Doubt on local distinguishability of non-inertial frames

Question

I'm watching a this video ("Can You Feel Force?") and have some doubts to clarify. My understanding is (and this is also mentioned in the video at this timestamp) that to conclude that some force is being exerted on some object, its acceleration is observed w.r.t. an inertial frame. And I thought the way to pinpoint an inertial frame would be to check the reading on an accelerometer that's at rest w.r.t. that frame.

However the video asserts a couple of things:

1. At this timestamp (watch till the 5:15 mark), it's mentioned that if one is in a room with an accelerometer that moves, then it's also possible some internal mechanism (e.g. magnetic force) of the room is causing that movement in the acclerometer. Thus to supposedly conclude that your frame is inertial, one (less precise) method is to consider "global effects" - i.e. check if one is accelerating w.r.t. majority of the matter/energy in the universe (see here)
2. Statements asserting local distinguishability of accelerated frames are not true (see here)

I'm a bit confused especially about the first point, since the accelerometer in the room could be uncharged and designed in a way that it doesn't respond to any of the known forces like electromagnetism. So it would indeed be possible to tell for the person in the room if the room is accelerating, which in turn removes the need to make "global measurements".

Would be grateful is someone could clarify these points so that I can better understand the concepts.

Answer 1

it's also possible some internal mechanism (e.g. magnetic force) of the room is causing that movement in the acclerometer

This point is incorrect. There are many different mechanisms and designs of accelerometers, and there are many different physical influences that could affect accelerometers. So, suppose that we have 5 different types of accelerometers and 3 different units of each type. We set them all to measure the acceleration of our room.

Now, suppose we find that one unit disagrees with all of the other units. Then we say that one unit is broken and needs to be replaced or repaired.

But if all three of one type of unit disagree with the others then we say that type is sensitive to some environmental effect. We take other measurements of the environment and investigate the physics of the device to see if we can understand both what it is sensitive to and how. We can then either correct the measurement for the effect, or ignore it whenever the environmental factor is affecting it.

Although you mentioned B fields, by far the most common environmental factor is temperature. Most devices only work well in a certain temperature range and they fail either above or below it. As a result, most manufacturers will specify the operating range of temperature in their documentation. So usually this sort of information is actually known a priori, and what I described isn’t even needed. But what I described is essentially what the manufacturer does to figure out the characteristics of a given type of device.

So, these environmental effects, like the B field and temperature, etc are all local effects and can be measured locally. Now, you can come up with various logistical, economic, or engineering reasons why some local environmental effect on the measurement devices may be unknown, but that only tells you about your logistics, economics, or engineering, not about physics.

So from a physics perspective it is correct to say that an accelerometer is a local measurement of proper acceleration. Concerns about B fields etc are merely logistical issues, and not principled physics objections.

Answer 2

I haven't watched the video but your point about "uncharged and designed in a way that it doesn't respond to any of the known forces like electromagnetism" is quite correct. The issue here is that if one does not know ahead of time what kinds of forces may be possible, then it is quite a long job to rule out the possibility that an accelerometer may be being influenced by something one failed to take into account.