# If the distance between two objects is increasing with increasing rate, can we determine which object is under influence of force?

Suppose two bodies, A and B, are together in free space. One of them, let’s say- A, accelerates away, then retards, stops, accelerates back and stops again when it reaches B.

Although we can see the objects separating and reuniting, can we be certain about the fact that it was A which really accelerated and not B? Can we determine which object was actually under influence of force? Can any experiment conducted by A or B settle the dispute?

I think that the answer is 'no'. I will explain why I think so presently. But interestingly, if I am correct, and there is no certain way of knowing which object it was that accelerated, then how can one of them end up being younger than the other on their reunion?

So, can we determine which object accelerated? I think no. Suppose A decides to conduct an experiment to find out whether it is under influence of a force or not. To conduct an experiment, A needs an experimental setup. Now, it would be wise for A to keep his experimental setup at rest with him. This means that if A is accelerating, so would his laboratory.

What I mean is this- if a person is confined in a room where all the objects are at rest with respect to him, also meaning that all objects are under influence of same force per unite mass if need be, then no experiment conducted in the room can determine whether the room is accelerating or not.

So, let’s say that A and B are holding a glass of water each. Now, when our experiment starts, one of them accelerates. Let’s say A's glass spills due to inertia while B's does not. B would argue that this is because A has accelerated. A can argue that this is because B and the water in his own glass accelerated together (they were charged, and accelerated when an electric field was introduced). B's glass does not spills because the whole of B, with the glass and the water, can be considered uniformly charged.

Can this dispute be resolved? If not, I think there is symmetry in such situation, and both objects would observe the other object return younger, in parallel universes.

• You are seriously over-thinking this, in my opinion. A person subject to an acceleration/deceleration is subject to a force ($F=ma$) which can be felt or observed with the simplest of experiments like a pendulum. One can therefore not undergo an $a$ without experiencing it. – Gert Oct 18 '15 at 14:56
• Not really, though your examples are a little confusing to read... – Horus Oct 18 '15 at 14:57
• @Gert: You are, maybe, assuming that the person under influence of acceleration is accelerating non uniformly. Suppose each particle of an object accelerates uniformly. Assume that it is uniformely charged and is put under uniform electric field. Will it still feel experience acceleration. As for pendulum, who said the bob of the pendulum was not the thing which experienced an equal and opposite force? – Prem kumar Oct 18 '15 at 15:51
• @horus: I will try to edit so that my examples are less confusing. – Prem kumar Oct 18 '15 at 15:52
• @Raja: you need to understand equations of motion: the whole pendulum experiences the same $a$ but the inertial forces aren't the same. Most of the pendulum will remain stationary (with regards to the reference frame) but not the bob. Re. electrical fields, inertial forces always act, regardless of what field the object finds itself in. – Gert Oct 18 '15 at 16:02

The glass of water constitutes an accelerometer capable of measuring the acceleration of a vehicle. If the glass is held stationary with respect to the vehicle, movement of the water can reveal any acceleration with a component parallel to the surface of the water (and in special cases, perpendicular to it, but we'll ignore those for simplicity).

In the scenario you mentioned, one object accelerates away from the other but only A's glass spills. We can unambiguously take this to mean that A's ship accelerated, because otherwise there is no mechanism by which the water could be "pushed out" of the glass. (Actually, more accurately, the glass is pulled out from under the water, which stays still due to inertia.) This would occur whether there is a Ship B or not, because each object's inertia is independent of each other object. In other words, there would be no way for Ship B to cause A's water to spill simply by accelerating away.

In relativity, only velocity is relative. Acceleration is absolute in all cases in all reference frames.

• You say-"A's glass spills. We can unambiguously take this to mean that A's ship accelerated". This can also mean that B as well as the glass accelerate away from 'A'. Suppose B and the glass are negatively charged. Suppose the cause of acceleration is introduction of uniform electric field, which does not affects A or the water. So, although there would be no way for the Ship B to cause A's water to spill simply by accelerating away, both events might occur together. So, B accelerates. – Prem kumar Oct 18 '15 at 15:40
• What is your answer, by the way. Are you saying that A would be younger when they meet again. How do you explain this result given that B and the glass are charged and they accelerate away from A due to electric feild which was introduced? – Prem kumar Oct 18 '15 at 15:44
• @Raja If A accelerates by firing its engines, it observes B and the glass "accelerating" in the same direction, but B's glass doesn't spill. If B and the glass repel or attract each other with a charge, they accelerate in opposite directions, and B's glass spills because B is accelerating. It's simple to determine the difference. – Asher Oct 18 '15 at 16:00
• @Raja and as always, the one that doesn't accelerate ages more than the one that does. – Asher Oct 18 '15 at 16:02
• @Raja: I'm upvoting Asher's answer because it is correct, including the last line. – Gert Oct 18 '15 at 16:05