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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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  • what specific article in Wikipedia are you referring to? – Bob D Nov 27 '23 at 21:30
  • “Some sources, in particular Wikipedia, state, that …” please link to the specific Wikipedia article with the exact quote you are concerned about. I think you are misquoting, because I don’t recall seeing that – Dale Nov 27 '23 at 21:32
  • @BobD and Dale, I originally read it in Russian Wikipedia, now I quickly read the English version, and can't currently find such statement, so I providing the Russian version. I also added the link to the answer to the similar question – Stdugnd4ikbd Nov 28 '23 at 07:51
  • @Dale updated question – Stdugnd4ikbd Nov 28 '23 at 07:51
  • This can be helpful (possible duplicates): https://physics.stackexchange.com/q/615436/226902 https://physics.stackexchange.com/q/17459/226902 https://physics.stackexchange.com/q/615433/226902 https://physics.stackexchange.com/q/199791/226902 https://physics.stackexchange.com/q/492219/226902 – Quillo Nov 28 '23 at 08:05
  • @Quillo, the problem, is that most of answers are different from each other, and seems to be even conflicted with each other. Some posters refer to gravity, some to the fact, that constantly moving frame moves constantly only in some another frame, and in other may not move constantly. I'd also want to get answer on my question, marked as first. – Stdugnd4ikbd Nov 28 '23 at 08:23
  • Simply put: an inertial observer is a free-falling point particle. This is a mathematical statement. In the "real world" an inertial observer is anything that can be described as a free falling point particle well enough (i.e. within the requested precision for a particular situation/phenomenon and the needed amount of time). – Quillo Nov 28 '23 at 09:13
  • @Quillo 1) As other posters, even You mentioned, stated - mathematical models, instead of real are or can be "true", "ideal", "absolute". 2) Free-fall is just a particular case of gravitational interaction - between bodies with huge difference in mass. Or not? Just two neutrinos, for example, being attracted to each other by gravity are in free-fall? 3) Whatever, free fall means non-constant moving, but then, in such frames, bodies that are not affected by forces, and hence should move constantly, will move accelerated, and then those are not inertial frames – Stdugnd4ikbd Nov 28 '23 at 09:42

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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  • Sorry, for late reply. You confirm, that absoluteness and perfection can be obtained only in math, unlike the real world, but prove it, in particular, with such absolute and idealised math model of a free fall, since, as I understand, free fall assumes constant acceleration, while in real world, again, as I understand, gravity does not produces constant acceleration (You mentioned, that in modern physics gravity is not considered as a force, however, acceleration due to it, is still non constant, is not it?). Because of that, Your answer seems contradictory to me. – Stdugnd4ikbd Dec 02 '23 at 12:16
  • I think I will ask a lot of additional questions, and since comments are not intended for that, if You are interested in answer them, I invite You to a chat – Stdugnd4ikbd Dec 02 '23 at 12:18
  • @Stdugnd4ikbd I don’t like the chat feature here. Just ask your questions in the usual way. My answer is not contradictory. Free fall isn’t an idealized math model, so your objection seems like looking for an argument rather than looking to learn. I am not interested in arguing today. Maybe some other day – Dale Dec 02 '23 at 17:48
  • Okay, I will continue here then. Can You please provide a definition of a free fall? – Stdugnd4ikbd Dec 02 '23 at 20:35
  • @Stdugnd4ikbd free fall is when an attached accelerometer would read 0. – Dale Dec 02 '23 at 21:26
  • So, when there is no attached accelerometer, it is not a free fall?
    • – Stdugnd4ikbd Dec 03 '23 at 09:39
  • Will the attached accelerometer read zero, if the acceleration of the body, accelerometer attached to, is changing?
    • – Stdugnd4ikbd Dec 03 '23 at 09:41
  • @Stdugnd4ikbd said “when there is no attached accelerometer, it is not a free fall?” I explicitly used the word “would” to provide for that case. The fact that you deliberately misinterpreted my statement shows that you are not interested in learning but arguing. You are more interested in twisting words than learning concepts. I have better things to do than try to help someone who doesn’t want to learn. I am done and will not respond further here. It is a waste of my time. Goodbye and good luck – Dale Dec 03 '23 at 12:31
  • In Your sentence "would" is related to "read 0", but not to "attached accelerometer", You didn't write "if there would be an accelerometer, that read 0", so this is the reason why I asked You for clarification Your definition of free fall, since, from Your definition free fall requires an attached accelerometer.
    • – Stdugnd4ikbd Dec 03 '23 at 12:52