# Acceleration vs. uniform motion: There are three rockets in deep space

## Main Question or Discussion Point

The sun is far, far away. The earth is far, far away. No stars. Nothing but unbounded spacetime. And three rockets.

Rocket #1: Velocity (according to its odometer): 700 mph Towards Earth (constant speed)

Rocket #2: Accelerating (according to its odometer) to 800mph towards some galaxy far away from Milky Way

Rocket #3: Engines are off. It's "at rest."

Since space has no boundaries and thus direction has no (absolute) meaning, I cannot see why being at rest is any different from being accelerated. Rockets #1 and #2 are not really going anywhere, just like rocket #3.

This is why proper acceleration is not making any sense. Sure, rocket man in rocket #2 feels the force of the engines, or does he? Can you have acceleration (feel that jerk) without gravity (a gravitational field)? Additionally, if you can feel that jerk in deep, deep space, what is causing you to feel it, while keeping in mind that space(-time) is unbounded and that direction is meaningless?

What am I missing?

Edit: I guess the one thing I may not be accounting for is that direction here would be one rocketship moving away from the other, but to me, neither is really going anywhere in a significant sense.

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Since space has no boundaries and thus direction has no (absolute) meaning, I cannot see why being at rest is any different from being accelerated. Rockets #1 and #2 are not really going anywhere, just like rocket #3.
Going nowhere ? You said that 1 is heading towards Earth and 2 is heading out of the galaxy.

This is why proper acceleration is not making any sense. Sure, rocket man in rocket #2 feels the force of the engines, or does he? Can you have acceleration (feel that jerk) without gravity (a gravitational field)? Additionally, if you can feel that jerk in deep, deep space, what is causing you to feel it, while keeping in mind that space(-time) is unbounded and that direction is meaningless?
He does feel the force from his engines. His inertia causes him to feel it.
Direction is not meaningless. What do you mean by that ?

I think you should make an effort and study Newtons laws before getting yourself into this state.

Seminole Boy. Take time out of the equation for it does not exist.Gravity in space is universal (equal from every direction)= not detectable but exist so in the presents of G you would feel acceleration.

Mentz:

Here is what I'm saying. If we can't physically describe the placement of our universe, or its direction, as there are no boundaries in space, it has to suggest that placement and direction, when gravitational forces are not at work, are meaningless concepts. We are not x,y,z in the realm of existence. We are just existing. You can't physically put coordinates on our existence, so therefore direction and placement (position) seem not to carry any absolute meaning. Without boundaries, and space has none, these two words carry no (absolute) meaning.

Mentz:

Here is what I'm saying. If we can't physically describe the placement of our universe, or its direction, as there are no boundaries in space, it has to suggest that placement and direction, when gravitational forces are not at work, are meaningless concepts. We are not x,y,z in the realm of existence. We are just existing. You can't physically put coordinates on our existence, so therefore direction and placement (position) seem not to carry any absolute meaning. Without boundaries, and space has none, these two words carry no (absolute) meaning.
In order to describe physical setups we introduce coordinates and directions ( basis vectors ). They are not absolute but are necessary sometimes.

pervect
Staff Emeritus
The sun is far, far away. The earth is far, far away. No stars. Nothing but unbounded spacetime. And three rockets.

Rocket #1: Velocity (according to its odometer): 700 mph Towards Earth (constant speed)

Rocket #2: Accelerating (according to its odometer) to 800mph towards some galaxy far away from Milky Way

Rocket #3: Engines are off. It's "at rest."

Since space has no boundaries and thus direction has no (absolute) meaning, I cannot see why being at rest is any different from being accelerated. Rockets #1 and #2 are not really going anywhere, just like rocket #3.

This is why proper acceleration is not making any sense. Sure, rocket man in rocket #2 feels the force of the engines, or does he? Can you have acceleration (feel that jerk) without gravity (a gravitational field)? Additionally, if you can feel that jerk in deep, deep space, what is causing you to feel it, while keeping in mind that space(-time) is unbounded and that direction is meaningless?

What am I missing?
I am confused. Are the rockets at a constant speed, or do they have their engines on?

Let's get the earth, and the other galaxy out of the picture, since they are far, far away and supposedly out of the picture.

What is the speed of rocket #1 relative to rocket #3, the one with its engines off. Is it constant as you claim?

(Rather than use an odometer, I'd use a doppler radar. If it wouldn't confuse things too much for you. If it does confuse things, hmmm, well, let me know it's confusig for starters.)

How about the speed of rocket #2 relative to rocket #3?

If the speed of rocket #1 relative to rocket #3 is constant, and the speed of rocket #2 relative to rocket #3 is constant, NONE of the rockets is accelerating. I don't see why you think they are. You do know that acceleration is the rate of change of speed, right?

Mentz:

Here is what I'm saying. If we can't physically describe the placement of our universe, or its direction, as there are no boundaries in space, it has to suggest that placement and direction, when gravitational forces are not at work, are meaningless concepts. We are not x,y,z in the realm of existence. We are just existing. You can't physically put coordinates on our existence, so therefore direction and placement (position) seem not to carry any absolute meaning. Without boundaries, and space has none, these two words carry no (absolute) meaning.
Directions are never absolute. What someone calls up on one side of the globe is called down by someone on the other side. It all depends on the reference frame you choose. Just because they aren't absolute doesn't mean they don't have meaning.

I guess I'm saying something that Einstein was saying: gravity = acceleration.

I don't really know.

Pervect wrote:

Are the engines on?

Yes, they're on on #1 and #2 (but #2 is pushing the gas harder--he's accelerating). Rocket man piloting #3 turned his off.

What is the speed of rocket #1 relative to rocket #3, the one with its engines off. Is it constant as you claim?

Speed = distance over time. If it's just deep space (with no direction), how can we have distance? That's what I'm saying!

(Rather than use an odometer, I'd use a doppler radar. If it wouldn't confuse things too much for you. If it does confuse things, hmmm, well, let me know it's confusig for starters.)

Okay, fine.

How about the speed of rocket #2 relative to rocket #3?

I don't know how to answer this. That's why I just threw out 700mph according to the speedometer. I'm not even sure how a speedometer would calculate this stuff in deep space.

If the speed of rocket #1 relative to rocket #3 is constant, and the speed of rocket #2 relative to rocket #3 is constant, NONE of the rockets is accelerating. I don't see why you think they are. You do know that acceleration is the rate of change of speed, right?

Okay, so how, in deep space, can we be accelerating?

A.T.
Can you have acceleration (feel that jerk) without gravity (a gravitational field)?
Yes

Additionally, if you can feel that jerk in deep, deep space, what is causing you to feel it,
Inertia. As for the cause of that, we don't really have a deeper model I think. There where some attempts to attribute inertia to the influence of the rest of the Universe (Machian priniciple) but it never reached the state of an actual quantitative theory.

pervect
Staff Emeritus
?

Speed = distance over time. If it's just deep space (with no direction), how can we have distance? That's what I'm saying!
Basically, you'd use a radar set to measure the distance. A doppler radar could measure the velocity as well (but only the radial component, I suppose, if we're completely literal, this could be confusing).

wiki said:
A Doppler radar is a specialized radar that makes use of the Doppler effect to produce velocity data about objects at a distance. It does this by beaming a microwave signal towards a desired target and listening for its reflection, then analyzing how the frequency of the returned signal has been altered by the object's motion. This variation gives direct and highly accurate measurements of the radial component of a target's velocity relative to the radar.
So we do have instruments that can measure distance (regular radar) and the radial part of the velocity (doppler radar) in deep space. Given the existence of such instruments, your question of "how can we have distance" doesn't really make sense to me. We can have distance, and we can measure it , too. Perhaps you need to study how such insturments work, but that isn't a relativity question.

me said:
How about the speed of rocket #2 relative to rocket #3?
?
I don't know how to answer this. That's why I just threw out 700mph according to the speedometer. I'm not even sure how a speedometer would calculate this stuff in deep space.
Using a spedometer /odometer doesn't make sense to me unless you're on a road. And there aren't any roads in space. But spedometers are just one way of measuring speed, and odometers are just one way of measuring distance. There are lots of ways that would actually work, radar would be my first choice.

Rather than say "you can't do it" (measure distance in deep space), you might want to start thinking about how you can do it - that seems to me to be the only way to resolve your confusion.

me said:
If the speed of rocket #1 relative to rocket #3 is constant, and the speed of rocket #2 relative to rocket #3 is constant, NONE of the rockets is accelerating. I don't see why you think they are. You do know that acceleration is the rate of change of speed, right?
?
Okay, so how, in deep space, can we be accelerating?
Very easily. We have assumed that rocket #3 has its engines off. Now let's assume that rocket #1 has its engines on. Then by Newton's laws, the relative velocity between rocket #1 and rocket #3 will NOT be constant, but will be constantly changing. This is the *definition* of acceleration. The rate at which velocity changes.

We can measure this velocity change directly with a doppler radar (it's helpful for rocket #1 to be moving directly away from rocket #3 so that the radial velocity is the entire velocity). We can measure the distance with a regular radar, and take the rate of change of distance with respect to time to get the velocity as well.

Furthermore, we can say that ALL rockets with their engines off will measure a constant velocity to ALL other rockets with their engines off, this is a consequence of Newton's laws.

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
The rockets, with their engines off, have no forces applied to them, and they are therefore in a state of uniform motion, and have a constant relative velocity.

If we turn a rockets engine on, we DO apply a force to it, it is NOT in a state of uniform motion, and our instruments detect that.

Thanks, Pervect. I think you cleared it up. I guess I'm forgetting that the velocities are based off speeds of relativistic natures, if I'm saying that right. I still feel, though, that something is not being accounted for.

Dale
Mentor
Seminole Boy, I would highly recommend that you pay close attention to tensor33's excellent post:
Directions are never absolute. What someone calls up on one side of the globe is called down by someone on the other side. It all depends on the reference frame you choose. Just because they aren't absolute doesn't mean they don't have meaning.