Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a m...Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a much deeper understanding … of the theory of relativity”. The deeper understanding of resolving the paradox is by applying more explicit definitions of proper time interval, Lorentz transform, time dilation, and aging time.展开更多
This paper provides a clear analysis of how hypothetical concepts not allowed in Special Relativity should be treated and exposes hidden assumptions in space-time diagrams used on YouTube, where some prominent physici...This paper provides a clear analysis of how hypothetical concepts not allowed in Special Relativity should be treated and exposes hidden assumptions in space-time diagrams used on YouTube, where some prominent physicists have taken to publishing on popular topics that may not survive peer review. Such casual graphical treatment conceals the fact that space-time diagrams provide only for the Einstein synchronization convention for all observers, not the many other valid synchronization protocols, and also obscure that relativity’s equality of reference frames is rebutted if concepts outside relativity, such as instant communication, are introduced. These omissions of unconscious assumptions have been used to “prove” the existence of block time and time travel or time paradoxes. We will show the contradictory assumptions amount to assuming time travel, rather than the more mundane need to adjust synchronization conventions. We further show a new result that the use of the space-time diagrams as proposed by these “explainers” leads to discontinuities in which a differential change in communication speed leads to a sudden jump from present to long-past arrival time, strongly suggesting invalidity of the method.展开更多
In this paper, the solution of the time-dependent Fokker-Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein-Podolsky-Rosen （EPR） paradox. Th...In this paper, the solution of the time-dependent Fokker-Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein-Podolsky-Rosen （EPR） paradox. The analytics and numerical calculation show the influence of pump depletion on the error in the measurement of continuous variables. The optimum realization of EPR paradox can be achieved by adjusting the parameter of squeezing. This result is of practical importance when the realistic experimental conditions are taken into consideration .展开更多
In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected proces...In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.展开更多
The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To prov...The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.展开更多
The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if <i>K</i> = <i>f'/f</i> (frequency ratio of the shift, <i>f'</i> the shi...The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if <i>K</i> = <i>f'/f</i> (frequency ratio of the shift, <i>f'</i> the shifted frequency), then the value of the series at time = t occurs in the shifted series at time = <i>t/K</i>. That is because in each harmonic the sin(<i>f't</i>) and cos(<i>f't</i>) became sin(<i>Kft</i>) and cos(<i>Kft</i>). The original series could be the number of photons in area of a beam with encoded information. Therefore the number of observed photons and information has the same resultant Doppler shift as frequency. Resultant is total effect of axial, transverse and gravitational shifts. Mass and energy of light do not have the same Doppler shift which may indicate missing parts that Doppler shift and that mass traveling at the speed of light is different from other mass and energy. The second proof (Section 5) the vector equations of space time require observed time to have 3 dimensions if the speed of light is constant in all directions, but the Doppler shift in each direction is not the same. The blue shift (compression) of time has paradoxes. If time has many dimensions, that would solve the paradoxes, but break conservation laws. No solution of that is given here. It is not expected that radical a solution will have any followers.展开更多
This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leon...This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.展开更多
The twins or clock paradox has been a subject of lively discussion and occasional disagreement among both relativists and the public for over 100 years, and continues to attract physicists who write papers giving new ...The twins or clock paradox has been a subject of lively discussion and occasional disagreement among both relativists and the public for over 100 years, and continues to attract physicists who write papers giving new analyses or defending old ones, even though many physicists now consider the matter only of educational interest. This paper investigates the number of papers, which is increasing, and trends in explanations, some of which are now targeted at professional physicists and other of which are targeted at optical or radar visualization rather than problem solving. Observations of students indicate that the latest techniques help but only somewhat. An analysis is made of 21 previous treatments appearing in the education related American Journal of Physics, Einstein’s discussions and several other pedagogical papers. A new memory aid for simultaneity transformation is given that puts it on a par with “time dilation” and “length contraction” for quick and easy problem visualization. The point of view of a trailing twin is introduced to show how simultaneity changes account for missing time in the turnaround. Length contraction is treated on equal footing with time dilation, and Swann’s insight into clocks is extended to lengths. Treatments using the conventionality of simultaneity are seen as equivalent to choice of co-moving frames. Responses to difficult questions are suggested which avoid being dismissive, and engage students’ critical thinking.展开更多
文摘Professors Mohazzbi and Luo [1] published “Despite several attempts have been made to explain the twin paradox … none of the explanations … resolved the paradox. If the paradox can be ever resolved, it requires a much deeper understanding … of the theory of relativity”. The deeper understanding of resolving the paradox is by applying more explicit definitions of proper time interval, Lorentz transform, time dilation, and aging time.
文摘This paper provides a clear analysis of how hypothetical concepts not allowed in Special Relativity should be treated and exposes hidden assumptions in space-time diagrams used on YouTube, where some prominent physicists have taken to publishing on popular topics that may not survive peer review. Such casual graphical treatment conceals the fact that space-time diagrams provide only for the Einstein synchronization convention for all observers, not the many other valid synchronization protocols, and also obscure that relativity’s equality of reference frames is rebutted if concepts outside relativity, such as instant communication, are introduced. These omissions of unconscious assumptions have been used to “prove” the existence of block time and time travel or time paradoxes. We will show the contradictory assumptions amount to assuming time travel, rather than the more mundane need to adjust synchronization conventions. We further show a new result that the use of the space-time diagrams as proposed by these “explainers” leads to discontinuities in which a differential change in communication speed leads to a sudden jump from present to long-past arrival time, strongly suggesting invalidity of the method.
文摘In this paper, the solution of the time-dependent Fokker-Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein-Podolsky-Rosen （EPR） paradox. The analytics and numerical calculation show the influence of pump depletion on the error in the measurement of continuous variables. The optimum realization of EPR paradox can be achieved by adjusting the parameter of squeezing. This result is of practical importance when the realistic experimental conditions are taken into consideration .
文摘In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.
文摘The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.
文摘The first proof (Sections 2 - 4), applies Doppler shifts to the Fourier time sine series. It shows if <i>K</i> = <i>f'/f</i> (frequency ratio of the shift, <i>f'</i> the shifted frequency), then the value of the series at time = t occurs in the shifted series at time = <i>t/K</i>. That is because in each harmonic the sin(<i>f't</i>) and cos(<i>f't</i>) became sin(<i>Kft</i>) and cos(<i>Kft</i>). The original series could be the number of photons in area of a beam with encoded information. Therefore the number of observed photons and information has the same resultant Doppler shift as frequency. Resultant is total effect of axial, transverse and gravitational shifts. Mass and energy of light do not have the same Doppler shift which may indicate missing parts that Doppler shift and that mass traveling at the speed of light is different from other mass and energy. The second proof (Section 5) the vector equations of space time require observed time to have 3 dimensions if the speed of light is constant in all directions, but the Doppler shift in each direction is not the same. The blue shift (compression) of time has paradoxes. If time has many dimensions, that would solve the paradoxes, but break conservation laws. No solution of that is given here. It is not expected that radical a solution will have any followers.
文摘This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.
文摘The twins or clock paradox has been a subject of lively discussion and occasional disagreement among both relativists and the public for over 100 years, and continues to attract physicists who write papers giving new analyses or defending old ones, even though many physicists now consider the matter only of educational interest. This paper investigates the number of papers, which is increasing, and trends in explanations, some of which are now targeted at professional physicists and other of which are targeted at optical or radar visualization rather than problem solving. Observations of students indicate that the latest techniques help but only somewhat. An analysis is made of 21 previous treatments appearing in the education related American Journal of Physics, Einstein’s discussions and several other pedagogical papers. A new memory aid for simultaneity transformation is given that puts it on a par with “time dilation” and “length contraction” for quick and easy problem visualization. The point of view of a trailing twin is introduced to show how simultaneity changes account for missing time in the turnaround. Length contraction is treated on equal footing with time dilation, and Swann’s insight into clocks is extended to lengths. Treatments using the conventionality of simultaneity are seen as equivalent to choice of co-moving frames. Responses to difficult questions are suggested which avoid being dismissive, and engage students’ critical thinking.
