The Problem with Nonaccelerated Inertial Reference Frames

Oct 13, 2025 by wbrum.org 21 views

Could it be that just specifying that an inertial reference be nonaccelerated still allows for Newton's third law to be violated?

In the realm of physics, particularly in the context of Newtonian Mechanics and Special Relativity, the concept of inertial reference frames plays a crucial role. An inertial reference frame is a coordinate system that is at rest or moving at a constant velocity relative to an observer. The fundamental assumption underlying inertial reference frames is that they are nonaccelerated, meaning that they do not experience any acceleration. However, a question arises: does specifying that an inertial reference be nonaccelerated still allow for Newton's third law to be violated? In this article, we will delve into the intricacies of inertial reference frames, Newton's third law, and explore the possibility of violating the latter in the context of the former.

Newton's third law, also known as the law of reciprocal actions, states that for every action, there is an equal and opposite reaction. This fundamental principle is a cornerstone of classical mechanics and has far-reaching implications in various fields of physics. The law is often expressed as:

F12 = -F21

where F12 is the force exerted by object 1 on object 2, and F21 is the force exerted by object 2 on object 1.

An inertial reference frame is a coordinate system that is at rest or moving at a constant velocity relative to an observer. The fundamental assumption underlying inertial reference frames is that they are nonaccelerated, meaning that they do not experience any acceleration. In other words, an inertial reference frame is a frame of reference in which the laws of physics remain unchanged.

The Problem with Nonaccelerated Inertial Reference Frames

The concept of nonaccelerated inertial reference frames seems straightforward, but it raises a question: does specifying that an inertial reference be nonaccelerated still allow for Newton's third law to be violated? In other words, can we still have a situation where the action and reaction forces are not equal and opposite, even if the reference frame is nonaccelerated?

Let's consider a thought experiment to illustrate the problem. Imagine two objects, A and B, interacting with each other in a nonaccelerated inertial reference frame. Object A exerts a force F12 on object B, and object B exerts a force F21 on object A. According to Newton's third law, F12 = -F21. However, what if the inertial reference frame is not perfectly nonaccelerated? What if there is a small acceleration, no matter how small, in the reference frame?

Coordinate systems play a crucial role in describing the motion of objects in physics. A coordinate system is a set of axes used to describe the position and motion of objects. In the context of inertial reference frames, the choice of coordinate system can affect the apparent motion of objects. For example, if we choose a coordinate system that is accelerating, the motion of objects will appear different from what it would be in a nonaccelerating coordinate system.

Symmetry is a fundamental concept in physics, particularly in the context of special relativity. Symmetry refers to the idea that the laws of physics remain unchanged under certain transformations, such as rotations or translations. In the context of inertial reference frames, symmetry plays a crucial role in ensuring that the laws of physics remain unchanged.

If we can violate Newton's third law in a nonaccelerated inertial reference frame, it would have far-reaching implications in various fields of physics. For example, it would challenge our understanding of the behavior of objects in classical mechanics and would require a reevaluation of the laws of physics.

In conclusion, specifying that an inertial reference be nonaccelerated does not necessarily prevent the violation of Newton's third law. The concept of inertial reference frames is more complex than it initially seems, and the choice of coordinate system can affect the apparent motion of objects. The connection to symmetry and the implications of violating Newton's third law are also crucial aspects of this problem. Further research is needed to fully understand the implications of this result and to determine whether it has any practical consequences in the real world.

Brown, K. (2018). Physics in Space and Time (3rd ed.). Academic Press.
Feynman, R. P. (1963). The Feynman Lectures on Physics. Addison-Wesley.
Landau, L. D., & Lifshitz, E. M. (1976). The Classical Theory of Fields. Pergamon Press.
Q&A: Could it be that just specifying that an inertial reference be nonaccelerated still allows for Newton's third law to be violated?

Q: What is an inertial reference frame?

A: An inertial reference frame is a coordinate system that is at rest or moving at a constant velocity relative to an observer. The fundamental assumption underlying inertial reference frames is that they are nonaccelerated, meaning that they do not experience any acceleration.

Q: What is Newton's third law?

A: Newton's third law, also known as the law of reciprocal actions, states that for every action, there is an equal and opposite reaction. This fundamental principle is a cornerstone of classical mechanics and has far-reaching implications in various fields of physics.

Q: Can we still have a situation where the action and reaction forces are not equal and opposite, even if the reference frame is nonaccelerated?

A: Yes, it is possible to have a situation where the action and reaction forces are not equal and opposite, even if the reference frame is nonaccelerated. This can occur if the inertial reference frame is not perfectly nonaccelerated, or if there are other external forces acting on the system.

Q: What is the role of coordinate systems in describing the motion of objects in physics?

A: Coordinate systems play a crucial role in describing the motion of objects in physics. A coordinate system is a set of axes used to describe the position and motion of objects. In the context of inertial reference frames, the choice of coordinate system can affect the apparent motion of objects.

Q: How does symmetry relate to inertial reference frames?

A: Symmetry is a fundamental concept in physics, particularly in the context of special relativity. Symmetry refers to the idea that the laws of physics remain unchanged under certain transformations, such as rotations or translations. In the context of inertial reference frames, symmetry plays a crucial role in ensuring that the laws of physics remain unchanged.

Q: What are the implications of violating Newton's third law in a nonaccelerated inertial reference frame?

A: If we can violate Newton's third law in a nonaccelerated inertial reference frame, it would have far-reaching implications in various fields of physics. For example, it would challenge our understanding of the behavior of objects in classical mechanics and would require a reevaluation of the laws of physics.

Q: Is it possible to have a situation where the action and reaction forces are not equal and opposite, even if the reference frame is nonaccelerated, and the system is isolated?

A: Yes, it is possible to have a situation where the action and reaction forces are not equal and opposite, even if the reference frame is nonaccelerated, and the system is isolated. This can occur if the inertial reference frame is not perfectly nonaccelerated, or if there are other external forces acting on the system, even if they are not directly observable.

Q: How does the concept of inertial reference frames relate to the concept of special relativity?

A: The concept of inertial reference frames is closely related to the concept of special relativity. In special relativity, the laws of physics are the same in all inertial reference frames, and the speed of light is constant in all inertial reference frames. The concept of inertial reference frames is a fundamental aspect of special relativity.

Q: What are some of the key differences between inertial and non-inertial reference frames?

A: Some of the key differences between inertial and non-inertial reference frames include:

Inertial reference frames are at rest or moving at a constant velocity relative to an observer, while non-inertial reference frames are accelerating or rotating.
Inertial reference frames are used to describe the motion of objects in classical mechanics, while non-inertial reference frames are used to describe the motion of objects in general relativity.
Inertial reference frames are used to describe the behavior of objects in special relativity, while non-inertial reference frames are used to describe the behavior of objects in general relativity.

Q: Can we use inertial reference frames to describe the motion of objects in general relativity?

A: No, we cannot use inertial reference frames to describe the motion of objects in general relativity. In general relativity, the laws of physics are not the same in all inertial reference frames, and the speed of light is not constant in all inertial reference frames. Instead, we use non-inertial reference frames, such as rotating or accelerating frames, to describe the motion of objects in general relativity.

Q: What are some of the key implications of using non-inertial reference frames in general relativity?

A: Some of the key implications of using non-inertial reference frames in general relativity include:

The laws of physics are not the same in all non-inertial reference frames.
The speed of light is not constant in all non-inertial reference frames.
The motion of objects is described in terms of the curvature of spacetime, rather than in terms of the motion of objects in a fixed reference frame.

Q: Can we use inertial reference frames to describe the motion of objects in quantum mechanics?

A: No, we cannot use inertial reference frames to describe the motion of objects in quantum mechanics. In quantum mechanics, the laws of physics are not the same in all inertial reference frames, and the motion of objects is described in terms of wave functions and probability amplitudes, rather than in terms of the motion of objects in a fixed reference frame.

Q: What are some of the key implications of using non-inertial reference frames in quantum mechanics?

A: Some of the key implications of using non-inertial reference frames in quantum mechanics include:

The laws of physics are not the same in all non-inertial reference frames.
The motion of objects is described in terms of wave functions and probability amplitudes, rather than in terms of the motion of objects in a fixed reference frame.
The behavior of particles is described in terms of quantum fields, rather than in terms of the motion of particles in a fixed reference frame.