I can't understand inertial reference frames

[vanesch]

No, i never said that. What i said was that one can derive all results from classical physics by using just a simple Euclidean background that you need to define the necessary vectors.

Hehe, let's see what you wrote in post #11:

Well with respect to the uniform background that you need to define. I mean, without an Euclidean background, Newtonian mechanics (which is described in terms of vectors) has no meaning.

In this context, an inertial frame of reference is that frame onto which no net forces is acting. Thus, a frame with constant velocity with respect to the Euclidean background-space.

This "Euclidean background-space" = an absolute space.
It is a way to identify points in space for different times, and that's exactly what it means, "absolute space".

There's no such thing in Galilean relativity. Of course, ONCE YOU HAVE CHOSEN AN INERTIAL FRAME, its COORDINATE REPRESENTATION corresponds to an Euclidean space. A coordinate frame is nothing else but a way to identify the different fibres of the bundle. But your coordinate representation is NOT the original space manifold ; the difference being that the coordinate frame has an arbitrary choice to it, while the object that is supposed to describe physical reality can of course not have an arbitrary choice to it.

So yes, intro courses in classical mechanics work in an Euclidean space, but this space is a *coordinate frame*, it is not the representation of physical space. If, *by definition* it is already an inertial frame, then of course everything applies in this "background (coordinate) space".
But the difficulty is now to find an operational definition which links this hypothetical coordinate frame to any empirical procedure.

Again, you don't need to bring in the concept of fibre bundles into this discussion because it is irrelevant. Again, i never stated that space is absolute.

You don't need to bring in the concept of fibre bundles in order to do computations in a coordinate representation that has already been postulated to be an inertial frame, which is what happens in intro mechanics courses. In "pseudo-real-world" problems either, you do not need to bring in that concept, because it is ASSUMED, erroneously, that the "embedding frame" is an inertial frame. Exercises "at the surface of the earth" are supposed to be in an inertial setting ; which is, strictly speaking, wrong of course: You'd need to explain why the gravity force of the sun MUST NOT be taken into account - your frame is in fact not "inertial" but "freefalling towards the sun" so any naive mind who would include the force of gravity of the sun into its problem to be "more accurate" would in fact commit an error. It is exactly that error which makes it unintuitive to explain why tidal effects have TWO bulges and not ONE, for instance.

Now, for most textbook exercices of pulleys, ropes, weights, bullets, stones, ladders and so on, this seems to work more or less, but it only works because things happen to be so that the numerical values of what we do are such that the errors are numerically relatively small. But that's a coincidence, because the Earth is big, we are small, and we use time scales in these problems which are very small compared to the natural periods of the motions which are erroneously described with our "inertial frame fixed to the earth" which is always tacitly assumed in these problems of ropes and pulleys and other textbook problem material.

However, if someone, like the OP, REALISES these issues, and wonders (rightly) what IS now an inertial frame, then I'd say that you'd need to be more careful. The best mathematical explanation of what's *IN PRINCIPLE* meant with galilean relativity (which is the principle that one cannot discern an absolute space from a uniformly moving one), is the idea of the fibre bundle.

This is a poor formulation i my opinion since if he would have restored Galilean relativity, the physicality of absolute time cannot be rejected.
I would say that after special relativity, the issue of absolute velocity was solved but general relativity solves the issue of absolute acceleration.

No, this is not correct. If there wouldn't have been an absolute velocity of light, then Galilean relativity was correct, and ALREADY contained the issue of "velocities are relative". However, what was contained in the Newtonian framework was ALSO a different concept, namely absolute time (which has nothing to do with absolute space or not a priori). And this was dropped, in order to permit another concept, which was absoluteness of light velocity.

No, you are wrong. It was NOT solved by Galileo because the transformation of velocity under Galileo is incorrect because c is not an universal constant here.

But this has nothing to do with the absoluteness of space. It has to do with the absoluteness of time.

Just look at when the velocity transformation under Galileo and Lorentz are equal (only very small velocities). The Galileo Transformation is wrong and therefore does not solve the absolute v issue. Only special relativity does.

The galilean transformation is not "wrong", it is just the juxtaposition of GALILEAN RELATIVITY and ABSOLUTE TIME, while special relativity is the juxtaposition of GALILEAN RELATIVITY and ABSOLUTE LIGHT VELOCITY.

Both are equivalent concerning the rejection of absolute space, and the issues in both, concerning the operational definition of an inertial frame, are identical.

Well, err, the formalism may be logically all right but if one starts from incorrect postulates, the model is just plain wrong. That's all there is to it. Aso, like you say yourself, our universe does not behave like that...Err, i think that says it all.

Yes, but the part that is discussed here, which is the galilean principle of relativity, which states that there is no absolute space, IS THE SAME IN BOTH special relativity and Newtonian physics.

Well, that's what i have been saying all along. The only difference between you and me is that i say : just pick the reference frame with it's origin in the Earth's center and all is ok. No need for "defining" an inertial frame properly and no need for relativity all along.

So, the statement of a beginning course of Newtonian physics is then:
"the sun is immobile in absolute space, its position doesn't change because it is at the origin (eh, in Euclidean space ?) "

As I said before, in principle this is WRONG, and the problem of defining, in all generality, what is an inertial frame is a difficult (and in fact impossible) one. It is just that IF YOU CLAIM THAT THE SUN IS FIXED, PINPOINTED IN ABSOLUTE SPACE, that you make a terrible conceptual error, but that you obtain *reasonably good* numerical results for mechanical textbook problems, and this is just due to the choice of numerical values of periods, velocities and distances in these problems. If we would have been an ant in a lab on a dust particle in a turbulent airflow, the concept would be entirely accute.
It is just because the tidal effects of the sun and even the Earth are very small numerically, and the centrifugal force due to the rotation of the Earth around the sun is perfectly compensated by its gravity (why ? ), that textbook problems work out up to the accuracy of these effects.
And this is why, except for smart students, not much questions often arise when discussing "inertial frames". If students would have been ants, there would be miriads of questions on the operational definition of an inertial frame, and the significance of Galilean relativity.
But we are lucky and the accuracy demanded in textbook problems is numerically less precise than the fundamental conceptual errors that are made by them. Nevertheless, it is thought-provoking to think about it in all generality, as the OP did.

For instance, textbook question: "an apple falls off an apple tree. Calculate the lowest-order corrections to its fall due to the Sun's and the moon's gravitation as a function of the position of the moon and of the location of the apple tree on the surface of the earth"

If more of these questions would be asked (even though they are numerically ridiculous), reflection of what IS an inertial frame would be more stimulated.

 

[Andrew Mason]

What can i calculate with relativity that would make our lives better ?

The timing of GPS signals to provide accurate locations to within a few metres on the Earth surface! This accuracy requires special relativity calculations to account for time dilation.

AM

 

[marlon]

Hehe, let's see what you wrote in post #11:

Hehe, i never said that in post #11. I think you are reading things that you want to be reading

This "Euclidean background-space" = an absolute space.
It is a way to identify points in space for different times, and that's exactly what it means, "absolute space".

It does not matter whether this space is absolute or not. So, what is your point ?

So yes, intro courses in classical mechanics work in an Euclidean space, but this space is a *coordinate frame*, it is not the representation of physical space. If, *by definition* it is already an inertial frame, then of course everything applies in this "background (coordinate) space".
But the difficulty is now to find an operational definition which links this hypothetical coordinate frame to any empirical procedure.

But it does not matter whether this space is a representation of physical space. The reason being that classical physics works. Besides, i disagree that this space does not represent physical space. You cannot make such statements because it is the ONLY frame you are working with. Beware, this is not equivalent to saying that space is absolute.

Now, for most textbook exercices of pulleys, ropes, weights, bullets, stones, ladders and so on, this seems to work more or less, but it only works because things happen to be so that the numerical values of what we do are such that the errors are numerically relatively small.

Indeed but that clearly shows how important classical physics is and how, err "important" relativity really is.

But that's a coincidence, because the Earth is big, we are small, and we use time scales in these problems which are very small compared to the natural periods of the motions which are erroneously described with our "inertial frame fixed to the earth" which is always tacitly assumed in these problems of ropes and pulleys and other textbook problem material.

Well, this sounds more like a bad lawer answer. One could also argue that it is a coincidence that relativity exists just because someone thought that c is an universal constant. Clearly, we don't need relativity in "most of the cases here on earth".

However, if someone, like the OP, REALISES these issues, and wonders (rightly) what IS now an inertial frame, then I'd say that you'd need to be more careful.

Ofcourse, i never argued that and i also explained to the OP how one defines an inertial frame.

No, this is not correct. If there wouldn't have been an absolute velocity of light, then Galilean relativity was correct, and ALREADY contained the issue of "velocities are relative". However, what was contained in the Newtonian framework was ALSO a different concept, namely absolute time (which has nothing to do with absolute space or not a priori). And this was dropped, in order to permit another concept, which was absoluteness of light velocity.

No, you are mistaken. In Galilean relativity, time is absolute. The issue of absolute velocity is NOT solved in Galilean relativity. Why do you think that the transformation laws for velocity are different in special relativity. The only reason is the universal c constant. Point Final.

But this has nothing to do with the absoluteness of space. It has to do with the absoluteness of time.

I wasn't referring to that, i was referring to the fact that velocity is still absolute in Galilean relativity.

The galilean transformation is not "wrong", it is just the juxtaposition of GALILEAN RELATIVITY and ABSOLUTE TIME,

No it is wrong because absolute time is a property of the Galileo Transformation.

while special relativity is the juxtaposition of GALILEAN RELATIVITY and ABSOLUTE LIGHT VELOCITY.

Given the definition of the Galilean transformation, that would be simply impossible. Time is NOT absolute here.

issues in both, concerning the operational definition of an inertial frame, are identical.

The definition of an inertial frame is identical in all versions of relativity. It is the definition i have given (and some other people too) in my very first post in this thread.

So, the statement of a beginning course of Newtonian physics is then:
"the sun is immobile in absolute space, its position doesn't change because it is at the origin (eh, in Euclidean space ?) "

NTED IN ABSOLUTE SPACE, that you make a terrible conceptual error, but that you obtain *reasonably good* numerical results for mechanical textbook problems,

That's a bit easy no ?

I clearly stated several times that classical physics has it's issues with relativity and inertial frames. I do realize that special and general relativity are valid physical theories, so...

and this is just due to the choice of numerical values of periods, velocities and distances in these problems.

Nope that is not true.

If we would have been an ant in a lab on a dust particle in a turbulent airflow, the concept would be entirely accute.

Not in ant's classical physics formalism it wouldn't.

really, such remarks do not have any value. We know the reality, we know what works and what doesn't...

It is just because the tidal effects of the sun and even the Earth are very small numerically, and the centrifugal force due to the rotation of the Earth around the sun is perfectly compensated by its gravity

This sounds like some intelligent design-type of answer.

For instance, textbook question: "an apple falls off an apple tree. Calculate the lowest-order corrections to its fall due to the Sun's and the moon's gravitation as a function of the position of the moon and of the location of the apple tree on the surface of the earth"

If more of these questions would be asked (even though they are numerically ridiculous), reflection of what IS an inertial frame would be more stimulated.

Indeed, but in that case, the definition of inertial frame that some of us gave here will do just fine.

Again, i resent the fact that you seem to be implying that i deny the validity of SR/GR. I never did that, what i was trying to say is something very different and i know you understand very well what i am talking about.

marlon

 

[marlon]

The timing of GPS signals to provide accurate locations to within a few metres on the Earth surface! This accuracy requires special relativity calculations to account for time dilation.

AM

Yeah, that's the answer you generally get. Any other technological applications ? Surely there must be at least 10 or 20, no ?


marlon

 

[vanesch]

Hehe, i never said that in post #11. I think you are reading things that you want to be reading

Just scroll back and read post #11 in this thread. I copied and pasted it.

It does not matter whether this space is absolute or not. So, what is your point ?

My point is that the concept of an inertial frame, in Newtonian/Galilean AS WELL AS IN SPECIAL RELATIVITY is a subtle concept that runs into circularity problems when one attempts to give an operational definition of it in a totally general way.
As such, saying that "an inertial frame is simply one that is in uniform motion wrt to absolute space" is totally missing the issue.

But it does not matter whether this space is a representation of physical space. The reason being that classical physics works. Besides, i disagree that this space does not represent physical space. You cannot make such statements because it is the ONLY frame you are working with. Beware, this is not equivalent to saying that space is absolute.

It simply means you miss the gist of the Galilean relativity principle if you do so, and that there are potential textbook problems which are totally within the scope of classical physics to which wrong answers will be given. Unfortunately, one doesn't often find these problems in most textbooks.

Well, this sounds more like a bad lawer answer. One could also argue that it is a coincidence that relativity exists just because someone thought that c is an universal constant. Clearly, we don't need relativity in "most of the cases here on earth".

You really missed the issue I think. I'm NOT arguing against classical physics, or its practical applicability (on the contrary!). I'm explaining a subtlety about its conceptual framework.
You sound like someone to whom one is explaining the proof of the irrationality of the square root of 2, and your answer would be that for all practical purposes, an 8 digit development is good enough, so all this stuff about irrationality is irrelevant.

Ofcourse, i never argued that and i also explained to the OP how one defines an inertial frame.

Yes, and that definition is WRONG, in all generality.
To quote you again:

In this context, an inertial frame of reference is that frame onto which no net forces is acting. Thus, a frame with constant velocity with respect to the Euclidean background-space.

In order for this definition to have operational meaning, you need to INTRODUCE the "Euclidean background space" which is impossible to define (as of Galilei's relativity principle).
Moreover it is even wrong in this way, because you could have a ROTATING frame "onto which no net forces are acting".

The correct (circular) definition of an inertial frame is:
"a coordinate frame, which is such that the motion of a particle on which no net forces act, is a uniform straight motion".

And, as I explained in the beginning of this thread, the circularity resides in the "on which no net forces act", because IN ORDER TO DETERMINE THE FORCE ACTING ON A PARTICLE, you have to apply Newton's second law *in an inertial frame*.

So, imagine a toy universe, in which there is an electric field, which is given by E = E0 cos(w.t) 1_z
(Coulombian electricity, no B field).
We now have charged and uncharged test particles in our universe.
The charged ones undergo this up and down oscillating E field, while the uncharged ones don't. But how do we know which ones are the "free" ones ? We could just as well take (erroneously) the charged ones as "free" particles, and then define the inertial frames as those which accelerate up and down in sync with these charged particles. In this reference frame, the uncharged ones seem to undergo an oscillatory acceleration, while the charged ones undergo uniform straight motion in this frame.
So how do you operationally define an inertial frame in this universe ?


Silly example ? Gravity does the same with normal particles in our universe.

No, you are mistaken. In Galilean relativity, time is absolute. The issue of absolute velocity is NOT solved in Galilean relativity. Why do you think that the transformation laws for velocity are different in special relativity. The only reason is the universal c constant. Point Final.

You seem to confuse the galilean relativity principle (which states that there is no absolute background space) and the galilean transformations, which take the galilean relativity principle, together with the notion of absolute time, to determine the transformation laws.

I wasn't referring to that, i was referring to the fact that velocity is still absolute in Galilean relativity.

? is it ? Galilean relativity says exactly the opposite: that there is NO absolute velocity. That's explained in "about two new sciences" by Galileo, where he gives the example of the experiments on a ship, which are indistinguishable from the experiments on shore.

No it is wrong because absolute time is a property of the Galileo Transformation.

Yes, which is obtained from the galilean principle of relativity, PLUS the assumption of absolute time.

The definition of an inertial frame is identical in all versions of relativity. It is the definition i have given (and some other people too) in my very first post in this thread.

You mean, the one with "the frame on which no net forces act ?"

This sounds like some intelligent design-type of answer.

I guess you say this because you didn't realize the point I was making.

Ok, here we go again. Let's take the Earth's center as a good inertial frame. Now, consider that I make a spring + weight which is tuned to have an oscillation frequency with a period exactly equal to one year, fixed to some place on the Earth's surface.
Question: will the sun's force of gravity drive this oscillator or not ?


Indeed, but in that case, the definition of inertial frame that some of us gave here will do just fine.

Again, i resent the fact that you seem to be implying that i deny the validity of SR/GR. I never did that, what i was trying to say is something very different and i know you understand very well what i am talking about.

I'm absolutely not insinuating this. I'm rather saying that there's a subtlety in the conceptual definition of "inertial frame" within the theoretical setup of Newtonian physics which has some circularity to it when you think about it (even in a toy universe where this law is perfectly valid).
I'm even saying that this issue has nothing to do with relativity, and remains intact in special relativity. It goes (partially) away in GENERAL relativity, but not because of its relativistic character, but rather because of its general covariance ; a reformulation of Newtonian physics on these grounds is also possible of course and has been done - but is a bit useless, given that general relativity is the better theory and even easier.


I'm NOT claiming that Newtonian physics is "wronger" than relativity on this issue, rather on the contrary.

However, the "answer" to the OP question, that "an inertial frame is simply a frame with constant velocity wrt some form of absolute space" is about the wrongest answer one could give to these interrogations: it has not only no operational meaning, but it even introduces a physical idea which is explicitly excluded by galilean relativity.

 

[rcgldr]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

 

[vanesch]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

Yes, of course, there's no problem with that. I'd even say that it is the starting point for doing Newtonian physics: you start with the postulate that there exists an inertial frame, you name it and you say that it is called x,y,z,t, and then you can do things in it.
The conceptual confusion is to think that this corresponds to some kind of absolute space, which it doesn't of course.

As long as things are abstract, and you SAY that x,y,z,t is an inertial frame, and you SAY which forces are acting upon which object, there's no problem, and this is what's usually done in textbooks (and textbook problems).
The difficulty resides in giving an *operational definition*: to define a lab procedure in all generality that will guarantee you that you have an inertial frame. And without such an operational definition, there's no LINK between the abstract, mathematically invented set of coordinates x,y,z,t and any number you could get out of any measurement procedure: in other words, without an operational definition of an inertial frame, Newtonian mechanics makes no empirically testable predictions.

In practice this is not a problem, because "a coordinate set at the surface of the earth" or "a coordinate set through the center of the earth, pointing to the fixed stars" or "a coordinate set through the center of the sun" turn out to be quite good. But clearly those are "accidental" cases and they have a circumstantial ad hoc definition. If you take that as a definition of "inertial frame" it would imply, for instance, that there's no Newtonian mechanics before the formation of our solar system :-)

The fundamental problem is that there are no "free particles" on which "no forces act", because on all things acts at least the force of gravity, and maybe others - which you might ignore.

 

[loom91]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

The question is not whether it's a reality or whether classical physics is more useful than GTR. This is theoretical physics, usefullness is a very minor consideration. The problem is that the concept of inertial reference frame is not internally self-consistent. It has a circular definition.

Q:What is an inertial reference frame?
A:It is a reference frame in which particles free of forces are unaccelerated.
Q:What is force?
A:Force is the time-derivative of momentum IN AN INERTIAL REFERENCE FRAME.

You see the problem? It is not possible to opertionally determine a particle to be free of forces, but even before that the very definition of inertial reference frames is problematic. Irrespective of whether or not classical mechanics with galilean relativity can be formulated in E^3xE^1, it remains that it is theoretically impossible to determine anyhting's velocity against it without assuming the existence of ether. Classical mechanics is defnitely usefull, but all the usefullness in the world won't save a theory in theoretical physics if it's not the right picture of the world. That's why the field is called theoretical physics and not applied enginnering.

Molu