Inertial Reference Frame Proof

[SirCurmudgeon]

Consider a specific reference frame (0XYZ) attached to Earth. A point (origin) being selected, coordinates are ascribed along with a vector basis. This reference is non-inertial because it is locked to Earth and the acceleration of Earth is not zero.

Suppose upon rising one morning I felt very certain the acceleration of Earth had become constant over night and the frame was now an inertial frame. How would prove this.

 

[Dale]

Suppose upon rising one morning I felt very certain the acceleration of Earth had become constant over night and the frame was now an inertial frame. How would prove this.

Get a 6 degree of freedom accelerometer (3 axes linear acceleration and 3 axes rotation) and measure it.

 

[jbriggs444]

Consider a specific reference frame (0XYZ) attached to Earth. A point (origin) being selected, coordinates are ascribed along with a vector basis. This reference is non-inertial because it is locked to Earth and the acceleration of Earth is not zero.

Suppose upon rising one morning I felt very certain the acceleration of Earth had become constant over night and the frame was now an inertial frame. How would prove this.

Personally, I'd look for the sun. The fact that it was night and is now morning would act as a very strong clue that the Earth's rotation had not stopped overnight. If the Sun was still low in the east after I'd showered, shaved, eaten, driven to work, put in an eight hour day and was driving home then I'd be inclined to give some increased credence to the idea that the Earth had stopped rotating at some point.

Or I might consider general relativity. If upon rolling out of bed I found myself floating in mid-air rather than thumping heavily onto the floor, I might give some credence to the idea that objects at rest in the local Earth frame no longer had a 1 g proper acceleration.

 

[FactChecker]

Suppose upon rising one morning I felt very certain the acceleration of Earth had become constant over night and the frame was now an inertial frame.

You mean the velocity is constant and the acceleration is 0.

 

[SirCurmudgeon]

Thanks to all for responding.

Dale: "Get a 6 degree of freedom accelerometer (3 axes linear acceleration and 3 axes rotation) and measure it."
I assume the accelerometer would say, "0, 0, 0, 0, 0," and "0." (All null). This would not be a proof.

FactChecker: Constant velocity is also zero acceleration.

I checked some of the "refs" offered. Apparently Einstein was no certain about this...

Jim

[Mentor's note: This post has been edited to remove some unnecessary snark that violated Physics Forums guidelines]

 

[FactChecker]

T
FactChecker: Constant velocity is also zero acceleration.

Yes. But you said constant acceleration. That is not enough. You should have said 0 acceleration.

 

[Dale]

I assume the accelerometer would say, "0, 0, 0, 0, 0," and "0." (All null).

That is a bad assumption to make since it has never been true on Earth in the past and since the whole point of making the measurement is precisely so that you don't need to assume the outcome.

This would not be a proof.

Yes, it would, at least locally.

 

[Nugatory]

Suppose ... the acceleration of Earth had become constant over night and the frame was now an inertial frame.

Constant acceleration doesn't make an inertial frame - that requires constant and zero acceleration. There's also some ambiguity about which frame you mean when you say "the frame" - is this the frame in which the center of the Earth is at rest, or a frame in which the point on the surface of the Earth at which you are standing is at rest?

"Get a 6 degree of freedom accelerometer (3 axes linear acceleration and 3 axes rotation) and measure it."
I assume the accelerometer would say, "0, 0, 0, 0, 0," and "0." (All null). This would not be a proof.

How would that not be a proof? It's one of the most direct measurements imaginable, by a device whose purpose is specifically to detect deviations from inertial motion. Set one up on the non-inertial surface of the Earth and it will show 1g acceleration towards the center of the Earth and rotation about the Earth's axis with a 24-hour period; if it reads zero in all six degrees of freedom then any frame in which it is at rest (or moving with a constant coordinate velocity) is proven to be inertial.

 

[SirCurmudgeon]

Nugatory, Thanks...

My apologies to all. I screwed this up from the git go writing "constant acceleration" when I meant "constant velocity."
Sorry. The 6DoF device is astounding, for sure. My basic question (phrased differently a bit) is "considering one's self as
residing in an actual physical reference system, how would one know whether the frame was inertial.

I think the device you describe works. If there were an inertial position, the device would actually read 0, 0, 0, 0, 0, 0.
By inertial I do not mean "almost inertial" or "inertial enough." Seems to me the device would always say non-inertial.
The device itself has mass. But, it might read "inertial" self-propelled in deep space with no other mass anywhere whatsoever.

Newton spoke of inertial frames. But did he physically know one when he saw one. If so, I wonder, how so.

Thank you for your patience, jp

 

[jbriggs444]

My basic question (phrased differently a bit) is "considering one's self as
residing in an actual physical reference system, how would one know whether the frame was inertial.

Do objects subject to no external forces move in straight-line trajectories at constant speed when measured against that reference system?

i.e. do Newton's laws hold good?

 

[SirCurmudgeon]

Thank you...

My idea is:
1) Yes. "...objects subject to no external forces move in straight-line trajectories at constant speed when measured against that (an inertial) reference system." Newton says yes. But there iis a problem. There are ALWAYS external forces (non-zero sum).
2) Newton's laws are approximate. Serve quite well, great accuracy for events of short time and/or short distance.

 

[jbriggs444]

T
1) Yes. "...objects subject to no external forces move in straight-line trajectories at constant speed when measured against that (an inertial) reference system." Newton says yes. But there iis a problem. There are ALWAYS external forces (non-zero sum).

Newton's second law takes care of that nicely.

 

[Dale]

My basic question (phrased differently a bit) is "considering one's self as
residing in an actual physical reference system, how would one know whether the frame was inertial.

I already answered this. Use an accelerometer! The phrasing is fine, I am answering the content of the question.

But there iis a problem. There are ALWAYS external forces (non-zero sum).

Even that is OK. Not only does an accelerometer tell you if it is inertial or not, but if it is non inertial it tells you how much and in which direction it is accelerating. You can use that to determine which reference frames are locally inertial, even if that happens to not be the accelerometers frame.

2) Newton's laws are approximate. Serve quite well, great accuracy for events of short time and/or short distance.

All physical laws are approximate. The best that any law can do is to explain measurements within their experimental uncertainty.

 

[FactChecker]

objects subject to no external forces move in straight-line trajectories at constant speed when measured against that (an inertial) reference system.

This is just a form of accelerometer. Combinations of them could serve as both accelerometers and pseudo-gyroscopes (I think).

But there iis a problem. There are ALWAYS external forces (non-zero sum).

If you mean forces within the accelerometer, that just means that it might be difficult to make an accurate accelerometer. But there are types of accelerometers and gyroscopes that are very accurate.
If you mean external forces effecting the reference frame in question, that just means that it would be difficult to have a perfect inertial reference frame. A lot of things do not require perfection.

PS. I said "pseudo-gyroscope" because I think the curvature of the paths of combinations of devices could be used to measure rotation rate without actually using a gyroscope.