If there is no absolute reference frame, why do fictitious forces exist?

Question

According to relativity (both Galilean and Special) no reference frame is fixed, but if that were the case, why do we feel fictitious forces when being in a car that's accelerating with respect to a road?

And why is that force proportional to the car's acceleration with respect to the road?

Wouldn't it imply that the road was a fixed, absolute reference frame?

It would be folly to admit that the road was an absolute reference frame, that's true, but since it's not an absolute frame (because such things don't exist) why is the fictitious force exercised?

Answer 1

why do we feel fictitious forces when being in a car that's accelerating with respect to a road?

We don't feel them, just like we don't feel gravity force. Although they are present in accelerated frames, what we usually feel e.g. in accelerated bus are the actual interactions - pressure, friction (real forces) - due to contact with bodies moving with the bus in accelerated motion (bus floor, seat, handle).

Fictitious forces are mathematical terms introduced into $\mathbf F'_{net}$ in order to achieve validity of the Newton 2nd law equation $\mathbf F'_{net}=m\mathbf a'$ in non-inertial frames. In different accelerated frames, acceleration is different, net force is different, but real force is the same in all frames, thus the sum of all fictitious forces is different in different frames.

The fact this (preservation of the 2nd law equation) can be achieved by introducing fictitious forces does not single out any single inertial reference frame though.

Answer 2

According to relativity (both Galilean and Special) no reference frame is fixed.

This is correct. However, they do single out a set of frames, the so called inertial frames. These are the frames, in Galilean relativity, where objects with no net force on them travel at uniform speed in a straight line or remain at rest (this is just a specialisation of the former for zero speed).

but if that were the case, why do we feel fictitious forces when being in a car that's accelerating with respect to a road

This is because an accelerating frame is not an inertial frame. The frame, to accelerate, must feel a force and then for the car frame, this force is transmitted to your body. And so you feel a 'fictitious force'. However, in this case the force is real.

Instead, consider a ball freely moving in space. Thus it is moving in a straight line at constant speed. Then suppose you shoot by in an accelerating rocket. Then the ball, from the rocket frame looks as though it is accelerating. Thus it, by Newton's second law, looks as though a force is applied to the ball to make it accelerate. This is a fictitious force.

Answer 3

Acceleration is a change in velocity, which everyone can agree on even if they don't agree on which velocity is "moving" and which is "stationary". As an analogy, the concept of "here" is relative. Bob says "here" is London, Alice says "here" is Paris, so they disagree on here; but they agree that they are in different places and even on the relative distance between them.

Answer 4

The centripetal force is considered 'real' caused by Lorentz force (Electrodynamics) between wheel spokes atoms. The centrifugal force is considered fictitious.

Consider the following paper: https://arxiv.org/pdf/1112.5618

It appears even inertial frames in relative motion disagree on the direction of the real forces, though disagreement on simultaneity has to be considered.

@Ján Lalinský

Fictitious forces are mathematical terms introduced into F′net in order to achieve validity of the Newton 2nd law equation F′net=ma′ in non-inertial frames. In different accelerated frames, acceleration is different, net force is different, but real force is the same in all frames, thus the sum of all fictitious forces is different in different frames.

Ján, please, are there real forces bending the wheel spokes in the primed frame?

Answer 5

Fictitious forces exist because there is no such thing as an absolute reference frame - the magnitude, direction, or even existence of a fictitious force depends entirely on your choice of reference frame. They're simply bookkeeping tools that are used to explain motion from the point of view of a non-inertial (accelerating) reference frame. Note that there are an infinite number of inertial (non-accelerating) reference frames, none of which utilize fictitious forces.

The inertial frame of the road isn't an "absolute" frame since there are many other frames that also don't use fictitious forces, in which the free body diagram looks exactly the same. Inertial frames as a class do tend to be preferred in many cases, since all the forces acting in that frame have real physical causes - friction, drag, engine torque, etc. But this is also true in any other inertial frame, like the frame of a car driving straight down the road at a constant speed. From the point of view of a passenger in a turning car, on the other hand, there is a fictitious force with no apparent physical cause.