where the narrator says regarding the protagonist
“He wondered how he could ever have thought of planets, even on Earth, as islands of life and reality floating in a deadly void. Now, with a certainty which never after deserted him, he saw the planets - the 'earths' he called them in his thought - as mere holes or gaps in the living heaven - excluded and rejected wastes of heavy matter and murky air, formed not by addition to, but by subtraction from, the surrounding brightness.”
I love the space trilogy.
Out of the silent planet helped me think of what the “heavens” are.
I’d definitely recommend them, though I love thinking of t he symbolic nature of things.
There are some great comments here, incredibly enlightening.
Yet somehow, I still find myself on Wolfram's side, suspecting that the entire QM/GR formulation is going to turn out to be the wrong way to understand the universe and that something quite different (e.g. cellular automata) will eventually be seen as much better.
The situation seems quite analogous to the one with fluid mechanics: we can use the continuously valued models that involve concepts like rate, turbulence, friction, etc. and be happy that we can reason about the system even though we fundamentally do not know what these properties are and can reasonably doubt that they are real. Or we can use cellular automata models, which use discrete math and have no "properties" that we can reason about. The outcomes are broadly similar in terms of prediction, but the approaches are totally different.
I will not be alive in 300 years, but if I were to be, I'd be willing to wager right now that most of the QM/GR formalisms will have been replaced by something entirely different.
"John Wheeler, the famous physicist, put forward the idea that all of the material world is constructed from the geometry of the spacetime. Our research strongly supports this kind of natural philosophy. It means that the material world always corresponds to some geometric structures of spacetime."
This is also the Platonic-Pythagorean perspective, that the world is literally made of math.
Maybe something along the lines of regions of charged space time resist compression while charged and non charged regions more spontaneous compress? Attraction/repulsion?
I can’t follow the math but he seems to be talking about general relativity in empty space, and he seems to be talking about classical electromagnetism not quantized. So it doesn’t seem to be the holy grail of quantum general relativity, in any case.
I had a quick look at their paper. I haven't understood everything and looked into all steps in detail but I think what they doing is (roughly) the following:
Let g be the spacetime metric, and A be the electromagnetic 4-potential.
1. Suppose you could write the metric as g_{μν} = A_μ A_ν, i.e. the symmetric product of A with itself.
2. Conclude that the Einstein-Hilbert action is just the electromagnetic action plus a correction term A_μ ∇^μ ∇_ν A^ν = g(A, grad(div A)).
3. Assume that J^μ = ∇^μ ∇_ν A^ν = grad(div A).
4. The correction term from step 2 then becomes the usual electromagnetic coupling A_μ J^μ. As a consequence, the Einstein-Hilbert action for g is just the usual full (non-vacuum) action of electrodynamics on a background curved by g = Sym(A⊗A).
5. Consider the vacuum Einstein equations and, thus, a Ricci-flat spacetime. Show that this is equivalent to ∇² A^μ = J^μ which are the inhomogeneous Maxwell equations in Lorentz gauge. The fact that we're in a vacuum spacetime but still considering electromagnetism seems odd but I guess their idea is that if electromagnetism is a purely geometric property of spacetime, then the electromagnetic action (including any potential electric current) shouldn't appear on the right-hand side of Einstein's equations in the first place – because the Einstein equations are Maxwell's equations.
6. Identify the 4-current J^μ with terms involving the electromagnetic field tensor and the metric's Weyl curvature. (Meaning, once again, that J^μ can be non-trivial even though we're considering a vacuum/Ricci-flat spacetime.)
7. Identify the remaining (homogeneous) Maxwell equations with the first Bianchi identity for the Riemann tensor.
8. Impose the continuity equation ∇_μ J^μ = 0, i.e. assume conservation of charge.
9. Conclude from 3) and 8) that div(A) fulfills a homogeneous wave equation.
-----
Comments and observations:
- In step 5, I don't see how Maxwell's equations (18) are supposed to follow from equation (17). But it's late, maybe I'm just being blind.
- As other comments have already pointed out, step 1 seems unreasonable because the metric will no longer be of Lorentzian type (with determinant -1) but instead will be positive-semi-definite. (To see this, diagonalize the metric at a given point => g = (A_μ)² (dx^μ)².) In particular, the metric might even be degenerate(!) It seems section 2.1 in their paper is supposed to address the signature issue but from my POV it's insufficient.
- The paper basically claims that gravity is just the theory of a vector 4-potential. That doesn't seem right, given that much effort was spent in the past 100 years to find such a theory. AFAIK it's pretty much ruled out these days.
- Given step 5 and the fact that the EM field no longer seems to contribute to the field equations, I have even more doubts this theory could ever turn out to be true. There are lots of solutions to the Einstein-Maxwell equations and I'm sure some of them have been confirmed experimentally by now. (I'm thinking of black hole jets etc.)
- For instance, IIRC there's a paper showing that from Einstein-Maxwell's equations it follows that photons move along null geodesics (which in the beginning of GR was merely an axiom of the theory). I wonder what would happen to this result. Hypothetically, photons might no longer move along geodesics in this new gravito-electromagnetic theory but the theory might still reproduce gravitational lensing. I don't think that's very likely, though.
- More generally, I think their theory is even difficult to reconcile with classic electrodynamics in the first place. In the absence of strong gravitational and quantum effects, we know that Maxwell's equations describe ED very well. However, the equations ∇² A^μ = J^μ above no longer are the classic (linear!¹) vacuum Maxwell equations we know – they are now highly non-linear since the covariant derivative ∇ now also involves the vector potential A. To reobtain classic ED in flat space one would basically need to ensure that in every-day situations A is "constant enough" not to produce any significant curvature through g = Sym(A⊗A) but still dynamic enough to reproduce the classic wavey nature of light. This doesn't seem likely. Plugging any known (experimentally proven) solution to the Maxwell equations into the equations here should invalidate the theory.
No opinion on this paper but I'll note something related of interest:
You can see how special relativity is true by just taking Maxwell's equations seriously. They show the speed of light is the same in every reference frame.
I like the idea intuitively (the idea that infinite discrete photons are required to mediate continuous fields from a single electron over infinite distances never sat well with me), so are they claiming here that there is a relativity-version of Maxwell's Equations? Does it require an additional spatial dimension to account for charge, or does it operate it on the same spacetime as gravity? Regardless, if I'm understanding this nontechnical overview correctly, it's a large claim requiring a lot of work. Probably worth a Nobel Prize if it they actually pull it off.
There seems to be something tantalizing in the relation between the EM and gravity field. Whether this is an accurate description of that remains be seen.
The idea of combining electromagnetism into space time field isn't exactly new; Weyl's theory of the combined gravitational-electromagnetic field [0], proposed by Hermann Weyl, some 100 years ago, did just that.
Yes, and the paper the article is based on does mention Weyl:
> 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].
Gravity is extremely well described by general relativity. What we do lack is a quantum version of GR, but that does not change the fact that we understand gravity very well, at least in the sense of the word that physicists are used to.
> we understand gravity very well, at least in the sense of the word that physicists are used to
(emphasis mine)
As someone with a background in mathematical relativity, I would like to note that GR actually is not very well understood at all. Physicists seem to focus on the few simple solutions to Einstein's field equations that people have found through educated guessing, but there a ton of questions about the field equations that are open to this day.
wrote two very well cited articles [1,2] on this in the context of string theory. but this was just extending kaluza klein, where by adding one compact dimensions (with some assumptions) you get maxwell out of einstein for free. this result is from 1919, 102 years old.
i'm glad i can write all gravitation, electromagnetism, yang mills and string theory in two equations (1.6 in [2]]) but honestly i don't that's a breakthrough.
i might be wrong, yet it smells more like PR than important discovery.
btw you can as as well find solutions of GR that are dual to navier stokes equs.
What would the EM field of a photon look like if you moved along with the photon? Would the magnetic part disappear just like it disappears when you move along with a moving electron?
Basically, from the photon's point of view, all travel is the universe distorting until origin and destination are literally the same point. Photon's don't experience movement, the universe does an instant jig around them while they sit still.
I dream of faster than light travel by bending the space time fabric in “U” shape (like pinching a piece of paper) and allowing to travel across the two planes of reference.
folding the paper isnt enough. you also need to reform the paper to make the hole attach at both ends. ripping apart spacetime may not even be possible.
Sure, it would take an enormous amount of energy to do it though.
Oh yeah, and you'd also be annihilated as you were completely turned to energy as you tried to go through it of course. But you'd sure fire a hell of a lot of randomized high energy particles out the other side after the amount of time it would have taken light to get there.
Not my preferred kind of "travel", I'll just freeze myself and go the slow way or something.
This common desire for FTL should be an object lesson in how wishful thinking distorts objectivity. We see a constant stream of ideas that spring from simply not understanding the domain of a function. You can put a negative value into mass or energy. That doesn't mean it means anything.
There really is no plausible theory for FTL of any kind. Maybe there will be in the future. Personally I'd put everything I have on the speed of light being an absolute limit to causality.
Look at it this way: if FTL travel were possible we probably wouldn't exist. Whoever came first would probably colonize the Universe and sterilize it of competition. So there's that.
if FTL travel were possible we probably wouldn't exist. Whoever came first would probably colonize the Universe and sterilize it of competition
FTL doesn't necessarily mean infinite/instant travel. Also the scenario you propose could be part of the Great Filter, and we just haven't been culled yet. Or FTL civilizations tend to get so large they fracture & turn to in-fighting or encounter other resource bottlenecks that limit exponential expansion.
Or C is the law and going FTL spawns a cosmic traffic cop like the meatball head things in Rick & Morty.
Or FTL is simply impossible, but perhaps not constant and various factors impact the local C
Here's about the same idea with formulas: http://estfound.org/quantum.htm. TL;DR if we assume that the ds2 invariant oscillates a bit, and apply the lorentz transforms, we'll get the stationary Schrodinger equation. I can't judge the math or physical soundness of the approach, but it looks legit.
The idea that strong electromagnetic fields affect the local curvature of spacetime is nothing short of revolutionary. Imagine the possibilities of that! This may be the beginning of the road to a functional warp drive at last.
Controlled experiments are very rare if you are talking about gravity, since the force is so weak. Observational experiments (astronomy) is where most of the evidence comes from.
The most obvious inclusion of it for me is the radiative (also known as the photon) component of the matter density in Lambda CDM models (that is, they need to account for the proportion of the energy density of the universe which is related to electromagnetic fields to rule it out as dark matter).
I'm not sure what you're looking for. EM fields so strong that they affect spacetime noticeably?
We haven't observed any Reissner-Nordstrom/Kerr-Newman black holes iirc. That said, _anything_ with stress-energy-momentum is held to affect spacetime curvature in GR.
I think there are no experiments in the lab or a direct measurement of this. Anyway, if the light is blended during an eclipse, the that light should have accelerated the Sun just a tiny tiny ... tiny tiny bit in the opposite direction.
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