# Can you know which reference frame is accelerating?

• B
Gold Member
Person A is in car A and person B is in car B. These people don't know if their car is moving (i.e. there is no scenery and their engines don't vibrate or make noises). Car A is stopped and car B is moving with a velocity v. Person A thinks that car B is moving with a velocity v while person B thinks that car A is moving with a velocity of -v. Except for the fact that I said that car B was the one moving, it would be impossible to tell, correct?

Does it work the same way with acceleration? Is it possible to know whether car A is accelerating with an acceleration a or car B is accelerating with an acceleration -a? If so, why is that different from how it works with velocity (I'd prefer more of a mathematical/scientific reason, not just "because that is how physics works")?

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Person A is in car A and person B is in car B. These people don't know if their car is moving (i.e. there is no scenery and their engines don't vibrate or make noises). Car A is stopped and car B is moving with a velocity v. Person A thinks that car B is moving with a velocity v while person B thinks that car A is moving with a velocity of -v. Except for the fact that I said that car B was the one moving, it would be impossible to tell, correct?
If v is close to the speed of light you would be able to observe time dilation. See: twin paradox.
Does it work the same way with acceleration? Is it possible to know whether car A is accelerating with an acceleration a or car B is accelerating with an acceleration -a? If so, why is that different from how it works with velocity (I'd prefer more of a mathematical/scientific reason, not just "because that is how physics works")?
You would need some reference to apply a force to create that acceleration and from that interaction you would be able to gauge which vehicle is moving.

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Dale
Mentor
Except for the fact that I said that car B was the one moving, it would be impossible to tell, correct?
Correct.

Is it possible to know whether car A is accelerating with an acceleration a or car B is accelerating with an acceleration -a?
Yes, just use an accelerometer

Gold Member
If v is close to the speed of light you would be able to observe time dilation. See: twin paradox.
But the twin paradox is solved by acceleration. If acceleration weren't a factor, wouldn't both twins think the other's time was dilated?
Yes, just use an accelerometer
What I don't quite get is that if car B is accelerating forward at 1 m/s2, at t=1 person A will think that car B is going forward at 1 m/s while person B thinks that car A is going backwards at 1 m/s, at t=2 person A will think that car B is going forward at 2 m/s while person B thinks that car A is going backwards at 2 m/s, etc. Is that correct? Since it is impossible which one is moving, why can you tell which one is accelerating?

But the twin paradox is solved by acceleration. If acceleration weren't a factor, wouldn't both twins think the other's time was dilated?
Ah yes, you are correct. My apologies. The twin paradox solves your second inquiry then! xD

jbriggs444
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Since it is impossible which one is moving, why can you tell which one is accelerating?
As @Dale said, use an accelerometer. If you are pushed back into your seat, your car is accelerating. No need to look out the window.

[If you want to know which is "really" accelerating, e.g. in an elevator and which is "really" stationary, e.g. in a gravitational field then the equivalence principle says that locally there is no difference]

• Isaac0427
Gold Member
As Dale said, use an accelerometer. If you are pushed back into your seat, your car is accelerating. No need to look out the window.

[If you want to know which is "really" accelerating, e.g. in an elevator and which is "really" stationary, e.g. in a gravitational field then the equivalence principle says that locally there is no difference]
Ah, ok. So if you accelerate you will feel a fictitious force. And the person who is not accelerating will not feel any force.

• jbriggs444
Ah, ok. So if you accelerate you will feel a fictitious force. And the person who is not accelerating will not feel any force.
If you accelerate, you feel a real force in an inertial frame. To explain the acceleration in the non-inertial frame requires a fictitious force.

jbriggs444
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2019 Award
If you accelerate, you feel a real force in an inertial frame. To explain the acceleration in the non-inertial frame requires a fictitious force.
Real forces are real. They are present in every frame, inertial or not.

If a frame is non-inertial then fictitious forces can explain why the observed frame-relative acceleration does not match what would be predicted based on the real forces alone. To be technically correct, what you "feel" is the strain associated with a real force pair.

I think you are trying (correctly) to point out that fictitious forces cannot be felt. This is technically true. You don't feel the fictitious force pushing you into the seat. What you feel is the compression of backside into upholstery. [One could also argue the opposite -- that the human brain is a sophisticated device that is able to subtract out expected inputs and presents a filtered sensation that actually does reflect the fictitious force. The eyes and visual cortex are especially good at post-processing of this sort]

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• PeroK
PeroK
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Person A is in car A and person B is in car B. These people don't know if their car is moving (i.e. there is no scenery and their engines don't vibrate or make noises). Car A is stopped and car B is moving with a velocity v. Person A thinks that car B is moving with a velocity v while person B thinks that car A is moving with a velocity of -v. Except for the fact that I said that car B was the one moving, it would be impossible to tell, correct?
You could potentially tell how fast you are moving relative to the Earth and to the atmosphere. The absence of scenery is not really the issue: how would you know it's not the scenery that is moving?

The real issue is that you cannot ascribe a specific, absolute velocity to your motion. You might see the scenery, the Sun, the distant stars and calculate your velocity relative to them. But this does not give you an absolute velocity. Whether you can see the scenery or not doesn't change that.

PeroK
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If v is close to the speed of light you would be able to observe time dilation. See: twin paradox.
It makes no difference how large the relative velocity is. Time dilation is just another observation relating to relative motion.

Dale
Mentor
What I don't quite get is that if car B is accelerating forward at 1 m/s2, at t=1 person A will think that car B is going forward at 1 m/s while person B thinks that car A is going backwards at 1 m/s, at t=2 person A will think that car B is going forward at 2 m/s while person B thinks that car A is going backwards at 2 m/s, etc. Is that correct? Since it is impossible which one is moving, why can you tell which one is accelerating?
Are you familiar with the concept of spacetime diagrams?

The modern understanding of relativity is very geometric. You can consider a point particle to trace out a curve in spacetime, where the slope of the curve gives the speed. The principle of relativity basically says that the laws that govern the figures work the same regardless of which direction you put as the "up" direction on your paper. So you can rotate the picture and it is still a valid representation of the same physics.

Rotating a drawing changes the slope of all of the lines (velocity) but does not change which lines are straight (inertial) and which ones are bent (acceleration).

In the passenger seat of the car is a little girl.

She is holding a helium balloon on a string, which is fully suspended by the string; that is, it is freely floating and not touching the roof of the car's cab.

Observing this balloon should indicate all you need to know about the car's acceleration.

What behavior does the balloon exhibit? How does this work and why?

diogenesNY

Gold Member
[If you want to know which is "really" accelerating, e.g. in an elevator and which is "really" stationary, e.g. in a gravitational field then the equivalence principle says that locally there is no difference]
Now I am a little confused, can you elaborate? Wouldn't that mean you can't tell which one is actually accelerating?

PeroK
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But the twin paradox is solved by acceleration. If acceleration weren't a factor, wouldn't both twins think the other's time was dilated?

What I don't quite get is that if car B is accelerating forward at 1 m/s2, at t=1 person A will think that car B is going forward at 1 m/s while person B thinks that car A is going backwards at 1 m/s, at t=2 person A will think that car B is going forward at 2 m/s while person B thinks that car A is going backwards at 2 m/s, etc. Is that correct? Since it is impossible which one is moving, why can you tell which one is accelerating?
You have to understand more precisely what "all motion is relative" means. If you look at post #10, I said you cannot assign an absolute velocity to motion. You can, however, measure that something is accelerating and that over a period of time its motion relative to you has changed and, moreover, this is because it accelerated and not you.

But, what you cannot say is that at any time it was absolutely travelling at a given velocity.

In short: you can tell when something is changing its velocity (relative to an inertial reference frame); but you cannot assign an absolute value to its velocity at any time. The value of its velocity must be relative to something.

PS and that is true in good old classical physics. It does not hinge on the special or general theories of relativity. The issue is only obscured by dragging relativity into it, IMHO.

PeroK
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PPS to give an example. Suppose a particle acclerates at ##2 m/s^2## for ##5s##.

In one IRF (inertial reference frame), that particle might have started at rest and acclerated to ##10 m/s##.

In another IRF, that particle might have started at ##30 m/s## and acclerated to ##40m/s##.

And in yet another IRF that particle might have started at ##-10 m/s## and decelerated to ##0 m/s##.

The point is that all IRF's agree about the accleration, but they all record different values for the initial and final velocities (and indeed the velocity at each time). The particle is not absolutely at rest at any time; only at rest relative to a single IRF. Nor is it ever absolutely travelling at ##10 m/s##; only at ##10m/s## relative to a single IRF.

• Isaac0427
Gold Member
In short: you can tell when something is changing its velocity (relative to an inertial reference frame); but you cannot assign an absolute value to its velocity at any time. The value of its velocity must be relative to something.

PS and that is true in good old classical physics. It does not hinge on the special or general theories of relativity. The issue is only obscured by dragging relativity into it, IMHO.
So, essentially, acceleration is not relative, right?

PeroK
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So, essentially, acceleration is not relative, right?
Yes, exactly, acceleration is absolute. All inertial reference frames will measure the same value.

• Isaac0427
Gold Member
Yes, exactly, acceleration is absolute. All inertial reference frames will measure the same value.
Then what was the post about the equivalence principle saying? Is it that, for the case of the twin's paradox, the earth twin would think the space twin is accelerating while the space twin will think that he is in a gravitational field and the earth twin is the one moving? In both cases, both would agree that the space twin is in a non inertial frame, right?

PeroK
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Gold Member
Then what was the post about the equivalence principle saying? Is it that, for the case of the twin's paradox, the earth twin would think the space twin is accelerating while the space twin will think that he is in a gravitational field and the earth twin is the one moving? In both cases, both would agree that the space twin is in a non inertial frame, right?
Not quite. The major difference between classical physics and general relativity is that in GR gravity is not a force and acceleration under gravity becomes a different matter. The equivalence principle is part of the transition from classical physics to general relativity.

It's late for me, so I'm signing off now. But, there must be lots of threads already on the equivalence principle!

Nugatory
Mentor
So, essentially, acceleration is not relative, right?
Proper acceleration, the thing that an accelerometer measures, is not relative.

Coordinate acceleration, the thing that is produced by fictitious forces, is relative - it only happens in non-inertial frames and it cannot be detected by an accelerometer.

If I am in free fall in the earth's gravitational field, my proper acceleration is zero; my coordinate acceleration relative to an observer standing on the surface of the earth is 1G. The earthbound observer attributes this acceleration to a fictitious force called "gravity".

• jbriggs444
A.T.
Proper acceleration, the thing that an accelerometer measures, is not relative.

Coordinate acceleration, the thing that is produced by fictitious forces, is relative - it only happens in non-inertial frames and it cannot be detected by an accelerometer.
Coordinate acceleration (dv/dt), exists in inertial frames too, it's just equal to proper acceleration there.

Nugatory
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Coordinate acceleration (dv/dt), exists in inertial frames too,
Ah - yes of course you're right. All you need is a non-fictitious force to produce some proper acceleration and you'll have to have some coordinate acceleration as well.
it's just equal to proper acceleration there.
Only in the inertial and momentarily comoving frame in which the accelerating object is at rest - at least if ##v## is intended as the coordinate velocity.