#### phinds

Gold Member
@Nearlynothing

You said :
"His acceleration can be measured locally, with accelerometers, so this can be defined in absolute terms, with no reference to coordinates. Now in this frame he sees the station failing to remain stationary, he interprets his own acceleration as a means to remain stationary in that frame."

An interesting angle, i'll have to let that sink in for a while.
Well, that's not right. He is clearly NOT staying stationary in that frame. Since it is moving away from him, he is moving away from it. What his acceleration does is keep him from being dragged along with that frame, since without acceleration, he is stationary in that frame.

From HER frame of reference, the guy on the train is stationary and the train station is accelerating away from both of them.

Here's another way of looking at it:

Take a frame of reference and grid it as XY coordinates. In that frame, there is a pretty girl at 0,0.

At 10,0 there is a train station and a train.

Through some means that we don't care about, the train station, in our XY frame of reference, begins accelerating in the negative Y direction. The guy on the train doesn't want to lose sight of the pretty girl, so he has to accelerate to stay on the X axis while the train station moves away from him. From HIS frame of reference, he is moving relative to the train station but NOT moving relative to the girl, he is maintaining his position is her frame of reference.

#### Nugatory

Mentor
Actually, it is. SR is based on inertial frames.
Because this misunderstanding has been so widely propagated in the pop-sci press, because so few first-year courses try to correct it, and because Einstein himself back in 1905 did not fully appreciate what he had wrought, people can be forgiven for believing that SR is based on inertial frames.

But it's not - it works for all frames in flat space-time. Whether the frame is inertial or not is just a simple coordinate transformation as long as the space-time is flat (that is, described by the Minkowski metric in $x,y,z,t$ coordinates). For a good example of a purely SR treatment of a non-inertial frame in flat space-time, google for "Rindler coordinates", and note that the Rindler coordinates are just a transformation of the Minkowski coordinates.

#### Kyle.Nemeth

Not quite, SR does stress the equivalence of all inertial frames, but it's not at all a theory confined to them. You can define frames that are not inertial in minkowski space, nothing about space-time is changed by the use of these coordinates
I agree.

For the sake of trying to help @NoaDrake understand the idea, I thought it was necessary to remain within the elementary context of SR. But you are correct in the context of a Minkowski Space.

#### nearlynothing

Well, that's not right. He is clearly NOT staying stationary in that frame. Since it is moving away from him, he is moving away from it. What his acceleration does is keep him from being dragged along with that frame, since without acceleration, he is stationary in that frame.
I have no idea why you say it's not right.

the train frame is not stationary in the station frame, that's clear, the train is stationary in its own frame.

What i say is that someone in the train frame interprets his own acceleration as whats keeping him stationary in his OWN frame.

#### nearlynothing

I agree.

For the sake of trying to help @NoaDrake understand the idea, I thought it was necessary to remain within the elementary context of SR. But you are correct in the context of a Minkowski Space.

Yeah I agree non-inertial frames can be more tricky. But they are needed in this scenario, I dont think simply saying that the thought experiment goes beyond the range of applicability of SR is enough.

#### phinds

Gold Member
I have no idea why you say it's not right.

the train frame is not stationary in the station frame, that's clear, the train is stationary in its own frame.

What i say is that someone in the train frame interprets his own acceleration as whats keeping him stationary in his OWN frame.
Nothing is EVER necessary to keep something stationary in its own frame of reference. It is stationary there by definition.

#### nearlynothing

Nothing is EVER necessary to keep something stationary in its own frame of reference. It is stationary there by definition.
Lets not call it its own frame then, lets call it the non-inertial frame frame.

The train needs a force to stay stationary in this non-inertial frame, and interprets the station as "falling".

So the station is moving in this non-inertial frame as opposed to the train which is not, whereas the train is moving in the inertial frame of the station while the station itself is not.

Last edited:

#### phinds

Gold Member
Lets not call it its own frame then, lets call it the non-inertial frame frame.

The train needs a force to stay stationary in this non-inertial frame, and interprets the station as "falling".

So the station is moving in this non-inertial frame as opposed to the train which is not, whereas the train is moving in the inertial frame of the station while the station itself is not.
It doesn't matter whether or not YOU choose to call it "the frame of the train", it IS the frame of the train. You can call it green if you like, it is still the frame of the train (and yes, it is a non-inertial frame)

#### nearlynothing

It doesn't matter whether or not YOU choose to call it "the frame of the train", it IS the frame of the train. You can call it green if you like, it is still the frame of the train (and yes, it is a non-inertial frame)

All i am saying is that it's never possible to determine which is moving absolutely, no matter if you remember being accelerated or not.

I realize i phrased it wrong, i meant the train needs a force to stay in a non-geodesic path.

Last edited:

#### bahamagreen

Looks to me like the problem starts from remembering the acceleration, or looking at the printout of the accelerometer, or any other record keeping device or system that reveals a past real period of acceleration... prior to achieving the inertial reference frame.

... and the problem then comes from thinking that you were "still" before the acceleration, but now are "moving" as a result of it... shades of absolute space.

This is not a technical answer, but an inertial reference frame is "still" when it is yours no matter what history of previous accelerations might have been. In essence, an IRF has no "mechanical history" of accelerations (no lingering, ontological, causative, or otherwise potent effects). Another way to say it is that any and all possible acceleration histories are "equal" in their nonexistent effect after an IRF has been established - all IRF are physically identical despite any historical differences with respect to acceleration.

If you think about the implications of this, you will see that it never makes sense to say, "My IRF is moving and I know it because of this piece of evidence of past acceleration..."

As phinds often says, sort of, "You are moving and not moving at all possible speeds, depending on who is measuring and their relative motion, but do you feel any different?", or something like that... :)
Which means that to somebody somewhere in relative motion to your IRF, they might account for your relative motion to themselves by suggesting any and all possible combinations and configurations and durations of acceleration history to account for your observed relative velocity... each acceleration history unique, and all acting prior to your same final relative motion.

#### PeterDonis

Mentor
I know that i had to startup the train from 0 km/h to start leaving the station.
No, you don't know this. All you know is that you had to start up the train from 0 km/h *relative to the station*. You don't know whether you started "moving" in any absolute sense when you started leaving the station, or if you were "moving" when you were in the station, and gradually stopped "moving" as you accelerated, until you reached a state of "rest" when the train stopped accelerating. You can't just assume that moving at 0 km/h relative to the station means you are "really at rest". (If you're inclined to say that you can, consider that the station is on a rotating Earth, which is moving relative to the Sun, which is moving relative to the galaxy, which is moving relative to other galaxies. The fact that the station *seems* to be at rest to you is not a good reason for claiming it is "really at rest" in any absolute sense.)

In other words, just knowing that you accelerated in the past doesn't show that you are "moving", because you don't know which state of motion is "really" at rest to begin with. All acceleration does is change your state of relative motion; it doesn't, and can't, let you determine which state of relative motion is "really moving" or "really at rest".

#### Noa Drake

Ok, thank you for these various comments, i am learning.

#### phinds

Gold Member
Excellent. That's what all the Science Advisors and Homework Helpers and Mentors here love to hear. They spend a lot of time here trying to do just that and it is sometime an underappreciate task. I, on the other hand, am just here to kibitz

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving