Hacker News Reader

Comment by immmmmm | Hacker News Reader

Physicist here, gravity is a force, just a different one.

Also, like everything else in physics: it depends how you observe it.

For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself.

Also gravity on Earth (weak gravitational field) is mostly curvature of time, namely the spacelike curvature can be ignored, and the g_{00} component of the metric can be seen a a gravitational potential. see p 80 of this:

http://www.blau.itp.unibe.ch/newlecturesGR.pdf

View on HN

Newton's first law tells us that in the absence of external forces, a body will keep going in the same direction, uniformly, ie its wordline will be straight.

However, that concept is not available in arbitrary manifolds, you need additional structure: The covariant connection, which allows you to parallel transport velocity vectors, enabling you to define the concept of straight lines (autoparallels, which will be geodesics if the connection is 'metric').

According to general relativity, gravity hooks into that. So from that perspective, the gravitational force on a test particle will be a consequence of (the generalization of) the first law instead of the second one, making it into a pseudo-force like the Coriolis force.

correct!

but if you introduce a derivative which is covariant under diffeomorphisms and u(1) transformations

D = d + \omega + A

you see that gravitation (connection \omega) enters on a somewhat same footing as the electromagnetic potential (A). there are nuances ofc, but the view (force/curvature) depends from where you're looking.

also in real life particles don't real exist... they're excitations in a field

"Come now, do you really expect me to do derivatives that are covariant under diffeomorphisms and u(1) transformations in my head while strapped to a centrifuge?"

"No, Mr Bond, I expect you to die."

Obligatory https://xkcd.com/123/

hahaha thanks!

"This ultimately led [Einstein] to the realisation that gravity is best described and understood not as a physical external force like the other forces of nature but rather as a manifestation of the geometry and curvature of space-timeitself." This is in the introduction of the paper you shared...

Give the commentor some credit -- I doubt they'd link a paper they are not familiar with.

Also in the paper:

"In a certain sense the main effect of curvature (or gravity) is that initially paralleltrajectories of freely falling non-interacting particles(dust, pebbles,. . . ) do not remainparallel, i.e. that gravity is an attractive force that has the tendency to focus matter."

Maybe don't immediately look for ways to discredit someone's contribution to the discourse without examining all of the content they have shared?

> best described and understood not as a physical external force

"best described as not a force" is not the same statement as "is not a force".

In physics and mathematics there can be multiple different, complementarity descriptions of the same thing. In fact, if you can reach the same result by two very different routes that seems to make it more robust.

I was trying to say three things:

1) it still somehow works like other fundamental forces since it derives from asking invariance under a local symmetry group

2) it is different from other forces since the symmetry group associated to it is directly symmetries of space-time (rather than some internal U(1) vector bundle like maxwell or SU(3) nuclear strong force)

3) in weak fields like on earth it mostly reduces to a conservative force driven by a gravitation potential (what you experience while climbing a mountain)

3 bis) like (mostly) anything in physics there is a duality i.e. there are regimes where you can consider it as a force, and there are regimes where you cant.

read the textbook, i know it's a 1000 pages but it's a great introduction :)

As the parent comment says, everything in physics depends on how you observe ("... best described").

Like Sean Carroll said in the Veritassium video about the "many worlds" [1], there's no such such thing as "pressure", it is just the interaction of fluid molecules. For practical purposes though, it is best described as a scalar called "pressure".

[1] https://youtu.be/kTXTPe3wahc?t=1043

I think I've read the same thing about temperature.

And now I'm wondering if it also applies to matter if matter is just an excitation of a quantum field.

Perspective is everything.

A simple example to understand how perspective can alter reality is to imagine being a point floating in a 3-D space where you are able to see the X-Y-Z axes. Now, imagine tracing (0,0,0) when you are at (500,500,500). Trivial.

Now, trace (0,0,10^100). That is a huge Z-line you would say. This is the side view.

Now, move to (0,0,10^100) from (500,500,500). This is the top view. What do you see?

Another example: When viewed from perpendicular to X-Y plane, a circular motion on X-Y plane looks properly circular.

When the same motion is viewed standing far away on the X-axis, the motion resembles an oscillation.

Same motion, different perspectives, seemingly different results.

> Physicist here, gravity is a force, just a different one.

Isn't gravity an acceleration, and weight a force? Otherwise gravity would accelerate heavier objects more slowly.

suppose you have an electric field described by a potential \phi, the force is

F = - q * d\phi/dx

where q is the electric charge

now suppose you're in a gravitational potential \phi_g, the force is

F_g = - m * d\phi_g/dz

where m is the mass. as you can see it's like the newton equation, so yes looks like an acceleration :)

Heavy objects are made of many light objects[0], so no, they would still accelerate at the same rate.

[0] with the exception of light, which is very light[1], but made of light particles rather than light particles.

[1] Homographs ahoy

There are heavy objects that are not made of lighter objects as far as we can tell, such as the Higgs boson or quarks. As far as we currently know, they should also fall at the same speed near the earth.

Fair point — I was just rehashing a very simple thought experiment that showed why the acceleration should be the same for heavy and light objects alike, but you are totally correct, it isn’t really ok for me to count all bradyons as equivalent.

The thing is that this thought experiment is interesting, but it is wrong. It is true that it is not logically possible for a system of two objects to fall faster than both of its constituent parts, but that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects - the lighter object would slow down the heavier object somewhat, so the new "combined" object would fall slower than the heavier of the two objects, but it would fall faster than the lighter of them.

In fact, the fact that heavy and light objects fall at the same speed is a profoundly special property of the gravitational interaction. No other fundamental force behaves this way: in an electric field, objects with more charge will accelerate more quickly than objects with less charge (and the same is true for the weak and strong forces).

In fact, the acceleration of an object or particle in a field is proportional to its field-specific charge divided by its inertial mass. The really interesting thing about the gravitational interaction is that the "charge" associated with the gravitational field is exactly equal to the inertial mass of that object, so all objects accelerate at the same rate because of the gravitational field.

This truly special property of the gravitational field had no explanation until Einstein's theory of general relativity, which discarded the idea that the gravitational field is a field at all, and described the motions of objects only in terms of rectilinear movement in a curved space-time (the reason why inertial mass curves space time is still unexplained though - it seems to simply be a property of the universe).

> that does not mean that it is a priori logically impossible for heavier objects to fall faster than lighter objects

Right, but if this were the case, a dumbbell would fall about twice as fast when its axis is perpendicular to the ground, than when it's parallel to the ground. Realizing this is not true from lived experience completes the thought experiment.

The difference between the total force acting on the horizontal dumbbell and the total force acting on the vertical dumbbell is 2/(height-dumbbell_length)^2. Given that height should be measured from the center of the Earth, this is ~0 for any length of dumbbell you can conceivably imagine. So even if lighter objects fell more quickly than heavier objects, you wouldn't expect to see oriented dumbbells fall at different rates.

However, what you could expect to see is that dumbbells with different weights for the two parts would never fall horizontally, they would tend to reorient vertically, with the heavier end first. Not sure how likely it would be to have noticed that this is not the case from lived experience.

You are making a semantic argument, so let's clear it up.

Gravity is the natural phenomena, or experimental observation, whereby bodies with mass appear to gravitate towards each other. One model and explanation of this phenomena is Newton's Law of Gravity used within the framework of Newton's dynamics (or laws of motion). The Law claims that gravity is a force, with a very specific formula we are all aware of.

If you ignore Newton's third law (about action-reaction pairs) for the gravitational phenomena of small bodies near a planet, and assume that the planet doesn't move at all, then we call the force on the small body its weight.

Now, returning to your question, in daily lingo, physicists use the word gravity to refer to the phenomena, the force law, or the weight. You have ascertain from context. In summary, gravity is a force is a perfectly valid and understandable statement within the slang of physics.

A person who has studied physics in a good school here.

Weight is the force a body exerts on its support.

Force of gravity is a force exerted by each body in a system onto every other body.

Physics does not magically become different outside the confines of a good school.

On the other hand, the Internet is black with the ink of people who think they understand physics but do not. Credentials do help you to distinguish someone who has a chance of knowing what they're talking about.

I mean, it's… true? My own (very highly upvoted) comment on the main thread of this article contains the text "I only took four lectures of General Relativity before I gave it up in favour of computability and logic", which is helpful context for anyone who reads it, because it lets the reader know in a fairly objective sense that I am familiar with some of the concepts of GR but am unlikely to understand everything in detail. You can't know whether someone on the Internet knows what they're talking about, but they can give you some of their context to help you decide. Admittedly "a good school" is not the most useful context, but it's better than no context.

Correct me if I'm wrong please, but the 'curved space' strategy describes the velocity of two objects in a 2 body scenario, but it doesn't describe the behavior when the two objects have zero velocity relative to each other, right?

The 'two spheres in a box' experiment for testing the gravitational constant has no relative velocity at all, so how could 'curved space' describe the force between them?

As I understand it, even objects with no velocity in space still have velocity in time, and the curvature of spacetime shifts it from the time component into the spatial components. In other words an object's velocity is a 4 dimensional vector, and the curvature of spacetime causes the angle in 4d spacetime of that vector change, while still preserving total momentum, thereby accelerating the object in space while decelerating it in time. So as an object falls into a gravity well, it actually moves more slowly through time, transferring more and more of its total momentum from temporal motion and into spatial motion.

Correct. And just making the trajectory to appear straight by modifying the reference grid doesn't change anything. For example, once can see even exponential curve appear in a logarithmic grid. Force is a relation between the reference frame and the object. It is possible to consider either one as straight or flat.

While the apparent straightness of a curve depends on the choice of coordinates, there's also an invariant notion defined in terms of the connection.

This affects our understanding of forces: Accelerations live in the double tangent bundle, which gets split into a horizontal and vertical part by the connection. The horizontal part is the contribution by inertia, yielding pseudo-forces (including gravity according to GR). The vertical part is due to non-inertial forces.

A fun little physical experiment: a density gradient of the water in a fish tank (caused say by putting sugar in the water) will cause a laser to bend: https://www.youtube.com/watch?v=DhNZP2KgMLw

How this can be connected to gravity I do not exactly know. I suppose the change in the refractive index of the water is akin to g_{00} component of the Riemann metric, since it produces a compensating change in the wave vector at that point. Whether you could imagine GR consistently in terms of changes in the local speed of light a.k.a. changes in the permittivity of free space, again, I do not know.

I was always wondering if there is a way of distinguishing a straight line in a curved space from a curved line in a flat space, given that you cannot 'look' at space time from the outside. Would that be possible?

The usual suspects; lasers and mirrors. That's how gravitational waves were detected.

Physicist (BSc) turned software developer here, I understood around 2% of your comment :)

(Thanks for the effort, though, it might just be me, in the end I changed profession for a reason)

Ah sorry, i did 8 years of GR and strings..

I was replying to the headline: 'umm, yes and no...'

Physics is the study of making simple things complicated.

Physics is the study of tearing off the mask of simplicity to reveal the horrible complexity hiding underneath.

Once again, it's largely down to your frame of reference.

Is there any science other than physics more adept at describing extremely complex phenomena with extremely simple laws, with known, bounded error?

I'm currently doing a BSc in Physics too.

However, when I've graduated I don't think I would ever call myself a physicist like yourself unless I actually went on to do research in physics as a career, which likely means following the traditional academic path of doing a PhD (since I'm not Freeman Dyson).

Sorry for the nitpick but such titles should be earned don't you think?

i did a phd, got highly cited and was promised to a successful career. i did not continue tho because:

1) the high-energy field is in deep crisis, unlike in Dyson era there is almost no new experimental data.

2) seeing people trying to get a temporary position looked pretty much like a pack of dog on a single bone with few left scraps of meat. for getting to the bone marrow (aka permanent pos) one basically had to kill all the other dogs then wait the bone crack open (i can tell you the resulting science is not always of high quality)

3) i wanted to do sth useful for mankind.

so yes i was not masochistic enough to become a career physicist, even if i am a respected expert in my field. also i don't think you can compare present day physics to Dyson era, science careers these days are more about social skills and PR.

so you're correct: i'm an aborted / half-backed physicist, who is highly p* of what the field has become, converted to computer sciences, just to realise my new field is as scientifically crooked as the first one.

i'll try to get it right next time :)

... at least this time i didn't get down voted too much on HN

Isn't gravity somewhat like the forces that one observes in non-inertial frames of reference in classical mechanics?

umm, yes and no...

the key principle of general relativity is the equivalance principle: there is no (local) way to tell if you're being accelerated (in a spaceship for instance) or in a gravitational field. in other terms the inertial mass is the same as the gravitational mass.

this, and lorentz invariance, yields general relativity almost uniquely, so it's a very strong principle.

so yes, in some sense gravitation shift the notion of "inertial frame of reference"

Original page kinda doesn’t explain the idea in simple terms. This Veritasium video gives detailed “popsci” explanation:

https://youtu.be/XRr1kaXKBsU

But the principle of equivalence is not included in the Poincaré group.

neither is local gauge invariance for maxwell

No , is not a force

Before downvoting , prove Einstein wrong

This is like that silly discussion of the centrifugal force.

Forces are mathematical models, not fundamental properties of reality (we don't know what the fundamental properties of reality are).

It's one of a general class of problems: "we are each using a word to mean something different". Taboo the word "force" and see if you still disagree :P

Reply on news.ycombinator.com