# Is acceleration relative? (In the same way that velocity is)

1. Apr 21, 2010

### Georgepowell

Velocity is relative because when describing something's velocity you have to say relative to what. i.e. "A particle is traveling at 5m/s" doesn't make sense. "A particle is traveling at 5m/s relative to me" does make sense.

Does "A particle is accelerating at 5m/s²" make sense?

I have seen this argued before and people sometimes say "Acceleration is not relative because you can feel yourself accelerating" (And this means that you can tell you are accelerating a certain amount, not relative to anything). I disagree with that reasoning because you are feeling yourself being squished, you don't feel yourself accelerating. If your whole body is accelerating equally (or we are just talking about particles accelerating, not bodies) then you cannot measure the acceleration of yourself.

So if there are two particles, one is accelerating at 5m/s² directly away from the other. Is it valid to say that one is accelerating and the other one isn't?

2. Apr 21, 2010

### espen180

Acceleration is relative. If two bodies are accelerating by an equal ammount in the same direction in one frame, how does it look in the bodies' rest frame?

3. Apr 21, 2010

### Mentz114

Suppose both particles are in geodesic motion. If a force, such as a rocket motor, acts on one particle it goes into a non-geodesic trajectory. The other particle stays in geodesic motion. It is not relative, one is geodesic, the other is not.

4. Apr 21, 2010

### Hurkyl

Staff Emeritus
(In special relativity) the question of whether acceleration is zero or non-zero is absolute. If non-zero, then the specific magnitude* and direction is relative.

*: I mean 3-magnitude. The magnitude of the acceleration 4-vector is an invariant

Similarly, the question of geodesic/non-geodesic motion in GR is absolute.

5. Apr 21, 2010

### neyzenilhan

acceleration is relative for accelerated frames.

6. Apr 21, 2010

### Hurkyl

Staff Emeritus
Blarg, good catch. Somehow, my intent to mention orthonormal coordinates didn't make it into my post.

7. Apr 21, 2010

### bcrowell

Staff Emeritus
This is a nice way of putting it. Maybe an even more compact formulation is that in both SR and GR, it's geodesic versus nongeodesic motion that is absolute. (In SR, the notion of a geodesic just happens to also coincide with the Newtonian idea of an inertial frame.)

8. Apr 21, 2010

### Staff: Mentor

In relativity there are often multiple related concepts that you will need to distinguish. In this case there are two acceleration concepts: "proper acceleration" and "coordinate acceleration". Coordinate acceleration is relative, and includes the "non-squishing" acceleration you describe. Proper acceleration is absolute and is the "squishing" acceleration that you can feel and which causes deviations from a geodesic.

9. Apr 22, 2010

### yuiop

Let us say that both particles have accelerometers attached to them and the accelerometer of one particle (A) indicates an acceleration of 5m/s² and the other (B) indicates zero acceleration. It would then be valid to say that A has a force acting on it while B does not. As far a motion through space is concerned there is a symmetry or relative nature. Both particles are entitled to consider themselves as stationary. B says that he is stationary in flat space and a force is accelerating A away from him. A says he is stationary in a gravitational field and B is falling away from him.
A particle with proper acceleration of 5m/s² makes more sense, in that all observers would agree on what that means. Without the "proper" qualification the statement is open to interpretation. For example let us say that A is initially at rest with B and accelerates away with constant proper acceleration of 5m/s² as measured by his onboar accelerometer. B remains stationary and observes that A's acceleration relative to B's frame is less than the proper acceleration and decreasing over time. The acceleration measured by B is called the coordinate acceleration and is observer dependent.
Trivially they will of course both agree that they are at rest with respect to each other if they are right next to each other. However if they are separated by a distance parallel to the direction of acceleration, they will see the distance between them as expanding over time and so they do not see themselves at rest with each other, even when they agree that they both measure the same proper acceleration / force acting on them and even when an external inertial observer agrees they are accelerating at the same coordinate rate and the distance between them is constant in the inertial frame. This is basically Bell's paradox.

10. Apr 23, 2010

### Altabeh

The acceleration is an absolute quantity in SR because all observers agree whether an object is accelerating or not! For example, if a particle has a vanishing acceleration in one frame, this will be the same in any other frame. Looking at the transformation formula of acceleration in SR confirms this conclusion. But in GR there are different kinds of acceleration; one being the coordinate acceleration which, owning to its name, one can conclude that this type of acceleration is coordinate-dependent so not absolute. Thus if it is zero in one coordinate system, it will not be the same in any other. Some other kind of acceleration exists which is called "proper acceleration" and is quite different from the other: this is measured independently of the chosen coordinate system by some inertial observer moving relative to the object being observed.

AB

11. May 20, 2010

### Passionflower

Depends on what you mean by acceleration. But because you say: "In the same way that velocity is", then the answer is: yes of course acceleration is relative.

However proper acceleration is not!

But two bodies can certainly move inertially and accelerate with respect to each other. For instance when an satellite is in orbit around a planet.

12. May 21, 2010

### LukeD

All motion is relative.

If we have a cloud of dust and move the whole cloud together, none of the particles within the cloud can tell that they are moving just by the interactions of the dust particles.

The only "absolute" motion is the internal motion of the particles of the cloud. An example would be the entire cloud getting smaller or larger.

13. May 21, 2010

### Staff: Mentor

This is not correct, please see the previous posts for details.

14. May 21, 2010

### Caelus

wait, but you can mesure yourself accelerating. but an indopendant observer could mesure it diferently

15. May 21, 2010

### Staff: Mentor

See posts 8, 9, 10, 11. All obeservers in any reference frame using any coordinate system whether inertial or non-inertial and regardless of the curvature of spacetime will all agree on the proper acceleration.

16. May 21, 2010

### LukeD

All motion is relative.

It's more a slogan than a mathematical statement. I'm pretty sure Einstein said it at one point though, and taken in a certain context, it's true.

Even proper acceleration cannot be taken as "absolute" because it is defined in terms of the metric. The metric gives the intrinsic geometry of spacetime given by the gravitational curvature from every other particle in the universe. So if we measure the proper acceleration, we are measuring against every other particle in the universe. It is a very relative measure.

Even in special relativity, proper acceleration is a relative measure. To measure it, we first have to find an inertial frame, which is one in which all free particles (and all centers of mass) move inertially. You then measure your acceleration relative to the inertially moving particles. If you cannot find an inertial frame (which is a notion defined relative to the other particles moving in the universe), then you cannot measure the proper acceleration (without needing to use a metric).

17. May 21, 2010

### yuiop

Finding an inertial frame is not too difficult. Just cut the wires on an elevator and if you are really picky remove all the air from the elevator and its shaft. Believe it or not, NASA have built one of these ;)

Now calibrate your accelerometer to read zero in the free falling elevator. This could be as simple as a bunch of masses on springs and when they are deflected or stretched then you have non zero proper acceleration. Where does the rest of the universe come into it?

18. May 21, 2010

### Staff: Mentor

All obeservers in any reference frame using any coordinate system whether inertial or non-inertial and regardless of the curvature of spacetime will all agree on the proper acceleration. That is absolute. It is certainly not relative "in the same way that velocity is" as the OP is asking.

19. May 23, 2010

### GRDixon

My take is that the particle that is accelerating relative to an inertial frame is the one that is accelerating. The other particle, if at rest in some inertial frame, is not accelerating. If both particles are accelerating relative to inertial frames, then I would say they are both accelerating. I have read that the purpose of Newton's 1st law is to define the set of inertial frames. That is, any particle that experiences zero force, but is measured to accelerate, is being observed from a non-inertial frame. In any case, acceleration (like all kinematic quantities) doesn't quantitatively make much sense to me unless the frame, relative to which it's being measured, is identified.

20. May 23, 2010

### atyy

The rest of the universe comes into it, because you must ensure that your accelerometer reads nonzero when the acceleration is nonzero. After all, an accelerometer that reads zero all the time will read zero in free fall.