Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects seem more natural by connecting with more elementary aspects of physics, particularly the physics of waves.

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and
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,”
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,”
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H. R.
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H. R.
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,
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,
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), pp.
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80
.
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H. R.
Brown
and
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, “
The origins of the spacetime metric: Bell's ‘Lorentzian pedagogy’ and its significance in general relativity
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H. R.
Brown
and
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, “
Minkowski space-time: A glorious non-entity
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H. R.
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12.

These authors also proposed the label “dynamical” for this viewpoint, which we have adopted Ref. 10.

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D. J.
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Mermin
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(
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W. M.
Nelson
,
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, 2nd ed. (
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,
Charleston, SC
,
2013
).
16.
A similar “water-world” conception has been discussed in
M.
Shupe
, “
The Lorentz-invariant vacuum medium
,”
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53
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127
(
1985
).
17.
One can still define rigidity within relativity as a contrast to the malleability of, e.g., a box of gas. Physically speaking a “rigid” object is one whose shape is determined by a quantized wavefunction which is separated from others by a significant energy gap; cf. also <http://en.wikipedia.org/wiki/Born_rigidity>.
18.

See, e.g., Ref. 14 or Ref. 15.

19.

Of course there is also no reason a priori to expect that the effects could fit together to produce the Lorentz transformation. Ultimately, it is simply a mathematical fact that some field theories are Lorentz invariant, while none (to the author's knowledge) exist in which effects conspire to cancel rate changes.

20.
A.
Hirose
and
K.
Lonngren
,
Fundamentals of Wave Phenomena
(
SciTech Publishing
,
Raleigh, NC
,
2010
).
21.
See, e.g.,
N.
Mott
, “
The wave mechanics of alpha ray tracks
,”
Proc. Roy. Soc. A
126
,
79
84
(
1929
).
22.

Another possibility for the coupling involves one time derivative, e.g., ϕ(x)ξξ̇, which is similar to the coupling of an electric potential. A coupling with two time derivatives would be analogous to a gravitational potential.

23.

Derivatives convert the cosines of Eq. (5) into sines, however, the packet built on sines is approximately equal to the packet built on cosines and shifted by Δx=π/2k.

24.
For a recent treatment, see
C.
Wells
and
S.
Siklos
, “
The adiabatic invariance of the action variable in classical mechanics
,”
Eur. J. Phys.
28
,
105
112
(
2007
);
Also
Goldstein
,
Classical Mechanics
, 2nd ed. (
Addison-Wesley
,
Reading, MA
,
1980
), chap. 11-7.
25.
See the prize essay “Wave Momentum” by Charles Peskin, <http://silverdialogues.fas.nyu.edu/object/silver.charliepeskin>.
26.

This can be shown using conservation of angular momentum, but this is of course one aspect of Lorentz invariance, since the Lorentz group contains rotations.

27.
W. M.
Nelson
, “
A wave-centric view of special relativity
,” e-print arXiv:1305.3022.
28.
This calculation is described in standard texts such as
J. D.
Jackson
,
Classical Electrodynamics
, 2nd ed. (
John Wiley & Sons
,
New York
,
1975
). A more schematic understanding is presented in Ref. 27.
29.
An alternate form of the calculation is described in
V. P.
Dmitriyev
, “
The easiest way to the Heaviside ellipsoid
,”
Am. J. Phys.
70
,
717
718
(
2002
);
and
B. Y.
Hu
, “
Comment on ‘The easiest way to the Heaviside ellipsoid’ by Valery P. Dmitriyev
,”
Am. J. Phys.
71
,
281
(
2003
).
30.

Ideas for calculating explicit shape change can be found in Refs. 13 and 8 (the latter proposes numeric calculations of orbiting systems undergoing acceleration). Calculations to lowest order in v/c are also feasible.

31.
The contraction process has been analyzed by
H.
Nikolic
, “
Relativistic contraction of an accelerated rod
,”
Am. J. Phys.
67
,
1007
1012
(
1999
).
32.

The other part of the mass change is actually an increase, because the electron in a lower energy state moves faster and hence has a larger relativistic mass. The virial theorem guarantees that this increase is more than offset by the decrease in field energy.

33.
F.
Wilczek
, “
Happy birthday, electron
,”
Sci. Am.
306
,
24
(
2012
).
34.
W. M.
Nelson
, “
On back-reaction in special relativity
,”
Am. J. Phys.
81
,
492
497
(
2013
).
37.

One can question whether slow carrying is a valid method of synchronization, but if it is not, then there is no clear reason to believe that observers have any useful way to define synchronization (a real possibility in non-Lorentz-invariant scenarios, cf. Sec. IV).

38.
Slow transport appears to have been first presented in
A.
Eddington
,
The Mathematical Theory of Relativity
(
Cambridge U.P.
,
Cambridge
,
1923
).
39.
For Einstein's train see, e.g., Ref. 14, Ch. 5; <http://en.wikipedia.org/wiki/Relativity_of_simultaneity>; A. Einstein, Relativity: The Special and General Theory, Springer, 1916, available in the public domain at <http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory>.
40.

For further discussion of these “perspectival” changes between observers, see Ref. 13.

41.

The fact that formal quantities, especially the metric, may not have their expected operational meaning within the theory, has also been discussed by Brown (Ref. 4) and Brown and Pooley (Ref. 9).

42.
We don't claim that no other interesting classes of field theory exist; examples are Lorentz invariant theories with background field values. Lorentz violation is an active topic of research, e.g.,
T.
Jacobsen
,
S.
Liberati
, and
D.
Mattingly
, “
Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints
,”
Ann. Phys.
321
,
150
196
(
2006
).
43.

This helps understand the question of conventionality of the definition of simultaneity (see, e.g., Ref. 11). If Lorentz invariance holds then there is a preferred definition of simultaneity and little reason to consider any other; otherwise one will need to consider conventions, but probably no really ideal convention will exist. In no case can a field/wave world be converted back to Newtonian behavior by means of conventions.

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