Problems with Inertial Reference Frames

[JDoolin]

2) worse, it is against the genius of GR to encorporate fundamentally observer-dependent concepts into the structure of the theory. To understand GR (and SR for that matter), it is necessary to recognize the importance of the difference between what is an objectively supportable statement about the nature of some situation, which must be expressed in invariant form, versus what is just a matter of coordinates, which is like a word that sounds different in English and Italian. In English, we have the word "love", in Italian, "amore". The words sound totally different, so in your approach to the concept of love, we would have the statement that love is language dependent because amore sounds completely different. However, the whole point of the concept of love is that it ought to be there no matter what language you use, or even if you have invented language at all. When the same cannot be said about the concept of a global inertial frame, it exposes the fact that such a concept is not a physically real object that should appear in any theory of physics. Rather, it is simply a matter of coordinates, which is important in the practice of getting useful numbers, but has no place in any theory of physics. Indeed, that is pretty much the breakthrough realization that underpins all of relativity.
GR says no such thing, nor does this claim have anything to do with the concept of a global inertial frame. You are confusing "happening at a place and time" with "being able to be given coordinates that exist in some particular global system." Those are just not the same thing.

There is a big difference between language dependence, and observer dependence.

(To distinguish between observer dependency and description dependency: http://www.spoonfedrelativity.com/pages/Types-of-Transformations.php )

With language dependency love is the same thing whether I say it in Latin or English.

But with observer dependency, my experience of love is certainly a different experience than your experience of love. We don't love the same things; we don't love the same people; we don't even know the same people.

If ANY theory of physics cannot account for observer dependency, it is flawed.

 

[Ken G]

Does General Relativity categorize the reference frame of an accelerating observer as an "inertial reference frame?"

GR postulates are usable by any observer, accelerating or not. There is no need to even define the term "inertial reference frame", it doesn't mean a whole lot in GR-- if you know what an observer's accelerometer reads, you are fine to use GR. One of the main accomplishments of GR is to describe motion, including gravity, with postulates and laws that are completely coordinate free, so they are also completely general for any observer-- accelerating or not (as long as you know what the accelerometer reads).

Does General Relativity categorize the reference frame of a rotating observer as an "inertial reference frame?"

Again the term "inertial reference frame" is not needed in GR, you may forget the concept ever even existed. However, the nature of spinning observers is still debated by GR experts, especially around Mach's principle. I would say the issue of "what is a spinning observer" remains a disputed concept in GR, because of the need for boundary conditions to solve the differential equations that GR relies on.

Does General Relativity categorize the reference frame of a free-falling observer as an "inertial reference frame?"

To the extent that special relativity applies in a locally (i.e., too local for tidal effects) free-falling frame, yes. To the extent that the entire need for "inertial reference frames" ceases to exist, and to the extent that the global meaning breaks down in the presence of tidal effects, who cares? The concept is simply no longer required, this is one of the great accomplishments of GR.

Does General Relativity have a word for the reference frame of an observer who is NOT accelerating, NOT rotating, and NOT free-falling?

No. And why should it? Any observer who is not accelerating is free-falling, the words are synonymous in GR.

 

[Ken G]

But with observer dependency, my experience of love is certainly a different experience than your experience of love. We don't love the same things; we don't love the same people; we don't even know the same people.

If ANY theory of physics cannot account for observer dependency, it is flawed.

Yet the analogy with love is purposefully flawed-- we have the word "love" in different languages because we imagine objectively shared aspects, whereas the aspects of love that are inherently observer dependent are its subjective aspects, which do not appear in physics theories (and are a problem for language translation also)! Hence, in physics, the only allowed "observer dependence" is of the language type (i.e., the objective type). There is no difference between description dependence and observer dependence, I think that article you cited has this quite wrong. Even in the example they give, the location of a table changes when you transform between observers-- but that doesn't mean that locations are observer dependent, it means there is no such thing as location in the laws of physics, there is only relative location. This is also the mathematical meaning of a vector-- what is not observer dependent is the vector from observer A to the table, and the vector from observer B to the table (more correctly events at the observers and events at the table), and so all laws of physics must manipulate only those latter entities-- never the coordinate location of the table in either an absolute or an observer-dependent sense. This is because the location is not absolute, while anything that is observer-dependent must not be part of the laws of physics (until you get into quantum mechanical measurement theory, but that's a whole other story).

 

[harrylin]

The initial presentation of Newton’s Laws of Motion (NLM) to students often proceeds as follow: 1. The 3 laws are presented, 2. The caveat that the laws are only valid in Inertial Reference Frames (IRFs) is (sheepishly) mentioned, 3. An attempt is made to define an IRF, and 4. Some examples of IRFs and Non-Inertial Reference Frames (NIRFs) are given. After struggling with some of the commonly given examples of IRFs/NIRFs I believe that they are often flawed – even in well respected textbooks. There are 3 such example categories in particular:
1. All inertial frames are in a state of constant, rectilinear motion with respect to one another.
2. An inertial frame of reference is a frame of reference that is not accelerating.
3. We can usually treat reference frames on the surface of the Earth as inertial frames. (Since the Coriolis effect is generally small enough to be ignored.)”

Before criticizing these three examples, let me point out perhaps the most glaring problem with IRFs, which is that if we are to be rigorously precise we must acknowledge that IRFs are only conceptual approximations of reality valid only in infinitesimally small volumes. They simply do not physically exist anywhere in nature, and thus NLM are, strictly speaking, never valid. Nevertheless, assuming for the moment that they do serve some purpose consider the first example above. [..]

The reason for your frustrations is probably historical: textbooks that teach Newton's laws of motion do not teach Newton's theory of mechanics but a "classical mechanics" which doesn't follow his postulates and definitions. However, Newton's laws are based on those.
http://gravitee.tripod.com/definitions.htm
(press "cancel" and carefully read through "scholium")

Harald

 

[D H]

The reason for your frustrations is probably historical: textbooks that teach Newton's laws of motion do not teach Newton's theory of mechanics but a "classical mechanics" which doesn't follow his postulates and definitions. However, Newton's laws are based on those.

Nonsense, Harald.

The OP questioned why we teach Newtonian mechanics at all. He did something quite invalid in the first four posts, taking the concept of a local inertial frame from general relativity to the domain of Newtonian mechanics.


There is no reason, zero, zilch, nada, to teach Newtonian mechanics as described by Newton in his Principia. That would be a huge step backwards. No calculus, no algebra, no vectors, no concept of energy. Why would we do that? Just because that is how humanities are taught does not mean that that is the right way to teach science.

There is very little in science that is taught as originally described by the person who came up with the idea. There's nothing special about Newtonian mechanics in this regard. Electromagnetism, thermodynamics, relativity, quantum mechanics: Not a single one of them is taught in its original form. Chemistry and biology have gone through similar transformations. Chemists don't teach chemistry as described by Lavoisier, biologists don't teach evolution as described by Darwin. Lavoisier and Darwin were the starting points, not the culmination of modern chemistry and modern biology.

 

[D H]

OK, this has gone on far too long.

Thread locked pending moderation.