Cause of Inertia

[worzel]

talkorigins[/url]]Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

[Grand Vizier]

talkorigins[/url]]Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

Weird, worzel. I was just thinking about starting a thread to ask about the current status of Mach's Principle when I read your post (I was pondering all that geocentric stuff). I know that the term was coined, not by Mach, but by Einstein. And I know that it means that, if true, the properties of mass, including inertia, can only be defined with regard to the 'Fixed Stars' (as Mach would have put it). But it still seems like 'spooky action at a distance', (as Einstein would have put it).

And I've seen it described as obsolete on several sites. But if Mach's Principle is metaphysical nonsense, what have we replaced it with, exactly?

[Grey]

Is this true? I thought it was just an idea.

My understanding is that although Einstein was intrigued by Mach's Principle, and it was part of the inspiration for general relativity, general relativity does not in fact incorporate it. That is, it's entirely possible to accept general relativity without considering Mach's Principle to be true.

I've always wondered if it's more of a philosophical point anyway. The obvious experimental test would be to check and see whether an object still shows inertial effects if you remove everything else from the universe, but it seems like that would be difficult to arrange.

Of course, if the Higgs boson is eventually found and indeed proves to be the cause of inertia, that would seem to show this to be false, but it might still be possible to reconcile the two ideas, I suppose.

[Grand Vizier]

Is this true? I thought it was just an idea.

My understanding is that although Einstein was intrigued by Mach's Principle, and it was part of the inspiration for general relativity, general relativity does not in fact incorporate it. That is, it's entirely possible to accept general relativity without considering Mach's Principle to be true.

I've always wondered if it's more of a philosophical point anyway. The obvious experimental test would be to check and see whether an object still shows inertial effects if you remove everything else from the universe, but it seems like that would be difficult to arrange.

Depends how big the funding we can get is...

Of course, if the Higgs boson is eventually found and indeed proves to be the cause of inertia, that would seem to show this to be false, but it might still be possible to reconcile the two ideas, I suppose.

Thanks. I understand that the Higgs Boson 'may be responsible for many of the properties of matter', but I have not seen it linked with, or opposed to, Mach's Principle on this forum, or anywhere else, come to that. The 'God Particle' has somehow failed to interest me to date, but if these are the stakes...

[George]

talkorigins[/url]]Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

That doesn't sound right to me. Newton felt the bucket water would become concave due to absolute space. Einstein showed space is not absolute, but spacetime is absolute. I think he called it "invariance theory" but others, media especially, liked calling it relativity instead.

The bucket test would work independent of other stars. However, their mass/energy affect spacetime. It is this interaction with space that gives some connection to Mach.

Unfortunately, I am not a GR person, but thought I'd throw that out at you anyway. Hopefully, others will elaborate and correct.

[dgruss23]

Bondi discussed this in his 1952 Cambridge Monographs on Physics book titled Cosmology.

He began the Chapter IV titled "The Problem of Inertia" by noting that the Earth's rotation speed can be measured by terrestrial experiments such as the focault pendulum and by astronomical measurements with respect to the fixed stars. Since both measurements agree, Bondi asks if this can be a coincidence or if it requires a dynamical explanation.

In Mach's view an explanation is required.

Bondi then proposes that if it is assumed the coincidence of the terrestrial and astronomical reference frames is not a result of Newton's laws or GR, then it becomes necessary to postulate a causal connection between the motions of the stars and the motions of local inertial frames. Bondi concludes that since the local frame cannot be influencing the motions of the stars, then the stars must influence the local inertial frame.

This is Bondi's statement of Mach's Principle: "the local inertial frame is determined by some average of the motion of the distant astronomical objects."

It seems quite philosophical.

[worzel]

It seems quite philosophical.

Yes, I always thought it was. But what I read suggested that it is implicit in GR. As you can explain all the local phenomena on a stationary earth using GR, it wouldn't suprise me if it were true, except that I've never heard it claimed before.

[Evan]

My understanding is not that the "distant remote fixed stars" actually somehow cause inertia. Thet are simply what was considered an absolute reference point for the frame of motion locally.

Mach wrote: "All masses and all velocities, and consequently all forces, are relative. There is no decision about relative and absolute which we can possibly meet, to which we are forced, or from which we can obtain any intellectual or other advantage. (Mach, The Science of Mechanics, ch.2, vi-3, Open Court, 1960, 279)"

http://www.bun.kyoto-u.ac.jp/~suchii/mach.pr.html

Since all bodies locally can be observed to be moving relative to one another we need a reference that is not observed to be moving. Unfortunately it was not appreciated that the universe was expanding and the distant "fixed" stars are no such thing.

Well, maybe they are fixed. Here is a different interpretation of redshift.

http://www.halos.com/reports/arxiv-1998-redshift.pdf

[A Thousand Pardons]

My understanding is not that the "distant remote fixed stars" actually somehow cause inertia.

If you are talking about Mach's Principle, I would have to disagree. Here's a short pithy statement of it from Mathworld:

What this implies is that the inertia of a body here is influenced by matter far distant.

[Evan]

I dunno about that. It seems Einstein was "putting words" into Mach's mouth.

"The above version of the principle is largely due to Albert Einstein, who brought the principle into mainstream physics whilst working on general relativity. Indeed it was Einstein who first coined the phrase Mach's principle. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly. He is more concerned with criticising Newton's mechanics, in particular the idea of absolute space."

http://www.wordiq.com/definition/Mach's_principle

I would like to find a copy of Mach's work in the original German and see what he really wrote. A lot can be lost in translation. I have found quite a few references and excerpts here

"Was fuer ein Ziel will und kann die Wissenschaft erreichen, der ich mich hingebe? Inwiefern sind deren
allgemeine Ergebnisse ”wahr“? Was ist wesentlich, was beruht nur auf Zufaelligkeiten der Entwicklung?"

Here Einstein asks Mach what results can he expect to use from the work (Mach's) . What has been shown to be "true" and what actually useful developments can he expect.


In "Die Mechanik" Mach claims the "Fixsternhimmel" as a reference frame. This is where subtle translation errors can creep in. That means "Fixed star sky" or the universe, NOT necessarily the fixed stars themselves.

I don't have time now to do more reading on this now but I believe there is room to interpret what Mach meant differently from what is given as accepted.

[A Thousand Pardons]

I dunno about that. It seems Einstein was "putting words" into Mach's mouth.

more or less, but the result was what we know as Mach's Principle.

Einstein thanked Mach for his contribution to general relativity, but I think Mach disowned the results, so you probably won't find a lot of support for Mach's Principle in Mach's works, other than a general push in that direction.

[Normandy6644]

Didn't Einstein eventually abandom Mach's principle with GR anyway?

[A Thousand Pardons]

Didn't Einstein eventually abandom Mach's principle with GR anyway?

It doesn't seem to be that Einstein abondoned Mach's Principle with General Relativity. Pais says Einstein was disappointed that General Relativity didn't lend strong support to Mach's Principle, and eventually quit his insistence on Mach's Principle. However, there are still physicists today who accept General Relativity, and support Mach's Principle.

[ToSeek]

My explanation of inertia is that stuff is lazy.

[A Thousand Pardons]

My explanation of inertia is that stuff is lazy.

Close to my own--my answer to inertia is a stuffed lazyboy

[worzel]

I guess the lack of a resounding "yes" means that it isn't implicit in GR.

[Grand Vizier]

The whole issue seems like a major dangling loose end to me. But Grey mentioned the Higgs Boson. While Googling gives few link-ups between this and Mach's Principle, there are a few more with regard to the Higg's Field. Like this AIP abstract:

A vacuum—generated inertia reaction force

My physics isn't that great, but it seems to me that the authors here are suggesting that the Higgs Field resists acceleration like air resistance with velocity, which would make inertia a local phenomenon, I guess. But I'm not sure how the Higgs Field provides some sort of reference framework. (I'm getting muddled.)

They do seem very definite:

This analysis strongly supports the concept that inertia is indeed an opposition of the vacuum fields to any attempt to change the uniform state of motion of material bodies. This also definitely shows that inertia should be viewed as extrinsic to mass...

And then go on to say that:

It is also briefly discussed why a strict version of Mach's Principle does really contradict this view, though a broad sense version of Mach's Principle may be in agreement.

So it seems the Principle is still with us in some form...

[A Thousand Pardons]

I guess the lack of a resounding "yes" means that it isn't implicit in GR.

yes and no

[worzel]

I guess the lack of a resounding "yes" means that it isn't implicit in GR.

yes and no

Philosophical then.

[Padawan]

I would define Inertia as


The reluctant force within you that strongly prevents you from doing your job, studying, or carrying out any other task you know that you have to do.

Inertia is also known as lazyness :P

[A Thousand Pardons]

Philosophical then.

You mean me? Of course. Just ask soupdragon2.

[Evan]

A small reminder. General Relativity deals with gravity, how it results and the effects that are due. It does not deal with the speed of light. General relativity incorporates the laws of motion as stated by Newton and expands upon them.

Special Relativity deals with the speed of light and the concepts of simultaneity, the constancy of the speed of light and time.

Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity. Special relativity deals with the relative motions of objects up to and including the speed of light.

It is amazing to me to think that these people, Einstein, Mach, Lorentz et al were formulating these fundamental concepts that still hold true today when thier likely primary mode of transportation was a horse and buggy.

The two theories are related but not the same. General relativity went through many revisions by Einstein until its final form as published in 1916.

[Jerry]

...Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity. Special relativity deals with the relative motions of objects up to and including the speed of light...

The two theories are related but not the same. General relativity went through many revisions by Einstein until its final form as published in 1916.

This is not correct, Special Relativity is a linear application of GR that shows up when you drop out all the unneeded terms. One can argue you can pull GR out of SR, but you must first define gravity as a tensor with space and time bending attributes.

However, if mass is assumed to slow the speed of light via a Lorentz transform, rather than bending time and space, a variant form of (time constant) SR can be expanded to (time constant) GR without introducing any new parameters.

We should not consider this unfathomable: We change the speed of light inside dense molecular structures without a second thought. Why isn't this EM effect assumed to be the same as gravitational lensing? Are not the results the same?

[A Thousand Pardons]

A small reminder. General Relativity deals with gravity, how it results and the effects that are due. It does not deal with the speed of light. General relativity incorporates the laws of motion as stated by Newton and expands upon them.

General relativity incorporates the laws of special relativity as well.

Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity.

O yes it is. Special relativity restricts itself to observers in inertial reference frames, as a basis, whereas general relativity expands that to all observers, even those in non-inertial reference frames.

It is amazing to me to think that these people, Einstein, Mach, Lorentz et al were formulating these fundamental concepts that still hold true today when thier likely primary mode of transportation was a horse and buggy.

And (gasp) wrote letters and posted them, as their primary means of communication

[Evan]

General relativity incorporates the laws of special relativity as well.

Implict, yes. Explicit, no.

I have a small puzzle for anyone to explain...

Einstein was particularly fond of what he called a "thought experiment". In
his explanation of the General Theory he refers to a "man in a chest" (read
elevator) being drawn at a constant rate by a never ending force, that is,
the elevator is being accelerated at a constant rate. He further postulates
that the man within the "chest" cannot perform any experiment that will
permit him to distinguish that he is in an accelerating frame of reference
rather than in a gravitational well created by matter. Einstein specifically
makes reference to a mass suspended from a hook on the ceiling of the
"chest" by a rope. This constitutes a pendulum.

When the pendulum in the accelerating frame of reference is swung it will
have a period that is determined by the length of the rope and the degree of force caused by the acceleration of the closed frame of reference (the elevator). In the spirit of Einstein we shall ignore friction, internal heating of the fibers of the rope etc. We concern ourselves with only the elements of the problem that are relevant to the Theory.

Here follows what may be a flaw in Einstein's theory, or, is it not a flaw, and if
not, please explain why.

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing. It describes an arc as it
swings. At the end of the arc it is closer to the "roof" of the elevator
than when it is at the mid-point of the swing, yet the force due to
acceleration is exactly the same at all points within the closed frame of reference.

When a pendulum swings in a gravitational field this is not the case. We
imagine the "chest" as resting on the surface of a gravitational body so
that the pendulum "feels" exactly one gee gravity at the mid-point of the
swing. Since gravity is created as a consequence of the existence of matter
and agglomerations of matter take a spherical shape when present in large
quantities, the pendulum experiences a different gravitational force when it
is at the ends of the arc as opposed to the force experienced at the
mid-point. Gravity decreases as the inverse square of distance from the body
that produces the field. At the ends of the arc of the pendulum it is
further from the centre of the gravitational mass and therefore experiences
less gravitation. Einstein was well aware of this. It would seem that the
pendulum swinging in the gravitational well should have a slightly longer
period. Does it?

If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?

[ngc3314]

General relativity incorporates the laws of special relativity as well.

Implict, yes. Explicit, no.

I have a small puzzle for anyone to explain...

Einstein was particularly fond of what he called a "thought experiment". In
his explanation of the General Theory he refers to a "man in a chest" (read
elevator) being drawn at a constant rate by a never ending force, that is,
the elevator is being accelerated at a constant rate. He further postulates
that the man within the "chest" cannot perform any experiment that will
permit him to distinguish that he is in an accelerating frame of reference
rather than in a gravitational well created by matter. Einstein specifically
makes reference to a mass suspended from a hook on the ceiling of the
"chest" by a rope. This constitutes a pendulum.

(...snip...)

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing. It describes an arc as it
swings. At the end of the arc it is closer to the "roof" of the elevator
than when it is at the mid-point of the swing, yet the force due to
acceleration is exactly the same at all points within the closed frame of reference.

When a pendulum swings in a gravitational field this is not the case. We
imagine the "chest" as resting on the surface of a gravitational body so
that the pendulum "feels" exactly one gee gravity at the mid-point of the
swing. Since gravity is created as a consequence of the existence of matter
and agglomerations of matter take a spherical shape when present in large
quantities, the pendulum experiences a different gravitational force when it
is at the ends of the arc as opposed to the force experienced at the
mid-point. Gravity decreases as the inverse square of distance from the body
that produces the field. At the ends of the arc of the pendulum it is
further from the centre of the gravitational mass and therefore experiences
less gravitation. Einstein was well aware of this. It would seem that the
pendulum swinging in the gravitational well should have a slightly longer
period. Does it?

If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?

This is why Einstein (or at least his later interlocutors I've read) specify that the equivalence is local - that is, the experiment is specified to encompass such a small region that the nonparallel direction of gravitational acceleration due to proximity to the center of attraction, or "vertical" extent changing the acceleration, are not measurable. The issue is not whether you can decide from a finite experiment whether you are near a mass or accelerating, but (as I understand it, the main point) that as one approaches a truly local set of measurements, the effects become indistinguishable. Thought experiments can be such wonderful things - you seldom need to get a proposal funded...

[Evan]

as one approaches a truly local set of measurements, the effects become indistinguishable.

Don't think so. As a thought experiment you have at your disposal instruments of infinite sensitivity. Was Einstein wrong or did he just oversimplify in some manner? Or, is there a reason that the pendulum DOES have exactly the same period in both cases?

[ToSeek]

Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

[worzel]

Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

But the equipment available in this thought experiment could be an infinitely large planet with a fintie gravitional pull

[Evan]

Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

Care to explain?