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Comment by geomark | Hacker News Reader

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?

View on HN

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.

If I understood it right,

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

> ...Being accelerated by such a pseudo-force won't register on an accelerometer...

Just checked the accelerometer on my phone. It reads around 9.8m/s/s pointing downwards.

Assuming you're standing on the surface of the earth, that's wrong: You're being accelerated upwards, not downwards. Cf the introductory paragraph and "Physical principles" section of https://en.wikipedia.org/wiki/Accelerometer

If you're standing, you're not accelerating anywhere. Acceleration is a change in velocity, which is a change in position. The forces on you are balanced: the force of gravity is balanced by the force exerted upon you by the ground. You're not going anywhere, and therefore you're not accelerating.

An accelerometer works by comparing the difference between some mass that is acted upon by an external force and a related mass that is loosely connected to it (e.g. by a spring-like linkage. whose strain we can measure) as not to be acted upon by that force directly.

If you move the casing of an accelerometer, the sprung mass inside it lags behind, and thereby the acceleration can be measured via strain gauges or whatever.

Gravity defies accelerometers because, unsurprisingly, gravity acts on all of the the masses contained in an object equally.

(At least any gravitational field you are likely to encounter in ordinary experience is going be almost perfectly uniform across an everyday object.)

It is when you are in free-fall, that is when you're accelerating due to gravity. And that's exactly when the accelerometer doesn't tell you anything, because every part of the object is in the same free-fall; all of you is accelerating. The accelerometer is differential. It doesn't see a difference, so it doesn't see acceleration.

You now that free-fall is acceleration because orbiting satellites are in free fall and they follow circular paths. Objects will not move in a circle unless a force accelerates them toward the center. Like when you spin a mass on the end of as string, it goes in a circle due to the centripetal force exerted by the tension carried in the string.

When you're standing on the planet, your accelerometer is lying to you. Gravity is acting on the sprung mass inside the accelerometer, and it's also acting on the case which holds that mass. But the case is constrained from moving, whereas the sprung mass isn't. So a differential strain develops, which "looks and feels" like acceleration.

In summary, an accelerometer is an instrument which measures the acceleration due to a force which is applied just to its casing, and not to some critical piece of mass held inside. Gravity causes equal acceleration of the casing and that piece of mass, and so gravitational acceleration is immeasurable by that accelerometer.

Acceleration can be measured with regard to some frame of reference via distance and time calculations.

Sorry, I interpreted the - sign in the opposite direction.

Either ways, the accelerometer is registering something. If gravity was purely a ‘pseudo force’ as GGP said, I should’ve expected a 0 reading.

Am I misunderstanding the point made about the accelerometer?

The feeling you have of force is due to resting on something that's holding you up. If you take that away, you would be in the same gravitational field but feel no forces on you and your accelerometer would measure 0m/s/s.

If you jump off a bridge, during your brief flight you could look at your accelerometer and see zero. The gravitational influence on you hasn't changed at all by jumping off a bridge- the only change was removing the upward force that stopped you from falling.

Or record your screen and drop your phone from a second floor balcony to see what the accelerometer reads

You're at rest relative to Earth's surface. From the perspective of that particular frame, the gravitational (pseudo-)force gets balanced by the normal force. But the gravitational force is 'actually' zero, leaving the normal force accelerating you upwards to be measured by your accelerometer.

That’s because you aren’t in free fall.

If I step off a bridge, why does the distance between me and the very large nearby spherical mass begin decreasing at an, umm, accelerating rate?

The surface is accelerating up at you relative to the gravitational field.

What happens if two people jump off bridges on opposite sides of the earth? How does that work in that interpretation?

Same thing? For each of them, they see themselves non-accelerating with respect to the gravitational field. But they do see the soil accelerating towards them against the gravitational field.

Why is the soil not in free-fall? Because it feels normal force of all the earth below.

And why is not the whole earth in free fall towards its core? Because it has an electrostatic force (a real one!) which keeps all the atoms and molecules from collapsing on itself. If it would collapse on itself, it would first become a neutron star and then a black hole.

It still isn’t obvious to me how, if “the surface is accelerating up at you relative to the gravitational field” on both sides of the earth, the earth isn’t pulling itself apart.

To be clear, my confusion is about how this interpretation is consistent with the facts, not the facts themselves (I think).

ah, that is where the curvature of spacetime comes in. That field is curved between both observers on each side of the earth, because there is a massive object between them: the earth.

So the field is going radially inwards towards the center of the massive object.

[blinks in paradigm shift]

"Gravity" is the curvature of spacetime. An inertial "straight line" follows that curvature, like going "straight" on the Earth's surface draws a spatial curve. Remove what's supporting me (dirt, bridge) and I'll continue on my inertial straight line, which actually orbits and settles down to the center. Even "at rest" at the center/bottom of the gravity well is not zero inertia per se, it is a continuing inertial line orbiting with still-constant velocity at zero radius. Ergo gravity isn't a force; gravitational attraction is just masses' inertial lines being distorted by the infinite-reaching distortions of other masses. There is no "gravitational force" to unify with other forces. OMG.

I've been trying to get my head wrapped around gravity for years. You just tied the knot.

Next questions: why does mass distort spacetime? As E=mc^2, does/can energy distort spacetime? Mass & energy being just different units of the same thing, what's the nature of that thing without thinking in terms of divided mass/energy colloquial thought? And then questions on to weak & strong nuclear forces, and reconsideration of electromagnetic force.

I'm willing to accept it as yet another thing I don't understand, but it still isn't obvious to me how the field being curved solves the issue. Even if we have bent our coordinate system around the earth (which I think is equivalent to what you're saying), how can the two sides of the earth both be accelerating "upwards", or now "outwards", without the earth being pulled apart?

Do you know of any diagrams that might illustrate this idea to a layperson?

Layperson here. As I understand it, if there were no bonds or repulsive forces between the atoms that made up Earth, they would all be in free fall, and they would all fall toward the center of the Earth's mass. Since these are inertial paths, there's no force compelling them to fall; they're just following the curvature of spacetime.

The electrostatic forces and bonds between atoms are exactly what prevents these atoms from following inertial paths. The atoms act on each other, and collectively produce a force radially outwards from the center of Earth supporting its mass.

Earth isn't pulling itself apart because nothing is pulling in the first place. All the mass is pushing against itself, refusing to be packed tighter, despite the flow of spacetime around it drawing it together over time.

When we're standing on Earth, our particles are following the same flows of spacetime toward the core of Earth. From our inertial frame, the ground below us is moving toward us, because as noted Earth resists being compacted further. So we meet the surface, we both resist being compacted by the other, and we experience a stable force.

"From our inertial frame, the ground below us is moving toward us" makes a lot of sense to me, but doesn't seem to be quite the same as "the surface is accelerating up at you relative to the gravitational field". The former is with respect to the inertial frame of the faller(s), the latter seemingly with respect to the inertial frame of some shared gravitational field.

That said, your description does kind of explain it for me, unless I am misunderstanding, though at the moment I only get it as a "negative" argument: we are being accelerated upwards/outwards with respect to the field's reference frame, because otherwise we would be moving along our natural inertial path.

It is still a bit puzzling that if the ground disappears we appear to accelerate, whereas my current reading of what you wrote seems to imply that we would immediately return to our "inertial path".

What I'm really wondering is if all of this "acceleration relative to the field" business is a misleading abstraction, and "relative reference frames" fix it (and indeed that was my very primitive understanding of relativity). However, on balance it seems much more likely that I'm simply misunderstanding things.

> The former is with respect to the inertial frame of the faller(s), the latter seemingly with respect to the inertial frame of some shared gravitational field.

Fair, and I'm not sure I follow that, either. I'm not sure how an entire field can really have a reference frame in the first place.

> though at the moment I only get it as a "negative" argument: we are being accelerated upwards/outwards with respect to the field's reference frame, because otherwise we would be moving along our natural inertial path.

That pretty succinctly captures my understanding.

> It is still a bit puzzling that if the ground disappears we appear to accelerate, whereas my current reading of what you wrote seems to imply that we would immediately return to our "inertial path".

Yes, that's the sticky bit! I think "appear" is load-bearing here, because what are you measuring relative to? The surface of the Earth is not an inertial reference frame (according to general relativity, it's accelerating!).

It might be easier to think about if we use centrifugal force -- the fictitious force you feel when being swung in a circle from some central point. From an inertial reference frame, you have some velocity in the tangential direction, and a rope (say) is pulling on you in the radial direction. This force accumulates with the existing velocity over time to produce a circular path.

From your perspective, however, you feel a force pushing you outwards, which is resisted by the rope you're attached to. You would feel that, if the rope was cut, you'd be "pulled" out into space (radially away). But this is because you're not aware of -- you don't sense -- the tangential velocity you possess, because it's canceled by the choice of a frame that's moving with you.

The change to an inertial frame introduces an extra velocity term, and this in turn allows us to replace the unattributable outward pull of the centrifugal force with a force merely attributed to the tension of the rope you're attached to. (In fact, this might be a good intuition for what an "inertial frame" even is: it's a frame in which all forces are equal and opposite to other forces. Gravity and the centrifugal force are unbalanced in this sense.)

The gravitational field (curvature of spacetime) plays the same role that the hidden velocity does. In an Earth surface frame, the feeling of being pulled "down" is attributed vaguely to the fact that there's a bunch of mass "down there". In an inertial frame, the feeling of being pulled "down" is attributed to the ground pushing "up" at you.

In both scenarios, we can find a frame involving an extra term that lets us redescribe the phenomenon we observe in terms of forces attributable to physical entities.

The "Fictitious forces" Wikipedia page has some pretty good schematic animations for the centrifugal force, FWIW.

[0] https://en.wikipedia.org/wiki/Fictitious_force

Lots of good stuff for me to think about. Thanks for taking the time!

Compared to the radius of the earth the Bridge is on the surface of the earth. In other words you don’t travel far enough / long enough to observe any difference in g.

If you were in free-fall, (preferably in a stable orbit and not falling off a tall building) and checked your accelerometer, you would read zero. Even though you are still being accelerated by gravity.

You misread. Your phone is accelerating upwards at 9.8m/s^2. That is also what it displays. If you have an accelerometer that displays a history (I recommend the app phyphox), you will also see that acceleration while your phone is falling.

The phone will measure zero acceleration while it's falling.

Apparently I forgot to type the "go away" that was supposed to go between the "acceleration" and "while" in that sentence ^^.

Any skydivers wish to confirm this? But the wind would push on the phone. So any lunar skydivers wish to confirm?

A better analogy is something that is in a stable orbit.

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.

Dimensional analysis seems to me to be a far more fool-proof way of knowing whether a quantity should be used with a particular formula.

Also the other issue is that the word "force" in physics doesn't just refer to F=ma, it also refers to the general concept of an interaction mediator. That's why they're called the four fundamental forces -- meaning that saying "gravity is not a force, it's a field" is not only overly pedantic but is also arguably wrong if you take it literally.

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.

Acceleration being independent of the mass of the test particle being acted upon only holds true for two types of forces: Inertial forces, and the gravitational force.

According to General Relativity, this is no coincidence: Free-fall spacetime trajectories ('worldlines') get modelled as straight lines ('autoparallels'/'geodesics'), indicating an absence of net forces. Apparent gravitational forces then arise the same way any of the other inertial forces do.

Such an interpretation of gravity is natural insofar that it handily explains the measurements of accelerometers, which only will measure nonzero values if motion deviates from free-fall due to the presence of non-gravitational forces.

But note that as is often the case, it boils down to a semantic argument about the definition of 'force'. The effects of 'fictitious' forces can certainly be as real as the effects of 'real' forces (in case of gravity, eg tidal heating, or the extreme example of spaghettification, ...); personally, I have no issue with calling gravity a force.

It's a pseudoforce in the same way centrifugal acceleration is "fictitious"

It's a consequence of massive objects following geodesic motion on a curved space; e.g. To keep an ant on a sphere you would need "something" to ensure the ant's velocity doesn't lead the ant's position "off" the sphere. That something is interpreted as gravity.

Here's a more technical explanation: https://physics.stackexchange.com/questions/212167/what-is-a...

And massless. Light follows a geodesic in GR. Also i don’t think intrinsic curvature is well explained by the ant analogy. The apparent force isn’t to stay in the manifold but to stay on the geodesic thru space time (which is free fall).

Yep, though massless particles must follow null geodesics specifically.

Yeah, the ant analogy isn't the best, though it does show off that movement on a curved surface needs "corrections" from the movement on a flat surface (and the degree to which that occurs happens to entirely characterize curvature itself).

If you force the ant to always travel on a great circle, then it might be a little more precise :)

It's neither massive nor massless object that follow geodesics, it's objects with energy (including the mc^2 kind).

Yes, and "massive" and "massless" exhaustively covers both, with the special highlighting of massless particles which are further constrained to follow null geodesics.

Massive particles don't have that limitation but they only travel time-like geodesics (as far as we know).

> with the special highlighting of massless particles which are further constrained to follow null geodesics.

Only to an approximation. Photons generate gravitational fields, and the planets they travel near are attracted to the photons (not much obviously). (See: Kugelblitz)

Gravity does not treat photons specially, the rules are the same as for other particles.

For extra credit imagine a Kugelblitz traveling by at light speed - it's moving so fast, it doesn't have time to add any mass. Yet, mass transited inside the event horizon of this object.

Interesting, thank you.

Gravity is sort of special compared to the 3 forces in the standard model because of its relation to inertia.

For all 3 SM forces, there is a distinction between the charge of a particle and how easy it is to move that particle.

For gravity no such distinction has ever been measured - the "gravity charge" of an object seems to be the same thing as its tendency to oppose movement (its inertial mass) in any experiment ever conducted, which has led to Einstein's observation that gravity seems to be a dual of acceleration in a curved space time. No similar explanation is required for the other forces, as they are not intimately tied to inertia in the same way.

Now, unfortunately general relativity's curved space time has never been successfully meshed with QM's Uncertainty principle and/or wave function. Most physicists, at least particle physicists, do tend to believe that it is in fact GR that is limited in its description, since QM (in particular QFT) is the most precisely confirmed experimental theory ever devised, while GR is extremely difficult to work with for making precise experimental predictions (Einstein's equations are non-linear, and almost all predictions are actually based on linear approximations of the equations) - so there is much more "room" for GR to be modified at very low scales without contradicting the high scale results than the other way around.

A force is considered an interaction mediated by a carrier.

When we learn, a force will be described in a way that adheres to the new/modified framework.

How long can that definition of a force have existed? 60 years? "Carriers" (carrying particles if I understand you correctly) only makes sense in the context of the standard model. It rubs me the wrong way when a field co-opts layperson definitions of something and redefines them to be something incompatible with the original definition, but I can understand that maybe physicists are not interested in helping people maintain what little physical intuition can be gleaned from the world around them.

But I digress, are gravitons not a carrier of gravity?

There're no gravitons in the standard model and every attempt to introduce them has failed. That's the problem. Our current theoretical framework describes all fundamental forces but gravity.

> Mathematically all interactions can be described as fields.

Is there any other way a field can be described? What's the physical reality of a field?

Particles as shown in most introductory particle physics courses. Because of particle/wave (alternatively particle/field) duality the question of whether particles or fields are the fundamental constituents remains open but the current consensus is the later (fields).

Describing a field in terms of particles seems circular if particles are excitations of a quantum field.

Indeed. That's why it is a hard question to answer which is fundamental.

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.

Thank you for your explanation.

If you haven't seen it yet, this thread hes devolved into a refutation of OPs recollection of their teacher's explanation. There are other people rice chimed in about why Gravity isn't a force: Basically because gravity is space-time curvature and it's objects in free fall that are at rest.

Right. Just like the force between opposite charges. That's how I've always thought of it.

Small nit - I think it is actually called electrostatic force, at least when we are talking about charges at rest.

Is there a way to describe electrostatics as objects following inertial trajectories through curved space?

This video really helped me understand why it’s not a force. Also awesome physics channel as well.

https://youtu.be/XRr1kaXKBsU

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.

Veritasium made a cool video about this some months ago: https://www.youtube.com/watch?v=XRr1kaXKBsU

Isn't the same true of electromagnetism?

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.

What about the opposite? A clear explanation of what the strongest evidence for gravity NOT being fictitious but rather being a real force is?

Such a point of view is pretty much incongruous with contemporary physics. I'm not sure how one would go about even formulating the case.

Despite its central presence in physics 101 the notion of force is actually not all that clearly present in fundamental physics.

Newton's innovation might be said to be the representation of gravity as a force, but even in the Principia he doesn't commit to the idea because of an intuitive rejection of the non-locality implied by such a conception. So the idea that gravity is a force of the same sort as you pushing on a cart full of apples (whatever _that_ is) was never a particularly strongly held idea. I'm not an expert on the history of physics (I have read the Pricipia in translation, though) and I suspect Newton, if questioned appropriately, might have himself admitted there are issues with the conception that go beyond just non-locality.

Even at the level of Lagranian physics in the contemporary style (which despite that description is hundreds of years old) the idea of forces has an ad-hoc quality to it. The description of a completely closed system doesn't really contain forces unless you explicitly include them in the form of lagrange multipliers for the constraints, and then the forces that you calculate are, in a sense, provided "externally" by processes outside of the system itself.

For instance, the easiest way to represent the motion of two particles held together by a perfectly rigid rod doesn't mention the force exerted by the rod to maintain that constraint and yet simulates the motion perfectly. If we are interested in how much force the rod must exert to maintain the constraint, we can add in a largrange multiplier, but what that quantity tells us is in a sense a summary of the non-represented physics of the rod itself, which is still excluded from the system. A force then is a kind of interface between that which you are considering in detail and that which is assumed to be part of the external world. If everything in the world were simulated, then nothing would deviate from its expected motion, and thus there would be no forces at all, since all a force is is a description of how something deviates from the path it would ordinarily take if not for the intervention.

On this view Newton's first law is much more important and fundamental than his second: objects always move in straight lines but we must take great care in understanding what a straight line actually is for a given physical system. Really, the seed of general relativity and the geometric formulation of field theories is right there in the first law. This explains why the second law is of so much less importance in modern physics.

I'm not a professional, just an interested failed physicist, so standard equivocations apply to the above.

This video by an actual professional hits on some of these ideas:

https://www.youtube.com/watch?v=IBlCu1zgD4Y

In General Relativity, gravity is not a force.

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 a Newtonian context, gravity is a force.

In an Einsteinian context, forces are not even discussed.

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.

Well, if you are currently at rest in relation to the surface of the earth, that means you are moving with speed c towards the future (the ct direction in Minkowsky space time). The shortest path from the past to the future, near a large mass like the Earth, is curved towards the center of the Earth. So, because of inertia, your trajectory in spacetime will be curved towards the center of the Earth. However, the surface you are standing on is preventing this motion via an electromagnetic interaction.

Do you feel a force from gravity? I thought you feel the electromagnetic force (normal force) of your chair pushing you away from the Earth and stopping your free fall.

If not for the gravitational force, the normal force would have nothing to exert. So I guess you feel the magnitude of the force from gravity via the normal force.

I’d highly recommend this explanation: https://m.youtube.com/watch?v=XRr1kaXKBsU

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.

This sums it up [1].

[1] https://www.youtube.com/embed/XRr1kaXKBsU

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

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