I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?"

I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong answer out there, please correct me.

Intuitive answer: the curve is indeed very gentle, and (e.g.) light will be deflected only very slightly by the curvature; but the ball is moving for a couple of seconds, and that's an eternity. On human scales, the time dimension is much "bigger" than the space dimensions (we're quite big in the time dimension and quite small in the spatial dimensions); the ball moves only a small distance through space but a very large distance through time, amounting to a big distance in spacetime, and so the slight curvature has a bigger effect than you might expect.

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

I've seen this explained elsewhere, and it does look very cool when displayed this way. But perhaps someone with more background can explain to a lay person -- what even is a force?

Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a transformation that causes charged particles travel on "straight" lines?

Veritasium just put out a great video on this: https://www.youtube.com/watch?v=XRr1kaXKBsU

My enlightening moment about general relativity: apples do not fall on the ground, instead, the earth is inflating, and the inflation of the earth is accelerating at 9.8 m/s^2. Eventually, the ground catches the apple.

Of course, you are going to tell me that the earth is not inflating, obviously, because it is still the same size after so many years.

But here is the trick: the earth is inflating at the same rate as spacetime contracts. If the earth didn't inflate, the contraction of spacetime would have collapsed it into a black hole.

Note: It is related to Einstein's elevator thought experiment. Here, the inflating earth replaces the rocket powered elevator.

Note 2: If the idea of an inflating earth bothers you, I suggest you start considering that the earth is flat, seriously! Flat Earthers took Einstein's thought experiment quite literally and consider the Earth to be a disk that is continuously accelerated upwards. And in fact, if free fall trajectories were parabolic, that would be the correct explanations. In reality, because the earth is not flat, free fall trajectories are elliptic, though it is only apparent on a large scale.

I'm curious, how does the "gravity is not a force" viewpoint relate to the hypothesized graviton particle [1]?

Are they incompatible viewpoints, or just different perspectives on the same thing? (E.g. are gravitons hypothesized to disappear depending on frame of reference?)

I'm assuming they're incompatible (that we need the theory of everything [2] to reconcile them) but would love to know if there's something I'm missing.

[1] https://en.wikipedia.org/wiki/Graviton

[2] https://en.wikipedia.org/wiki/Theory_of_everything

True gravitational force is something that can’t be transformed away by an arbitrary choice of frame (even an accelerating one).

As a brief example, consider two objects in downwards free fall toward the centre of some massive object. Since they head towards the centre, in a free falling frame the two objects actually get closer to each other until they collide as they reach the centre.

This is known as the tidal effect of gravity and is the actual physical content of general relativity. This effect can be shown to be obtained by an appropriate curvature of spacetime which itself can be shown to be related to the stress-energy of matter inhabiting spacetime.

This video really cleared up a lot of misunderstandings for me: https://www.youtube.com/watch?v=wrwgIjBUYVc

I had never visualized it this way in my head before, and it all makes a lot more sense now. Highly recommend!

The video for this page provides great context https://youtu.be/XRr1kaXKBsU

Here's another 'though experiment' I like which some people disagree with, by not understand reference frames:

Light always travels in straight lines. Even when light is experiencing a gravitational lensing and looks to us from earth that it's bending around a star or whatever, from the perspective of the light beam itself, it's moving in a straight line. It's entire reference frame is bent compared to ours (relativity) but nonetheless the correct view is that the light is still moving 'straight' in it's own reference frame.

Also if the light wasn't moving straight that would mean it's changing direction, which is the same as an acceleration, and a beam of light traveling thru a gravitational field feels no acceleration, because it's not accelerating. Again from this view you can say light is moving straight and experiencing no acceleration, just like an object in free-fall doesn't 'feel' any acceleration, even though they are accelerating from the perspective of some other reference frame other than it's own.

That brought up the verse from Pushkin [1]:

    One bearded sage concluded: there's no motion.
    Without a word, another walked before him.
    He couldn’t answer better; all adored him
    And all agreed that he disproved that notion.
    But one can see it all in a different light,
    For me, another funny thought comes into play:
    We watch the sun move all throughout the day
    And yet the stubborn Galileo had it right.

Both are right, in short. We observe parabolas and we are right counting on them - we have great successful experience using these prediction. GR theory predicts lines, they are right too, but in different context.

How is it not a force though? Regardless of curvature, a ball starts moving if you let it go without applying any force. Curvature alone can't account for that could it?

You might enjoy my special relativity interactive illustration: https://xixixao.github.io/cheetah-paradox/

Play with the accelaration to see some spooky seemingly faster-than-light movement.

I was taught that gravity is a force (like electromagnetism, or the strong and weak nuclear forces.)

The title says "gravity is not a force". In the article's perspective, why does a kitchen scale report a higher number when I place an object on it?

(In my perspective there is gravitational attraction between the object on the scale and the rest of the Earth, and the the scale, assuming it is "level" (set perpendicular to the direction of gravitation toward the center of the Earth) reports the magnitude of that attraction.)

If gravity isn't a force, then when the object and Earth are not in freefall or moving, what does the kitchen scale measure?

Speaking of reducing the dimensions of physical reality, a physics professor shared a very interesting video saying we should be thinking of photons and other massless objects as existing in 2d "areatime" as opposed to 3d "spacetime." I'm wondering if a revolution in simplifying the math behind physics is brewing.

https://www.youtube.com/watch?v=cb_PCuv0vcY&feature=emb_logo

Would not an electron and a positron trace out an identical line/parabola?

Would that mean electromagnetism is not a force either?

What is the difference between the two that makes one a force and one not a force?

I can't imagine how this applies to the whole earth. Assume there is 'top' and 'bottom' of the sphere, don't know how they do navigation in space, but assume it is like the usual earth maps. So how the things on the bottom get drawn to the earth, while they should go into the other side. Clearly there is something I don't understand, but I don't know what it is.

From the future here, gravity is just light reflecting off of stellar bodies, which causes the universe to "bend" space/time in all directions, just different strengths based on the reflectiveness of whatever it hit and the strength of the light source. The reason that a whole bunch of nothingness between planets keeps them spinning around one another is just light and the sheer force it applies by bumping into objects and then reflecting into the next one. Don't think of just one beam of light, think of a cacophony of endless bounces of light in varying degrees of strength.

Light is without mass, but not without energy. That energy causes what you could describe as "propulsion". Even the slightest bit of propulsion in the emptiness of space will cause matter to move around.

It's like light being a big ladle. And using that ladle to spin the water + tiny floating objects in a bath. They will all affect one another until the heat death of the bath occurs and all life grinds to a halt.

Somewhere I read that a free fall parabola does not even take into account earth's curvature. Although I cannot remember, what kind of function describes the reference system specific ``path, as a function of time''.

Could this be named more correctly: Gravity is not a force – free-fall hyperbolas are straight lines in spacetime (timhutton.github.io) ?

This is my favorite description of curved space time: bugs realizing the geometry of their space is not Euclidean. They discover their triangles are wrong.

https://www.feynmanlectures.caltech.edu/II_42.html

Always seemed pretty wild to me that for the tiny moment of time photons from my computer screen travel from the LEDs to my eyes, they're being dragged toward the floor at the same 9.8m/s^2 as everything else.

When standing on Earth we experience a frame of reference that is accelerating upwards, causing objects in free-fall to move along parabolas, as seen in the accelerating frame of reference on the left.

I'm trying to understand what is meant by this. When I drop an item on the floor it goes there in a straight line, not a parabola. Same if I drop something from a helicopter. Obviously I'm missing something here. Can someone with more insight ELI5 this to me please?

Gravity is a force, because if it is not for this reason then probably neither are the other forces. Many physicists believe we will achieve grand unification of the forces, which means that in some way they are all related to the curvature of spacetime and each force can be viewed as applying acceleration in a straight line. It's just that the geometry defining that line, the frame of reference, is different for each force.

Hasn't it been shown that mass originates from coupling with the Higgs field and it's mass that deforms spacetime? Given the large size of the Higgs boson, I don't understood why the lack of gravity in QM is viewed as a problem. Why does gravity have to be fundamental? What if it just shows up right around the same time as electroweak symmetry breaks down?

Someone watched Veritasium...

but the real question is: can you counter your own arguments? Because that's where absolutely fascinating science happens.

Has any papers been written describing/modelling spacetime as a fluid? You also see diagrams of space time as a plane with the gravity coming from the dip in that plane. But that model would hold in a 360 degree view, so I think we should model spacetime as a fluid with the density of that fluid going rise to drag and therefore gravity effects

The first explanation that actually worked for me: https://youtu.be/jlTVIMOix3I?t=55

(also nice engineering on the physical "space time stretcher" he built)

I understood it rationally before, but only with this video it also feels right.

A pretty good model. Thank you.

The model shown is for 1D space and 1D time, and this 2D spacetime is curved, remaining 2D. Can you though show us a 3D model of curved 2D spacetime? Maybe as a rotatable, scaleable 3D scene, where more complex phenomena, like planetary motion around a star, would be possible to show?

I saw this and the related Veritasium video, but am still scratching my head about something. Does this mean that away from all gravity a body does not experience any time? ie a person on a spacecraft stopped in intergalactic space would not age relative to persons on planets?

Wonderful lecture series on Audible by Benjamin Schumacher:

https://www.audible.com/pd/Black-Holes-Tides-and-Curved-Spac...

The scrollbars in the demo feel backwards to me. Like Mac trackpad scrolling vs mouse scrollwheels.

I want left to be 0 frame acceleration and left to be backwards in time. I kind of also want the graphs to be reverse order too, but I get why it's all presented this way. :)

If I throw a ball straight up, it loses speed. The speed at the top of the parabola is exactly zero. So how is the change in speed explained if there is no force involved? Even in a straight path, a change in speed implies a force acting on the object.

I'm a bit confused, how does a 2D graph with a curved X axis work?

Does this just mean to say that if we saw things distorted with an outward curve, then something that is moving in a curve would look to be moving in a straight line?

And what's the point of such an observation?

If gravity is not a force, how is spaghettification a thing? If you are stationary when you're weightless, how can different stationary parts of your stationary body move at the different speeds required for spaghettification to take place.

I recently finished "We Have No Idea" by Jorge Cham and Daniel Whiteson. Its a masterpiece of science communication and I cannot recommend it enough as a way for non-physicists to get a grasp on this concept, as well as related ones.

Does this mean that space time is ‘bent’ and objects follow an apparent parabola along that bend, or that space time is flowing towards a mass and the object is following a straight line on a ‘moving’ space time?

Don't we always consider gravity as "acceleration"?

In f = m * a, for objects falling from sky, it will be f = m * g where g is gravity, m is mass & f is force

Sorry, I think I am missing the point of the article.

Veritasium recently posted an excellent video on the subject: https://youtu.be/XRr1kaXKBsU

Ok, great opportunity for me to ask a dumb question that's been bothering me for a while, for practical reasons I won't go into.

How is gravity like a force at all, even in Newtonian physics? It seems like mismatched units. Gravity is an acceleration, not a force. F=ma, right? So if gravity were a force, it would produce an acceleration that was dependent on the mass, and it doesn't, so it seems to me like the only sense in which gravity is a force is if you define force as "something you can't see that makes things move", which is a pretty useless definition.

Given the small 'g' acceleration due to gravity, can we calculate the mass and dimensions of the object that is the reason for that value of g ?

Is there such thing as a force then, I heard they invented some model in which fundamental forces are just curves in folded dimensions or something.

Gravity is a force in the same way the centrifugal force is a force

An artifact of rotating coordinate frames in one, the curvature of spacetime in the other

What I don't get is when I'm standing on the Earth, I'm in an accelerating frame, but what direction am I accelerating in?

Not just free-fall parabolas. Think about the path airplanes traverse when they go to another continent. Still a parabola, but flattened.

The way I understand it. We are moving towards the ball the ball dis not fall back it just accelerated away from us for a while.

Seems rather tricky to invent anti-gravity when gravity is just an emergent phenomenon of distortions in the spacetime fabric.

Gravity creates the stage (spacetime) upon which other forces (electromagnetism, strong and weak nuclear forces) can play out?

(off topic) i thought the title is "gravity is not free", hmm thanks that's an interesting topic for a story..

General Relativity may be a theory with an excellent prediction power but to me it is the one that's lacking in realism (as in the philosophical definition)

It's not a fundamental problem, nobody has abandoned Maxwell's equations for EM except for the most specific cases, but it's a similar case.

There's probably a better explanation than just "distortion of space time" which is a great way of viewing it, but it's a bit of a stretch (pun intended)

So gravity is not a force even though it acts on mass as a force? This is really confusing.

Can anybody sane tell us what gravity is in the case of flat space-time?

but the calculation of time dilation due to a gravitational force results in a DIFFERENT amount than time dilation due to accelerating in a spaceship at one G. So the equivalence principle would fail- I can tell if I am accelerating due to gravity or if I am accelerating due to motion by measuring time dilation. Without doing the math you can know this is true by looking at the age of a person on the ground on earth and the age of a person in a spaceship accelerating at 1 G. The spaceman will experience greater time dilation (age slower) as his speed approaches that of light. In a spaceship people will age slower. But both people will only feel 1 G.

my physics teacher would always say that "Gravity is not a force, but we experience a force due to gravity and call it weight"

So ... what is terminal velocity then?

You could call inertia a force then.

if it is not force how come there is movement? where is the force coming from?

How would you define it ?

F = ma

F means force. Gravity is a type of acceleration, not a force without being multiplied by a mass!

Sooooo planet Earth is actually flat? :)

How can we manipulate gravity?

relevant XKCD

https://xkcd.com/123/

How would periodic “free-fall” motion look in this setup? E.g. a point mass orbiting around a body, or a point mass oscillating back and forth in a 1D gravity well.

Bullshit. Space-time is just an abstract concept.

Gravity is not a force. The surface of the Earth is moving up to the object in free-fall at an acceleration of 9.8 m/s^2. The force pushing the surface, and the pressurized atmospheric shell, upward is a result of the processes occurring within the Earth (likely, in particular, those within the the core).