A solution of the time paradox of physics
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Z. Phys. Chem. 2020; aop
Grit Kalies*
A solution of the time paradox of physics
https://doi.org/10.1515/zpch-2020-1659
Received March 13, 2020; accepted July 29, 2020; published online August 27, 2020
Abstract: Quantum mechanics for describing the behavior of microscopic entities
and thermodynamics for describing macroscopic systems exhibit separate time
concepts. Whereas many theories of modern physics interpret processes as
reversible, in thermodynamics, an expression for irreversibility and the so-called
time arrow has been developed: the increase of entropy. The divergence between
complete reversibility on the one hand and irreversibility on the other is called the
paradox of time. Since more than hundred years many efforts have been devoted to
unify the time concepts. So far, the efforts were not successful. In this paper a
solution is proposed on the basis of matter-energy equivalence with an energetic
distinction between matter and mass. By refraining from interpretations pre-
dominant in modern theoretical physics, the first and second laws of thermody-
namics can be extended to fundamental laws of nature, which are also valid at
quantum level.
Keywords: entropy; irreversibility; quantum thermodynamics; special relativity;
time paradox of physics.
1 Introduction
The experience of irreversibility, i.e. the empirical reality that processes have a
direction and that yesterday can be distinguished from tomorrow, has occupied
philosophers and physicists for centuries.
On the one hand, the theories of modern physics interpret processes as time-
reversal invariant, i.e. time-symmetric or reversible. The equations of quantum
mechanics, special relativity (SR), classical mechanics, electrodynamics, etc.,
remain unchanged under time-reversal. Even general relativity (GR), which is
applied for events on cosmological scales, contains no physical expression for
irreversibility. This would mean that each process in the universe can be reversed
in the same path.
*Corresponding author: Grit Kalies, HTW University of Applied Sciences Dresden, 1 Friedrich-List-
Platz, D-01069 Dresden, Germany, E-mail: grit.kalies@htw-dresden.de
Open Access. © 2020 Grit Kalies, published by De Gruyter. This work is licensed under the
Creative Commons Attribution 4.0 International License.2 G. Kalies
On the other hand, thermodynamics includes a physical term for the fact that
processes are irreversible and that a time arrow exists for the whole universe. In
1865, Rudolf Clausius formulated the second law of classical thermodynamics
according to that the extensive state quantity entropy S increases in any natural
process [1]. Thermodynamic process and equilibrium criteria are defined by en-
tropy relations and are used to design technical and industrial processes and to
describe the complex everyday world surrounding us.
The divergence between complete reversibility in quantum mechanics on the
one hand and irreversibility and time arrow in thermodynamics on the other, i.e.
“The Paradox of Time” [2], could not yet be explained by a physics approach.
Today, S is interpreted as a merely statistical property, whereby a dynamic chaos
on the micro level would break the temporal symmetry. In this way, the second law
of thermodynamics is further understood as a statement of probability, as already
concluded by Ludwig Boltzmann in the context of the kinetic theory of gases [3].
Modern quantum field theories assume time-reversal processes in line with Ein-
stein’s opinion who wrote in his letter of July 29, 1953, to his colleague and friend
Michele Besso:
“As far as our more direct knowledge of the elementary processes exists, there is a reversal of each
process. […] In the elementary, there is an inverse to every process.” (« Aussi loin que puisse
parvenir notre connaissance plus directe des processus élémentaires, on trouve, pour chaque
processus, son inverse. […] Dans l’élémentaire, tout processus a son inverse. » [4, p. 292])
Consequently, irreversibility is further understood as a subjective impression or
illusion, as Albert Einstein suggested in 1955:
“For us believing physicists, the distinction between past, present and future only has the
meaning of a persistent illusion.” („Für uns gläubige Physiker hat die Scheidung zwischen
Vergangenheit, Gegenwart und Zukunft nur die Bedeutung einer wenn auch hartnäckigen
Illusion.“ [5])
Up to the present day, physicists try to explain the origin of the arrow of time [6–11].
In this context, it should be noted that in modern theoretical physics, the theories
of relativity and the Copenhagen interpretation of quantum mechanics are
regarded as fundamental, while thermodynamics is understood as more deriva-
tive. Irreversible behavior is often neglected:
“Irreversibility as a fundamental problem is still not accepted today; the considerable effort
that was invested in it for several decades around a hundred years ago merely served to finally
displace it.” („Irreversibilität als Grundlagenproblem wird bis heute nicht akzeptiert; der
erhebliche Aufwand, der vor etwa hundert Jahren für einige Jahrzehnte dafür getrieben
wurde, diente lediglich seiner endgültigen Verdrängung.“ [12, p. 8])Time paradox of physics 3
Accordingly, the so-called world formula (Theory of Everything, ToE) is searched
today in the unification of two theories with reversible time concepts: the quantum
theory with CPT symmetry and the general theory of relativity that describes
gravity as a symmetric dynamic spacetime. In the unifying approaches of quantum
gravity such as string theory, loop quantum gravity, non-commutative geometry,
causal dynamical triangulation or asymptotic safety, an attempt is made to
quantize spacetime, with a consensual solution still missing [13]. The most popular
candidates of quantum gravity are the string theory and loop quantum gravity. The
intuitive approach of the string theory that real elementary particles cannot be
zero-dimensional1 is connected with a high-dimensionality of spacetime. For
example, the five popular superstring theories that predict supersymmetry (SUSY)
postulate 10 spacetime dimensions. Since a few years, the criticism of the string
theory is increasing:
“The experimental confirmation is the seal of quality of genuine natural science. Since string
theorists have not succeeded in proposing any possibility of experimental confirmation of
string theory at all, string theory should be retired now and today.” („Die experimentelle
Bestätigung ist das Gütesiegel echter Naturwissenschaft. Da die Stringtheoretiker es nicht
geschafft haben, überhaupt irgendeine Möglichkeit der experimentellen Bestätigung der
Stringtheorie vorzuschlagen, sollte die Stringtheorie jetzt und heute in den Ruhestand
geschickt werden.“ [F. Tipler, in: 14, p. 96])
Some of the co-founders of loop quantum gravity admit that their theory and
modern physics are in crisis, such as the theoretical physicists Lee Smolin [8, 11, 15]
and Sabine Hossenfelder [16]. Others, like the physicist Carlo Rovelli, argue,
contrary to Lee Smolin, that time does not exist and invoke the beauty of GR [17, 18].
This esthetic assessment cannot convince. A dynamic spacetime inevitably
means that even for macroscopic processes the arrow of time (the distinction
between yesterday and tomorrow) is irrelevant and that films cosmologically
might run backwards. The fundamental daily experience that things are subject to
temporality, including aging and death, is negated. From the viewpoint of ther-
modynamics, the approaches of quantum gravity are bound to fail since mecha-
nistic approaches such as relativistic mechanics and quantum mechanics are
based on idealizations that can only provide an incomplete picture of the real
world.
In this paper is shown that the divergence between complete reversibility in
quantum theory and irreversibility in thermodynamics can be resolved by means
of an energetic distinction between matter and mass. Matter-energy equivalence
1 A one-dimensional object like a string is closer to reality than a point-like, i.e. zero-dimensional
elementary particle in the Standard Model. However, one-dimensionality still remains a non-
physical assumption.4 G. Kalies
[19, 20] provides the theoretical justification for a realistic interpretation of
quantum phenomena, based on works of Hendrik Antoon Lorentz, William
Thomson (Lord Kelvin), Henri Poincaré, Walther Nernst, Louis de Broglie, Jean-
Pierre Vigier, David Bohm, etc. [21–23]. By adapting thermodynamics to quantum
theory, a realistic theory of quantum thermodynamics can be developed, which can
be understood as the connection between micro- and macrocosm.
After a short insight into the time concept of modern physics and the current
interpretation of entropy, a solution of the time paradox of physics is presented
that is in full agreement with the experimental evidence and newer findings of
quantum physics.
2 Special relativity and the time concept of
physics
The time concept of modern theoretical physics is essentially based on the special
theory of relativity (SR) of Albert Einstein [24, 25]. The conditionality of this time
concept can only be understood in the historical context. A brief summary is given
below that may differ from other reports in key points because it focuses on the
recognition of irreversibility.
Before 1905, the ideas of time were mainly influenced by Newton’s concept of
absolute time:
“Absolute, true, and mathematical time, of itself, and from its own nature flows equably
without regard to anything external, and by another name is called duration : relative,
apparent, and common time, is some sensible and external (whether accurate or unequable)
measure of duration by the means of motion, which is commonly used instead of true time;
such as an hour, a day, a month, a year.” [26, p. 77]
and the ideas of philosophers such as Immanuel Kant [27, p. 134] or Arthur
Schopenhauer [28, p. 67], who understood space and time as a priori categories.
In 1905, Albert Einstein created substantially new space and time concepts. Time
was identified by the clock time which is always variable because clocks, i.e. real
matter, can be influenced, e.g. by gravitational fields. He proposed a dynamic time
that depends on the state of the observer. Time was interpreted as relative while
abandoning absolute time and absolute simultaneity.2
2 A detailed analysis of the time concept of special theory of relativity is given in the textbook
“Vom Energieinhalt ruhender Körper” (“From the Energy Content of Resting Bodies”) [19] and will
be presented in the subsequent paper “A solution of the interpretation problem of Lorentz
transforms”.Time paradox of physics 5
In 1908, the mathematician Herman Minkowski derived from SR the idea of the
four-dimensional Minkowski spacetime:
“The views on space and time that I would like to develop for you are based on experimental
physics. This is their strength. Their tendency is a radical one. From now on, space for itself
and time for itself are to be completely reduced to shadows and only a kind of union of the two
is to maintain independence.” („Die Anschauungen über Raum und Zeit, die ich Ihnen
entwickeln möchte, sind auf experimentell-physikalischem Boden erwachsen. Darin liegt
ihre Stärke. Ihre Tendenz ist eine radikale. Von Stund‘ an sollen Raum für sich und Zeit für
sich völlig zu Schatten herabsinken und nur noch eine Art Union der beiden soll Selb-
ständigkeit bewahren.“ [29, p. 75])
For the physics of the early 20th century, the usability of theories was of primary
importance. In 1905, Ludwig Boltzmann stated that physics turns from an
explaining to a describing natural science [30, p. 1]. Also Einstein’s paper “On the
electrodynamics of moving bodies” in 1905 [24] was committed to a pragmatic and
positivistic spirit. By promising a unification of Newtonian mechanics and Max-
well’s electrodynamics, SR did fulfill the collective expectation of physics and
offered a way out of the long-lasting crisis that resulted from the fact that a me-
chanical ether fluid could not be found.
In light of the new time concept of SR, one spoke of a radical change in the
worldview. In 1909, Max Planck proclaimed a Copernican revolution:
“It hardly needs to be emphasized that this new understanding of the concept of time places
the highest demands on the abstraction ability and imagination of the physicist. […] The
revolution caused by this principle in the area of the physical world view can only be
compared in extent and depth with the introduction of the Copernican world system.“ („Es
braucht kaum hervorgehoben zu werden, daß diese neue Auffassung des Zeitbegriffs an die
Abstraktionsfähigkeit und an die Einbildungskraft des Physikers die allerhöchsten Anfor-
derungen stellt. […] Mit der durch dies Prinzip im Bereiche der physikalischen Weltan-
schauung hervorgerufenen Umwälzung ist an Ausdehnung und Tiefe wohl nur noch die
durch die Einführung des Copernikanischen Weltsystems bedingte zu vergleichen.“ [31, pp.
117–118])
This assessment is still shared today, and many textbooks and scientific papers
honor the revolutionary work of Albert Einstein and Hermann Minkowski.
Nevertheless, the time concept of SR is rather to be understood as a pragmatic
emergency solution, since a dynamic relative time inevitably means that time is
symmetric. In this way, all processes are reduced to reversible changes of position
in empty space, according to which objects can be transported back to their old
place without any changes. From experience we know that this represents an
idealization which is not able to fully grasp the complexity of nature:6 G. Kalies
“Predictable in the future is only what resembles the past, or what can be put together again
from elements that are like those of the past. This is the case of astronomical, physical and
chemical processes, of all those in general, in which only changes of position occur, in which
the idea that things can be brought back to the same place is not a theoretical absurdity, [/]. ”
(„Vorhersehbar an der Zukunft ist nur, was der Vergangenheit gleicht, oder was aus Ele-
menten, die denen der Vergangenheit gleichsehen, wieder zusammengesetzt werden kann.
Dies ist der Fall der astronomischen, physikalischen und chemischen Vorgänge, aller derer
überhaupt, ,beidenen nur Lageveränderungen vor sich gehen, bei denen der Gedanke, die
Dinge könnten an Ort und Stelle zurückgebracht werden, keine theoretische Absurdität ist,
[32, p. 34])
Beside the main postulate of the invariance of light velocity, SR is characterized by
energetic idealizations and assumptions such as [19, 20]:
– the movement of point masses in empty (matter- and field-free) space,
– the interpretation of the inertial system as a rigid body,
– the construction of space from inertial systems,
– the interpretation of time as clock time,
– the concept of the primacy of the observer.
Many scientists criticized the contra-intuitive assumptions of SR, which led to
partly emotional discussions, also in public. The majority of contemporary sci-
entists at the early 20th century did not believe in an empty, etherless space:
“Lorentz’s theory demanded an ether. He, and the great majority of his contemporaries, never
doubted the physical reality of the ether, as something that both had physical properties and
could serve as a standard of rest with respect to which ‘absolute’ velocities had a definite
meaning.” [33, pp. 115–116]
In his general theory of relativity (GR) of 1915 [34, 35], Einstein replaced, by
maintaining the geometric idea of symmetric spacetime, the matter- and field-free
space of SR by a space corresponding to space filling:
“According to the general theory of relativity, however, space has no special existence in
respect of the ‘space-filling’, dependent on the coordinates.” („Gemäß der allgemeinen
Relativitätstheorie dagegen hat der Raum gegenüber dem ‚Raum-Erfüllenden‘, von den
Koordinaten Abhängigen, keine Sonderexistenz.“ [36, p. 125])
Einstein gave priority to geometry, as he reinforced in 1917 and 1922:
“The thus completed geometry is then to be treated as a branch of physics.” („Die so ergänzte
Geometrie ist dann als ein Zweig der Physik zu behandeln.“ [36, p. 9])
„According to all these definitions, spatial and temporal statements have a physically real,
not merely fictive meaning.” („Nach all diesen Festsetzungen haben räumliche und zeitliche
Angaben eine physikalisch reale, keine bloß fiktive Bedeutung.“ [37, p. 32])Time paradox of physics 7
With the measurement of the deflection of light in the gravitational field of the sun
by Sir Arthur Eddington in May 1919, which was interpreted as confirmation of GR,
the concept of relative time gained worldwide fame. The triumph of GR was also
that of SR although the two theories are fundamentally different. Einstein
considered many experimental findings, such as the perihelion motion of Mercury,
the deflection of light in a gravitational field or the redshift of spectral lines [36, pp.
98–100], as confirmations of the theories of relativity. In his speech to the Royal
Society of London in 1921, he emphasized that relativity
“is not of speculative origin, but owes its discovery only to an effort to adapt the physical
theory as well as possible to the observed facts.” (“nicht spekulativen Ursprungs ist, sondern
dass sie durchaus nur der Bestrebung ihre Entdeckung verdankt, die physikalische Theorie
den beobachteten Tatsachen so gut als nur möglich anzupassen.” [38])
It was a multi-causal, not only scientific, but also social and science-political
process that SR and GR were gradually accepted. A minor role in this context
played the fact that single experiments allow only limited statements and can be
interpreted differently, whereby the previously fixed belief is often decisive. The
experience of temporal development in one direction being confirmed innumer-
able times was not taken into account. Because the relativistic time concept con-
tained internal inconsistences, not few famous philosophers criticized the theories
of relativity, such as Henry Bergson in his book “Durée et simultanéité. À propos de
la théorie d’Einstein” (Paris, 1922) [39] or Nicolai Hartmann in his book “Philoso-
phie der Natur” (Berlin, 1950) [40]:
“Completely transparent, however, is the size of the aporias themselves – up to the self-
contradiction of the statements – as well as the extremely small base of the initial position.”
(„Vollkommen durchsichtig ist indessen die Größe der Aporien selbst – bis zum Selbstwi-
derspruch der Aussagen –, sowie die äußerst schmale Basis der Ausgangsstellung.“ [40, pp.
245–246])
While the criticism of the relative time has continued until today, Einstein’s
conception of complete masse-energy equivalence was widely accepted. The idea of
an easy calculability of the total amount of energy of a body or, elementary particle
was seductive. The theories of relativity began to become established. In 1927, on
the basis of GR, Georges Lemaître developed the big bang hypothesis [41]. He
introduced a cosmological time that represents an absolute time because with a big
bang only one age for the whole universe can be defined. In this context, a “partial
reinstatement of absolute simultaneity into the actual world” [42, p. 65]) was
noted. However, absolute time (cosmological time) and relative time (dynamic
spacetime) were interpreted as mathematically compatible with each other, for
instance by Hermann Weyl.8 G. Kalies
The assumptions of SR and GR, e.g. complete mass-energy equivalence and
dynamic spacetime (including complete reversibility), became the basis for the
Standard Models of particle physics and cosmology developed in the middle of the
20th century. Selected features of SR were further criticized, especially the so-called
time dilation and the clock paradox, e.g. by the physicists Herbert Dingle and Louis
Essen, the constructor of the caesium atomic clock. Yet, after several years of letters
in the journal Nature, initiated by Dingle in 1956 and ended in the early seventies, SR
was officially classified as self-consistent and experimentally confirmed.
The absence of an alternative theory, the longstanding practice of evaluating
experimental results one-sidedly as confirmation for the spacetime theory, the
advanced interconnection of the mathematical models developed in the meantime
and the broad application of the theories of relativity which had been successfully
defended over decades and had become the basis of modern physics, had made the
theories unassailable. Although Dingle’s objections were not refuted by logical
arguments, but in a quasi-collective and emotionally heated rejection of dozens of
physicists [43], official criticism of the theory was no longer welcome. Welcome
were constructive contributions to strengthen the theories of relativity and to link
them to quantum theory.
In his book “Science at the Crossroads” from 1972, Herbert Dingle criticizes the
“totally irrelevant idea of time” [33, p. 118] of SR and the increasing dogmatism in
the acceptance of the theory:
“Anyone who cares to examine the literature from 1920 to the present day, even if he has not
had personal experience of the development, can see the gradual growth of dogmatic
acceptance of the theory and contempt for its critics, right up to the extreme form exhibited
today by those who learnt it from those who learnt it from those who failed to understand it at
the beginning.” [33, p. 126]
The physicist Mendel Sachs states in his paper “On Dingle’s Controversy about the
Clock Paradox and the Evolution of Ideas in Science” that Dingle “did not receive a
logical answer” [43, p. 331] and describes the scientific atmosphere in which it is
impossible to give up once formed convictions:
“I would contend that during the ‘normal science’ period, the leaders of the scientific com-
munity, as well as most of their followers, acquire vested interests and a strongly emotional
attachment to the ongoing paradigms about the way the world is, in their view. A state of
dogmatism is then reached in which it is literally impossible for most of them to give up these
ideas – in spite of any quantity of experimental and/or logical inconsistencies that may pile
up.” [43, p. 329]
Today there is an increasing number of empirical results that cannot be explained
with the Standard Models of elementary particles and cosmology. The crisis of
modern physics arises furthermore from the fact that many of its fundamentalTime paradox of physics 9
postulates (dark energy, dark matter, quantizability of everything, gravitons, su-
persymmetry, etc.) are still awaiting empirical confirmation and that the four
fundamental forces cannot be unified. Nevertheless, one continues to act on the
basis of the historical guidelines. The standard textbooks of physics present SR and
symmetric spacetime as undisputed truths being consistent with empirical facts.
Alternative approaches are not mentioned, or if they do, then in random remarks as
out-dated beliefs that have been abandoned for good reason. There are textbooks on
the theories of relativity or quantum theory in which the word ether does not appear
even once. And there is probably hardly a scientific theory in the history of the world
that has been called proven as often as Einstein’s theory of relativity and for which
further experimental confirmation is constantly being searched and presented to the
public.
Since the symmetric spacetime was officially accepted, space and time have
been entrusted to mathematics with physical ambitions. For several decades,
mathematical hypotheses have been generated that can neither be empirically
disproved nor confirmed, such as the 26-dimensional bosonic spacetime, the
11-dimensional supergravity, parallel worlds, the big bang and the inflation the-
ories or the multitude of hypothetical particles. Mathematically, many worlds are
conceivable. However, mathematics can only be an adequate tool to describe
nature if the physical assumptions on which it is based are correct:
„The correctness of the mathematical formalism is not sufficient to validate a scientific
structure as coherent and free from contradiction […]. In reality the two relativity theories are
brimming with paradoxes.” [44, p. 248]
Today the paradoxes associated with the special theory of relativity are called
seemingly. Time dilation, which can only be imagined by accepting breaks in logic
[19, pp. 192–193], is presented as a simple fact:
“Let’s begin with a simple fact: time passes faster in the mountains than it does at sea level.”
[18, p. 9]
Modern physics textbooks teach that time travel into the future is possible:
“Since time dilation is such a diversely tested consequence of SR, it seems anachronistic to
speak of a paradox at all in the case of the twin paradox [/]. The fact that SR allows time
travel into the future at a high velocity does not represent a paradox in terms of causality,
because unfortunately it does not go backwards.” („Da die Zeitdilatation eine so vielfältig
getestete Konsequenz der speziellen Relativitätstheorie darstellt, scheint es anachronistisch,
beim Zwillingsparadoxon überhaupt noch von einem Paradoxon zu sprechen. [/] Dass die
spezielle Relativitätstheorie bei entsprechend hoher Geschwindigkeit Zeitreisen in die
Zukunft erlaubt, stellt auch kein Paradoxon in Hinblick auf Kausalität dar, denn zurück geht
es leider nicht.“ [45, p. 338])10 G. Kalies
3 An unsolved fundamental problem of physics:
irreversibility
The first physical description of the daily experience that processes are irreversible
dates back to the second half of the 19th century. During the thermodynamic study
of cyclic processes, Rudolf Clausius defined an increase of the extensive state
quantity entropy S with each natural process [1]. The two last sentences in his paper
of 1865 are:
“1) The energy of the world is constant., 2)The entropy of the world is moving toward maximum.”
(„1) Die Energie der Welt ist constant., 2) Die Entropie der Welt strebt einem Maximum zu.“ [1,
p. 400])
These words led to a broad public debate. A maximum of the “entropy of the world”
signified the so-called heat death of the universe – an apocalyptic scenario, since a
maximum entropy in the Clausiusian sense means a statistical uniform distribu-
tion and lack of macroscopic processes: the thermodynamic equilibrium.
According to Clausius [1], the amount of entropy S in a thermodynamic system
can by changed in two ways: firstly by an entropy exchange daS between system
and surroundings and secondly by an entropy increase diS within the system with
any natural process. daS is realized by means of heat transfer dQ = T daS. Thus the
second law of thermodynamics is:
dQ
dS da S + di S + di S, (1)
T
(dS)U, V di S ≥ 0. (2)
In the thermodynamic equilibrium or for reversible processes, it applies diS = 0. In
any natural irreversible process, however, entropy is generated, i.e. diS is positive.
This means that S is not conserved, in contrast to the internal energy U described by
the first law of thermodynamics (energy conservation).
By connecting the first and the second laws of thermodynamics, the change in
the amount of internal energy U in a thermodynamic system is given by [46]:
k
dU ∑ ξ i dX i TdS − pdV + ∑μj dnj + σ dA + … − Tdi S, (3)
i1 j
U f S, V, nj , A, …, (4)
with the term –TdiS originating from the second law of thermodynamics. While dU
denotes quantitative changes in the energy of a system, the entropy production term
diS addresses changes in the quality of energy. The greater diS, the more energy isTime paradox of physics 11
dissipated in the process – in the sense that this energy is less suitable for performing
work. In modern text books, this qualitative change is often pejoratively connoted
and called devaluation or degradation of energy, while Clausius himself called diS:
“the disgregation, which is to be regarded as the transformation value of the ongoing
arrangement of the components” („die Disgregation, welche als der Verwandlungswerth der
stattfindenden Anordnung der Bestandtheile zu betrachten ist“ [1, p. 390]).
diS = 0, i.e. the maximum entropy, is the basis of all thermodynamic equilibrium
conditions. In classical phenomenological thermodynamics, the irreversibility of
processes is only reflected in the positive sign of diS in Equation (2). In thermody-
namics of irreversible processes, the basic equation describes the temporal entropy
production in the volume V of a system by means of the entropy production density σS:
1 di S
σS ≡ ∑ J α X α , α 1, 2, 3, ..., k. (5)
V dt α
Each irreversible process such as the equalization of concentrations by diffusion or
of temperatures by heat conduction contributes to increase the amount of entropy
S. Here, the generalized thermodynamic force Xα is the local gradient of an
intensive state quantity like the chemical potential μj or the temperature T, and the
thermodynamic flux Jα is the temporal transport of an extensive state quantity like
substance, energy or impulse. Force Xα and flux Jα are zero in equilibrium.
The second law of thermodynamics is of experimental origin. It was derived
from the Carnot cycle and is confirmed countless times and without exception. To
this day, it is the only physical law with which the direction of processes can be
determined. This is the special feature of thermodynamics.
In 1905, Einstein postulated that the mass of a body is a measure of its energy
content:
„Die Masse eines Körpers ist ein Maß für dessen Energieinhalt.“ [25, p. 641]
If each kind of energy is reflected in the mass, any change in the amount of the
internal energy U of a body (a thermodynamic system) should be reflected in a
change of its mass:
dU c2 dm TdS − pdV + ∑μj dnj + σdA + ... − Tdi S, (6)
j
m f S, V, nj , A, .... (7)
In previous work [19, 20] has been shown that Equations (6) and (7) contradict the
first law of thermodynamics. By keeping all other extensive state variables con-
stant, changes in spatial state quantities of a real body such as volume V or12 G. Kalies
interface A do affect U, but not m [20]. The assumption that the mass of a body is a
measure of its whole energy content, i.e. the complete mass-energy equivalence, is
connected with further restrictions:
i) Internal processes cannot be described by dU = c2dm.
The state of a thermodynamic system can change by exchange processes and /
or internal processes. On the right-hand side of Equation (6), the term –TdiS is a
criterion for the existence of internal processes, which can be described by
Equation (5). In dU = c2dm such a criterion is lacking. In an isolated system
(dU = 0), it always applies dm = 0. Since m is unaffected, no internal processes
can be described by dU = c2dm. This includes quantum processes (pair anni-
hilation or formation, neutrino oscillation, etc.) in a system, in which rest
masses of elementary particles are changed, even if the annihilation of
elementary particles is often interpreted as confirmation of the complete
equivalence and convertibility of mass and energy.
ii) Irreversibility cannot be described by dU = c2dm.
Since the term –TdiS is missing, the criterion for the direction of processes and
the time arrow is missing. This corresponds to the assumption of SR that time is
relative and depending on the motion states of the observers, from which the
four-dimensional Minkowski spacetime was derived. The becoming, i.e. the
distinction between yesterday and tomorrow, becomes vague as Einstein
described in 1917:
“Since there are no longer any sections in this four-dimensional structure that objectively
represent the ‘now’, the concept of happening and becoming is not completely eliminated, but it
is complicated. It therefore seems to be more natural to think the physically real as a four-
dimensional being instead of the becoming of a three-dimensional being.” („Da es in diesem
vierdimensionalen Gebilde keine Schnitte mehr gibt, welche das ‚Jetzt‘ objektiv repräsentieren,
wird der Begriff des Geschehens und Werdens zwar nicht völlig aufgehoben, aber doch kom-
pliziert. Es erscheint deshalb natürlicher, das physikalisch Reale als ein vierdimensionales Sein
zu denken statt wie bisher als das Werden eines dreidimensionalen Seins.“ [36, p. 121])
Einstein describes “a four-dimensional being” as more natural than the becoming.
If every change in the internal energy U can be expressed also as a (symmetrical)
mass change, every process will inevitably become symmetrical, too. It is then
neither possible to assess whether the process is voluntary or forced, nor equi-
librium criteria can be developed.
According to i) and ii), dU = c2dm does not fulfill the criteria of a process
equation. Instead of complete mass-energy equivalence, thermodynamics sug-
gests matter-energy equivalence with non-weighing potential energy, an energetic
distinction between matter and mass and the acceptance of irreversible processes
[19, 20].Time paradox of physics 13
Statistical thermodynamics represents the connection between the description
of systems by classical thermodynamics and the description of molecules (in-
dividuals). In 1877, Ludwig Boltzmann interpreted the entropy S molecular-
statistically within the kinetic theory of gases [3]. Convinced that physics have to
understand irreversibility, his life aim was to fundamentally justify the arrow of
time. By assigning to each finitely large microstate a molecule with discrete energy
values, he determined S as the total number of distinguishable microstates of
molecules in state space and calculated all possible permutations P:
S log P + const. (8)
Well-known is Max Planck’s interpretation of Boltzmann’s equation:
S kB ln W (9)
with the thermodynamic probability W and the Boltzmann constant kB = R/NA.3
The developed formula system allows complex structures and processes to be
described with sufficient precision for many technical applications, from electro-
chemical processes, mixed-phase and interfacial processes up to the self-
organization of molecules. As atomist and founder of statistical thermody-
namics, however, Boltzmann believed in the complete discretizability of energy. In
the context of kinetic gas theory in which only reversible positional changes of
particles (atoms, molecules) are described, he had to fail in his aim to prove the
time arrow. In 1895, he finally admitted that his H theorem and the second law of
thermodynamics are merely probability statements.
His failure was regarded as final. This opinion was supported by Constantin
Carathéodori, who published in 1909 a mathematical justification of thermody-
namics [47], which was gratefully adopted by Max Planck, Max Born and others.
Carathéodori’s work based on the description of reversible positional changes of
particles and confirmed the mechanistic approach to the second law of
thermodynamics:
“One can deduce the whole theory without assuming the existence of a physical quantity,
heat, which deviates from the usual mechanical quantities.” („Man kann die ganze Theorie
ableiten, ohne die Existenz einer von den gewöhnlichen mechanischen Größen abweichen-
den physikalischen Größe, der Wärme, vorauszusetzen.“ [47, p. 357]
3 Please note that in Equation (8), S is a dimensionless number. Only when Max Planck introduced
the Boltzmann constant kB [J/K] as conversion factor, S obtained the unit [J/K]. The reason for
introducing kB was that the state quantities entropy S and temperature T are conjugated to each
other, whereby the history of physics has resulted in T being expressed in Kelvin and not in units of
energy [19, p. 81].14 G. Kalies
The origin of the time arrow remained unknown. Because it was unsatisfactory to
give up a physical explanation, Ilya Prigogine and the so-called Brussels school of
thermodynamics tried to fundamentally explain irreversibility until the 1970s:
“But the whole concept of ‘elementary particles’ needs to be reconsidered! […] It is not
impossible that ‘becoming’, i.e. the participation of particles in the development of the
physical world, will play an essential role in this construction.” („Aber der gesamte Begriff der
‚Elementarteilchen‘ muß neu überdacht werden! […] Es ist nicht ausgeschlossen, daß bei
dieser Konstruktion das ‚Werden‘, d. h. die Beteiligung der Teilchen an der Entwicklung der
physikalischen Welt, eine wesentliche Rolle spielen wird.“ [48, p. 207])
Later, Ilya Prigogine and Isabelle Stengers rejected this plan because they accepted
the ideas of modern physics and the Big Bang theory as the birth of space and time
and thus the expansion of spacetime:
“Obviously, the Big Bang is an event. […] According to our hypothesis, the Big Bang can be
regarded as the irreversible process par excellence.” („Offensichtlich ist der Urknall ein
Ereignis. […] Der Urknall kann nach unserer Hypothese als der irreversible Prozeß
schlechthin betrachtet werden.“ [2, p. 271])
As a compromise solution in the sense of modern physics, they proposed a
mathematical resolution of the time paradox that follows Boltzmann’s view of
large populations:
“The irreversibility expressed in the time arrow is a statistical property. It cannot be intro-
duced at the level of individual trajectories (or wave functions).” („Die Irreversibilität, die sich
im Zeitpfeil äußert, ist eine statistische Eigenschaft. Sie kann nicht auf der Ebene individueller
Trajektorien (oder Wellenfunktionen) eingeführt werden.“ [2, p. 229])
Since an objectification of the time arrow was not achieved and the contradiction
between reversibility on the micro level and irreversibility on the macro level was
not solved, Prigogine’s shift of opinion can be understood as the final retreat of
thermodynamics from fundamental theoretical physics.
Today, the state of a system is considered the less probable the more ordered it
is. Therefore the origin of life is considered unlikely today. The assumed increase of
entropy S in the universe within a Big Bang model is interpreted as connected with
an increase in probability:
“We live in an ‘unlikely’ world, and the ‘arrow of time’, the distinction between past and
future, is simply the consequence of this fact. What we call ‘nature’, the totality of inter-
connected processes, […], are only manifestations of one and the same process: the pro-
gressive disappearance of the initial deviation from equilibrium.” („Wir leben in einer
‚unwahrscheinlichen‘ Welt, und der ‚Pfeil der Zeit‘, die Unterscheidung zwischen Vergan-
genheit und Zukunft, ist einfach die Konsequenz dieser Tatsache. Das, was wir ‚Natur‘
nennen, die Gesamtheit der miteinander verflochtenen Prozesse, […], sind nurTime paradox of physics 15
Erscheinungsformen eines und desselben Prozesses: des fortschreitenden Verschwindens
der anfänglichen Abweichung vom Gleichgewicht.“ [2, p. 49])
There are textbook authors who express their astonishment that an anthropo-
morphic state quantity such as the entropy S should dictate the world process.
In light of the concept of matter-energy equivalence, diS > 0 is not anthropo-
morphic at all, but the expression for the becoming in nature, the only expression
moreover that physics has found for it so far. It is likely that the state quantity S
could not yet be fully interpreted in the 19th century because at this time infor-
mation from quantum physics was missing. This means that the fundamental law
of nature described by the second law of thermodynamics is not yet fully
understood.
4 A solution of the time paradox of physics
Following Ilya Prigogine’s demand that “the whole concept of ‘elementary parti-
cles’ needs to be reconsidered” [48, p. 207], matter-energy equivalence leads to an
understanding of “elementary particles” that provides an extended discussion
basis for the fundamental justification of the direction of time.
In previous work [19, 20], the mass-equivalent intrinsic energy EQ of each
fermion or boson (called quanton Q [49]) was identified with the internal motion
energy of Q. By abandoning the assumption of point masses and granting to each
quanton a spatial area, the former rest mass of an elementary particle (point mass)
according to Einstein was replaced by the intrinsic mass mQ of a quanton [20]:
U Q ≠ E Q mQ c2 (10)
According to Equation (10), EQ represents only a part of the internal energy of Q.
Photons possess an intrinsic mass mQ like other quantons. If fermions such as
electrons or tauons with an intrinsic mass mQ (caused by the internal degrees of
freedom) are additionally moved as a whole, their masses increase in real terms.
This means that the abstracted state quantity mass is always due to motion, an
explanation for the equivalence of inert and heavy mass [20].
The question from what do fermions and bosons emerge due to their motion,
leads back to the quantum-theoretical approaches of Oliver Heaviside, Henri
Poincaré, Hendrik Antoon Lorentz [50–53], Louis de Broglie, Jean-Pierre Vigier,
David Bohm and others [21–23] including ideas of an ether [51] or a sub-quantic
medium [22].
The presence of non-weighing, non-gravitating energy results directly from
the process equations of thermodynamics. However, the incomplete mass-energy
equivalence in Equation (10) can only be explained on the basis of a non-16 G. Kalies
mechanistic ether theory, in which all quantons Q, which are created from the
ether by excitation (oscillation, etc.), represent only limited independent entities.
They possess both the mass-equivalent intrinsic energy EQ (excitation energy) and a
measurable part of the non-gravitating potential ether energy. There is no com-
plete demarcation from the non-excited ether medium [19].
In the following, an evolution theory of matter is presented that is self-
consistent and consistent with experimental facts. It is known that photons change
their wavelength during processes. For example, the sunlight that leaves the Earth
is on average more long-wave than the one that was absorbed. By emitting light of
lower temperature, entropy produced in the processes on Earth is emitted to the
surroundings, which is called entropy export. This so-called “photon mill” [54, p. 9]
is the motor for all processes on Earth. The emitted light of lower temperature is
less suitable for carrying out work. According to Equation (10), the long-wave
photons have lost intrinsic energy EQ (excitation energy) and accordingly mass mQ.
Similarly, when ultraviolet light is absorbed by a fluorescent dye, the absorbed
UV radiation is more short-wave than the emitted one in the visible frequency
range. The emitted photon of lower frequency and intrinsic energy EQ = mQ c2 = hν is
again less suitable to perform work than the originally absorbed photon. Also the
shift of the spectral lines of the sunlight on the way to Earth or the cosmological
redshift [55] can be interpreted as degradation of energy because longer-wave
photons are less able to do work. Due to real interactions, the photons lose EQ and
accordingly mass mQ during the movement in the ether medium.
Thermodynamics has already found an expression for the permanent degra-
dation of energy: the increase of entropy S. Thus, entropy S was generated during
the movement of photons. Unlike as postulated by Einstein, photons are not
eternal. Since photons and other quantons (cf. Equation (10)) as well as light and
matter are equivalent, it can be logically extended that entropy S is generated with
every movement of a quanton in the ether medium.
If each change of position generates entropy S, Rudolf Clausius’ definition of
diS as
“the disgregation, which is to be regarded as the transformation value of the taking place
arrangement of the constituent parts” [1, p. 390]
can be extended by the “transformation value“ of the constituent parts itself.
Since the entropy production diS and accordingly the time arrow are already
present on the quanton level, every process in universe becomes irreversible. There
is no reversal in the same way for any elementary process. In order to specify the
two parts of local entropy production, indices will be used in the extended second
law of thermodynamics:Time paradox of physics 17
di S di SD + di SA > 0 (11)
with
– the disgregation diSD > 0 of quantons or quanton clusters, which denotes the
statistically accessible increase of entropy as a result of an increasing uniform
distribution (the changing arrangement according to Clausius [1, p. 390]),
– the aging diSA > 0 of quantons, which denotes the continuous increase in
entropy as a result of the increase of the wavelength of quantons during their
motion in the ether medium (the changing constituent parts itself).
Once a quanton as ether excitation has gained temporality, his development becomes
irreversible. During the aging process, the energy of a quanton does not disappear,
but is converted into the non-weighing energy of the non-excited ether medium. In
this way, a violation of the first law of thermodynamics is excluded. If one thinks this
development to the end, then solitary photons that do not interact with other
quantons age gradually on their path through the ether medium, from which they
have once distinguished themselves as separate, yet not independent individuals.
They become more and more long-waved and progressively enter the ground state of
non-excitation. In gradual succession and inevitably, they are eliminated, lifted to a
higher level and preserved – in the dialectic Hegel’s threefold sense.
The photons are integrated into what they are not and what they are. This
vividly illustrates what the non-quantizable, non-weighable, uncharged, etc.,
ether medium might be: a dense and highly tensioned state: a standing wave with
fixed nodes, a Bose–Einstein condensate that behaves like a single particle and
can be described with a single macroscopic wave function [56] – the material base
of the universe, which can serve as an absolute reference system.4
In Table 1, the conception of quanton ether developed here is summarized in a
polarizing manner, with the boundaries as always being fluent. In rudimentary
form, all properties of quantons are also existent in the unexcited ether medium.
The bosonic condensate preserves residual oscillations in Euclidean space that are
called today “quantum fluctuations of vacuum”. Since quantons only represent
another state of the ether medium, the whole energy of the universe can be reduced
to matter: the primacy of matter.
That the current quantum-mechanical concept of elementary particles is not
sufficient to describe the essence of quantons becomes clear from the fact that
quantons are countable, but not autonomous because they depend on the ether
medium. The old dispute about the discontinuity or the continuity of energy
4 In the recent literature, there exist different concepts of the ether medium as condensed
quantum matter system, described for instance in [19, 57, 58] which are to be examined.18 G. Kalies
Table : The properties of matter = energy in the universe.
Quanton ether
Ether excitation (quanton) Non-excited ether medium
Individual Collective
Low correlated Strongly correlated
Quantizable properties such as No measurably quantizable properties
mass, charge, spin, etc.
Temporally finite Temporally finite
between atomists such as Ludwig Boltzmann and energeticists such as William
Thomson, Ernst Mach or Wilhelm Ostwald might be settled. According to Table 1,
there is no either-or, no discontinuity or continuity, but energy is always both
discontinuous and continuous.
In 1931, Sir Arthur Eddington published in his Nature paper “The End of the
World: from the Standpoint of Mathematical Physics” [59] a thermodynamic vision
of the end of the universe. Therein Eddington predicts that all particles in the
universe will once dissolve into radiation whose wavelength will increase further
and further. This hypothesis resembles the presented idea of the temporal evolu-
tion of photons. However, Eddington believed in the ideas of symmetric spacetime
and Big Bang so that he assumed an expanding radiation ball and thus the
beginning and the end of the world.
With matter-energy equivalence, another scenario becomes plausible because
both the excitations and non-excitations are temporally finite. There is no
temporally infinite state. The increase of entropy S in Equation (11) describes only
one side of becoming and passing away – only the finiteness of each quanton as
ether excitation. Not yet covered is the other side: the finiteness of the collective
non-excitation.
While quantons gradually pass away in the ether medium, as long as no
counter-strategies of interaction are developed, new quantons are created else-
where because always local non-equilibria in the oscillating ether interwoven with
excitations exist. The activity of the ether medium is empirically proven, even if the
quantum fluctuations of the so-called vacuum are interpreted today as the emer-
gence of (virtual) particles from nothing. In a seemingly coincidental, but always
causal process, real instable quantons as well as real stable quantons beyond the
Heisenberg uncertainty relation emerge.5
5 The mechanisms of quanton formation may be diverse, e.g. by continuous random emergence
without collective ether movements [19, 60] or by collective ether movements and phase transi-
tions [57, 58].Time paradox of physics 19
Short-wave quantons represent states of lower entropy than the collective
state of highest entropy. Thus it applies to the process of quanton creation:
di S < 0 (12)
While the creation of new quantons from the condensate means the negation of the
collective, the disappearance of a quanton in the condensed ether medium means
the negation of the individual. However, both poles mark only the outer limits,
which are never completely reached, so that one is preserved in the other. Between
these two extremes, there is a great scope for creativity, as quantons interact with
each other by real matter waves [19], i.e. de Broglie waves [22]. By means of
binding, the excitation energy of quantons is concentrated in a smaller spatial
area. The larger excitation energy of the network means a stronger local differ-
entiation from the highly entropic ether medium, which is connected with a sta-
bilization and a local reduction of entropy – the fundamental principle of the self-
organization of matter. Also a photon approaching a compound of quantons be-
comes more short-wave (gravitational blue shift), i.e. it will by stabilized and thus
loses entropy.
In order to create and preserve stable states of quanton clusters with low local
entropy, a tribute needs to be paid. The mass defect during a binding process, i.e.
the loss of excitation energy of the cluster, can be interpreted as quanton dis-
gregation diSD > 0 because electromagnetic radiation is emitted and dispersed into
the surroundings [19]. This argumentation is similar to that in modern thermo-
dynamics, according to which a reduction of the entropy S of a system becomes
possible by means of entropy export daS > 0.
Beside the two parts of entropy production in Equation (11), now two parts of
entropy elimination can be specified:
di S di SC + di SS < 0 (13)
with
– the creation diSC < 0 of quantons, which denotes the decrease in entropy due to
the formation of new quantons from the ether medium (creation of new in-
dividuals from the collective),
– the self-organization diSS < 0 of quantons, which denotes the decrease in
entropy due to the interaction of quantons or quanton clusters.
With Equation (13), there is a counterweight to the permanent increase of entropy
in the universe. This means that pejorative denominations of diSD > 0 as degra-
dation, dissipation, waste, devaluation of energy, etc., are purely technically
justified in order to assess the suitability of energy for performing work. On a
universal scale, the so-called dissipation of energy is no one-way street.20 G. Kalies
Irrespective of this, Equation (11) remains incorruptible in its statement that
there is temporality for each quanton and quanton cluster that once formed, and
thus irreversibility of each process and a distinction between past and future. The
difference to current interpretations is, however, that the temporal limitation of all
creations in the ether medium is not connected with a heat death of the universe or
an idea of a universal beginning.
On the contrary, rigorous process thinking does not permit a temporal
beginning or end of the universe. Process thinking logically includes that each
cause has an effect which in turn is the cause for the next effect. With the concept of
quanton ether, the being of matter turns into a becoming – a temporally infinite
evolution, in which all things only emerge once and pass away again: panta rhei.
Since the being exists only as transition, processes are the being of matter and
expression for its indestructibility. Thus the permanent imbalance that causes
processes reflects, in fact, an equilibrium of nature – between non-excitation on
the one hand and excitation on the other, between collectivity on the one hand and
individuality on the other, wherein the dialectic destruction and conservation of
one in the other represents a basic principle.
Equations (11) and (13) do not represent a contradiction, but make aware of the
essential law according to which infinity can and must arise from the permanent
finiteness of states in time. The creation and gradual aging of countable in-
dividuals (which distribute and organize themselves) happens – in relation to
single individuals – successively, i.e. the terms in Equations (11) and (13) describe,
as it were, a cyclic process, the eternal cycle of nature.
Now it is possible to describe what was already philosophically concluded:
“Time has neither beginning nor end, but all beginning and end is in it.” („Die Zeit hat keinen
Anfang noch Ende, sondern aller Anfang und Ende ist in ihr.“ [28, p. 67])
Equations (11) and (13) can be summarized (cf. Table 2):
di S di SC + di SA + di SD + di SS . (14)
Equation (14) describes the ever-changing quality of energy. This extended second
law of thermodynamics and the first law of thermodynamics for describing the
changing quantity of energy would than represent the most fundamental physical
laws which cannot be violated even at quantum level.
In light of an infinite cause-effect-principle, it is plausible that the four con-
tributions mutually nullify each other in the universe:
di S 0. (15)
According to Equation (15), there would be no maximum of entropy and no
endpoint of all development. There is only one process in never-ending nature: theTime paradox of physics 21
Table : The four contributions for changing quantons and the quality of energy = matter.
Creation Aging Disgregation Self-organization
diSC diSA diSD diSS
> 0 of quantons must appear to us as imperceptible in our time scales,
especially since quantons stabilize each other by means of interaction. Also the
creation diSC < 0 of new quantons in a macroscopic system may be imperceptible to
us. Here, it is approximately sufficient to describe changes in the arrangements of
unchangeable particles, which are increasingly equally distributed.
If we are dealing with the world view and the mathematical description of S
over cosmic time scales, however, this interpretation cannot be sufficient. It is not
enough, to calculate the number of distinguishable microstates from all possible
permutations of molecules. Boltzmann’s and Planck’s definitions are comfortable
because they permit to use discrete numbers for calculations as it corresponds to
the mathematics of Cantor, Hilbert, etc. And yet: If one wants to capture the
evolution of quantons, e.g. the increase of wavelengths by moving in the ether
medium, one deals with growing non-discrete numbers. In light of continual en-
ergy changes, it might become necessary to reconsider alternatives in basicYou can also read
