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This is a term from classical mechanics. A fictitious force is a force that is only present in a so-called non-inertial frame. This means that the observer is experiencing some kind of acceleration. The point is that if the observer is accelerating then he might see some forces that are not really forces at all.

If you are in a rotating frame you are accelerating, and you feel a centrifugal force. However anyone looking at you while not rotating themselves will say that there is no such force at all.

Imagine you are on a horse in a merry-go-around and the thing malfunctions and starts to rotate very rapidly. You will feel the centrifugal force trying to blow you away from the center. However someone standing next to the merry-go-around sees no such force. What he sees is you holding on to the horse, but it is YOU holding onto the horse that is providing a force, if you would let go you would just fly in a straight line and no force would work on you.

It is a little difficult to explain it very well in words, in the relevant links I have posted a link that points to the wikipedia article for the Coriolis force (a fictitious force) and figure 1 there shows a nice picture of the above.

In General Relativity however, there is no preference for inertial frames anymore and you are valid in claiming there is a force pushing outwards. This force is then gravity. This is direct consequence of the equivalence principle that states that gravity and acceleration are indistinguishable (in a suitable limit).

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Q: Why is the centrifugal force the ladybug feels in the rotating frame called fictitious force?
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