# Questions on the notion of an inertial frame of reference

Imagine an astronaut flying in an spaceship at a constant speed in completely empty space, with no acceleration whatsoever, and no outside references, just dark empty space.

Q: Can the astronaut tell at what speed is he moving? and how do you define speed in that case when you have no outside references. Can you refer to the speed relative to the empty space?

Q: Can you identify the direction of your movement? Let's say ship moving nose forward, or tail forward? Is there a sense of "direction of movement" in such an inertial frame of reference?

Q: Imaging that the speed of that spacecraft is almost the speed of light "c - 1 m/s". But no acceleration. Meaning it's an inertial frame of reference right? Will you be able to throw a ball in the direction of movement? What about the direction inverse to the movement? Does that means that there is a direction of movement in an inertial frame of reference?

• " Imaging that the speed of that spacecraft is almost the speed of light "c - 1 m/s". " In what frame, is this the speed of spacecraft ? You said, it is moving in dark, completely empty space. In that case, it does not make sense to say, this is the speed of the aircraft, because, there is no other frame of reference in this universe Commented Jun 15, 2021 at 9:30
• @silverrahul yeah, good point... Commented Jun 15, 2021 at 9:50
• No, No, and No.
– user178659
Commented Jun 15, 2021 at 13:28

Q: Can the astronaut tell at what speed is he moving? and how do you define speed in that case when you have no outside references. Can you refer to the speed relative to the empty space?

No. This is already the case in Newtonian mechanics. Speed is always relative to some reference frame.

Q: Can you identify the direction of your movement? Let's say ship moving nose forward, or tail forward? Is there a sense of "direction of movement" in such an inertial frame of reference?

Again, movement is defined only with reference to some frame. If you are on a moving train and you start walking toward a toilet at the front of the train, you are actually experiencing train moving backwards, even though someone stationed on the ground would swear it moves forward.

In your case there is only one reference frame and that is the frame of the spaceship and everything is at rest in its own frame of reference (things are not moving relative to themselves).

Q: Imaging that the speed of that spacecraft is almost the speed of light "c - 1 m/s". But no acceleration. Meaning it's an inertial frame of reference right? Will you be able to throw a ball in the direction of movement? What about the direction inverse to the movement? Does that means that there is a direction of movement in an inertial frame of reference?

Again, the same answer applies. Since there is no acceleration, the frame of spacecraft is inertial. You claim it moves with certain speed, but relative to what? You are also moving with the speed close to the speed of light relative to some neutrino that just passed through you.

There is a relativity principle that claims, that all inertial movements are equivalent. Meaning, even though you might be moving with enormous speed relative to someone else, you will always feel like you are at rest and never observe any weird physics in the spacecraft.

• I dont get it, as I correctly understand from school, the faster your speed is the more energy you need to increase your speed even further. If all the frames were the same, it would mean the same amount of energy is required to increase speed with a certain percent, which is not true. Commented Jun 15, 2021 at 8:47
• > You claim it moves with certain speed, but relative to what? That is my very question, we know that nothing can move faster than light, what is light speed relative to? > This is already the case in Newtonian mechanics. Lets look at the real world, because according to Newtonian mechanics you can accelerate forever and there is no limit to the speed. Commented Jun 15, 2021 at 8:51
• @CorneliuMaftuleac It would not mean that. You tagged the question as special relativity, but let me explain it in Newtonian terms. The work done on an object is $W=F\Delta s$, where $F$ is applied force and $Delta s$ is distance the object traveled. The applied force is the same, but the distance traveled is different in different reference frames. So how much energy is getting transferred to the spaceship depends on the observer. In particular, in your own frame your distance is always zero, meaning, there is no increase of kinetic energy, even though the force might be applied to you(cont.) Commented Jun 15, 2021 at 8:53
• @CorneliuMaftuleac "what is light speed relative to" that is the thing about STR, its relative to everyone. The speed of light is the same whether it is me measuring it, or my friend moving towards it. The speeds in STR are not added/subtracted but follow different formula en.wikipedia.org/wiki/Velocity-addition_formula Commented Jun 15, 2021 at 8:56
• @CorneliuMaftuleac you can accelerate forever, granting someone/something provides you with energy needed to keep the acceleration up. Why do you think you cant? What would stop you to accelerate? Commented Jun 15, 2021 at 8:59

Yes, the astronaut can easily tell the speed of his movement. The speed (in his frame) is zero. He can also quite easily calculate his speed in any other frame he cares to calculate in, though it's unlikely he'd find this interesting. As for imagining that the speed is close to $$c$$, it is automatically close to $$c$$ in some frames and not in others, just like your own speed right now.