The special theory of relativity
Around the
turn of the century, scientists could make predictions about the character of the
relationship between the temperature of a given body and the kind of wavelength of light
it gives off when radiating at that temperature. The means used to make such predictions
involved marrying the principles of statistical mechanics to Maxwell’s
electromagnetic equations. Unfortunately, the theoretical predictions which were made on
the basis of such a methodological union frequently did not agree with empirical
measurements.
Max Planck
had suggested in 1900 that one might be able to resolve the problem of black-body
radiation (e.g., what wavelength of light will be radiated by a given object or body that
is heated to a certain temperature) if one were to suppose light were emitted from such
bodies only at certain levels of energy. These energy packets would be multiples of a
value ‘h’, derived by Planck, and known, henceforth, as the Planck constant.
Einstein
made use of Planck’s proposal in the former’s 1905 paper on the photoelectric
effect, the phenomenon in which electrons were observe to be emitted from various solid,
liquid, or gaseous materials when exposed to radiation of certain wavelengths.
Essentially, Einstein argued the photoelectric effect could be understood as a function of
the absorption and emission of discrete bundles of energy.
While the
work of Planck and Einstein helped resolve some of the issues surrounding the problem of
black-body radiation, it also helped give rise to a further problem which had far-reaching
implications. For example, the idea of a discrete, particle-like, bundle of energy was
difficult, to say the least, to reconcile with Maxwell’s theory of electromagnetic
fields in which light, as one form of electromagnetic radiation, supposedly was propagated
in the form of a wave.
Einstein
began to look for principles he hoped would be capable of withstanding whatever
theoretical and methodological reconstruction might have to take place with respect to the
"classical" mechanics of Newton and Maxwell which were under assault by the
changes taking place in physics around the turn of the century. And, in another of his
famous three revolutionary papers of 1905, he advanced his theory of special relativity as
a way of helping to bridge the transformations taking place.
In 1905,
Albert Einstein put forth his ideas on special relativity. The "special" aspect
of his first paper on relativity reflects his focus on the relation of different frames of
reference that were traveling with a constant, rectilinear (either in straight lines or at
right angles) motion relative to one another.
One might
think of a frame of reference as the vantage point from which one methodologically engages
or measures a given phenomenon of physics. Frames of reference which traveled with a
constant, rectilinear relative to one another were known as "inertial frames of
reference". Consequently, because there were many other kinds of
non-linear motion possible for a given frame of reference, Einstein was initially
interested only in the special case of rectilinear relative motion.
According to
Einstein, the principle of special relativity was intimately connected with all physical
phenomena. In effect, this principle stipulates that irrespective of the motion of a given
observer relative to any other observer, the laws of nature will be the same for all
observers. Another way of stating the same idea is to say that the laws of
nature are independent of the kinds of motion which different observers have with respect
to one another.
In other
words, the special theory of relativity is, at heart, about the invariance of physical
laws and, therefore, about that which transcends the relative motion of observers within
different frames of reference. Unfortunately, many people have remembered the
"relative" part but the theory but entirely have forgotten (or never, actually,
knew) the real significance underlying Einstein’s seminal 1905 paper.
Ironically,
the popular misconception of the theory of relativity as being mainly about how reality
tends to appear, or look, differently, relative to one’s point of view was aided and
abetted by Einstein himself. More specifically, apparently, Einstein was once reported to
have glibly explained the theory of relativity as somewhat akin to how sitting on a hot
stove for a minute seems like an hour and sitting next to a beautiful girl for a minute
seems like an hour.
He may have
had his tongue firmly in his cheek when he said this. However, many people have been
misled by the imagery ever since that time.
In any
event, earlier, in the late 1500s, Galileo also had put forth a principle of relativity.
He maintained that various laws of motion he had been exploring retained their invariant
form as laws even if the coordinate framework of an observer was subjected to different
transformations such as rotation, translation (motion in which all the parts of an object
move in the same direction), and so on. In other words, physical laws of motion were
independent of the sorts of geometric transformations which might be performed on any
given coordinate system being used by an observer to represent the motion in question.
Nevertheless,
there is a major difference between Galileo’s principle of relativity and the
principle of relativity advocated by Einstein. This difference concerned the role which
time played in the two theoretical frameworks.
Galileo
believed the laws of motion were the same independent of the frame of reference being
considered. However, the transformations (which showed how one frame of reference was the
equivalent of other frames of reference vis-a-vis, say, a particular law of motion) in
Galileo’s theory only were performed on the "spatial" coordinates of the
frames of reference being considered.
Galileo
considered the time coordinate to be absolute. That is, the time coordinate was the same
for all observers in all inertial frames of reference. Consequently, according to Galileo,
there was no need to translate the time component from one frame of reference to another
as had been done in relation to the spatial component.
For Galileo,
spatial coordinates could be moved, rotated and twisted. Time, however, was inviolate and
not subject to the realm of changes.
One of the
revolutionary facets of Einstein’s special theory of relativity was the manner in
which it departed from the classical treatment of, or approach to, time as an absolute.
Indeed, Einstein argued there was, at least, one law of nature - namely, the Maxwell
equations for electromagnetic phenomena, in which time could not be treated as an
absolute.
Einstein
contended that if one treated time as an absolute, then Maxwell’s equations altered
their character in certain ways as one moved from one frame of reference to another.
Therefore, when time was treated as an absolute, the laws of physics which were given
expression through Maxwell’s equations became dependent on, and were a function of,
the character of the state of motion of a given observational frame of reference.
As indicated
previously, Einstein believed the laws of nature were invariant and independent of any
given observational frame of reference. Consequently, in order to maintain this view,
Einstein argued that as one moved from one inertial framework to another, there was a need
not only for the spatial coordinates of one framework to be translated into their
equivalent counterpart in the new frame of reference, but there also was a need for one to
translate the temporal coordinates of one frame of reference into their temporal
"equivalents" in a new frame of reference which had rectilinear motion relative
to the first framework.
In short,
Einstein agreed with Galileo concerning the invariance of the "laws" of nature
and that such laws were independent of the frames of reference through which these laws
were experienced or engaged. At the same time, he disagreed with Galileo concerning the
role which time played - for Einstein, time was part of the fabric of a frame of reference
and not part of the fabric of the invariant laws of nature.
However,
Einstein did not believe that a principle of relativity which emphasized the invariance of
physical laws was sufficient, in and of itself, to withstand the challenges to classical
mechanics (in the form of Newtonian and Maxwellian theories) which were in the air at the
turn of the century. Some additional factor was necessary.
This extra
factor turned out to be the constancy of the speed of light. More specifically, Einstein
assumed that, in ‘empty’ space, light would always be propagated at a constant
velocity "c". Furthermore, he maintained the velocity of light is independent of
the motion of the body which is emitting light, and, therefore, the speed of light would
have the same value for all frameworks which were in uniform, rectilinear motion relative
to one another.
The
foregoing position gave rise to the problem of how to account for the constancy of the
speed of light. After all, one might expect that the velocity of light should be subject
to the same variability as were other spatial and temporal features of inertial
frameworks.
Lorentz,
prior to Einstein, had suggested that one would have to assign different times and
distances to different frameworks which were in uniform, constant motion relative to one
another. Then, one would have to use a set of transformation equations to show how the
measured values in one framework could be related to the comparable variables being
measured in other frameworks moving in constant, uniform motion relative to the first
framework.
Lorentz
believed one would have different values for the observables - such as length, time, and
so on - being measured in inertial frameworks as a result of the effect that the ether
imparted to systems traveling through it. ‘The ether’ was a hypothetical idea
adopted by many physicists of the 19th and early twentieth century and was believed to be
the spatial medium through which all bodies were assumed to move.
This facet
of Lorentz’ perspective was unacceptable to Einstein. Einstein was interested in
developing a position which would be independent of considerations of ‘the
ether’- a problematic theoretical entity.
Although the
relativistic transformation equations derived by Einstein - in order to preserve the
constancy of the speed of light in all frameworks - had precisely the same form as
Lorentz’s transformations equations (which had been constructed with the idea of
taking the effect which movement through the ether was assumed to have on
physical/material objects), Einstein understood the same equations in a very different way
than did Lorentz. Einstein had been led to the Lorentz transformation equations, not
through the causal effects of the ether, but by rethinking the ideas of length, time, and
simultaneity.
In
Einstein’s relativistic theory, measurements involving time, length, and so on, could
have different values in different inertial frameworks despite being tied to
one-and-the-same observed event. Variability of such measurements relative to a given
event was permitted in order to be able to preserve the velocity of light as a constant,
and the constancy of the velocity of light is a fundamental building block in the
invariant character of the laws of classical physics involving the basic equations of
Maxwell and Newton.
By reworking
the mathematics of the Lorentz equations (which are still known as Lorentz transformations
despite the differences in the manner in which they were generated), Einstein showed that
the inverse of a Lorentz transformation is itself a Lorentz transformation. This meant
that in systems which were in uniform relative motion with respect to one another,
differences in measurements for length, time, and mass taken for a given event within one
inertial framework would be reflected reciprocally - through the Lorentz transformation
equations - in other inertial frameworks conducting their own set of measurements
involving the same event.
Thus,
despite differences in the values for length, time, mass, and so on, which might be
obtained in inertial frameworks linked to one-and-the-same event, each of the inertial
frameworks observed the same laws of physics in operation. In other words, when one looked
at an event through the glasses of the Lorentz transformations, one could "see"
that the cement which bound together the different measurement values of various inertial
frameworks linked to a common event, was the fact that the general character of physical
laws remained intact when one translated the results of measurement in one inertial
framework with the results of measurement in other inertial frameworks observing the same
event. In short, measurement across inertial frameworks could be shown to be relative, but
the laws of physics manifested in these same inertial frameworks remained invariant.
For
Einstein, the fact that the inverse of a Lorentz transformation could be shown to be a
Lorentz transformation as well, had another significant meaning. It meant there was no
inertial framework which could be demonstrated to have a preferred stationary position
relative to the ether, and, therefore, there was no framework which could be
used as a sort of ontological ground zero through which one could calibrate the
relationship of all other frameworks vis-a-vis some given physical event.
Another way
of saying the same thing is to maintain that the ether - if it existed at all, could not
be shown to have any causal effect on variables such as length, time, or mass within
inertial frameworks that were in uniform, constant motion relative to one another. For, in
order to be able to demonstrate that the ether did have such a causal impact, one would
have to be able to identify some framework as being stationary relative to the ether and,
therefore, capable of being used to establish a baseline against which the impact of the
ether on non-stationary frameworks could be measured.
Absolute
motion could not be detected. Only relative motion was measurable, and it was only the
relative motion of inertial frameworks tied to a given event which would affect the
measurements made in these linked systems. Yet, irrespective of whatever differences in
measurement might arise from one inertial framework to another relative to some given
event, each of the frameworks would be able to show, via the Lorentz transformation
equations, that the same laws of physics governed the event being observed, no matter
which framework of measurement and relative motion one selected.
Methodology, fields and uncertainty
Einstein's special theory of relativity is largely a theory about methodological
issues. There are, to be sure, certain ontological overtones which exist in Einstein's
special theory of relativity.
For example, one such overtone is his assumption that the speed of light is independent
of the state of motion of the body from which it is emitted. This sort of overtone aside,
however, most of his paper on the electrodynamics of moving bodies involves a
methodological reworking of concepts such as time, length, mass, synchronization, and so
on.
More specifically, the reworking is done, on the one hand, in terms of the manner in
which the process of measurement shapes one's understanding with respect to the character
of various aspects of experience. In other words, the way one operationalizes an idea
(which is a form of the process of characterization) shapes the way one engages and
understands ontology.
For instance, when Einstein says time is what a clock measures1, he colors
his understanding of the ontology of time. The coloring comes from the character of the
means he uses to operationalize, for purposes of quantifying and measuring, the ontology
of time.
There also is another aspect to Einstein's methodological reworking of the meaning of
some of the basic concepts of physics. This aspect concerns the manner in which one goes
about translating the measured values obtained in another framework that has relative
uniform motion with respect to one's own framework. In short, this aspect revolves around
the methodology of translation between or among different frameworks.
Each of the foregoing aspects of the methodological reworking of basic ideas of physics
doesn't really say much about the structural character of ontology, except indirectly. In
effect, Einstein is exploring some of the constraints and degrees of freedom of ontology
as far as how one can methodologically interact with that ontology in the context of doing
comparative studies with observers in other frameworks who have relative uniform motion
with respect to one.
The principle that the inverse of a Lorentz transformation is, itself, a Lorentz
transformation says absolutely nothing about the structural character of ontology. What it
does say is: (a) the methodologies of systems involved in relative uniform motion are tied
together in certain ways; (b) our perceptions and interpretations of how such
methodologies are employed in other observational frameworks is rooted in, and shaped by,
methodological considerations; and, (c) our understanding of what goes on in our own
observational framework is rooted in, and shaped by the manner in which we operationalize
terms in that framework in order to be able to quantify and measure events which occur in
that framework.
The idea of relativistic effects is often given an ontological flavor such that, for
example, time paradoxes are permitted to have ontological implications. Thus, supposedly,
one and the same clock can, in an ontological sense, run both faster and slower at the
same time, just as a Lorentz transformation and its inverse, which are mathematical
structures, can exist simultaneously.
Herbert Dingle, in his book Science at the Crossroads, seems to be taking
issue with just this aspect of the special theory of relativity. He is commenting on, and
criticizing, the tendency of people to interpret the special theory as an ontological
theory that provides an accurate description of certain aspects of reality. Indeed, if one
does suppose that the special theory of relativity is primarily about ontology, then one
does end up with a number of paradoxes, some of which are pointed out by Dingle.
On the other hand, if one likens the special theory of relativity to the invention of a
better calibrated ruler or measuring device, then, although the new measuring device does
not, in and of itself, say anything about ontology, it does alter the structural character
of one's engagement of ontology. As a result, the measuring device may improve certain
aspects of one's understanding of ontology because it provides a means of compensating for
certain factors that are capable of distorting the way in which one's mode of methodology
engages ontology during the measurement process.
The special theory of relativity leaves the laws of nature unchanged. The special
theory of relativity is intended to show that the laws of nature are invariant despite the
fact that the measurements for different variables such as time, mass, length, and so on,
may vary from one framework to another in relation to the observation of one-and-the-same
event.
Apparently, the best way Einstein could think of to demonstrate invariance among a
variety of frameworks which have uniform relative motion with respect to one another, was
to re-calibrate the methodology. He did this by using the constancy of the speed of light
as the value which is to guide the re-calibration process as one moves from one locality
to another. This re-calibration is accomplished through the transformation equations that
are themselves rooted in a reworking of the meaning of such basic concepts as time,
simultaneity, length and so on.
In a sense, what Einstein has done in the special theory of relativity is somewhat
analogous to what Maxwell has done in arriving at his electromagnetic field theory.
Maxwell used a method (namely, the method of analogies) which generated implausible
mechanisms in order to make certain relationships visible and certain calculations
possible.
Despite such implausibilities, Maxwell's method yielded results that not only were in
agreement with empirical results, but also tied together, in a unified way, a wide variety
of electrical and magnetic phenomena. So, even though the mechanisms utilized by Maxwell
did not appear to be likely candidates to accurately reflect how (in an ontological sense)
things happened in the context of electromagnetic field, they led to results that were
able to accurately reflect, to some extent, the invariant character of the effects
which ensued from the unknown hows of such fields.
Einstein, too, has employed a method (namely, the special theory of relativity) which
generated implausible mechanisms (e.g., time should simultaneously run both faster and
slower) in order to make certain relationships visible and certain calculations possible.
Despite such implausibilities, Einstein's method, nonetheless, yielded results that were
not only in closer agreement to empirical findings than were the results derived from the
methods of Newtonian mechanics, but which also tied together, in a unified way, a wide
variety of physical phenomena. Therefore, even though the relativity methodology did not
appear to be a likely candidate to accurately reflect how (in an ontological sense) things
actually happened in the context of, say, the electromagnetic field, it led to results
that were able to accurately reflect, to a degree, the invariant character which was
inherent in the unknown hows of such fields.
In short, Einstein's special theory of relativity didn't get one any closer to
understanding the ‘how’ of things, but it did bring one closer to a more
accurate representation of what that unknown how made possible. His method accomplished
this by sensitizing one to the way methodological engagement affected processes of
observation, operationalization, measurement, interpretation and translation. This leaves
open the possibility that just as Einstein found his way to a methodological improvement
concerning Newtonian mechanics, someone also might be able to discover a means of
improving on the methodology of Einstein's special theory of relativity in a way that
would not entail problems such as the twin paradox, or having one and the same clock
running both faster and slower at the same time, and so on.
What is essential in all of this is not so much Einstein's methodology in particular,
but the effect of that methodology in allowing one to generate a more accurate description
of certain aspects of our engagement of ontology, while preserving the invariance of the
laws of nature as one moves from one observational framework to another. If one could come
up with an alternative means of accomplishing what Einstein's methodology accomplishes,
yet, which is free from some of the problem's of Einstein's special theory of relativity,
then, this would constitute an improvement, once again, in the manner in which we
methodologically engage certain aspects of reality.
However, one might not be able to eliminate, or by-pass, the problems inherent in
Einstein's methodology, for such problems may give expression to certain limits in the
character of rational methodology itself. More specifically, there is a sense in which the
problems that occur in Einstein's special theory of relativity may serve as something akin
to Heisenberg's uncertainty principle.
Heisenberg indicated that the very process we use to observe phenomena can
disturb, if not distort, the character of what is observed and, thereby, place limits on
the extent to which reality can be known. So too, one of the effects of Einstein's special
theory of relativity may be to indicate that the very methodology which is used to
preserve the invariance of the physical laws of the universe interferes with our ability
to establish certain facts about the universe. For example, one might not be able to
determine the actual structural identity of a given event independent of its embeddedness
in a network of assumptions and methodological considerations concerning measurement and
relative motion.
Einstein's methodology permits one to see that a given event is law-governed. His
methodology also permits one to see how the form of the laws which are operative, manifest
themselves according to the manner in which different observational systems engage a given
event.
However, Einstein's methodology obscures one's vision of the actual ontological
character of that which underlies the event. One sees relative mass, velocity,
length, and time, but one does not see the actual mass, velocity, length or time of
an event.
One sees only what one's methodology permits one to see. In a sense, the methodology
becomes like a modern heir to the Kantian categories.
Consequently, Einstein's methodology introduces an element of uncertainty concerning
the nature of reality. As is the case with quantum phenomena, one can approach the actual
structural character of reality only up to a point. Beyond that, the methodology itself
prevents one from getting any closer. Indeed, the attempt to get closer only leads to
problems, paradoxes and distortions.
In other words, within certain limits, the methodologies of both quantum physics as
well as relativistic physics help one to grasp the structural character of certain aspects
of ontology. However, if the boundaries of these limits are ruptured or exceeded, an
increasing element of indeterminancy and/or uncertainty is introduced into the
proceedings. As a result, one's vision of certain aspects of ontology becomes obscured.
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