So, this is a really cool concept and I look forward to the determination if it is true or testable.
I find the "double copy of other forces" verbiage to be difficult to follow. Walking through a formula example would be helpful, and formaluae exist to communicate exactly this kind of clumpy-wumpy-lumpy-timey-wimey awkwardness language clods through in its quest to communicate mathematical structures.
(Passing comment from a phone, so forgive the brevity.)
The key predictions one typically calculates using quantum field theory are scattering amplitudes. Let’s consider both gravity and one of the other forces in the “weak”/perturbative limit — flat space time and force carriers as (quasi)particles Eg: photons, gluons, etc. Now let’s compare the algebraic expressions for the scattering amplitude in both cases (final answer after pages of calculations).
For gluons it turns out there is one piece due to how the gluons are moving when they collide (kinematic piece), multiplied by another piece for the charge they carry (aka color); surprisingly the two pieces have a somewhat similar form if you squint (called “color kinematics duality”). Also gluons are spin-1.
Now, gravitons don’t carry charge, but they’re spin-2. If you look at the algebraic expression for the amplitude of scattering gravitons (after a much more tedious calculation) — lo and behold — it looks like it just has kinematic-like piece multiplied twice! (and no color piece.)
This is what is commonly referred to as “double copy” (of kinematic term) or “gravity = gauge (force) squared”.
This is one of the seminal papers; it’s very short, and has very few equations (but they’re written in a very abstract form) — feel free to stare at them if you like: https://arxiv.org/abs/1004.0476
This is my complaint about most of what I read about advanced physics. I have enough understanding of math and basic physics that it seems within reach for me to follow an equation-driven explanation, but the papers are a bit too dense for me. And I suppose I'm not interested enough to invest the time to truly understand all of the notation.
If we find out we are living in a simulation it would be rather arbitrary to have a force that does not unify with the others. Consider buggy game physics and trying to harmoniously explain how those forces work together without knowledge of the fact it is a simulation with global variables, nodes, data corruption events ect
We only leave in a simulation at the first level, but the thing running the simulation live in a world with rules too and they must influence the shape of the simulator.
Saying God created the world or the universe is a simulation is as dissatisfying a response as saying humans were made on Earth. Sure why not but what made it, did it start, will it end, how does it work at the most fundamental level? How does God's processing of information actually works ? That s what we must understand, up to the end.
This probably isn't the right place for this question. But the right kind of people will be reading this thread so I will ask it.
In college physics my teacher insisted that, despite gravity being popularly referred to as a force, it is not a force. Weight is indeed a force, but gravity is more like a field. I understood it like this: Say you have a point mass in an isolated system. There is certainly gravity all around that mass, but there are no forces anywhere in the system. Not until another mass is introduced into the system do you have any forces. It is apparent from the formula for force since then you have that new mass times the acceleration of gravity.
Or is this just being pedantic and does it even matter?
Nope, that's not what a physicist means when they say gravity isn't a force. What is meant is that apparent gravitational acceleration can be understood as a consequence of Newton's first instead of his second law.
According to Newton's first law, a body on its own (ie with no net external forces acting) will continue to move uniformly in a straight line.
Now, drag a marker uniformly and in a straight line (from your perspective) across a spinning disc. It will trace out a curved line, meaning an observer sitting on the disc will conclude that a force must have been present as the line would have been straight otherwise. We call this particular apparent force the Coriolis force, one of the pseudo-forces (aka fictitious forces or inertial forces) present in rotating reference frames. Being accelerated by such a pseudo-force won't register on an accelerometer, and the force vanishes if we analyze the motion from an inertial reference frame.
According to General Relativity, gravity is like that, a pseudo-force, except that there's generally no frame that can make gravitational (pseudo-)forces vanish in an extended region.
Taking a differential-geometric perspective, we note that there's no inherent notion of "continuing on in the same direction" on arbitrary manifolds. We need additional structure such as a covariant derivative, which gives us a notion of velocity change along a trajectory. Gravity hooks into that, with bodies in free-fall moving in 'straight lines' according to the Levi-Civita connection of spacetime.
Others have answered your question rather well. Let me offer a perspective.
I believe it was Feynman who said that theoretical physicists have a very simple goal: they just wants to predict the future. Now this might be impossible in full generality, but in controlled circumstances (which we usually call "experiments") they can often do a pretty good job of predicting the outcome.
As far as we know, predicting the future requires mathematics which is therefore the physicists' main tool. In doing so it is practical to give a name, like 'force' or 'geodesic motion' or 'particle' or 'wave', to certain mathematical concepts. But in my view one should not get too hung up on the precise meaning of any of those words, simply because it is not productive if the mathematics is already clear enough.
In fact, I think this is the most common misconception for people with a passing interest in physics. (See also discussions elsewhere on this page...) So allow me to stress this: these words really mean very little without the equations.
Of course, mine is just a physicist's perspective. I imagine your question would be the bread and butter for a philosopher.
Seems needlessly pedantic to me, since by that definition electromagnetism isn't a force either -- it's not possible to have a force on a charged object without there being another object that creates the field the first object is interacting with (and vice versa). In fact, Newton's third law kind of implies that it's impossible to have any force in isolation. The same formula argument would apply to Coulomb's law.
Now, is it fair to point out that you can model these forces as fields, and that such a model is very useful? Yeah. But it's silly to argue that something is or is not a "force" but is instead a "field" -- these are mathematical constructs used in the models we use for physics. I mean, it's not really accurate to say that "forces" and "fields" exist in the first place (in the sense that the mathematical models themselves are a real thing that exist in the world -- they are simply models). And in the end it definitely doesn't matter, neither the maths nor the real world cares whether you personally consider gravity a force or not.
(I expect this is also the case for the strong and weak forces, but I haven't done post-grad physics.)
EM isn’t a force. EM flux is a force. The pedantry is important because it tells you which formulae/units are compatible with one-another.
Weight (~gravitational force), or EM flux (~electromotive force), being forces, can be directly translated into impulse in a dynamic system—reduced to an instantaneous acceleration upon a mass, and thus into the fundamental units of meters, seconds, and grams/mols.
Mathematically all interactions can be described as fields. Where gravity differs from other interactions/forces is that it lacks, according to standard model but hypothesized to exist, a carrier (boson). Instead gravity is described by general relativity as the result of curved spacetime.
Edit: This is what article is about and how double copy helps with this. The previous is described in the article's second section.
How does it being a consequence of curved spacetime make it not a force? When we learn the more fundamental origins behind the other forces, will they also cease to be forces? It's not helpful, IMO.
IANAP but wanted to say this - Same argument could be made for EM force. There is electric field around a charge but only when you place another charge the two charges attract or repel as per electromagnetic force. That way gravity and EM seem to be similar. But gravity does seem to be different as it can be thought of as not a force (in agreement with your physics teacher). It curves space and time and objects just move along the geodesics (straight lines on curved surfaces). So gravity gives rise to space time geometry. Once that happens, you can stop thinking about gravity as a force. Worth emphasizing again - IANAP.
See, that makes sense. I've heard it said before that gravity is not a force, and my thoughts were just that it obviously is a force. And of course here we are, cutting through the pedantry to learn that they were in fact not communicating anything actually meaningful with the phrase. You could simply say that potential energy and kinetic energy are different and it would be just as meaningful as what people mean when they say gravity is not a force. It's misleading. A single particle creates a gravitational potential that exerts nothing on its own. Okay. I say this as someone with a BS in Physics.
Gravity is what we call it when objects interact via their masses. Other fundamental interactions are electromagnetism, the weak or the strong interaction (often also called "weak (nuclear) force", "strong (nuclear) force").
In the static case (i.e. time-independent), there is a (let's e.g. focus on electric / gravitational) potential. It's spatial change ("gradient" / "derivative in space") is its electric / gravitational field which is also the ratio of the force on an infinitesimally small charge/mass at the given distance to the charge/mass (it has to be negligibly small so that it does not influence the field).
So there are few different concepts that usually all get mixed up and lead to some confusion. It hope the overview helps a bit.
If you want to read more, look up the italic terms in Wikipedia.
Yes, gravity is "more like a field". But what kind of field? A force field.
The right kind of object in the right kind of force field experiences a force.
A mass experiences a force in a gravitational field; a charge experiences a force in an electric field.
A point mass is difficult to reason about because a point mass has infinite density, and a gravitational field that gets arbitrarily large the closer that the point is approached.
Non-point masses, like uniform spheres, have a gravitational field that increases up to their surface, and then decreases. A particle at the exact centre of a uniformly dense field experiences no net force.
Also, a particle floating inside a hollow sphere of uniform thickness experiences no net force; the field sums to zero everywhere inside. This is why the field gets weaker toward the centre of a solid sphere. Every point inside a solid sphere can be regarded as simultaneously being inside a hollow sphere (experiencing no net force from that), and being just on the surface of a smaller interior sphere: that part of the sphere which is deeper than the particle.
I say that 'weight is the force due to gravity' - that weight is the force and gravity is the abstract concept (in college-level physics terms).
Same for 'EM force' and 'electromagnetism'
Conflating the two is a type of 'metonym' that is common in every-day and journalistic speech as here. If it's obvious what aspect you mean, then it doesn't really matter.
Whether it is pedantic depends on your goals and perspective, but if you are interested in a history and philosophical development of Force that culminates in the observation that gravitational forces are fictitious, I can heartily recommend "Concepts of Force" by Max Jammer.
Despite the fact we know that GR is broken and can't be a description of reality, even educated physicists seem to persist in speaking as if it is absolutely true, even though they know better.
See also all the talk about "what happens in a black hole", which should almost always be qualified with "in General Relativity". When we have a unified theory a lot of the crazy stuff, like rotating singularities leading to "other universes", will probably disappear.
Is gravity going to be a force in the Unified Theory? Probably. I believe it is in our current best candidates. But they aren't right either yet, so I don't know.
Edit: Some modders seem to be confused and are probably reading this as some sort of criticism of science itself or something. It is not. It is literally true. It is not a force in GR, but that doesn't make it "not a force", because GR is known to be false. It is an exceedingly good approximation to something, but we know it is not the underlying truth, which is why we are still seeking out a Unified Theory... precisely because GR isn't it. Thus, I find confident proclamations about whether or not gravity is or is not a force to be premature. We don't know. The thing it is definitely not a force in is known to be not the truth.
So to the extent you are confused about why it isn't a force... well, stay tuned, because this whole area is ripe for reconsideration in the next few decades. There are also theories that have attempted to rewrite all of physics as "not a force"s like gravity too, turning all forces into geometry. While these are not currently favored, IIRC these are the orginal physics theories that added rolled-up dimensions. String theory built on those.
They are, in the context of F=ma where m is the inertial mass and an object is deviating from a spacetime geodesic, which explains why we feel a force from gravity as we sit here.
I thought it was an abstraction trick. Just like they derive the electric field of a charge from abstracting away the second charge from the classic electric force equation.
You can have a gravitational field with waves in it without any charges at all. Place a single test particle in this field and it be affected by the field
> Most theorists assume that gravity actually pushes us around through particles
Is this true, and if so, why? The interpretation of gravity as something that warps spacetime very elegantly yields its “gravitational force” via its effect on the action integral, and is easily understood using a path integral style framework. It seems like a particle-based framework would necessarily be a lot more complicated, although maybe it’s necessary for some reason I don’t know.
So you're right that (low-energy) gravitational physics is understood because you know how to write down the action. The question is whether the sum over paths in the path integral should also include a sum over metrics. That sum over metrics is equivalent to saying that gravitons exist (in the same way that the sum over electromagnetic potentials is equivalent to saying that photons exist).
Now if you want to include gravitational effects and do it in a consistent way, you have to sum over metrics, meaning you have to have gravitons. That's because trying to treat gravity like it's classical but treating everything else like it's quantum mechanical is inconsistent. For example, classical gravity could tell you which slit an individual electron passed through in a double slit experiment, if you measured the gravitational field accurately enough--you could say definitively that it came through one slit or the other by measuring which way the gravitational field that it generated is pointing. This would destroy the interference pattern and you wouldn't be able to conduct the double-slit experiment at all.
> the path integral should also include a sum over metrics
Understood, thanks.
> That sum over metrics is equivalent to saying that gravitons exist (in the same way that the sum over electromagnetic potentials is equivalent to saying that photons exist).
Could you explain this? I'm not making the connection where "you should sum over this potential" implies "there exists a corresponding particle for the potential". If that implication is true, that feels like a pretty important generalizable principle that someone should have told me in undergrad...
>It seems like a particle-based framework would necessarily be a lot more complicated.
That’s true for the other forces as well! And yet after very careful study we know the electromagnetic field IS quantized, particles of light are photons, and to get them to do the right thing (exhibit interference, for example) you need a quantum mechanical framework.
Classically that’s true, but if we want consistency with quantum mechanics, the only starting point we know is to quantize the force carrying fields (gravitons, just like photos and gluons), but then it turns out we can’t get far from the starting point.
Why do we want to quantize gravity? Imagine you are doing a scattering experiment. To predict the full results consistently (in principle), you would need to include the gravitational forces between the scattering particles. This would be particularly important in early universe cosmology where you might have lots of heavy stuff zipping around at high speed! The classical GR picture is not too helpful in these situations.
> the only starting point we know is to quantize the force carrying fields
Sure, but what if there is no field for GR? The way I understand gravity to work (warping spacetime in such a way that proper time gets "crunched" towards mass, retarding the system's action, shifting the variationally stationary path towards the mass) does not require a force carrying field (as far as I can tell).
Everything else (that we know about) in the universe is quantised. (I don't know whether experiments have shown gravity to be quantised yet.) If something's quantised, that means there's a smallest possible unit of it (a “particle”).
Someone needs to do a better visual explanation of these particle interactions. If you can describe it mathematically then surely you can create a computer simulation.
What you have linked is just bog-standard entanglement simulations. There are a dozen free software apps to do that. It's basically just linear matrix algebra with complex numbers.
What the parent meant was real particle simulation, for example simulating the collision between two electrons or computing the dipole moment of a muon, from fundamental standard model constants. It requires numerically solving 12 dimensional PDE's. That's much more complicated than entanglement simulations.
People can and do make computer simulations of particle interactions? It's just that 12 dimensional PDE's are not exactly fast, but we can e.g. use them to compute the dipole moment of fundamental particles like muons.
Think of it like knowing the rules, but the rules not being efficient to compute with.
3D rendering was unbelievably slow for a long time too, the good thing about computers is they have storage so you can render 1 frame an hour if you want and just record it and play it back later.
Exactly my thought while reading the prose. A picture is worth a thousand words, a formula a thousand pictures. Yet having a bit of the three kinds is often needed to easily comprehend the concept for those who are neither particularly visual, logical, or patient.
Particle interactions are visualized with Feynman diagrams which can be used for mathematical calculations (ref: arXiv:1602.04182). Do you mean something better than them?
I've looked into why there's a total vacuum of numerical simulation, and the reason is simply snobbery. There's a philosophy that numerical methods are what mere engineers do, and not as intellectually pure as symbolic solutions.
You regularly hear comments like: "Such and such cannot be solved", what is often meant is: "It can only be solved numerically, but not with closed form algebraic expression."
People that say things like the former statement have excluded numerical solutions as valid in their mind. Such solutions may as well not exist, as far as they're concerned.
I see this attitude everywhere in theoretical physics.
The other issue is that because of the seventeen layers of assumptions and abstractions, most physicists are now at the point where they're not really making theories about physics, but instead they're debating the properties of the abstractions themselves. It's like kids trading basketball cards and saying one player is better than the other because his card is printed better.
This can all be boiled down to an acid test: Can you render your equations? As in, full 3D numerical simulation with an image as an output? Not a graph, not a scalar value, but a picture?
For simple (non-diffracting) optics? Yes! That's literally every 3D computer renderer!
For classical electromagnetics the answer is: yes.
For plasma physics the answer is: yes.
Even for special and general relativity, the answer is: yes.
For QED? Err... maybe? I've seen some toy examples in 2D, and I think I've seen a 3D example once. In principle, it's doable.
For anything else? Nothing. Or at any rate, I've seen nothing despite years of searching.
E.g.: Can you show me any "rendering" that extends a QED simulation with the weak interaction?
Can you find any animated examples of any particle interaction? E.g.: a free electron being captured by a proton, or an electron changing orbitals?
Again: Images or animations please. Not graphs or scalars. Everyone I ever challenge gets confused and links me to a paper with a histogram in it. That's not what I mean!
Well, there's Feynman diagrams. The problem is that there's a combinatorial explosion that severely limits certain simulations. Apparently this double-copy procedure can be used to cut down on the combinatorics, which is why physicists are excited about it.
Anybody here know if this double copy technique is related to the cobordism property found in Donaldson's Theory [1]. From wiki:
> Donaldson was able to show that in specific circumstances (when the intersection form is definite) the moduli space of ASD instantons on a smooth, compact, oriented, simply-connected four-manifold X gives a cobordism between a copy of the manifold itself, and a disjoint union of copies of the complex projective plane CP^2.
I imagine a very very slow moving rock in space - going at 1 m/s (relative to earth) in a straight line, the earths mass causes spacetime to bend making the rock head towards earth, but then the rock starts to accelerate
the bit I don't understand is why does the rock accelerate towards mass? Why does the bending of spacetime make it not carry on at 1 m/s towards earth
and since this rock has increased its speed due to accelation, where has this extra energy come from?
I really have no business answering this, but in the spirit of Cunningham's law I'm going to try to give an answer how I think of it. Would like some feedback and some guidance. This is purely a intuitive answer and not at all an academic one.
As we know from relativity and time dilation, as our GPS satellites need to be resynchronized as they move fast and at a lesser mass level. The center of the Earth is very heavy and is therefore going through time slower than the rock or surface objects. Gravity doesn't really exist. Gravity is merely the side-effect of heavy-mass objects going through time slower than lighter objects. This is what is meant when it is said that spacetime is curved.
So back to your question, where does the extra energy come from to accelerate the rock towards the Earth? An easy way to think of it, expanding on E=mc^2, Et=mc^2, where t is time. As the ball is now falling further and further into the Earth's gravity well, it is now going through time slower and slower. With t going slower, E must increase to balance the equation, which speeds it up.
thanks, so the rock that was heading towards earth at 1 m/s will technically not accelerate - with in its own reference point, but the rock will accelerate to the earth (from the earths reference point)
slight change of question, if the rock was heading directly in a straight line towards earth at 1 m/s, as the rock nears the earth it will accelerate (from the earths perpective) where has the extra energy come from? before it was heading at 1 m/s, but as it hits earth it will be travelling much faster
I’d like to learn more about this symmetry. Does anyone recommend a good article (or paper) about this?
> Researchers note that electromagnetism, the weak force and the strong force each follow directly from a specific kind of symmetry — a change that doesn’t change anything overall (the way rotating a square by 90 degrees gives us back the same square).
I'm _pretty_ sure that this is referring to gauge symmetry, so that's the term to search for.
I dunno of a good article as an introduction. As a grad student, I found Terry Tao's explanation [1] rather helpful, but of course it has a strongly mathematical flavor.
Thanks! It sounds like the next step is to look for curvature transformations associated with terms used for each of those three. (If someone knows more, always open to hear that too.)
> “Gauge theory” is a term which has connotations of being a fearsomely complicated part of mathematics – for instance, playing an important role in quantum field theory, general relativity, geometric PDE, and so forth. But the underlying concept is really quite simple:
Then goes on to write an incomprehensible novella length explanation.
I like Tao, but this is a problem in 'pure' maths. I feel the issue is exacerbated by the fact that if you can follow along with Terry then you likely will be unable to recognise the issue.
A good counter point is this series by Timothy Gowers developing a proof of "Pingala's Determinant".
When Gowers finds the proof he states:
> Since this clearly has determinant 1 and this clearly has determinant 1, so does their products, ie. Pascal's[sic] determinant is 1. Could have done that, but that would have been uh, well depends on what you find interesting, but that would have been really sort of rabbit out of the hat, look what a billiant clever mathematician I am. I can just sort of produce this fabulous identity out of nowhere and it's got a nice simple proof that also came out of nowhere. What I want to emphasize is these sort of proofs don't come out of nowhere.
The series is great and will show anyone outside the field of pure maths that even pure mathematicians use numerical reasoning while trying to reason about a subject.
"If +1, -1, and √-1 had been called direct, inverse and lateral units, instead of positive, negative, and imaginary (or impossible) units, such an obscurity would have been out of the question."
- Gauss (translated), a couple hundred years ago.
Of all the things to rename, this may be at the top of my list. I think some kids get lost in the abstraction specifically because the name "imaginary" isnt helpful in understanding the underlying concept.
Readit News
I find the "double copy of other forces" verbiage to be difficult to follow. Walking through a formula example would be helpful, and formaluae exist to communicate exactly this kind of clumpy-wumpy-lumpy-timey-wimey awkwardness language clods through in its quest to communicate mathematical structures.
The key predictions one typically calculates using quantum field theory are scattering amplitudes. Let’s consider both gravity and one of the other forces in the “weak”/perturbative limit — flat space time and force carriers as (quasi)particles Eg: photons, gluons, etc. Now let’s compare the algebraic expressions for the scattering amplitude in both cases (final answer after pages of calculations).
For gluons it turns out there is one piece due to how the gluons are moving when they collide (kinematic piece), multiplied by another piece for the charge they carry (aka color); surprisingly the two pieces have a somewhat similar form if you squint (called “color kinematics duality”). Also gluons are spin-1.
Now, gravitons don’t carry charge, but they’re spin-2. If you look at the algebraic expression for the amplitude of scattering gravitons (after a much more tedious calculation) — lo and behold — it looks like it just has kinematic-like piece multiplied twice! (and no color piece.)
This is what is commonly referred to as “double copy” (of kinematic term) or “gravity = gauge (force) squared”.
This is one of the seminal papers; it’s very short, and has very few equations (but they’re written in a very abstract form) — feel free to stare at them if you like: https://arxiv.org/abs/1004.0476
no wonder no one can follow any of this. they intentionally obfuscate everything.
I looked for a better entry into the subject and found this:
https://arxiv.org/abs/1810.08183
And a longer review article:
https://arxiv.org/abs/2003.12528
https://arxiv.org/abs/2103.16441
Saying God created the world or the universe is a simulation is as dissatisfying a response as saying humans were made on Earth. Sure why not but what made it, did it start, will it end, how does it work at the most fundamental level? How does God's processing of information actually works ? That s what we must understand, up to the end.
Dead Comment
Here's an old one for example that explains what they are doing at Fermi wit the G-2 machine:
https://www.youtube.com/watch?v=O4Ko7NW2yQo
And just check the science sites.
In college physics my teacher insisted that, despite gravity being popularly referred to as a force, it is not a force. Weight is indeed a force, but gravity is more like a field. I understood it like this: Say you have a point mass in an isolated system. There is certainly gravity all around that mass, but there are no forces anywhere in the system. Not until another mass is introduced into the system do you have any forces. It is apparent from the formula for force since then you have that new mass times the acceleration of gravity.
Or is this just being pedantic and does it even matter?
According to Newton's first law, a body on its own (ie with no net external forces acting) will continue to move uniformly in a straight line.
Now, drag a marker uniformly and in a straight line (from your perspective) across a spinning disc. It will trace out a curved line, meaning an observer sitting on the disc will conclude that a force must have been present as the line would have been straight otherwise. We call this particular apparent force the Coriolis force, one of the pseudo-forces (aka fictitious forces or inertial forces) present in rotating reference frames. Being accelerated by such a pseudo-force won't register on an accelerometer, and the force vanishes if we analyze the motion from an inertial reference frame.
According to General Relativity, gravity is like that, a pseudo-force, except that there's generally no frame that can make gravitational (pseudo-)forces vanish in an extended region.
Taking a differential-geometric perspective, we note that there's no inherent notion of "continuing on in the same direction" on arbitrary manifolds. We need additional structure such as a covariant derivative, which gives us a notion of velocity change along a trajectory. Gravity hooks into that, with bodies in free-fall moving in 'straight lines' according to the Levi-Civita connection of spacetime.
force = vector under specific coordinate system with physical source
isn't a force = vector + properties in specific coordinate system produce some kind of force-like phenomenon
Just checked the accelerometer on my phone. It reads around 9.8m/s/s pointing downwards.
I believe it was Feynman who said that theoretical physicists have a very simple goal: they just wants to predict the future. Now this might be impossible in full generality, but in controlled circumstances (which we usually call "experiments") they can often do a pretty good job of predicting the outcome.
As far as we know, predicting the future requires mathematics which is therefore the physicists' main tool. In doing so it is practical to give a name, like 'force' or 'geodesic motion' or 'particle' or 'wave', to certain mathematical concepts. But in my view one should not get too hung up on the precise meaning of any of those words, simply because it is not productive if the mathematics is already clear enough.
In fact, I think this is the most common misconception for people with a passing interest in physics. (See also discussions elsewhere on this page...) So allow me to stress this: these words really mean very little without the equations.
Of course, mine is just a physicist's perspective. I imagine your question would be the bread and butter for a philosopher.
Deleted Comment
Now, is it fair to point out that you can model these forces as fields, and that such a model is very useful? Yeah. But it's silly to argue that something is or is not a "force" but is instead a "field" -- these are mathematical constructs used in the models we use for physics. I mean, it's not really accurate to say that "forces" and "fields" exist in the first place (in the sense that the mathematical models themselves are a real thing that exist in the world -- they are simply models). And in the end it definitely doesn't matter, neither the maths nor the real world cares whether you personally consider gravity a force or not.
(I expect this is also the case for the strong and weak forces, but I haven't done post-grad physics.)
Weight (~gravitational force), or EM flux (~electromotive force), being forces, can be directly translated into impulse in a dynamic system—reduced to an instantaneous acceleration upon a mass, and thus into the fundamental units of meters, seconds, and grams/mols.
Edit: This is what article is about and how double copy helps with this. The previous is described in the article's second section.
Is there any other way a field can be described? What's the physical reality of a field?
Thank you for your explanation.
Small nit - I think it is actually called electrostatic force, at least when we are talking about charges at rest.
https://youtu.be/XRr1kaXKBsU
In the static case (i.e. time-independent), there is a (let's e.g. focus on electric / gravitational) potential. It's spatial change ("gradient" / "derivative in space") is its electric / gravitational field which is also the ratio of the force on an infinitesimally small charge/mass at the given distance to the charge/mass (it has to be negligibly small so that it does not influence the field).
So there are few different concepts that usually all get mixed up and lead to some confusion. It hope the overview helps a bit.
If you want to read more, look up the italic terms in Wikipedia.
The right kind of object in the right kind of force field experiences a force.
A mass experiences a force in a gravitational field; a charge experiences a force in an electric field.
A point mass is difficult to reason about because a point mass has infinite density, and a gravitational field that gets arbitrarily large the closer that the point is approached.
Non-point masses, like uniform spheres, have a gravitational field that increases up to their surface, and then decreases. A particle at the exact centre of a uniformly dense field experiences no net force.
Also, a particle floating inside a hollow sphere of uniform thickness experiences no net force; the field sums to zero everywhere inside. This is why the field gets weaker toward the centre of a solid sphere. Every point inside a solid sphere can be regarded as simultaneously being inside a hollow sphere (experiencing no net force from that), and being just on the surface of a smaller interior sphere: that part of the sphere which is deeper than the particle.
Same for 'EM force' and 'electromagnetism'
Conflating the two is a type of 'metonym' that is common in every-day and journalistic speech as here. If it's obvious what aspect you mean, then it doesn't really matter.
Despite the fact we know that GR is broken and can't be a description of reality, even educated physicists seem to persist in speaking as if it is absolutely true, even though they know better.
See also all the talk about "what happens in a black hole", which should almost always be qualified with "in General Relativity". When we have a unified theory a lot of the crazy stuff, like rotating singularities leading to "other universes", will probably disappear.
Is gravity going to be a force in the Unified Theory? Probably. I believe it is in our current best candidates. But they aren't right either yet, so I don't know.
Edit: Some modders seem to be confused and are probably reading this as some sort of criticism of science itself or something. It is not. It is literally true. It is not a force in GR, but that doesn't make it "not a force", because GR is known to be false. It is an exceedingly good approximation to something, but we know it is not the underlying truth, which is why we are still seeking out a Unified Theory... precisely because GR isn't it. Thus, I find confident proclamations about whether or not gravity is or is not a force to be premature. We don't know. The thing it is definitely not a force in is known to be not the truth.
So to the extent you are confused about why it isn't a force... well, stay tuned, because this whole area is ripe for reconsideration in the next few decades. There are also theories that have attempted to rewrite all of physics as "not a force"s like gravity too, turning all forces into geometry. While these are not currently favored, IIRC these are the orginal physics theories that added rolled-up dimensions. String theory built on those.
In an Einsteinian context, forces are not even discussed.
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[1] https://www.youtube.com/embed/XRr1kaXKBsU
Is this true, and if so, why? The interpretation of gravity as something that warps spacetime very elegantly yields its “gravitational force” via its effect on the action integral, and is easily understood using a path integral style framework. It seems like a particle-based framework would necessarily be a lot more complicated, although maybe it’s necessary for some reason I don’t know.
Now if you want to include gravitational effects and do it in a consistent way, you have to sum over metrics, meaning you have to have gravitons. That's because trying to treat gravity like it's classical but treating everything else like it's quantum mechanical is inconsistent. For example, classical gravity could tell you which slit an individual electron passed through in a double slit experiment, if you measured the gravitational field accurately enough--you could say definitively that it came through one slit or the other by measuring which way the gravitational field that it generated is pointing. This would destroy the interference pattern and you wouldn't be able to conduct the double-slit experiment at all.
> the path integral should also include a sum over metrics
Understood, thanks.
> That sum over metrics is equivalent to saying that gravitons exist (in the same way that the sum over electromagnetic potentials is equivalent to saying that photons exist).
Could you explain this? I'm not making the connection where "you should sum over this potential" implies "there exists a corresponding particle for the potential". If that implication is true, that feels like a pretty important generalizable principle that someone should have told me in undergrad...
That’s true for the other forces as well! And yet after very careful study we know the electromagnetic field IS quantized, particles of light are photons, and to get them to do the right thing (exhibit interference, for example) you need a quantum mechanical framework.
So why not for gravity too?
Why do we want to quantize gravity? Imagine you are doing a scattering experiment. To predict the full results consistently (in principle), you would need to include the gravitational forces between the scattering particles. This would be particularly important in early universe cosmology where you might have lots of heavy stuff zipping around at high speed! The classical GR picture is not too helpful in these situations.
Sure, but what if there is no field for GR? The way I understand gravity to work (warping spacetime in such a way that proper time gets "crunched" towards mass, retarding the system's action, shifting the variationally stationary path towards the mass) does not require a force carrying field (as far as I can tell).
To the point, I've founded a startup precisely for that: https://quantumflytrap.com/
What the parent meant was real particle simulation, for example simulating the collision between two electrons or computing the dipole moment of a muon, from fundamental standard model constants. It requires numerically solving 12 dimensional PDE's. That's much more complicated than entanglement simulations.
Think of it like knowing the rules, but the rules not being efficient to compute with.
Squiggles. Little arrows. Hand-drawn scribbles.
I've looked into why there's a total vacuum of numerical simulation, and the reason is simply snobbery. There's a philosophy that numerical methods are what mere engineers do, and not as intellectually pure as symbolic solutions.
You regularly hear comments like: "Such and such cannot be solved", what is often meant is: "It can only be solved numerically, but not with closed form algebraic expression."
People that say things like the former statement have excluded numerical solutions as valid in their mind. Such solutions may as well not exist, as far as they're concerned.
I see this attitude everywhere in theoretical physics.
The other issue is that because of the seventeen layers of assumptions and abstractions, most physicists are now at the point where they're not really making theories about physics, but instead they're debating the properties of the abstractions themselves. It's like kids trading basketball cards and saying one player is better than the other because his card is printed better.
This can all be boiled down to an acid test: Can you render your equations? As in, full 3D numerical simulation with an image as an output? Not a graph, not a scalar value, but a picture?
For simple (non-diffracting) optics? Yes! That's literally every 3D computer renderer!
For classical electromagnetics the answer is: yes.
For plasma physics the answer is: yes.
Even for special and general relativity, the answer is: yes.
For QED? Err... maybe? I've seen some toy examples in 2D, and I think I've seen a 3D example once. In principle, it's doable.
For anything else? Nothing. Or at any rate, I've seen nothing despite years of searching.
E.g.: Can you show me any "rendering" that extends a QED simulation with the weak interaction?
Can you find any animated examples of any particle interaction? E.g.: a free electron being captured by a proton, or an electron changing orbitals?
Again: Images or animations please. Not graphs or scalars. Everyone I ever challenge gets confused and links me to a paper with a histogram in it. That's not what I mean!
So it's only doable for tiny N.
> Donaldson was able to show that in specific circumstances (when the intersection form is definite) the moduli space of ASD instantons on a smooth, compact, oriented, simply-connected four-manifold X gives a cobordism between a copy of the manifold itself, and a disjoint union of copies of the complex projective plane CP^2.
[1] https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_equations#D...
I imagine a very very slow moving rock in space - going at 1 m/s (relative to earth) in a straight line, the earths mass causes spacetime to bend making the rock head towards earth, but then the rock starts to accelerate
the bit I don't understand is why does the rock accelerate towards mass? Why does the bending of spacetime make it not carry on at 1 m/s towards earth
and since this rock has increased its speed due to accelation, where has this extra energy come from?
As we know from relativity and time dilation, as our GPS satellites need to be resynchronized as they move fast and at a lesser mass level. The center of the Earth is very heavy and is therefore going through time slower than the rock or surface objects. Gravity doesn't really exist. Gravity is merely the side-effect of heavy-mass objects going through time slower than lighter objects. This is what is meant when it is said that spacetime is curved.
So back to your question, where does the extra energy come from to accelerate the rock towards the Earth? An easy way to think of it, expanding on E=mc^2, Et=mc^2, where t is time. As the ball is now falling further and further into the Earth's gravity well, it is now going through time slower and slower. With t going slower, E must increase to balance the equation, which speeds it up.
No need to feel dumb about asking questions, that's how we all learn :)
With regards to your question, looks like someone answered this in another comment chain: https://news.ycombinator.com/item?id=27096279
slight change of question, if the rock was heading directly in a straight line towards earth at 1 m/s, as the rock nears the earth it will accelerate (from the earths perpective) where has the extra energy come from? before it was heading at 1 m/s, but as it hits earth it will be travelling much faster
> Researchers note that electromagnetism, the weak force and the strong force each follow directly from a specific kind of symmetry — a change that doesn’t change anything overall (the way rotating a square by 90 degrees gives us back the same square).
Physics From Symmetry by Jakob Schwichtenberg
Also, (though I've not read it) this appears to be a longer, more detailed text in the same vein:
Quantum Theory, Groups and Representations: An Introduction by Peter Woit
This one gets to the EM field on page 573 :-/
I dunno of a good article as an introduction. As a grad student, I found Terry Tao's explanation [1] rather helpful, but of course it has a strongly mathematical flavor.
[1] https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
Also, a textbook is revealed on what seems to be this exact topic. Does this seem right? https://physicstoday.scitation.org/doi/pdf/10.1063/PT.3.2421
> “Gauge theory” is a term which has connotations of being a fearsomely complicated part of mathematics – for instance, playing an important role in quantum field theory, general relativity, geometric PDE, and so forth. But the underlying concept is really quite simple:
Then goes on to write an incomprehensible novella length explanation.
I like Tao, but this is a problem in 'pure' maths. I feel the issue is exacerbated by the fact that if you can follow along with Terry then you likely will be unable to recognise the issue.
A good counter point is this series by Timothy Gowers developing a proof of "Pingala's Determinant".
When Gowers finds the proof he states:
> Since this clearly has determinant 1 and this clearly has determinant 1, so does their products, ie. Pascal's[sic] determinant is 1. Could have done that, but that would have been uh, well depends on what you find interesting, but that would have been really sort of rabbit out of the hat, look what a billiant clever mathematician I am. I can just sort of produce this fabulous identity out of nowhere and it's got a nice simple proof that also came out of nowhere. What I want to emphasize is these sort of proofs don't come out of nowhere.
Timestamped to quotation: https://youtu.be/m8R9rVb0M5o?t=886
The series is great and will show anyone outside the field of pure maths that even pure mathematicians use numerical reasoning while trying to reason about a subject.
Of all the things to rename, this may be at the top of my list. I think some kids get lost in the abstraction specifically because the name "imaginary" isnt helpful in understanding the underlying concept.
I think more confounding is that the electron carries a negative charge.
This mistake goes back to Franklin but we can’t blame him; from the data he had he had a 50/50 chance of getting it right.