# Einstein's STR is valid for systems that are not accelerating.

• lalbatros
In summary: Einstein's Special Theory of Relativity is valid for systems that are not accelerating. This means that it can be used to predict measurements of an accelerated observer. However, it is unable to handle accelerated coordinate systems.
lalbatros
Hello,

Einstein's Special Theory of Relativity is valid for systems that are not accelerating.​

on this site: http://csep10.phys.utk.edu/astr162/lect/cosmology/gravity.html

Honestly I cannot understand that.

I have read the famous Gravitation by Wheeler and "Classical theory of fields" by Landau, and I know some of the motivations for going to GR from SR. I can imagine that strong gravitational fields or strong accelerations are a limit to the theory. Or even that gravitation doesn't fit well in the STR.

But is that not a bit exagerated to say that:

Einstein's Special Theory of Relativity is valid for systems that are not accelerating.​

What are the facts?

As long as we're talking about a flat spacetime (Minkowski space), then it's special relativity. SR can certainly handle objects that have a non-zero coordinate acceleration in an inertial frame, and it also includes coordinate systems that aren't inertial frames. It's possible to define a "crippled" version of SR that only allows inertial frames and no other coordinate systems, but that's not the theory that physicists in this century have in mind when they talk about special relativity (and even the "crippled" version of the theory can handle accelerating objects).

I think that historically, there's been a change in viewpoint and terminology. Originally people thought of SR as dealing only with inertial reference frames, with accelerated reference frames being part of GR as a "generalization" that also includes gravitation. Nowadays people think of SR as dealing with situations where gravitation can be ignored (flat spacetime), with GR being specifically a theory of gravity (curved spacetime).

I understand that sometimes it's convenient to use the mathematical tools of GR to work with accelerated reference frames, although they're not really necessary, as they are with gravitation.

Grammatically the statement that "Einstein's Special Theory of Relativity is valid for systems that are not accelerating" does NOT say it is not valid for some or all accelerating systems.

That's a good point. The first statement certainly suggests the second, but it doesn't imply it. I still think it's a strange thing to say though.

To elaborate on jtbell's point:

There is some confusion about where SR ends an GR starts.
According to Wald, the prefixes stem from the respective covariance principle, where special covariance means same form in all inertial systems, and general covariance means same form in all coordinate systems.
In that sense, the theories are defined by their mathematical formulation and not by their domain of applicability. Even if SR can be used to predict measurements of an accelerated observer, it is by definition unable to handle accelerated coordinate systems.
IMHO, general covaiance is nowadays so deeply ingrained that the definition of a theory by the allowed coordinate transformations seems quite artificial to many people. That's why it is common to make the distinction according to the domain of applicability, and regard SR as the "subset" of GR that is valid for flat spacetime.

## 1. How did Einstein come up with the theory of special relativity?

Einstein's theory of special relativity was developed through a series of thought experiments and mathematical equations. He was inspired by the work of Maxwell and Lorentz on electromagnetism and the idea that the speed of light is constant in all frames of reference.

## 2. What does it mean for a system to be accelerating?

An accelerating system is one that is changing its velocity, either by speeding up, slowing down, or changing direction. This can be caused by external forces such as gravity or by internal forces within the system.

## 3. How does special relativity apply to systems that are not accelerating?

Special relativity applies to any system that is moving at a constant velocity. This includes systems that are not accelerating, as long as they are not affected by external forces such as gravity. The laws of special relativity hold true for all frames of reference moving at a constant velocity.

## 4. Can the theory of special relativity be applied to large-scale systems?

Yes, the theory of special relativity can be applied to systems of any size. It has been tested and confirmed through various experiments, including those involving large-scale objects such as planets and stars. However, for very high speeds or large gravitational forces, the theory of general relativity may need to be used instead.

## 5. How does special relativity affect our understanding of space and time?

Special relativity shows that space and time are not absolute, but are relative to the observer's frame of reference. This means that measurements of space and time can be different for different observers, depending on their relative velocities. It also introduces the concept of spacetime, where space and time are interconnected and can be affected by gravity.

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