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Why is it impossible to determine a real inertial frame? We can determine the applied torque on a gyroscope by observing its precession. And thus we can evaluate the acceleration of our non-inertial frame. Is this acceleration relative to a real inertial frame? If so then it should be easy to determine a real inertial frame. Help me on this, IM really confused

Junaid
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  • Who says it's impossible to determine a real inertial frame? – John Doty Jun 02 '23 at 12:09
  • https://en.wikipedia.org/wiki/Inertial_reference_unit – John Doty Jun 02 '23 at 12:11
  • What do you mean by a "real" inertial frame? It isn't hard to tell when you're in an inertial reference frame. Are you referring to the fact that there are infinite inertial reference frames which are indistinguishable from one another? – Nuclear Hoagie Jun 02 '23 at 12:27

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Why is it impossible to determine a real inertial frame?

It is not impossible. An inertial frame is one where 6 degree of freedom accelerometers at rest in the frame measure 0 acceleration. These are common devices that can be purchased as a commodity.

Dale
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The answer by Dale is cogent and correct so I won't improve it. He makes clear what is possible. It is possible to determine whether or not a given frame is inertial. But for completeness I would like to comment on what is not possible. What is ruled out by relativity?

The important point is that, whether in Newtonian or Einsteinian physics, the physical effects within a given inertial frame have no dependence whatsoever on how fast that frame may be moving relative to other things. What happens in my room does not depend at all on how fast the room is moving relative to some distant asteroid, for example. As a result the concept of being "at rest" or "not moving" is more subtle than one might guess if one were not aware of this. In particular, there is no basis (in the equations of motion) on which one inertial frame can be singled out as the one that is "really" or "absolutely" at rest. They all have equal claim.

On the other hand, once one brings in the location and motion of particular physical things one may arrive at good reasons to claim one frame as preferred for the purpose of discussing some given set of behaviours. For local concerns, one might prefer the frame in which your home planet is not moving. For cosmic concerns one might prefer the frame in which the background radiation is isotropic. In cosmology this is called the "comoving frame" (it is comoving with the Hubble expansion). But unless you observe that radiation, or some physical effect that depends on it, there will be absolutely no way to tell how fast your chosen frame is moving relative to the cosmic comoving frame (for example). Similar things can be said for any other pair of inertial frames.

Andrew Steane
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