Definition of an Inertial Frame

[JustinLevy]

It's a system which is not accelerated nor rotating, a system in which Newtons laws hold true. Newtons first law, the law of inertia states that an object will stay at rest or move with uniform velocity unless acted upon by a force - if this law holds, you are in an inertial system.

Thank you for the reply, but some posters have already answered this question for me.
It turns out that Newton's laws are invariant to parity transformation and thus cannot be used to define inertial frames without requiring relativity to predict that the universe should have parity symmetry ... but experiment has shown the universe does not have parity symmetry, and thus that can't be a valid definition.

I guess I should just start a new thread with my follow up question.

Anyway, thanks everyone for your help.

 

[DrGreg]

This is a fact, no experiment to date has detected a light speed anisotropy.

I wonder if we are talking at cross purposes here.

Your statement above is meaningless unless you specify what clock synchronisation was used in the experiments. In the context you were using before, I assumed you were talking about Selleri coords.

My guess is that the experiments you quote were not synced using Selleri coords. They were probably synced by ultra-slow clock transport. So if you meant to say "This is a fact, no experiment to date has detected a light speed anisotropy measured using ultra-slow clock transport synchronisation", I would believe it.

But if you are really saying (as you seemed to be earlier) "This is a fact, no experiment to date has detected a light speed anisotropy measured using Selleri coordinates", that is simply a logical impossibility (excluding the trivial explanation that no such experiment has been carried out, or the implausible explanation that an incontravertible disproof of relativity has been found).

It's not just light that's anisotropic in Selleri coords. The formula for momentum as a function of coordinate velocity is also anisotropic, for example. So the coordinate equations for the laws of physics are different in Selleri coords compared with Einstein coords.

(For what it's worth, I didn't explicitly recommend the book by Zhang, although it might have been within the reference list of a paper I quoted.)

From your last message I can now see the source of your confusion over the word "rotation". The reference in post #22 to "spatial rotations" did not mean a rotating frame, i.e. a frame that continuously rotates as time progresses. It simply meant a comparison between two non-rotating coordinate systems, where one system's coordinate axes could be obtained by a spatial rotation of the other's axes.

 

[masudr]

I might be late here, but there are a lot of posts.

Is there some way to define an inertial coordinate system without being cyclical (defining it with terms that require an inertial coordinate system to define)?

Can't we just put two balls of different (negligble) mass in freefall and see if they move relative to each other?

 

[1effect]

My guess is that the experiments you quote were not synced using Selleri coords. They were probably synced by ultra-slow clock transport. So if you meant to say "This is a fact, no experiment to date has detected a light speed anisotropy measured using ultra-slow clock transport synchronisation", I would believe it.

The earlier ones were done by slow clock transport. The newer ones use the Mansouri-Sexl theory (parameter \epsilon). The point was that clock synchronization does not participate in the definition of an inertial frame. The other point was that the transforms relating inertial frames do not enter in the definion of an inertial frame. I repeated this point multiple times. The absence of acceleration as detected by an accelerometer is sufficient in defining an inertial frame.

It's not just light that's anisotropic in Selleri coords. The formula for momentum as a function of coordinate velocity is also anisotropic, for example. So the coordinate equations for the laws of physics are different in Selleri coords compared with Einstein coords.

Correct, and so is Maxwell's wave equation. Yet, none of the above differences is detectable experimentally. For all intents and purposes, the "Selleri Theory" is experimentally indistinguishable from special relativity. It is just one of the many theories that is experimentally indistinguishable from SR.
But this is straying from the main point: the main point is that neither the clock synchronization (Einstein,Galilei, Selleri,etc), nor the transforms resulting from the convention (Lorentz,Galilei,Selleri) do NOT enter in the definition of an inertial frame. The absence of acceleration as detected by a an accelerometer is sufficient.

From your last message I can now see the source of your confusion over the word "rotation". The reference in post #22 to "spatial rotations" did not mean a rotating frame, i.e. a frame that continuously rotates as time progresses. It simply meant a comparison between two non-rotating coordinate systems, where one system's coordinate axes could be obtained by a spatial rotation of the other's axes.

I answered this twice, once in the first context , the second time in the second context. I made quite clear that , in the latter case, one can easily separate the inertial frames into clases that depend on the orientation of their axes. For example, there is no reason to consider that frames with opposing orientation of Ox are in the same class.

 

[Aether]

...the main point is that neither the clock synchronization (Einstein,Galilei, Selleri,etc), nor the transforms resulting from the convention (Lorentz,Galilei,Selleri) do NOT enter in the definition of an inertial frame. The absence of acceleration as detected by a an accelerometer is sufficient.

All of Newton's laws must hold true for a frame to be inertial as defined in SR, not just Newton's first law. See http://www.mathpages.com/home/kmath386/kmath386.htm" :

The problem here, as in almost the entire literature on this subject, is the invalid extrapolation from Newton’s first law to all of Newton’s laws. Whittaker correctly notes that the first law is satisfied only in terms of space and time coordinates that are not accelerating, but then he jumps to the assertion that the Newtonian laws (plural) of motion are valid with respect to these same systems – an assertion that is demonstratably false. Compatibility with Newton’s first law is not sufficient to ensure compatibility with the second and third laws. To cement the confusion, the phrase “inertial coordinate system” is commonly used interchangeably to refer to (1) coordinate systems compatible with Newton’s first law, and (2) coordinates systems compatible with all three of Newton’s laws, despite the fact that the latter are only a subset of the former. There really ought to be two different terms for these distinct sets of coordinate systems, but unfortunately a single term is used for both.

Einstein's clock synchronization convention enters into the definition of an inertial frame in the context of SR through conservation of momentum (isotropy of coordinate speeds) according to Newton's third law.

 

[D H]

A reference for the cited paper would have been useful. Parts of the paper ring of quackery, for example "Essentially every textbook perpetuates this fundamental error, which consists of defining inertial coordinate systems (and frames) only using Newton’s first law". Perhaps the author of that paper is the one who is in error rather than "essentially every textbook", including Halliday & Resnick, Taylor & Wheeler, Marion, and so on, and so on.

 

[Aether]

A reference for the cited paper would have been useful.

I provided a link to the http://www.mathpages.com/home/kmath386/kmath386.htm" per se?

 

[D H]

Since I quoted from the article, isn't it rather obvious I am objecting to the article? By a reference, I meant providing a citation to the journal in which the article was published.

 

[paw]

or are you objecting to the contents of the http://www.mathpages.com/home/kmath386/kmath386.htm" per se?

I see nothing in that article that convinces me the quoted authors are wrong. Bodies that are in uniform motion before any series of ideal collisions are in uniform motion after the collisions. I can't see how this would change or add to the definition of an inertial frame based on Newtons first law.

It would be nice if the article cited some reliable source or if it was a peer reviewed article. Many internet pages sound authoritative but are really just someones unsubstatiated opinion.

 

[JustinLevy]

For all intents and purposes, the "Selleri Theory" is experimentally indistinguishable from special relativity.

I and DrGreg have tried to explain this to you several times. You seem to not be listenning. The "Selleri Theory" is NOT a theory. It is just a coordinate system. We can work out the predictions of SR for any coordinate system as long as spacetime is flat.

Continually referring to a coordinate system as a "theory" is very misleading. Of COURSE we can define coordinate systems in which the speed of light is anisotropic using those spatial and time labels. To say that experiment ruled out this option is just seriously misunderstanding what experiment can and cannot say. Experiment can say what the speed of light is in a given coordinate system. Experiment can NOT disprove coordinate systems however, and coordinate systems are NOT a theory by themselves.

In short, of course the predictions of SR in different coordinate systems will not contradict the predictions of SR... because it is the SAME THEORY, just different coordinate systems.

The absence of acceleration as detected by an accelerometer is sufficient in defining an inertial frame.

Then, as explained to you several time, but you seem to keep ignoring, your definition includes coordinate systems in which the postulates of special relativity don't hold. Therefore under your definition, special relativity is wrong. The fact that you don't think this is a blow against your definition seems bizarre to me.

What exactly would you like us to show you before you will believe this?

A reference for the cited paper would have been useful. Parts of the paper ring of quackery, for example "Essentially every textbook perpetuates this fundamental error, which consists of defining inertial coordinate systems (and frames) only using Newton’s first law". Perhaps the author of that paper is the one who is in error rather than "essentially every textbook", including Halliday & Resnick, Taylor & Wheeler, Marion, and so on, and so on.

The point that article is making is that the term "inertial" has several meaning which causes confusion. One meaning is supplied by Newton's first law.

The following point thought is that this is NOT sufficient to test whether a coordinate system is an inertial coordinate system. For, as demonstrated explicitly in previous posts, it is easy to define coordinate systems in which Newton's first law holds but empty space is not describe isotropically (nor the speed of light) and I think we can all agree that this would not be considered an inertial coordinate system in the context of relativity.

My initial question in this thread was answered long ago.
I am thankful for the help.
I am also confused why there is still debate regarding whether Newton's first law is just a necessary property as opposed to a sufficient property to define inertial frames, for it seems this has been answered definitively.

 

[1effect]

The "Selleri Theory" is NOT a theory. It is just a coordinate system. We can work out the predictions of SR for any coordinate system as long as spacetime is flat.

This is of course wrong, The Selleri theory is a particular case of the Mansouri-Sexl theory. I recommend that you read the Zhang book, it is really good :-). Failing to do that, you can read the John Baez web page I already cited when talking about theories experimentally indistinguishable from SR. See the word "theories"? :-)

Then, as explained to you several time, but you seem to keep ignoring, your definition includes coordinate systems in which the postulates of special relativity don't hold.

As I explained to you several times, you are mixing up several things: the definition of a refence frame (a mathematical system of assigning labels) , the definition of inertial reference frame (a physical construct determined by the absence of acceleration) and, finally the notion of coordinate transforms (another physical construct that relates differen reference frames). The latter has no bearing on the definition of inertial frames. This is the last time I will explain this to you. Good luck with whatever you are researching :-)

I am also confused why there is still debate regarding whether Newton's first law is just a necessary property as opposed to a sufficient property to define inertial frames, for it seems this has been answered definitively

You should stop being confused, I've told you repeatedly (and the textbooks confirm it) that the absence of acceleration condition is sufficient. So, the strange coordinate transforms have no bearing on the definition. Are you saying that you are convinced now that you saw the textbook references that the absence of acceleration is a sufficient condition for defining inertial reference frames? This is progress :-)

 

[JustinLevy]

This is of course wrong, The Selleri theory is a particular case of the Mansouri-Sexl theory. I recommend that you read the Zhang book, it is really good :-). Failing to do that, you can read the John Baez web page I already cited when talking about theories experimentally indistinguishable from SR. See the word "theories"? :-)

I gave you an example of a coordinate system (defined by giving a coordinate transformation from a coordinate system that was stated to be inertial), and you called it a theory. This is wrong. It is a coordinate system. You can name it a Selleri or Mansouri-Sexl coordinate system, I don't care. But it is a coordinate system, not a theory.

I gave you this example of a coordinate system in which the speed of light did NOT agree with the second postulate of relativity. Therefore, you need to either:
A) agree that coordinate system is not an inertial coordinate system, despite accelerometers reading zero while at rest according to this coordinate system
or
B) claim that coordinate system is an inertial coordinate system and therefore relativity is wrong by your definition

You keep trying to choose an invalid option where the coordinate system is inertial, and yet relativity is correct. You can't mix and match like that.

Further more you say some coordinate transformations predict (your word) anisotropic light speed, and then claim experiment shows "no such anisotropy has ever been observed" which alludes to some strange belief that these coordinate systems are experimentally disproven. But then you later claim that experiment can't distinguish these coordinate system. You are making all kinds of self-contradicting claims.

You can only choose A or B.
I've talked to some theoretical physicists and they all chose A, as would I, and as would anyone accepting the answer given my DrGreg, Mentz and others. For the record, and for clarity, which do you choose?

As I explained to you several times, you are mixing up several things: the definition of a refence frame (a mathematical system of assigning labels) , the definition of inertial reference frame (a physical construct determined by the absence of acceleration) and, finally the notion of coordinate transforms (another physical construct that relates differen reference frames).

An inertial reference frame is a special case of a reference frame. And a reference frame is a set of coordinate systems. Do you agree with those two statements?

If not, please explain.

If yes, for clarity please explain how, by your definition, the set of coordinate systems in one inertial reference frame are related.

You should stop being confused, I've told you repeatedly (and the textbooks confirm it) that the absence of acceleration condition is sufficient.

It is sufficient to say that the absence of acceleration of an object (as measured by the accelerometer) means it is moving inertially.
But this is not sufficient to define an inertial coordinate system. I gave you an explicit counter example. If you call that example an inertial coordinate system then relativity is wrong. And I truly hope you are not claiming relativity is wrong.

Are you saying that you are convinced now that you saw the textbook references that the absence of acceleration is a sufficient condition for defining inertial reference frames? This is progress :-)

I've said no such thing.

 

[1effect]

I gave you an example of a coordinate system (defined by giving a coordinate transformation from a coordinate system that was stated to be inertial), and you called it a theory. This is wrong. It is a coordinate system. You can name it a Selleri or Mansouri-Sexl coordinate system, I don't care. But it is a coordinate system, not a theory.

I suggest at this point that you take it up with either John Baez or with Zhang.

It is sufficient to say that the absence of acceleration of an object (as measured by the accelerometer) means it is moving inertially.
But this is not sufficient to define an inertial coordinate system. I gave you an explicit counter example. If you call that example an inertial coordinate system then relativity is wrong. And I truly hope you are not claiming relativity is wrong.

So, you agree with the author of the mathpages (you are copying his opinion word for word, including the counterexample based on the funny coordinate tranforms) and disagree with all the textbooks quoted.:-)

I gave you this example of a coordinate system in which the speed of light did NOT agree with the second postulate of relativity.

You are still confusing frames with coordinate transforms between frames. See my previous post.:-)

 

[Aether]

I recommend that you read the Zhang book, it is really good :-).

This is from the preface of Zhang's book:

The key point in Einstein's theory is the postulate concerning the constancy of the (one-way) velocity of light...This postulate is needed only for constructing well-defined inertial frames of reference or, in other words, only for synchronizing clocks (i.e., defining simultaneity). It is not possible to test the one-way velocity of light because another independent method of clock synchronization has not yet been found.

Then from section 1.3 of Zhang:

We emphasize again that the key point for constructing an inertial frame is the clock synchronization.

Zhang calls inertial frames constructed with Einstein clock synchronization "Einstein's inertial frame of reference, or an Einstein frame for short."

 

[JustinLevy]

I suggest at this point that you take it up with either John Baez or with Zhang.

As noted above, they do not support what you saying.

And as for your red-herring, yes there is a possibility of theories that are experimentally indistinguishable from special relativity. But what I gave you was not a theory, but an example coordinate system (defined by writing the coordinates in terms of coordinates given/stated to be an inertial coordinate system).

Regardless of the existence of such theories (and hence why it is a red herring), this does NOT in anyway affect our ability to calculate the predictions of special relativity and compare them to experiment. The point is, if you state that a coordinate system in which the speed of light in anisotropic is an inertial coordinate system (which you did), then by your definition the postulates of special relativity are incorrect and the theory is wrong. You continue to contradict yourself by calling these coordinate systems inertial and denying that this contradicts relativity.


You refuse to listen to direct evidence given to you.
You also refuse to answer direct questions.
You need to consider the possibility that you are incorrect in order to learn here.

So, you ... disagree with all the textbooks quoted.:-)

You keep saying this, but you have quoted no textbooks. The only thing you have quoted is wikipedia. Furthermore, as shown above, the book you have referred to actually supports what everyone else here has been saying... and contradicts your "definitions".

Please go back and answer my direct questions.

 

[matheinste]

Hello all.

At the risk of appearing ignorant, what have all these various coordinate systems got to do with the definition of inertial frames. I thought that coordinates were just a set of labels assigned to a frame and did not affect how the laws physics are.

To quote from Rindler's Special Relativity """ An Inertial Frame is one in which spatial relations are determined by rigid scales at rest in the frame, are Euclidean and in which there exists a universal time in terms of which free particles remain at rest or continue to move with constant speed along straight lines ( Newton' first law )------""""

There are many caveats attached to this definition but it does not seem to me to have anything to do with non Euclidean coordinate systems which are our own invention and which we are free to choose as suits are purpose.

My preferred definition is that in which an inertial frame in SR is one in which an accelerometer registers zero force. ( The absence of matter, and therefore gravity appears later on in Rindler's discusion and is relevant but is ignored for the purpose of definition ). But if you take change in velocity over time as a definition of acceleration then i suppose in coordinate systems which are not homogeneous a body can be said to be acceleratng even if no force is acting on it.

But these are just ramblings not based upon a real understanding of such things on my part. So as a genuine question, what is wrong with defining a frame as inertial if an accelerometer registers zero and the frame includes all objects at rest relative to the accelerometer with a Euclidean coordinate system attached ie. with an origin at a certain point in that frame. ( In the absence of any mass ). Of course the homogeneity of the spatial and time dimensions is assumed by the choice of a Euclidean system and perhaps it is naive to think that spacetime is 'really' like this, but i am looking for a working definition not a philosophical, though such arguments are valid, nicity.

Matheinste.

 

[1effect]

For a more involved sample, the following transformation from an inertial coordinate system yields another coordinate system that labels spatial distances according to physical rulers that would agree with an inertial frame, and labels time coordinates as what a clock would measure, and Newton's law still holds, yet the speed of light is not constant.

x' = gamma (x - beta ct)
y' = y
z' = z
ct' = ct / gamma

where gamma = 1/sqrt(1 - beta^2), and beta = v/c, where v is the velocity of the new coordinate system's spatial origin according to the inertial frame.

It is very easy to show that your "counterexample" is plain wrong.
First, a correction, the speed of light is constant, it is just that it is not isotropic.
Now, the the disproof: in frame S(x,y,z,t), light speed is isotropic.
In any other frame S'(x',y',z',t') light speed is not isotropic. It is easy to show that the absolute values of light speed in S' are :

c_-=\gamma^2(c-v) and
c_+=\gamma^2(c+v)

Now, it is easy to show that :

\frac{1}{c_-}+ \frac{1}{c_+}=\frac{2}{c}

so, for any length L we have:\frac{L}{c_-}+ \frac{L}{c_+}=\frac{2L}{c}This means that the Sellery theory predicts the same result (null) as SR for the Michelson-Morley experiment. About 60 years ago Robertson demonstrated that any theory that predicts the same results as SR for three experiments:

1. Michelson-Morley
2. Kennedy-Thorndike
3.Ives-Stilwell

is indistinguishable from SR. As John Baez says, the predicted anisotroy is not detectable experimentally.Like the author of the mathpages, you stopped your reasoning too early, at the point of deriving the light speed anisotropy from the transforms (actually, you didn't even do that, I calculated it for you). This is why both you and him contradict the mainstream definition of inertial frames.
Now, turns out that the Selleri theory, described by the transforms that you listed above , predicts the same exact results as SR for all 3 experiments, thus is indistinguishable from SR, thus your "counterexample" is wrong. See my demonstration above for MMX case, I will leave for you as an exercise to demonstrate it for Kennedy-Thorndike and for Ives-Stilwell. It is a fun exercise, I highly recommend it :-)

 

[yuiop]

What kind of coordinate system is this?


Imagine a rocket is moving with constant velocity, across the field of vision of an observer. The observer films the rocket but rather than keeping the camera stationary he pans with the rocket so that when the film is played back the rocket appears to be stationary.

In the playback, the "stationary" rocket is length contracted. Light signals going from the back of the rocket to the front take longer than the reflected signal takes to return giving an apparent anisotropic speed of light in the playback. (Light signals going from the back of the rocket to the front take longer than light signals going in the opposite direction in the played back movie.). The time taken for the light signal to travel from the back of the rocket to front and back again is 2L/c seconds according to an observer onboard the rocket and (2L/c)y seconds as seen on the "movie" due to time dilation. The two way speed of light inside the rocket as seen on the in the played back film is c/y^2.

Assume that the film is processed by a computer to correct for light travel times from the rocket to the camera to remove visual artifacts such as Terrell rotation. It might even be better to imagine a network of automated clocks and cameras that record events of the rocket moving relative to the network, and presents the measurements in real time to the observer in a form a computer graphic that keeps the rocket centered on the screen.

Is there a formal coordinate system that corresponds to the one I have just described?

 

[Aether]

...what have all these various coordinate systems got to do with the definition of inertial frames.

As distinct from "inertial motion", "inertial frame" is another term for an inertial system of coordinates.

I thought that coordinates were just a set of labels assigned to a frame and did not affect how the laws physics are.

Coordinate choices do not affect the results of actual experiments, but they do affect the form of the physical laws.

To quote from Rindler's Special Relativity """ An Inertial Frame is one in which spatial relations are determined by rigid scales at rest in the frame, are Euclidean and in which there exists a universal time in terms of which free particles remain at rest or continue to move with constant speed along straight lines ( Newton' first law )------""""

There are many caveats attached to this definition but it does not seem to me to have anything to do with non Euclidean coordinate systems which are our own invention and which we are free to choose as suits are purpose.

He then goes on to limit this definition with three axioms:

Our next axiom is that all inertial frames are spatially homogeneous and isotropic, not only in their assumed Euclidean geometry but for the performance of all physical experiments...This is a very strong assumption...It may be noted that, whereas our definition of inertial frame determines the rate of time (as that in which free particles move uniformly), the isotropy axiom determines the clock settings.

My preferred definition is that in which an inertial frame in SR is one in which an accelerometer registers zero force. ( The absence of matter, and therefore gravity appears later on in Rindler's discussion and is relevant but is ignored for the purpose of definition ). But if you take change in velocity over time as a definition of acceleration then i suppose in coordinate systems which are not homogeneous a body can be said to be accelerating even if no force is acting on it.

We aren't talking about accelerated frames at all. The issue is that simultaneity remains undefined by your definition of an inertial frame, so this definition is incomplete. Rindler added three axioms to his definition of inertial frame.

...what is wrong with defining a frame as inertial if an accelerometer registers zero and the frame includes all objects at rest relative to the accelerometer with a Euclidean coordinate system attached ie. with an origin at a certain point in that frame. ( In the absence of any mass ). Of course the homogeneity of the spatial and time dimensions is assumed by the choice of a Euclidean system and perhaps it is naive to think that spacetime is 'really' like this, but i am looking for a working definition not a philosophical, though such arguments are valid, nicity.

For a working definition you could add Rindler's three axioms to this definition. As noted in the mathpages.com article (by https://www.physicsforums.com/showpost.php?p=1177652&postcount=1") cited above:

...the phrase “inertial coordinate system” is commonly used interchangeably to refer to (1) coordinate systems compatible with Newton’s first law, and (2) coordinates systems compatible with all three of Newton’s laws, despite the fact that the latter are only a subset of the former. There really ought to be two different terms for these distinct sets of coordinate systems, but unfortunately a single term is used for both.

It is very easy to show that your "counterexample" is plain wrong.

What is wrong with the counterexample? It is just a case of an empirically valid coordinate system where Newton's first law holds, but not all three.

As John Baez says, the predicted anisotroy is not detectable experimentally.

The isotropy predicted by the standard formulation of SR is not detectable experimentally either, it is assumed. That article (by Tom Roberts and Siegmar Schleif) says that:

...while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic.

 

[JustinLevy]

1effect,
Again you ignore my direct questions. And you ignore that the books you say we should refer to actually disagree with you. And you ignore the examples given you. I'm not sure what more to say.

It is very easy to show that your "counterexample" is plain wrong.
First, a correction, the speed of light is constant, it is just that it is not isotropic.

It may not be time depedent, but it is not constant. Far from it, the speed of light becomes depedent on which direction the light is travelling.

Now, the the disproof: in frame S(x,y,z,t), light speed is isotropic.
In any other frame S'(x',y',z',t') light speed is not isotropic.

Forget the rest of your 'disproof' as we can stop right here. In your givens you already admit the speed of light is not a constant value, it "is not isotropic" and thus the value changes with direction.

Now, it is easy to show that :

for any length L we have:

\frac{L}{c_-}+ \frac{L}{c_+}=\frac{2L}{c}

All this shows is that the average speed of light for a round trip according to this coordinate system is a constant. Are you saying that you wish to consider the second postulate of relativity to refer to the average speed of light for a round trip instead?

Even if so, then you need to consider the other counter-example already given to you... take an inertial coordinate system, now define another coordinate system using galilean transformation from this given frame. Newton's first law will hold, but not your "round trip average speed of light".

The fact is, you are disagreeing with the mainstream view here. For the mainstream view is that the predictions of relativity match experiment, but by your definition the postulates of relativity are incorrect.

Now, turns out that the Selleri theory, described by the transforms that you listed above , predicts the same exact results as SR for all 3 experiments, thus is indistinguishable from SR, thus your "counterexample" is wrong.

You completely misunderstand the point here. The point is that:
1) the coordinate system meets your definition of an inertial frame
2) the speed of light is not constant in that coordinate system
3) special relativity postulates that the speed of light is constant in inertial frames
4) therefore either your definition is wrong OR relativity is wrong by definition

I think it is clear that your definition is wrong. It is unclear why you continue to cling to it, for you keep making contradictory statements.

It is a fun exercise, I highly recommend it :-)

You seem to be using that smile to indicate a smirk. I would appreciate it if you consider the possibility that you are wrong instead of thinking you know all, as this back and forth with you ignoring most of what is presented is becoming frustrating.

 

[JustinLevy]

What kind of coordinate system is this?


Imagine a rocket is moving with constant velocity, across the field of vision of an observer. The observer films the rocket but rather than keeping the camera stationary he pans with the rocket so that when the film is played back the rocket appears to be stationary.

In the playback, the "stationary" rocket is length contracted. Light signals going from the back of the rocket to the front take longer than the reflected signal takes to return giving an apparent anisotropic speed of light in the playback. (Light signals going from the back of the rocket to the front take longer than light signals going in the opposite direction in the played back movie.). The time taken for the light signal to travel from the back of the rocket to front and back again is 2L/c seconds according to an observer onboard the rocket and (2L/c)y seconds as seen on the "movie" due to time dilation. The two way speed of light inside the rocket as seen on the in the played back film is c/y^2.

Assume that the film is processed by a computer to correct for light travel times from the rocket to the camera to remove visual artifacts such as Terrell rotation. It might even be better to imagine a network of automated clocks and cameras that record events of the rocket moving relative to the network, and presents the measurements in real time to the observer in a form a computer graphic that keeps the rocket centered on the screen.

Is there a formal coordinate system that corresponds to the one I have just described?

Since you are using the same time, length, and simultaneity definitions from the original frame it sounds like you are looking for the coordinate system defined by a galilean transformation from the original frame.

x' = x - vt
t' = t

This gives a round trip average speed of light as:

\Delta t' = \frac{L}{c-v}+\frac{L}{c+v} = \frac{2L}{c(1-v^2/c^2)}

So, as you said, the two way average speed of light is c/y^2 for this coordinate system.

 

[1effect]

You completely misunderstand the point here. The point is that:
1) the coordinate system meets your definition of an inertial frame
2) the speed of light is not constant in that coordinate system
3) special relativity postulates that the speed of light is constant in inertial frames
4) therefore either your definition is wrong OR relativity is wrong by definition

All this shows is that the average speed of light for a round trip according to this coordinate system is a constant. Are you saying that you wish to consider the second postulate of relativity to refer to the average speed of light for a round trip instead?

No, it shows a lot more than what you are willing to admit : it shows that the Selleri theory is experimentally indistinguishable from SR, its prediction of light speed anisotropy is not detectable experimentally (as explained in the FAQ).
More importantly ,it shows that , despite the prediction of anisotropy, the set of transforms result into a null prediction for MMX, exactly like SR.
This means that your counterexample is invalid. I suggest that you go thru the exercise of using the transforms that you provided to convince yourself that the prediction for the other two experiments is identical to the one made by SR. Have you tried the exercise? What results did you get?

 

[1effect]

Hello all.

At the risk of appearing ignorant, what have all these various coordinate systems got to do with the definition of inertial frames. I thought that coordinates were just a set of labels assigned to a frame and did not affect how the laws physics are.

Correct.

To quote from Rindler's Special Relativity """ An Inertial Frame is one in which spatial relations are determined by rigid scales at rest in the frame, are Euclidean and in which there exists a universal time in terms of which free particles remain at rest or continue to move with constant speed along straight lines ( Newton' first law )------""""

Correct again.

My preferred definition is that in which an inertial frame in SR is one in which an accelerometer registers zero force.

Correct again.

So as a genuine question, what is wrong with defining a frame as inertial if an accelerometer registers zero and the frame includes all objects at rest relative to the accelerometer with a Euclidean coordinate system attached ie. with an origin at a certain point in that frame.

...and again :-)

 

[JustinLevy]

You completely misunderstand the point here. The point is that:
1) the coordinate system meets your definition of an inertial frame
2) the speed of light is not constant in that coordinate system
3) special relativity postulates that the speed of light is constant in inertial frames
4) therefore either your definition is wrong OR relativity is wrong by definition

All this shows is that the average speed of light for a round trip according to this coordinate system is a constant. Are you saying that you wish to consider the second postulate of relativity to refer to the average speed of light for a round trip instead?

No, it shows a lot more than what you are willing to admit : it shows that the Selleri theory is experimentally indistinguishable from SR, its prediction of light speed anisotropy is not detectable experimentally (as explained in the FAQ).
More importantly ,it shows that , despite the prediction of anisotropy, the set of transforms result into a null prediction for MMX, exactly like SR.
This means that your counterexample is invalid.

Here is a direct question:
Do you agree with statements 1-3 I gave there?

You continue to ignore all the content, and questions, and maintain contradictory statements... at this point it is difficult to resist writing you off as either a crackpot or a troll. I truly hope you will prove those worries baseless by having a logical discussion here.



May I remind you that the book you recommended did not support your opinion:

We emphasize again that the key point for constructing an inertial frame is the clock synchronization.

I am NOT saying that your definition of an inertial frame is a priori incorrect. After all it is just a definition. What I am saying is that your definition makes one of the postulates of special relativity incorrect by definition. Your definition is incompatible with special relativity.

Showing that calculations performing in another coordinate system agree with the calculations of SR in an inertial coordinate system in no way invalidate this point. The second postulate of SR isn't that the Michelson-Morley, Kennedy-Thorndike, or Ives-Stilwell experiments give particular results... those would be derived experimental predictions. The postulate is that the speed of light is a constant in inertial frames. Your definition contradicts this postulate. You can't have it both ways.

 

[1effect]

Here is a direct question:
Do you agree with statements 1-3 I gave there?

You continue to ignore all the content, and questions, and maintain contradictory statements... at this point it is difficult to resist writing you off as either a crackpot or a troll. I truly hope you will prove those worries baseless by having a logical discussion here.



May I remind you that the books you recommend, do not support your opinion:





I am NOT saying that your definition of an inertial frame is a priori incorrect. After all it is just a definition. What I am saying is that your definition makes one of the postulates of special relativity incorrect by definition. Your definition is incompatible with special relativity.

Showing that calculations performing in another coordinate system agree with the calculations of SR in an inertial coordinate system in no way invalidate this point. The second postulate of SR isn't that the Michelson-Morley, Kennedy-Thorndike, or Ives-Stilwell experiments give particular results... that would be derived experimental predictions. The postulate is that the speed of light is a constant in inertial frames. Your definition contradicts this postulate. You can't have it both ways.

This is the fourth time you have contradicted the FAQ in this thread. There is no point in continuing this discussion.

 

[ZapperZ]

Then this is a good time to close this thread.

Please note: if you think someone posted something that is crackpottery, or someone is being a troll, use the REPORT post button. If you continue to respond, then you are feeding the trolls and crackpots.

Zz.