So how is it accelerating (two rockets in space)

[Avalon_18]

Assume that there are 2 rockets in deep space or a place where there is nothing around to compare their motion to. Rocket A starts its thrusters but the observer in rocket A doesn't know about it. So my question is, if rocket A is considered to be stationary by the observer then how can he describe the acceleration of B which is not firing its thrusters. (Sorry for the bad framing of the question)

 

[gleem]

(Sorry for the bad framing of the question)

I think you should try again, If rocket A fires its thrusters Observer in A will know it. How is B accelerating if nothing is around to affect B and he is not firing his thrusters?

 

[phinds]

Rocket A starts its thrusters but the observer in rocket A doesn't know about it

So, is he asleep or what? If you mean the acceleration is so low that he doesn't feel it then that's possible but if he were standing on a sensitive enough scale, he WOULD know it.

 

[hilbert2]

The observer will feel the acceleration of the rocket. Free fall in gravitational field is pretty much the only situation where you can't feel your acceleration (but even then there's a small tidal effect that can be observed in principle).

 

[Avalon_18]

The observer will feel the acceleration of the rocket. Free fall in gravitational field is pretty much the only situation where you can't feel your acceleration (but even then there's a small tidal effect that can be observed in principle).

What if we assume that every part (atom) inside the rocket accelerates simultaneously so that every thing in rocket A relative to itself doesn't move.

 

[Nugatory]

What if we assume that every part (atom) inside the rocket accelerates simultaneously so that every thing in rocket A relative to itself doesn't move.

The only force that can do that is gravity - you're describing free fall, not what happens when a rocket is running its thrusters.

If both objects are freely falling under the influence of gravity, then it is completely arbitrary which one we say is really accelerating. In fact, in the modern theory of gravity (Einstein's general relativity) we don't even try to answer that question - the thing we calculate is the distance between them and how it is changing.

 

[russ_watters]

What if we assume that every part (atom) inside the rocket accelerates simultaneously so that every thing in rocket A relative to itself doesn't move.

When you are in an elevator, can't you tell when it starts and stops moving, even with your eyes closed?

A broader way to look at this is that if you deny an observer information, they may not be able to tell what is happening in a certain situation. But their inability to tell what is happening does not change/affect what is happening.

 

[Nugatory]

if rocket A is considered to be stationary by the observer then how can he describe the acceleration of B which is not firing its thrusters.

There's an answer at the bottom of this long post... I promise :)

The word "acceleration" is used for two different things: coordinate acceleration and proper acceleration. You've mixed the two up in this question (probably without realizing it).

Proper acceleration is caused by a force that you can feel: if you're standing on a spring scale in a spaceship, you'll know when its motors are firing and proper-accelerating you because you'll feel heavier and the scale will give you numerical confirmation that your weight has increased. You don't need any external reference to determine whether something is experiencing proper acceleration; either the springs in the scale are compressed or they aren't, and all observers everywhere will agree about this.

Coordinate acceleration is something you calculate for things that you're observing (perhaps including yourself). You pick an arbitrary point and declare it to be "not moving"; now we can define velocities for things that are moving relative to that point. (Often the arbitrary not moving point is the surface of the Earth and then we may not even recognize that we've made an arbitrary choice - if I say that a car is moving at 100 km/hr you'll assume that I mean "relative to someone standing at the side of the road" instead of, for example, "relative to the center of the solar system"). Now we can calculate the coordinate acceleration; it's just the rate at which the velocity is changing.

When we say that a dropped object is accelerating, we're talking coordinate acceleration, not proper acceleration. We've chosen to consider the surface of the Earth as not moving, the object starts with a speed of zero when we drop it, one second later it's moving at 10 m/sec relative to the surface of the earth, two seconds later it's moving at 20 m/sec, and so on until it collides with the ground.

And so with that long explanation, we can answer your question: whichever rocket is firing its thrusters is experiencing proper acceleration. Either observer is free to consider himself at rest and describe the situation as "I'm at rest; the other ship is coordinate accelerating" and analyze the physics from that point of view.

 

[cb83]

Does the observer need to know that they are moving to react.
Example: When you are in your car stopped (with your foot on the brake) on an incline at a stop light, another car pulls up beside you and stops. While you are looking at the light you notice the car next to you rolling backwards. How do you react? By pushing down harder on the brake. So, the follow-up question: Should perception of motion be allowed when discussing motion?

 

[russ_watters]

Should perception of motion be allowed when discussing motion?

As opposed to what?

I suppose if we outlaw the use of all sensors and perceptions we can make motion undetectable. But what do we win?

 

[jbriggs444]

I suppose if we outlaw the use of all sensors and perceptions we can make motion undetectable. But what do we win?

A Helen Keller kewpie doll?