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I wanted to ask the same question in different ways.

1.Consider the below example whereby we have a man M in a box B in outer space. B is acted upon by a force, F. B moves in direction of F. As the force F acts on B & not on M, M appears to move in the opposite direction to that of B(though M isn't really moving). M doesn't know that B is acted upon by F as he cant perceive it. But what he feels is that he himself is acted upon by a force F1 which is in opposite direction to F. F1 is the fictitious force acting on M in response to the real force F.

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So if in a context where you now consider B as the spacetime & F1 as the gravity, then what is F? In this context, notice that because you now consider B as spacetime, there are now no walls for B. Is F an effect of say, a mass (near to man M) on its nearby spacetime ? So is it that the mass applies an unnamed real force F on the spacetime around it causing it to curve and the curvature being produced is the fictitious force called gravity? Or in other words, we have the centripetal force as counterpart for centrifugal force. Centripetal force is a real force. So is there any for gravity? Or if there isn't any, why gravity can't be thought of similarly in this way to suspect a real force counterpart?

2.Asking this in a different way (but basically the same question), if fictitious forces arise in a non inertial reference frames, and if gravity is a fictitious force, that could imply the spacetime is a non inertial reference frame. So Why is spacetime a non inertial reference frame or accelerating reference frame in the first place? What specifically makes it so? Is it due to some real force acting on it? If so, what is it? Or is it that we never thought to think that way? (Because usually you get a non inertial or accelerating reference frame when a real force acts on it externally. That's why I am searching for a real force in this context.)

3.If gravity is a fictitious force & is basically the curvature of spacetime (hence not a real force) & mass (or stress-energy tensor whatever!) is what that causes the curvature, could it be said that the mass curves the spacetime by applying an unnamed real force directly on the nearby spacetime ?

4.My question asks basically don't we need a real force to explain why mass (or stress-energy tensor whatever!) curves spacetime? (atleast locally)

5.Lets say a mass or its stress energy tensor causes nearby spacetime to curve. Other masses near this mass move along their respective geodesics that appear to the 1st mass as if its curved & hence accelerating. (Even if these masses are moving with constant four velocity on geodesics, there is acceleration because of change in direction of motion of these masses as viewed by the 1st mass).So it can be thought as a 2 step process-1.effect of mass on nearby spacetime & 2.the effect of this nearby curved spacetime on the motion of other masses.So lets think the 1st step is due to a real force the mass acts on the nearby spacetime.(You might ask me why I think the effect of mass on nearby spacetime as a real force or even a force? A force is something that acts on a mass. But how can it act on spacetime? Spacetime has no mass. But spacetime has mass, right? Because it has zero point energy & energy is mass). And the motion of other masses appear to be accelerating due to the curvature produced by that real force. Note that the real force I asked to imagine acts on the nearby spacetime; not directly on the other masses. So even if the real force acts on the nearby spacetime of the 1st mass, it affects indirectly the motion of other masses in the vicinity. What 1st mass appears to see is that it directly affected the motion of other masses. As for the 2nd step, there is no force by which the spacetime acts on other masses. Its just because spacetime is curved, the masses follow their respective curved paths. Its due to the curvature. There's no real force there. So a fictitious force could play the role of a force in the 2nd step. Now if that fictitious force is what we name as gravity, what plays the role of real force for the 1st step? Or does gravity play roles in both the steps (in which case its both a real & a fictitious force)? But how can a thing be both real & fictitious force? A Fictitious force causes the same acceleration in objects of different masses unlike a real force. Gravity exactly does this (atleast locally). So its counterintuitive to think its also a real force. But I think you can come up saying that gravity is also a real force because it is different from our usual notion of concept of force in that when it acts on a mass B due to a mass A so as to cause a change in the motion of mass B, it acts so by disturbing the spacetime in between the 2 masses by curving, pulling & twisting. Usually forces act linearly. But maybe gravity doesn't. But that's a whole new idea to come up saying that gravity acts curvilinearly. I am sceptical about it. So given the fact that forces act linearly only, what is then the general consensus about whether its a fictitious force or a real force or both? I think that its fictitious locally but acts as a real force globally as globally the gravitational field is no longer uniform. But then if its fictitious force locally, what plays the role of real force locally?

There were related questions in this site but are not same.

Intuition for why mass and energy curve the space-time fabric and for why this relationship is linear?

Why exactly space curves due mass in space

Does spacetime have a "mass" value? or What is "Spacetime" made out of?

EDIT: I did some amount of reading. My question above holds true if gravity is fictitious. But I found that gravity is not fictitious. And in short, that is the head-on way to tackle this question. Because the question is closed , I cant answer this below.

In most scenario's of freefalling objects, we tend to miss the motion of the earth towards the object. If we take that into account, we come into conclusion that the heavier mass fall & reach the ground first. So to a person standing on earth the heavier mass has more acceleration. This is not what happens with a fictitious force. For fictitious force the person on earth would measure same acceleration for heavy & light masses.

CuriousMind9
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    If there is no friction between the man and the box then the man will not feel anything until he hits the wall. Are you assuming some force that keeps the man at rest relative to the box? (Somewhat of a hint here) – BioPhysicist Oct 22 '19 at 16:49
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    I see you have edited your picture. If the man is just floating in the box then he will not feel any forces until he hits the wall of the box when it reaches him – BioPhysicist Oct 22 '19 at 17:13
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    @AaronStevens He may, on the other hand, feel fear, surprise, or confusion, as the end of the wall starts moving towards him (probably all depends on the velocity). – JMac Oct 22 '19 at 17:16
  • The man in the example isn't at rest wrt the box during the time when he moves towards the wall of the box due to the fictitious force. I specifically mentioned the box was in outer space .This is the reason why you see the man M floating in the box. But my question is different. B is a non inertial frame of reference. If B is the spacetime & F1 is the fictitious force which is gravity, what is F ? We have counterpart for centrifugal force which is the centripetal force. Centripetal force is a real force. So is there any for gravity? – CuriousMind9 Oct 22 '19 at 17:21
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    If you are in a frame accelerating with $B$ then you also see the man accelerating. In your frame of reference you can explain the acceleration of the man through the use of fictitious forces. But this is in the accelerating frame. What the man feels has nothing to do with the frame you choose to do your physics in. He will just float there until the wall hits him. – BioPhysicist Oct 22 '19 at 17:33
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    Centripetal force is not the counterpart of the centrifugal force. They just end up canceling out for objects undergoing circular motion when viewed from a reference frame rotating with the object. But in general you can have a centrifugal force without any centripetal forces. And you can have only centripetal forces if you are not working in a rotating reference frame. Therefore, they are not counterparts of each other at all. – BioPhysicist Oct 22 '19 at 17:59
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    Fictitious forces arise when working in a certain non-inertial reference frame. They have nothing to do with the system being analyzed. – BioPhysicist Oct 22 '19 at 18:08
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    @Aaron Stevens- By counterpart I meant centripetal & centrifugal forces to be action reaction forces (Newtons 3rd law). Anyways I didn't know that generally fictitious forces could exist without real forces. It was a new insight. – CuriousMind9 Oct 22 '19 at 18:11
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    No, that is incorrect. Newton's third law breaks down in non-inertial reference frames when you bring in fictitious forces. The fictitious forces do not have a force paired with them. They exist due to working in a non-inertial frame only. That is why they are called "fictitious". – BioPhysicist Oct 22 '19 at 18:13
  • @Aaron Stevens- Ok got it. – CuriousMind9 Oct 22 '19 at 18:16
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    @Aaron Steven- If fictitious forces arise in non inertial reference frames, and if gravity is a fictitious force, that could mean the spacetime is a non inertial reference frame. Why is spacetime non inertial reference frame? What specifically makes it so? Is it due to some real force acting on it? Because usually you get a non inertial reference frame when a real external force acts on it. – CuriousMind9 Oct 22 '19 at 18:29
  • Because fictitious force isn't a force really acting on an object,I understand Newtons 3rd law doesn't apply there.But Is there any example where there is no corresponding real force for a fictitious force? I couldn't think of any.Even in the example of tides, at first glance gravity between the earth & the moon sort of acts like the real force.But because its fictitious, you might conclude that the scenario has only fictitious forces.But any scenario in which gravity appears to play as real force, its actually played by gravity's real force counterpart.So it again boils down to this question. – CuriousMind9 Oct 26 '19 at 15:55

1 Answers1

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Your question is based on a misunderstanding.

Einstein's argument about gravity as a fictitious force in an accelerating reference frame was posed as an argument for the equivalence principle, which says that all objects in a uniform gravitational field should fall the same way regardless of their mass. However, it's not really a model for gravity. For example, the accelerating-box model doesn't account for gravitational tides, which are a real and important effect.

In general relativity, gravitation is a "curvature force." Mass and energy distributions alter the curvature of spacetime, and the trajectories of low-mass particles are geodesics on this curved spacetime.

rob
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  • 'However, it's not really a model for gravity. For example, the accelerating-box model doesn't account for gravitational tides, which are a real and important effect.'. I didn't understand it. Why cant this model of accelerated box explain tidal forces? Because I think I can – CuriousMind9 Oct 26 '19 at 19:18
  • I understand that differential effects of gravity due to moon on either side of earth produce tidal force which is fictitious – CuriousMind9 Oct 26 '19 at 19:19
  • There is more gravity on side of earth near to moon than on opposite side.Its same to say a box kept on that side accelerates more towards the moon than the another one kept on the other side. Hence a man inside that box feels differently about the fictitious force acting on him than another man inside the other box on the opposite side of earth. This differential effect results in tidal force. – CuriousMind9 Oct 26 '19 at 19:19
  • so I explained it with accelerated box model.Then why may I know you are saying its not a model for gravity? – CuriousMind9 Oct 26 '19 at 19:20
  • The question was basically if gravity is fictitious, whats the real force in the scenario? For example if you are in a box.An external force F accelerates the box. You experience a fictitious force F1.In this example F is the real force. So whats the real force corresponding to gravity? – CuriousMind9 Oct 26 '19 at 19:21
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    Those give the stretching part of the tidal force, but not the squeezing action in the transverse plane. – rob Oct 26 '19 at 19:21
  • Because you cant explain the squeezing action in the transverse plane by accelerated box model, is gravity then not fictitious? – CuriousMind9 Oct 26 '19 at 19:35
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    At the risk of repeating myself, gravitation (in general relativity) is a curvature force. – rob Oct 26 '19 at 20:36
  • What is a curvature force? – CuriousMind9 Nov 05 '19 at 10:21
  • @CuriousMind9 See https://physics.stackexchange.com/a/186630/44126 – rob Nov 05 '19 at 12:59
  • So do you mean curvature force as a force that acts between 2 (or more) curvatures so as to reduce the overall curvature of the system? – CuriousMind9 Nov 05 '19 at 15:21
  • If so, I think it relates to how we view gravity globally. – CuriousMind9 Nov 05 '19 at 15:53