CONFIGURE UP RESEARCH PROFILE ON ALL THE BEST POSSIBLE PARADOXES IN ASTROPHYSICS AND QUANTUM MECHANICS
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3.Zermelo’s recurrent paradox
Poincare’s recurrency theorem suggests that Boltzmann H-function is periodic.
According to Boltzmann’s H-theorem H-function is decreasing and it doesn’t
require the possibility of its returning to the initial state.
Towards the end of the 19th century physicists employed the knowledge based on: Newton’s
classical mechanics, classical thermodynamics and Maxwell’s electrodynamics (only just
formed). Combined, Newton’s classical mechanics and classical thermodynamics lead to
Loschmidt’s and Zermelo’s paradox.
Poincare used Zermelo’s paradox and proved that the initial states of Newton’s equations would
repeat suggesting, however, that this is not real irreversible process. The recurrent paradox is
based on Poincare’s theorem.
Ernst Zermelo (Ernst Friedrich Ferdinand Zermelo, 1871-1953), a student of Max Planck and
successor of his thermodynamic understanding of the world, published in 1896 an article entitled
On a Theorem of Dynamics and the Mechanical Theory of Heat (Zermelo, 1896), in which he
applied Poicare’s theorem to the Second principle of thermodynamics.
Zermelo’s conclusion does not originate from a real phenomenon, accessible to human senses. It
is speculative and originates from a phenomenon formulated by thought. This paradox is a
thought experiment. The paradox is of theoretical nature; it arises from a debate on the
theoretical concepts of statistical nature of the explanation.
Zermelo’s recurrent paradox is of distinct theoretical character and was formed in the process of
defining Boltzmann’s formulation of statistical physics as a critical review of the principles and
opinions adopted by him. The paradox enables a better comparison of the formulations of
statistical physics and it can be categorized as a transitional paradox.
Zermelo based his paradox on the view that if a process is periodic it could not be simultaneously
irreversible. Thus, by applying Poincare’s theorem, the term entropy in the Second principle of
thermodynamics becomes absurd.
Twice does Boltzmann substantiate his views and provides a kind of a solution to Zermelo’s
paradox. He is conscious of the metaphysical character of the principle that all was created from
the least likely state and physical tendency to change the state of a system (Universe) and a
subsystem to a more probable state. According to him, Poincare’s theorem is “less general” than
the adopted principle and although recurrency is to be expected after a long enough period of
time, generally speaking, system entropy increases.
4.Mpemba effect
In two equal containers with equal volume of water at non-drastically different
temperatures, the freezing of their contents begins using the same process. Under
certain conditions, the water that was initially warmer will start to freeze first.
The phenomenon that warmer water freezes quicker than colder was know back in Aristotle’s
days (384-322 BC). It was discussed during the early middle ages by Roger Bacon
(1214-1294)12, then Giovanni Marliani in the 15th century, and in the late middle ages it was
described by Francis Bacon (1561-1626)14 and Rene Descartes (1596-1650)15. In a strange way
the phenomenon was neglected and forgotten by the scientific public until, thanks to a Tanzanian
student Mpemba (Erasto B. Mpemba) it returned to public attention in 1969. This is why the
phenomenon is also known as the Mpemba effect. The reason why warmer water freezes quicker
than colder is not yet known. Since common sense tells us that it is illogical the effect is also
called a paradox.
This renewed interest in why warmer water freezes quicker than colder has its own anecdote now
that Mpemba rediscovered it. Namely, while Mpemba was still in secondary school student of
Eugene Marschal in Mkwawa School in Iringa16 in 1964, he was making ice cream. He mixed hot
milk with sugar and rather than wait for it to cool placed it in the refrigerator. To his surprise he
noticed that his hot milk ice cream had frozen quicker than the ice cream of other students whose
milk wasn’t hot. When he asked his science teacher to explain it, he couldn’t. The first person to
take him seriously was Denis G. Osborne in 1969, who repeated the experiment after Mpemba
inquired about the reason why warmer water froze quicker than colder. They described this effect
together and returned it to the focus of scientific public’s attention. (Mpemba & Osborne, 1969).
As it happens, the same year Kell (Kell. G. S) published his work, independently from Mpemba
and Osborne, in which he endeavoured to explain the phenomenon by evaporation. He was not
familiar with Denis Osborne’s experiment which showed that evaporated mass is not enough to
explain the effect.
Poincare’s recurrency theorem suggests that Boltzmann H-function is periodic.
According to Boltzmann’s H-theorem H-function is decreasing and it doesn’t
require the possibility of its returning to the initial state.
Towards the end of the 19th century physicists employed the knowledge based on: Newton’s
classical mechanics, classical thermodynamics and Maxwell’s electrodynamics (only just
formed). Combined, Newton’s classical mechanics and classical thermodynamics lead to
Loschmidt’s and Zermelo’s paradox.
Poincare used Zermelo’s paradox and proved that the initial states of Newton’s equations would
repeat suggesting, however, that this is not real irreversible process. The recurrent paradox is
based on Poincare’s theorem.
Ernst Zermelo (Ernst Friedrich Ferdinand Zermelo, 1871-1953), a student of Max Planck and
successor of his thermodynamic understanding of the world, published in 1896 an article entitled
On a Theorem of Dynamics and the Mechanical Theory of Heat (Zermelo, 1896), in which he
applied Poicare’s theorem to the Second principle of thermodynamics.
Zermelo’s conclusion does not originate from a real phenomenon, accessible to human senses. It
is speculative and originates from a phenomenon formulated by thought. This paradox is a
thought experiment. The paradox is of theoretical nature; it arises from a debate on the
theoretical concepts of statistical nature of the explanation.
Zermelo’s recurrent paradox is of distinct theoretical character and was formed in the process of
defining Boltzmann’s formulation of statistical physics as a critical review of the principles and
opinions adopted by him. The paradox enables a better comparison of the formulations of
statistical physics and it can be categorized as a transitional paradox.
Zermelo based his paradox on the view that if a process is periodic it could not be simultaneously
irreversible. Thus, by applying Poincare’s theorem, the term entropy in the Second principle of
thermodynamics becomes absurd.
Twice does Boltzmann substantiate his views and provides a kind of a solution to Zermelo’s
paradox. He is conscious of the metaphysical character of the principle that all was created from
the least likely state and physical tendency to change the state of a system (Universe) and a
subsystem to a more probable state. According to him, Poincare’s theorem is “less general” than
the adopted principle and although recurrency is to be expected after a long enough period of
time, generally speaking, system entropy increases.
4.Mpemba effect
In two equal containers with equal volume of water at non-drastically different
temperatures, the freezing of their contents begins using the same process. Under
certain conditions, the water that was initially warmer will start to freeze first.
The phenomenon that warmer water freezes quicker than colder was know back in Aristotle’s
days (384-322 BC). It was discussed during the early middle ages by Roger Bacon
(1214-1294)12, then Giovanni Marliani in the 15th century, and in the late middle ages it was
described by Francis Bacon (1561-1626)14 and Rene Descartes (1596-1650)15. In a strange way
the phenomenon was neglected and forgotten by the scientific public until, thanks to a Tanzanian
student Mpemba (Erasto B. Mpemba) it returned to public attention in 1969. This is why the
phenomenon is also known as the Mpemba effect. The reason why warmer water freezes quicker
than colder is not yet known. Since common sense tells us that it is illogical the effect is also
called a paradox.
This renewed interest in why warmer water freezes quicker than colder has its own anecdote now
that Mpemba rediscovered it. Namely, while Mpemba was still in secondary school student of
Eugene Marschal in Mkwawa School in Iringa16 in 1964, he was making ice cream. He mixed hot
milk with sugar and rather than wait for it to cool placed it in the refrigerator. To his surprise he
noticed that his hot milk ice cream had frozen quicker than the ice cream of other students whose
milk wasn’t hot. When he asked his science teacher to explain it, he couldn’t. The first person to
take him seriously was Denis G. Osborne in 1969, who repeated the experiment after Mpemba
inquired about the reason why warmer water froze quicker than colder. They described this effect
together and returned it to the focus of scientific public’s attention. (Mpemba & Osborne, 1969).
As it happens, the same year Kell (Kell. G. S) published his work, independently from Mpemba
and Osborne, in which he endeavoured to explain the phenomenon by evaporation. He was not
familiar with Denis Osborne’s experiment which showed that evaporated mass is not enough to
explain the effect.
Answered by
11
This paradox originates from a real phenomenon, accessible to human senses, and is not a
thought experiment. The above mentioned experiment entails that this is an experimental
paradox.
Since this is a paradox without an explanation of the temperature change speed in different
physical states of water, clearly hierarchically differentiated, it could be classified as a
hierarchical paradox.
In order to solve Mpemba effect it is necessary to define precisely the initial conditions (water
mass, shape and type of the vessel, temperature difference, heat convection in the water, volume
of air in the water, freezing method, surrounding system,...) in which the effect is expected to be
demonstrated. In the case of drastic difference in water temperature or volume of water the effect
will not occur. It needs to be precisely defined whether the time interval observed will be until
the beginning of freezing or until the complete freezing of the entire volume of water.
The problem is that Mpemba effect is inconsistent with modern heat theory.
One of the explanations is that since at first we have equal volumes of water at different
temperatures, the volume of water at the higher temperature evaporates more, so that at the
moment of freezing the volumes of water will not be equal and the smaller amount of water will
freeze quicker. Certain authors claim that evaporation process alone is insufficient to explain
Mpemba effect.
It is generally believed that there is an infinite number of ways to combine relevant experiment
parameters that set up the conditions under which Mpemba effect will or will not apply. One
cannot say that Mpemba effect has been solved, since the values of the parameters within which
warmer water will freeze quicker than cold have not been precisely determined.
“Imagine a creature capable of following every single molecule along its path. Such
creature, whose characteristics would basically be as final as our own, would be capable of
something that we are not. This is because the molecules in an air-filled container, at a
regular temperature, move at velocities that are not regular at all, although the average
velocity of a large, randomly selected, number of molecules is almost completely regular.
Assume that such a container would be divided into two compartments, A and B, by a screen
with a small hole in it. The creature that can see individual molecules would open and close
the hole so that only the faster molecules may pass from A to B and only the slower from B to
A. Thus, the temperature in B would increase and the temperature in A would diminish
without work, which contradicts the Second law of thermodynamics”
Maxwell’s demon paradox is given here in its original form. James Maxwell published the
paradox in 1871 in a footnote in a textbook called Theory of Heat, and the paradox was first
mentioned in December of 1867 in Maxwell’s letter to Tait (Peter Guthrie Tait, 1831-1901). The
“demon” will be introduced later instead of the “being” that is arranging molecules according to
their speed, that “considers the way in which, when two objects are in contact, the wormer object
takes over heat from the colder without external intervention.”
This paradox does not originate from a real phenomenon, accessible to human senses. It is
speculative and originates from a phenomenon formulated by thought. This paradox is a thought
experiment. (Cucić, 2001) The paradox is of theoretical nature created as a thought speculation
in order to help in presenting a theoretical concept.
What makes this fictitious experiment paradoxical is the approach to the Second principle of
thermodynamics that heat can never be transferred from a colder to a warmer object without
external intervention. Maxwell found a way to “shake the foundations” of classical
thermodynamics owing to different principle of addressing the problem of heat transfer.
This paradox appeared as a consequence of paradigm mixing. In this case the paradigms of
classical physics and quantum physics are mixed. A quantum mechanical problem is approached
from the viewpoint of classical physics.
The thought experiment is paradoxical because the “being” that is arranging the molecules
belongs to a world of classical physics. The “being” acts according to the rules of the macrocosm
in the microcosm. If the paradox is viewed from a quantum mechanical standpoint the existence
of the “demon” must be understood as active intervention, since it does work while choosing
molecules.
thought experiment. The above mentioned experiment entails that this is an experimental
paradox.
Since this is a paradox without an explanation of the temperature change speed in different
physical states of water, clearly hierarchically differentiated, it could be classified as a
hierarchical paradox.
In order to solve Mpemba effect it is necessary to define precisely the initial conditions (water
mass, shape and type of the vessel, temperature difference, heat convection in the water, volume
of air in the water, freezing method, surrounding system,...) in which the effect is expected to be
demonstrated. In the case of drastic difference in water temperature or volume of water the effect
will not occur. It needs to be precisely defined whether the time interval observed will be until
the beginning of freezing or until the complete freezing of the entire volume of water.
The problem is that Mpemba effect is inconsistent with modern heat theory.
One of the explanations is that since at first we have equal volumes of water at different
temperatures, the volume of water at the higher temperature evaporates more, so that at the
moment of freezing the volumes of water will not be equal and the smaller amount of water will
freeze quicker. Certain authors claim that evaporation process alone is insufficient to explain
Mpemba effect.
It is generally believed that there is an infinite number of ways to combine relevant experiment
parameters that set up the conditions under which Mpemba effect will or will not apply. One
cannot say that Mpemba effect has been solved, since the values of the parameters within which
warmer water will freeze quicker than cold have not been precisely determined.
“Imagine a creature capable of following every single molecule along its path. Such
creature, whose characteristics would basically be as final as our own, would be capable of
something that we are not. This is because the molecules in an air-filled container, at a
regular temperature, move at velocities that are not regular at all, although the average
velocity of a large, randomly selected, number of molecules is almost completely regular.
Assume that such a container would be divided into two compartments, A and B, by a screen
with a small hole in it. The creature that can see individual molecules would open and close
the hole so that only the faster molecules may pass from A to B and only the slower from B to
A. Thus, the temperature in B would increase and the temperature in A would diminish
without work, which contradicts the Second law of thermodynamics”
Maxwell’s demon paradox is given here in its original form. James Maxwell published the
paradox in 1871 in a footnote in a textbook called Theory of Heat, and the paradox was first
mentioned in December of 1867 in Maxwell’s letter to Tait (Peter Guthrie Tait, 1831-1901). The
“demon” will be introduced later instead of the “being” that is arranging molecules according to
their speed, that “considers the way in which, when two objects are in contact, the wormer object
takes over heat from the colder without external intervention.”
This paradox does not originate from a real phenomenon, accessible to human senses. It is
speculative and originates from a phenomenon formulated by thought. This paradox is a thought
experiment. (Cucić, 2001) The paradox is of theoretical nature created as a thought speculation
in order to help in presenting a theoretical concept.
What makes this fictitious experiment paradoxical is the approach to the Second principle of
thermodynamics that heat can never be transferred from a colder to a warmer object without
external intervention. Maxwell found a way to “shake the foundations” of classical
thermodynamics owing to different principle of addressing the problem of heat transfer.
This paradox appeared as a consequence of paradigm mixing. In this case the paradigms of
classical physics and quantum physics are mixed. A quantum mechanical problem is approached
from the viewpoint of classical physics.
The thought experiment is paradoxical because the “being” that is arranging the molecules
belongs to a world of classical physics. The “being” acts according to the rules of the macrocosm
in the microcosm. If the paradox is viewed from a quantum mechanical standpoint the existence
of the “demon” must be understood as active intervention, since it does work while choosing
molecules.
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