Lorentz ether frame, Relativistic Mass, and Inertia

[kmarinas86]

It is obvious from particle accelerators that accelerating a mass increases its inertia. That should be a valid observation in all frames.

But if the angle between the acceleration vector and the velocity vector is relative to the observer, then whether the mass is accelerating or 'de'celerating should be relative as well. If so, this means disagreement between different inertial frames as to whether the inertia is increasing or decreasing.

One could counter that in the frame co-moving with the accelerated object that the force has been reduced, rather than the mass and its inertia increasing. Then it would no longer apply that the inertia of an object is the same in every reference frame. The object's inertia would be observed to be increased in accelerator's frame, while constant in the object's frame. However, this leads to the conclusion that the inertia of the universe is relative. However, given the link between inertial mass and gravitational mass, it seems untenable that such a property of the universe, such as inertia, could depend on the observer. For example, you would have inertial frames of reference where the energy density of the universe can be 10^120 times than what is observed in our frame. How would that preserve constants such as $G$ without introducing additional normalization factors or other similar corrections? It can't.

A Lorentz ether (in the context of the absolutist neo-Lorentzian view) would solve this problem:

http://en.wikipedia.org/wiki/Lorentz_ether_theory#Later_activity_and_Current_Status

Viewed as a theory of elementary particles, Lorentz's electron/ether theory was superseded during the first few decades of the 20th century, first by quantum mechanics and then by quantum field theory. As a general theory of dynamics, Lorentz and Poincare had already (by about 1905) found it necessary to invoke the principle of relativity itself in order to make the theory match all the available empirical data. By this point, the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it became both empirically and deductively equivalent to special relativity. The only difference was the metaphysical[C 7] postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory. As a result, the term "Lorentz ether theory" is sometimes used today to refer to a neo-Lorentzian interpretation of special relativity. The prefix "neo" is used in recognition of the fact that the interpretation must now be applied to physical entities and processes (such as the standard model of quantum field theory) that were unknown in Lorentz's day.

Subsequent to the advent of special relativity, only a small number of individuals have advocated the Lorentzian approach to physics. Many of these, such as Herbert E. Ives (who, along with G. R. Stilwell, performed the first experimental confirmation of time dilation) have been motivated by the belief that special relativity is logically inconsistent, and so some other conceptual framework is needed to reconcile the relativistic phenomena. For example, Ives wrote "The 'principle' of the constancy of the velocity of light is not merely 'ununderstandable', it is not supported by 'objective matters of fact'; it is untenable..."[C 8]. However, the logical consistency of special relativity (as well as its empirical success) is well established, so the views of such individuals are considered unfounded within the mainstream scientific community.

A few physicists, while recognizing the logical consistency of special relativity, have nevertheless argued in favor of the absolutist neo-Lorentzian view. Some (like John Stewart Bell) have asserted that the metaphysical postulate of an undetectable absolute rest frame has pedagogical advantages [B 22], while others have suggested that a neo-Lorentzian interpretation would be preferable in the event that any evidence of a failure of Lorentz invariance were ever detected.[C 9] However, no evidence of such violation has ever been found (despite strenuous efforts) → see Test theories of special relativity.

Any acceleration relative to this Lorentz ether frame would result in the increase of inertia agreed upon by all frames. Any deceleration relative to this Lorentz ether frame would result in the decrease of inertia agreed upon by all frames. Whether more energy goes from an object A, to object B, than from object B, to object A, can be agreed upon by all observers if a Lorentz ether frame existed.

Based on this, it is apparently not true that a Lorentz ether frame cannot be detected. It most certainly can. If, by applying a force on a charge, the inertia of a charge falls towards a minima, and then subsequently rises again, then such a charge has approached the Lorentz ether frame and then receded from it. That does not mean it has actually reached it. It only means that, for a brief period of time, it was closer to it. Multiple such measurements can ultimately lead to a more precise determination of the the Lorentz ether frame. Claims that it cannot be distinguished from SR are simply wrong. It may have a connection with the cosmic background anisotropy as well as Mach's principle. Notice that if the cosmic background is the signature of a thermal equilibrium of an early state of this universe, then any significant observed anisotropy would result from an observer's relative motion with respect to a universal inertial frame, which would be indeed coherent with the idea that there exists a Lorentz ether frame. Also true is that, for line-of-sight motion:

$$\gamma=\frac{1}{\sqrt{1-\beta^2}}=\frac{1}{2}\frac{1}{z+1}+\frac{1}{2} \left(z+1\right)=\frac{1}{2}\frac{f_{-o}}{f_{-s}} + \frac{1}{2}\frac{f_{+o}}{f_{+s}}=\frac{1}{2}\sqrt{ \frac{1-\beta}{1+\beta}} + \frac{1}{2}\sqrt{\frac{1+\beta}{1-\beta}}$$

Where:
$z$ is the redshift.
$f_{+s}$ is the peak-to-peak frequency of photons coming from a source in the forward direction, as measured at the source.
$f_{-s}$ is the peak-to-peak frequency of photons coming from a source in the backward direction, as measured at the source.
$f_{+o}$ is the peak-to-peak frequency of photons coming from a source in the forward direction, as measured at the observer.
$f_{+o}$ is the peak-to-peak frequency of photons coming from a source in the backward direction, as measured at the observer.

A perfect black-body emission pervading the universe would satisfy the condition $f_{+s}=f_{-s}$. Therefore, much of the anisotropy seen by an observer $o$ for a near-perfect black-body emission pervading the universe would correspond to $o$'s motions relative to such a medium. The Lorentz ether frame then may be regarded as a frame wherein the emission pattern of an all-pervasive near-perfect black body is seen with minimal anisotropies. Any object in that frame would be subject to conditions very near to $\gamma=1$ and $\beta=0$. In general, a particle's inertia is proportional to its $\gamma$.

http://en.wikipedia.org/wiki/Electromagnetic_mass#Modern_view

The concept that the mass of a body is the product of dynamical interactions of matter was superseded, when Albert Einstein found out in 1905, that kinematic considerations based on special relativity require that all forms of energy (not only electromagnetic) contribute to the mass of bodies (Mass–energy equivalence).[23][24] That is, the entire mass of a body is a measure of its energy content by E=mc^2, and Einstein's considerations were independent from assumptions about the constitution of matter.[B 2] By this equivalence, Poincaré's radiation paradox can be solved without using "compensating forces", when it is assumed that the mass of matter itself (not only the "fictitious" mass of the electromagnetic energy) is diminished in the course of the radiation process.[25]

Regarding the 4/3 problem: If it is assumed that the electron is a charged moving sphere, then also in special relativity the 4/3-factor is present when the electromagnetic momentum and the self-energy of the electron is considered. Therefore, Max von Laue showed in 1911[26] that Poincaré's introduction of a non-electromagnetic potential is formally correct, but it obtains its deeper, kinematic meaning when viewed from the principle of relativity and Hermann Minkowski's space-time formalism. That is, although electromagnetic momentum itself suggests a 4/3 factor, Laue's formalism required that there are additional components, which guarantee that also spatially extended systems are forming a "closed system" and thus transform as a four-vector, i.e., with rest mass of m=E/c^2. A more elegant solution was found by Enrico Fermi (1922),[27] Paul Dirac (1938)[28] and Fritz Rohrlich (1960),[29] who showed that the electron's stability and the 4/3-problem are two different things. By changing the definition of electromagnetic momentum, the electromagnetic mass can simply written as m_{em}=E_{em}/c^2, thus the 4/3 factor doesn't appear at all. However the Poincaré stresses are still necessary to prevent the electron from exploding due to Coulomb repulsion.[B 8] Today, such questions concerning the self-energy are also discussed on the basis of quantum mechanics, and as long as the electron is considered physically point-like, no electromagnetic mass exists. For distances located in the classical domain, the classical concepts including the Poincaré stresses come into play.[B 9]

Regarding the concepts of longitudinal and transverse mass: Those concepts were also used by Einstein in his first papers on relativity.[23] However, in special relativity they apply to the entire mass of matter, not only to the electromagnetic part. Later a similar concept was also used as relativistic mass

$$M=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}},\qquad m_{0}=\frac{E}{c^2},$$

by physicists like Richard Chace Tolman or Wolfgang Pauli[B 10] and is sometimes used in physics textbooks up to this day, although the term 'mass' is now considered by many to refer to invariant mass.

In a Lorentz ether frame, the relativistic mass would have a definite and real existence by being defined in terms of a relative speed $v$ with respect to this Lorentz ether frame. The mass $m_{0}$ would correspond to the minimum inertia which a particle may have, and thus, its minimum (and identical) inertial and gravitational masses. Despite what some claim, this can be detected experimentally. Failure to stand up to an adequate test would falsify the existence of a Lorentz ether frame. Given the possibility of such a test, the concept of a Lorentz ether frame is not strictly limited to metaphysics.

 

[danR]

In a Lorentz ether frame, the relativistic mass would have a definite and real existence by being defined in terms of a relative speed $v$ with respect to this Lorentz ether frame. The mass $m_{0}$ would correspond to the minimum inertia which a particle may have, and thus, its minimum (and identical) inertial and gravitational masses. Despite what some claim, this can be detected experimentally...

That's fine, but gimme the papers.

 

[Bill_K]

But if the angle between the acceleration vector and the velocity vector is relative to the observer, then whether the mass is accelerating or 'de'celerating should be relative as well. If so, this means disagreement between different inertial frames as to whether the inertia is increasing or decreasing.

In four dimensions the velocity 4-vector has a constant norm, and the acceleration 4-vector is orthogonal to it. You're absolutely correct, if you work in 3-dimensional terms then the angle between them is frame dependent. Your mistake lies in the interpretation of this.

Then it would no longer apply that the inertia of an object is the same in every reference frame.

You're confusing rest mass with relativistic mass, and using the word 'inertia' to refer to both. The rest mass is the same in every frame, the relativistic mass is not.

However, given the link between inertial mass and gravitational mass, it seems untenable that such a property of the universe, such as inertia, could depend on the observer.

Gravitational mass is linked to rest mass.

For example, you would have inertial frames of reference where the energy density of the universe can be 10^120 times than what is observed in our frame.

This is true. An observer in such a frame would meet an unfortunate demise.

How would that preserve constants such as G without introducing additional normalization factors or other similar corrections?

It has nothing to do with G or any other physical constant.

 

[Dale]

given the link between inertial mass and gravitational mass

What link between inertial mass and gravitational mass?

In general, the Lorentz aether will not cause nor resolve any problems you find with SR since they are experimentally identical.

 

[Bill_K]

What link between inertial mass and gravitational mass?

It is rumored that they are equal.

 

[Dale]

It is rumored that they are equal.

Mass isn't the source of gravity. The stress energy tensor is.