How can we understand the undetectability of acceleration in free fall?

[Ranku]

How does an altimeter detect altitude?
How does an accelerometer detect acceleration?

 

[Filip Larsen]

In aviation, an altimeter usually refers to the pressure altimeter which gets its height measure from the expansion of a closed, flexible container from drop in static air pressure as height increases. This altimeter shows altitude according to the reference pressure it has been set to (by the pilot).

Another common altimeter in aviation is the radio (or radar) altimeter which uses timing of reflected radio waves to measure the height above ground.

An accelerometer measures acceleration typical via some variation of the principle of inertia, that is, by applying Newtons law of motion to a mass in linear or rotational movement, but there are many different implementations depending on sensor speed, resolution, size and cost and pretty much any mechanical stretching, compression, bending, or change in vibration frequency can be used as basis for a sensor. I believe a typical modern accelerometer is a micro-electro-mechanical (MEMS) device measuring the change of resonance frequency due to acceleration on a vibrating part of the device, but there are also fiber-optic accelerometers that uses interferometry to measure the shift of a small mass, or gyroscopic devices that uses the gyroscopic forces on a rotating mass to measure rotational speed.

 

[Ranku]

An accelerometer measures acceleration typical via some variation of the principle of inertia, that is, by applying Newtons law of motion to a mass in linear or rotational movement, but there are many different implementations depending on sensor speed, resolution, size and cost and pretty much any mechanical stretching, compression, bending, or change in vibration frequency can be used as basis for a sensor. I believe a typical modern accelerometer is a micro-electro-mechanical (MEMS) device measuring the change of resonance frequency due to acceleration on a vibrating part of the device, but there are also fiber-optic accelerometers that uses interferometry to measure the shift of a small mass, or gyroscopic devices that uses the gyroscopic forces on a rotating mass to measure rotational speed.

I read that a person in gravitational free fall won't be able to detect his acceleration, even if he were consulting an accelerometer, because according to the principle of equivalence he is in a locally inertial frame, and therefore his accelerometer does not detect acceleration.
Is this true? If so, is there no way to build an accelerometer that will sense the acceleration of free fall?

 

[D H]

If so, is there no way to build an accelerometer that will sense the acceleration of free fall?

That is correct. There is no way to locally sense the acceleration due to gravity by any means.

First, in terms of what accelerometers sense:
From the perspective of Newtonian physics, accelerometers sense the acceleration due to the net non-gravitational real forces acting on the accelerometer. Accelerometers cannot sense centrifugal or Coriolis acceleration any more than they can sense gravitation; those are fictitious rather than real forces. The general relativistic explanation is a bit easier: Accelerometers sense the acceleration due to the net real forces acting on the accelerometer, Gravitation is a fictitious force in general relativity.

Now in terms of why:
The Newtonian explanation for why gravitational acceleration cannot be detected is that there is no way to shield the gravitational force. The gravitational acceleration experienced by the test mass in an accelerometer is pretty much the same as the gravitational acceleration experienced by the accelerometer as a whole. The sensed acceleration is the difference between the two, which is so close to zero as to be undetectable. The general relativistic explanation is once again easier. It is a direct consequence of the equivalence principle.

 

[rcgldr]

For an accelerometer to work in free fall, it would need an external reference, such as GPS satellite based telemetry systems.

 

[Filip Larsen]

I read that a person in gravitational free fall won't be able to detect his acceleration, even if he were consulting an accelerometer, because according to the principle of equivalence he is in a locally inertial frame, and therefore his accelerometer does not detect acceleration.

On a practical note you should be aware, that this is strictly speaking only true only for a point in any gravity field or for any object in a uniform gravity field, both being approximations to real life. For instance, in a spacecraft in orbit around Earth neither assumption is true, and in this case it is in principle possible to construct a set of accelerometers that can detect the gravity difference (gradient) between different ends of the spacecraft and hence detect that is is in a gravity field without measuring anything external to the spacecraft . However, as I said, this "merely" a practical consideration and does not change the validity of the principle of equivalence from a theoretical point of view.

 

[Ranku]

Thank you all for discussing this enigmatic phenomenon of undetectability of acceleration of free fall. Its 'conceptual brother' is of course the uniqueness of free fall, as discovered by Einstein's 'historical grandfather' Galileo!

There are different dynamic situations that could be elaborately analysed about how acceleration due to free fall must never be detectable - like more than one object in linear or orbital free fall.