Problems with Inertial Reference Frames

[D H]

This is my problem; that whenever I do a Lorentz Transformation, General Relativity Experts will claim that it is not possible. When I point out that I just did it, so it must be possible, they will continue to claim there is no possible exact theory in which inertial frames are global.

So I don't need GR to be all things to all people. I just need GR to stick to the incredibly tiny domain where it is valid, which is a zero-volume space.

Just because you have problems with general relativity does not mean it is wrong. Just because you want the universe to be simple and to be absolutely realistic does not mean that it is.

The fact is that general relativity is the best model of scientific reality we have. It is still a locally realistic theory. The windmill you should be tilting at is quantum mechanics, which is not even locally realistic. Bell's theorem.

You'd still be tilting at windmills, however.

 

[Ken G]

So I don't need GR to be all things to all people. I just need GR to stick to the incredibly tiny domain where it is valid, which is a zero-volume space.

I would say your problem here is conflating the usefulness of GR with the usefulness of the concept of global inertial frames. They aren't at all the same-- one works, the other doesn't. It's not GR's problem that the global inertial frame idea falls apart, indeed this is a feature of GR not a bug, and seems to be a crucial feature to match reality, "looking outside." I am in complete agreement with what D_H is saying also.

 

[JDoolin]

Just because you have problems with general relativity does not mean it is wrong. Just because you want the universe to be simple and to be absolutely realistic does not mean that it is.

The fact is that general relativity is the best model of scientific reality we have. It is still a locally realistic theory. The windmill you should be tilting at is quantum mechanics, which is not even locally realistic. Bell's theorem.

You'd still be tilting at windmills, however.

I'm not the one who said that physics has to be simple. That was you who suggested that we need to zoom-in to a level where the physics is simple. Remember, I want to zoom out to where physics has some complexity.

I am not saying I want the universe to be simple. I am saying that a theory should be compatible with the theories from which it is supposedly derived. If General Relativity is derived from Special Relativity, it should have at least some circumstance where the use of a Lorentz Transformation is permitted.

I'm not asking for something to be "realistic" because I don't know what you mean by realistic. What I would probably suggest instead is a rubric to evaluate a theory. Rather than just say "General Relativity is the best model of scientific reality we have" we need to actually break down General Relativity into the hundreds or thousands of ideas that it encompasses.

Because you have all these things in General Relativity

• Coordinate free General Relativity
• Schwarzschild Coordinates
• Rindler Coordinates
• free-falling-inertial-reference-frames
• Gravitational Lensing
• Parallel Transport
• Painleve Coordinates
• FLRW Coordinates
• Dark matter and dark energy
• de Sitter Universe
• Einstein Field Equations
• Gravitational Time Dilation

I don't have any desire to charge in and try to destroy the whole of General Relativity. There is a lot of good stuff in there. But those parts of General Relativity that are based on this concept that "Global Inertial Reference Frames Don't Exist" need to be surgically removed. Because the correct statement is that "Global Inertial Reference Frames are Observer Dependent."

Having said that, let's go back to this statement:

Just because you want the universe to be simple and to be absolutely realistic does not mean that it is.

Now, isn't it the assumption of General Relativity that there IS a mathematical model to describe the universe? My argument is not that the universe should be simple, but that the universe should be self-consistent, and shared. If an event happens in your universe at some place at some time, that same event must happen in my universe at some place, at some time.

Where GR goes wrong is that you say that if an event happens in your universe at some specific place at some time, it does NOT necessarily happen at any specific place and time in my universe. This is the point I disagree with.

I think if specific places and times can be established for events according to ONE observer, then specific places and times can be established for events according to ANY observer.

 

[Ken G]

If General Relativity is derived from Special Relativity, it should have at least some circumstance where the use of a Lorentz Transformation is permitted.

It does-- over any scales where the changes in gravitational potential are suitably much less than c². But note the key point here-- the length scale is limited, so again we find that the concept of an inertial frame has a necessarily local quality, or at least not completely global (as in cosmology, for example).

Rather than just say "General Relativity is the best model of scientific reality we have" we need to actually break down General Relativity into the hundreds or thousands of ideas that it encompasses.

It doesn't encompass that many ideas, the theory is based on a small set of postulates and ideas. That's why it is such a good theory (along with its spectacular accuracy). But this also means that applying the theory requires idealizations-- and as with any theory, this is a feature not a bug. Note also that a long list of different types of coordinates has very little to do with general relativity, any more than Cartesian vs. polar coordinates has much to do with Newton's laws. The whole point of GR is to be a theory whose "ideas" can be expressed in completely coordinate-free form. That is what makes it a fully objective theory (which, by the way, Newton's laws are not, in particular the first law).

I don't have any desire to charge in and try to destroy the whole of General Relativity. There is a lot of good stuff in there. But those parts of General Relativity that are based on this concept that "Global Inertial Reference Frames Don't Exist" need to be surgically removed. Because the correct statement is that "Global Inertial Reference Frames are Observer Dependent."

No, that is not the correct statement, and for two reasons:
1) there is usually no global inertial frame associated with any observer, because of the presence of horizons. For example, an accelerating observer has a Rindler horizon, and a spinning observer has a horizon at the distance where the angular speed is c. For the Earth, for example, that is roughly the distance of Jupiter, so the "global inertial frame" of an Earth-bound observer cannot even encompass the entire solar system.
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.

Where GR goes wrong is that you say that if an event happens in your universe at some place at some time, it does NOT happen at any specific place and time in my universe.

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.

 

[JDoolin]

1) there is usually no global inertial frame associated with any observer, because of the presence of horizons. For example, an accelerating observer has a Rindler horizon, and a spinning observer has a horizon at the distance where the angular speed is c. For the Earth, for example, that is roughly the distance of Jupiter, so the "global inertial frame" of an Earth-bound observer cannot even encompass the entire solar system.

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

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

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

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

(By the way, these aren't rhetorical questions. I'd really like a simple yes or no answer.)

 

[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.