Inertial frames in special relativity

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An inertial frame in special relativity (SR) is defined by the Minkowski metric, which incorporates the second postulate of SR regarding the constancy of the speed of light for all observers. While Newton's first law describes a freely moving object maintaining constant velocity, it does not adequately define inertial frames in SR due to the existence of non-inertial frames that still satisfy this law under Galilean transformations. The discussion emphasizes that simply identifying a freely moving observer does not establish a complete coordinate system necessary for defining an inertial frame. Ultimately, the definition of an inertial frame in SR relies on the geometric structure of spacetime, as described by the Minkowski metric. This understanding is crucial for distinguishing between inertial and non-inertial frames in the context of relativity.
JustinLevy
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What is used to define an inertial frame in special relativity?
Do I need to take one of the postulates as defining an inertial frame?

What is bothering me is that I used to use Newton\'s first law to define inertial frames (a freely moving object will have a constant velocity). This can not be the definition in SR because I could use the galilean transformations and Newton\'s first law would still hold (yet these are not inertial frames according to SR).

So how do you define an inertial frame in SR?
 
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JustinLevy said:
What is used to define an inertial frame in special relativity?
Do I need to take one of the postulates as defining an inertial frame?

What is bothering me is that I used to use Newton\'s first law to define inertial frames (a freely moving object will have a constant velocity). This can not be the definition in SR because I could use the galilean transformations and Newton\'s first law would still hold (yet these are not inertial frames according to SR).

So how do you define an inertial frame in SR?
An inertial frame in SR is the same as in Newtonian mechanics: the frame of reference of an observer who is experiencing no external force (dp/dt=0).

AM
 
Andrew Mason said:
An inertial frame in SR is the same as in Newtonian mechanics: the frame of reference of an observer who is experiencing no external force (dp/dt=0).
Specifying a freely moving observer only specifies one point (an origin if you will), but not an entire coordinate system. So unfortunately, that does not answer the question.

As I explained above, there are an infinite number of coordinate systems in which Newton\'s first law is true, yet the coordinate system is not an inertial one. You merely picked one of these freely moving points. If Newton\'s first law is not sufficient to define an inertial frame, definitely picking just one point will not be.


The more I think about it, I believe the answer is: an inertial frame in SR is defined by the Minkowski metric. Which in essence means the second postulate of SR is used to define an inertial frame.

Is this correct? Or are there other ways of looking at it?
 

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