# Gravity not a force

It's precisely because we identify the four-force as something that all freely-falling obsrevers agree on. An object that is freely falling experiences zero four-force, and hence, because the four-force is more useful than ordinary force, we tend to use that versus ordinary force. [..]
Thanks for the clarification! You seem to say that "Gravity is not a force" really means "Gravity is not a four-force". That is a concept that may need more elaboration, in particular for non-falling observers. And what happened to Einstein's gravitational field?

D H
Staff Emeritus
Science Advisor
You can explain the tides in terms of motion in a circle, with all the 'forces' we're familiar with.
No, you can't. At least not correctly. The centrifugal force explanation of the tides is fundamentally flawed; it happens to get the right result thanks to a lucky cancellation of errors. That circular motion explanation utterly fails for a Moon-sized object falling straight toward the Earth. When that object is at a distance of 384,400 km from the center of the Earth, the tidal forces exerted by it on the Earth would be exactly the same as those exerted by the Moon itself when it is 384,400 km from the center of the Earth.

The right way to explain tides from the perspective of Newtonian mechanics is to examine at the difference between the gravitational acceleration at a point on the surface of the Earth toward some other object (the Moon, the Sun, Jupiter, ...) and the gravitational acceleration of the Earth as a whole toward that object. In other words, compute the gravitational acceleration at a point on the surface relative to the Earth as a whole. Another way of looking at it: An Earth-centered frame is a non-inertial frame since the Earth is accelerating Moonward (and Sunward, and toward Jupiter, ...). The apparent gravitational acceleration at a point on the surface of the Earth is identically equal to this aforementioned difference.

Note that the motion of the tide-inducing object does not come into play here. All that comes into play is that this object causes other objects to accelerate toward it due to gravitation, and that this gravitational acceleration is not uniform. (There are no tides in Newtonian mechanics in a uniform gravitational field). When that Moon-sized object falling straight toward the Earth and the Moon are equidistant from the Earth, those two objects will exert the same tidal force on the Earth.

You don't need something as big as the Earth to observe these tidal forces. Outfit a spacecraft with an accelerometer placed far from the spacecraft's center of mass. If that accelerometer is sensitive enough, it will sense a tidal force because the spacecraft is a (more or less) rigid body and because gravitational acceleration at the accelerometer's location is falling at a slightly difference from that at the spacecraft's center of mass.

How can tidal forces not be taken care of in GR? They're only there because of what, presumably, GR predicts.
The spacecraft example above leads to how tidal forces can be addressed in GR. Suppose the distance between the spacecraft's center of mass and the accelerometer is many orders of magnitude less than the distance between the spacecraft and planet. This means we can linearize the tensor mathematics that describes the curvature of spacetime. What you'll get is the same prediction as the that predicted by in Newtonian mechanics. Things get hairier if that linearization isn't valid such as when the spacecraft is in the close proximity to an extremely massive object, but tidal forces can still be calculated. Tidal forces become much stronger than those predicted by Newtonian mechanics in case of extreme curvature of space-time.

I read somewhere that gravity is not a force. Is this true? What does it mean?
really gravity is not a force it is property of object by virtue of an object attract other object

Nugatory
Mentor
If these two travellers stop walking, do they experience anything? Is there any Force acting on them to make them continue getting closer to the Pole? I do understand this is just an analogy but I feel it is too far away from the point about the 'reality' or otherwise of a gravitational force. You would need to say what the equivalent of a force is for these two travellers. It certainly couldn't be the same as the 'force' that pulls two masses together because the analogy is not 1:1.
We are getting very far from OP's question, but the analogy is better than you're giving it credit for being; indeed, I've seen it used in serious introductions to GR. It works because in GR there's no such thing as standing still - in four-dimensional spacetime you're always moving in the time direction.

I can see that GR tries to explain the origin of a force like the one that the proximity of two masses causes but, if the effect is the same as that which occurs between two charges, then why is it not allowed to be called a force? What distinguishes the one 'force' from the other force apart from the difficulty in detecting it?

The essential difference is that with gravity you can always find a (local) frame of reference where the gravitational force is zero and test particles just continue moving inertially. This is the case for all the so-called "fictitious" forces; for example if you're standing on the surface of the earth and in the northern hemisphere, you'll believe that there's a force that deflects south-moving objects towards the west, but viewing the situation from space it's clear that the southwards-moving object is just moving in a straight line while the surface of the earth moves underneath it.

You cannot find a similar transformation with the so-called "real" forces; for example a charged and an uncharged particle test particle will always behave differently in the presence of an electric field.

The distinguishing characteristic of the "fictitious" forces such as gravity is that their strength is always proportional to the mass of the object being acted upon - this is why all objects accelerate at the same rate under the influence of gravity, regardless of mass. It is also why the fictitious forces can be made to disappear in some local frame, by choosing a suitable frame of reference.

BruceW
Homework Helper
Weight is a readily perceived and measured force - given the appropriate equipment - so why are we not 'allowed' to treat gravity as a force? It is such a tangible thing that it seems to me that the purist tail is wagging the dog of experience.
Then we should be allowed to treat centrifugal force as a real force too. In general relativity, you can't have one defined as a real force and not the other.

Edit: that's the beauty of general relativity - you can use whichever coordinate system you want. But this means we must accept that gravity and fictitious forces are one and the same.

Edit again: You could say that the coordinate system comoving with the expansion of the universe is the only true coordinate system, and use this coordinate system to judge what is gravity and what is fictitious force. But this seems like an unnecessary extension to me, without much insight gained.

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sophiecentaur
Science Advisor
Gold Member
2020 Award
No, you can't. At least not correctly. etc
Thanks for that. I learned sunnink today!

Then we should be allowed to treat centrifugal force as a real force too. In general relativity, you can't have one defined as a real force and not the other.

Edit: that's the beauty of general relativity - you can use whichever coordinate system you want. But this means we must accept that gravity and fictitious forces are one and the same.

Edit again: You could say that the coordinate system comoving with the expansion of the universe is the only true coordinate system, and use this coordinate system to judge what is gravity and what is fictitious force. But this seems like an unnecessary extension to me, without much insight gained.
Strictly speaking GR doesn't identify "real" or "fictitious"; it depends on the used coordinate system and one's interpretation what one calls fictitious and what real. That doesn't mean that gravity and fictitious forces must be one and the same - rather the contrary (see my post #20)!
It probably depends on what one means with "fictitious" in this context. In my world, "fictitious" forces are imaginary (or even occult) forces, without an identified corresponding physical cause (see also the footnote in my post #20).

EDIT: what is your definition of "field" in physics?
As I stated earlier I'm a purist, and consequently very recently due to a discussion here I recently adapted my definition of "field" to the original one, which is more logical.

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Nugatory
Mentor
It probably depends on what one means with "fictitious" in this context. In my world, "fictitious" forces are imaginary (or even occult) forces, without an identified corresponding physical cause

"Fictitious" is an unfortunate word, although given the history it's easy to see how it came into use and why it persists.

K^2
Science Advisor
It probably depends on what one means with "fictitious" in this context. In my world, "fictitious" forces are imaginary (or even occult) forces, without an identified corresponding physical cause (see also the footnote in my post #20).
The term "fictitious force" is strictly defined in physics. If you misunderstand it, that is your problem and yours alone.

Gravity is a fictitious force under General Relativity by definition of the former. This is not something that deserves an argument.

I think that True or False depend on our definition , anything's relative

The term "fictitious force" is strictly defined in physics. If you misunderstand it, that is your problem and yours alone.
http://en.wikipedia.org/wiki/Fictitious_force
As you say, "if you misunderstand it, then that is your problem"; but "yours alone" is not sure as there could be more people who misunderstand it. Importantly, the purpose of this forum is to help each other.
Gravity is a fictitious force under General Relativity by definition of the former. This is not something that deserves an argument.
Anyway, the question of this thread here does not concern "fictitious" but "force"; as someone brought it up it was useful to explain what people mean with it and why, but an argument about it is out of place and distracts from the topic.

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I think that True or False depend on our definition , anything's relative
Hi superbk welcome to physicsforums.
I largely agree that if gravity is a force depends on definitions, and many people have explained that here with more details.

Note: Suddenly it strikes me that markf has not come back yet with his feedback - and he already received 36 posts in answer! :uhh:

markf, can you give feedback? Did you find any answers helpful?

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as i told you before gravity is not a force it is the property of any thing which has mass

D H
Staff Emeritus
Science Advisor
as i told you before gravity is not a force it is the property of any thing which has mass
Here's what you said before:

really gravity is not a force it is property of object by virtue of an object attract other object
This is pretty much meaningless and doesn't answer the question. The ability of an object to attract another object? That is, in a sense, the definition of a force.

Whether gravity is or is not a (real) force is a matter of point of view. In Newtonian mechanics, objects subject to gravitation undergo acceleration when viewed from the perspective of a Newtonian inertial frame. So gravitation is a real force in Newtonian mechanics. In general relativity, gravitation is not a real force. It's a tautology. Objects that are subject to gravitation only are free-falling. A free-falling frame is a local inertial frame in general relativity, by definition.

As Khashishi said way back in post #8, "I think physicists don't get too worked up about what exactly constitutes a force." Or, quoting Shakespeare, "What's in a name? That which we call a rose by any other name would smell as sweet."

according to the theory of General Relativity, there is an equivalence to a body falling in free fall to an identical body out in free space traveling at a constant velocity.

what a big mass (like a planet) does is warp or curve space in such a way so that objects flying about freely in this curved space appears to us in our Euclidian space to be following a curve where it just appears that a force is acting on the body that causes its path to be curved toward the center of that big mass.

But it still takes force to escape curved spacetime. So what is curved spacetime? Is it akin to a hole in the ground? Isnt it any more a force, than a barrier in your way is, which you have to break through?

One more question, wouldnt that imply, that there is such a thing as maximum gravity? If we think of gravtiy as curved spacetime, then eventually spacetime reaches a point where it is bent by mass in such a way, that it exercises a maximum pull, with any further alteration of spacetime dimnishing its gravitaitonal pull.

K^2
Science Advisor
But it still takes force to escape curved spacetime. So what is curved spacetime? Is it akin to a hole in the ground? Isnt it any more a force, than a barrier in your way is, which you have to break through?

One more question, wouldnt that imply, that there is such a thing as maximum gravity? If we think of gravtiy as curved spacetime, then eventually spacetime reaches a point where it is bent by mass in such a way, that it exercises a maximum pull, with any further alteration of spacetime dimnishing its gravitaitonal pull.
Verstein, you need to learn a bit about differential geometry. The short answer to both of these is "no", but you need to understand how curvature in general manifolds works to go on further. How are your Calculus and Linear Algebra?