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According, to definition, provided, as I understand by Newton, there are frame of reference, where all constantly moving bodies keep their velocity constant, untill the force is not applied to such bodies.

Some sources, in particular Russian Wikipedia inertial frame of reference article, state, that there is no inertial frame of reference in the world (translated from Russian):

Absolute interial frames of reference are mathematical model, and do not exist in real world

Or, for example this answer from this forum:

When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics.

But each time sources either do not explain why, probably considering it obvious, or the explanation is not satisfying for me.

I do not know, do I understand the reason correctly.

  1. Is the condition of frame of reference to be inertial applied for any time? Do constantly moving bodies in such frame should always move constantly if the force is not applied, so if the force even only once is applied to the body, which is linked with inertial frame of reference, that frame will never be intertial? Or frame can variate: for some period it can considered absolutely inertial, even in real world, for some period not?

  2. Is there no inertial frame of reference because there is no constantly moving bodies, i.e. every body have at least tiny, yet acceleration? If yes, why all bodies have acceleration? Due to mass, and the fact, that gravity force goes to infinity? Okay, I understand, that massless particle will move at speed of light, but what if there is a particle, that doesn't not affected by gravity or eletric field, i.e. will be "fixed" at space? Will it have intertial frame?

  3. Also what about particle with speed of light? Since their speed is constant, don't they have interial frame of reference?

  4. (Extra) Also, since the motion, even non-constant (i.e. with acceleration), as I understand is relative, then for some frame of reference, attached to the accelerated body, there are "constantly" moving bodies, that "actually" move with acceleration, but relatively to such frame - constantly. I do not understand why this frame is not inertial? Because, by definition, bodies should move constantly and without a force being applied to them? But how do we know is the force applied? No, if someone punches a ball, okay, but what about fields of something like this?

Stdugnd4ikbd
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1 Answers1

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Absolute interial frames of reference are mathematical model, and do not exist in real world

In modern physics the term “absolute” refers to a quantity from a reference frame that is physically privileged. That means that the laws of physics uniquely identify that reference frame.

Such a frame does not exist because the laws of physics, as we know them, are the same in all inertial frames and none is uniquely identified. This is the principle of relativity.

When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics.

That answer is correctly objecting to the word “perfect” or “true”. Perfection is an unrealistic standard, so demanding it of something guarantees that the thing is not real.

Inertial frames are physical. Perfect inertial frames are not. The problem is “perfect”, not “inertial frame”.

Is the condition of frame of reference to be inertial applied for any time?

A frame may be locally inertial and local can include a restriction over time as well as over space. Such a locally inertial frame will typically not be inertial if you extend it beyond the local region of spacetime. If an extended reference frame has one part that is inertial and one part that is not, then the extended reference frame is not inertial.

can considered absolutely inertial

See above. Absolute has a different meaning. There are no absolute inertial frames, even locally.

If yes, why all bodies have acceleration? Due to mass, and the fact, that gravity force goes to infinity?

In modern physics gravity is not a force and a freely falling body is inertial. This can be seen by the fact that a freely falling accelerometer reads 0. In modern physics, a body whose accelerometers read 0 is not accelerating.

Also what about particle with speed of light? Since their speed is constant, don't they have interial frame of reference?

No. One of the defining characteristics of inertial frames is that $c$ is invariant. The frame of a particle means a frame where that particle’s speed is 0. It is not possible for the particle’s speed to be both 0 and $c$ in the same frame. So the particle’s frame cannot be inertial.

since the motion, even non-constant (i.e. with acceleration), as I understand is relative

Acceleration is not relative. It can be measured with an accelerometer. This is called proper acceleration and its magnitude is an invariant.

I do not understand why this frame is not inertial?

It is not inertial because accelerometers at rest in this frame do not read 0.

Because, by definition, bodies should move constantly and without a force being applied to them? But how do we know is the force applied?

We know because accelerometers read something other than 0.

Dale
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