JOURNAL OF APPLIED PHYSICS 107, 114105 2010
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program, Department of Chemical, Materials, and Biomolecular
Engineering and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 16 December 2009; accepted 13 March 2010; published online 3 June 2010
We develop a nonlinear thermodynamic model to predict the phase stability of ultrathin epitaxial
001 -oriented ferroelectric PbZr1−xTixO3 PZT films with x=1.0, 0.9, 0.8, and 0.7 on substrates
which induce anisotropic in-plane strains. The theoretical formalism incorporates the relaxation by
misfit dislocations at the film deposition temperature, the possibility of formation of ferroelectric
polydomain structures, and the effect of the internal electric field that is generated due to incomplete
charge screening at the film-electrode interfaces and the termination of the ferroelectric layer. This
analysis allows the development of misfit strain phase diagrams that provide the regions of stability
of monodomain and polydomain structures at a given temperature, film thickness, and composition.
It is shown that the range of stability for rotational monodomain phase is markedly increased in
comparison to the same ferroelectric films on isotropic substrates. Furthermore, the model finds a
strong similarity between ultrathin PbTiO3 and relatively thicker PZT films in terms of phase
stability. The combinations of the in-plane misfit strains that yield a phase transition sequence that
results in a polarization rotation from the c-phase polarization parallel to the 001 direction in the
film to the r-phase, and eventually to an in-plane polarization parallel to the 110 direction the
aa-phase is determined to be the path with the most attractive dielectric and piezoelectric
coefficients resulting in enhancements of 10 to 100 times in the dielectric permittivity and
piezoresponse compared to bulk tetragonal ferroelectrics of the same PZT composition. © 2010
American Institute of Physics. doi:10.1063/1.3386465
Sunday, October 3, 2010
Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films
Acta Materialia 58 (2010) 823–835
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics
Film thickness versus misfit strain phase diagrams for epitaxial PbTiO3 ultrathin ferroelectric films
PHYSICAL REVIEW B 78, 064117 2008
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy
Band structure of surface states and resonances for clean Cu(110) surface
Surface Science 601 (2007) 5779–5782
M.N. Read *, Q.Y. Qiu
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Available online 30 June 2007
Abstract
We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(110) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to 7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.
2007 Elsevier B.V. All rights reserved.
Keywords: Cu(110) surface electronic states; Surface electronic structure calculations; Shockley and Rydberg surface bands; Layer-by-layer KKR
scattering method
M.N. Read *, Q.Y. Qiu
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Available online 30 June 2007
Abstract
We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(110) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to 7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.
2007 Elsevier B.V. All rights reserved.
Keywords: Cu(110) surface electronic states; Surface electronic structure calculations; Shockley and Rydberg surface bands; Layer-by-layer KKR
scattering method
Theoretical investigation of polarization scaling in ultrathin epitaxial PbZrxTi1−xO3 films
JOURNAL OF APPLIED PHYSICS 102, 104113 2007
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007
We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007
We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334
Tuesday, September 28, 2010
丘乔羽: Scientific Research
丘乔羽: Scientific Research: "The Time Dilation Factor Could Not Obtain a Negative Time Qiao Yu Qiu** School of Materials Science and Engineering, University of New South..."
丘乔羽: Testing Time Dilation By Sunrays
丘乔羽: Testing Time Dilation By Sunrays: "AbstractSince the relativity theory published, the time dilation attracted the great interested. The time dilation had caused the debates fo..."
Testing Time Dilation By Sunrays
Abstract
Since the relativity theory published, the time dilation attracted the great interested. The time dilation had caused the debates for more than 100 years. It is difficult to do an experiment to test the time dilation on Earth. In this paper, we test the time dilation by an imagined experiment with Sunrays. The result shows that one would create paradoxes if he/she stands on different reference frameworks. Human being does not have the time dilation because they are in one reference framework only. The conclusion is that the time dilation can only be obtained in between two different reference frameworks.
Keywords: time dilation; relativity; unjustifiable hypotheses.
I. Introduction
The relativity theory predicts the time dilation of a transported clock. Einstein gave two unjustifiable hypotheses in his relativity[1]. Based on these two unjustifiable hypotheses he derived the Lorentz transformation and obtained the time dilation factor. Recently, many experts discussed the time dilation in details[2-10]. Jefimenko considered that the time dilation is a dynamic cause-and-effect phenomenon and not merely a kinematic effect[11]. Reinhardt et al. had tested the time dilation with fast optical atomic clocks[12]. Saathoff et al. had done an improved test of the time dilation using laser spectroscopy on fast ions at the heavy-ion storage-ring in Heidelberg[8]. Petit et al. had discussed the relativistic time dilation contribute to the divergence of universal time and ephemeris[10]. Peerally had detected the possible occurrence of a proportionality between the time dilation effects of special and general relativity in free-fall motion in Keplerian orbits[13]. The time dilation factor gives us a hope that one might find a way to go into the past of the world. Stephen W. Hawking pointed out this situation in his book “a brief history of time”[14]: “While this would be fine for writers of science fiction, it would mean that no one’s life would be safe: someone might go into the past and kill your father or mother before you were conceived!” Due to it is difficult to do an experiment to test the time dilation on Earth, let us do an imagined experiment with Sunrays to test the time dilation.
II. Analysis
The concept of the time dilation in relativity theory comes from two unjustifiable hypotheses. Einstein gave these two unjustifiable hypotheses in his relativity[1]:
(1) The time-interval (time) between two events is independent of the condition of motion the body of reference.
(2) The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.
Based on these two unjustifiable hypotheses, the time dilation factor γ can be obtained as follows[1]:
(1)Where v is the velocity of the motion, and c is the light speed.
Since Einstein published the formula of the time dilation factor, it caused the debates for more than 100 years. One will probably produce many paradoxes from the formula of the time dilation. The well-known example of misunderstanding the time dilation is the Twin Paradox. It says that X and Y are twins. While twin X travels in a high-speed rocket to outer space, twin Y remains on Earth. Many years later, twin X returns to Earth and reunites with twin Y. From twin Y’s point of view (on Earth), twin X has time dilation and twin X should be younger than twin Y when they reunite. From twin X’s point of view, twin Y has time dilation and twin Y should be younger than twin X when they reunite. The Twin Paradox had been discussed in many articles[15-41]. However, the Twin Paradox is produced from the viewpoints of different reference frameworks. Let us do an imagined experiment with Sunrays to test the time dilation.
We imagine that two beams of Sunrays begin to transmit from the Sun to the Earth at the same time. From our point of view (on Earth), two beams of Sunrays should arrive the Earth at the same time. We believe that both of them take 8 minutes. However, from ray1’s point of view, the time of ray2 is independent of the condition of motion the body of reference. Ray2 will have the time dilation and arrive the Earth earlier than ray1. Vice verse, from ray2’s point of view, the time of ray1 is independent of the condition of motion the body of reference. Ray1 will have the time dilation and arrive the Earth faster than ray2. It is clear that the paradox comes from the different viewpoints. We have to emphasize here that the time dilation can only be obtained in between two different reference frameworks in the relativity theory. From the viewpoint of one reference framework, one will obtain the time dilation on the other reference framework. Once the two different reference frameworks meet each other, the difference will disappear. There is no time dilation in one reference framework.
From the above Sunrays experiment, we can find that the Twin Paradox comes from the viewpoints of two different reference frameworks. Human being has the only one reference framework on Earth. When the Sunrays arrive the Earth, the two different reference frameworks become one reference framework on Earth. From Eq.(1) we can find that γ=1 at v=0. It is clear that human being does not have the time dilation when two different reference frameworks meet each other. Therefore, two beams of Sunrays will arrive the Earth at the same time.
Let us see the Twin Paradox. When twin X arrives the Earth to reunite with twin Y, they are in the same reference framework (on Earth). Once twin X arrives the Earth, the two different reference frameworks become one reference framework. They won’t have the time dilation on Earth. Thus, they are the same age while they reunite.
III. Conclusion
We conclude that the time dilation can only be obtained in between two different reference frameworks. Once the two different reference frameworks meet each other, the difference will disappear. There is no time dilation in one reference framework.
References:
[1] A. Einstein, Relativity The Special and the General Theory, 1916).
[2] R. Kanai, C. L. E. Paffen, H. Hogendoorn, et al., Journal of Vision 6, 1421 (2006).
[3] A. Gjurchinovski, American Journal of Physics 74, 838 (2006).
[4] J. R. Bray, Ieee Antennas and Propagation Magazine 48, 109 (2006).
[5] J. J. New and B. J. Scholl, Journal of Vision 9 (2009).
[6] G. Saathoff, U. Eisenbarth, S. Hannemann, et al., Hyperfine Interactions 146, 71 (2003).
[7] G. Saathoff, G. Huber, S. Karpuk, et al., in Special Relativity: Will it Survive the Next 101 years?, edited by J. Ehlers and C. Lammerzahl, 2006), Vol. 702, p. 479.
[8] G. Saathoff, S. Karpuk, U. Eisenbarth, et al., Physical Review Letters 91 (2003).
[9] G. Saathoff, S. Reinhardt, H. Buhr, et al., Canadian Journal of Physics 83, 425 (2005).
[10] G. Petit and S. Klioner, Astronomical Journal 136, 1909 (2008).
[11] O. D. Jefimenko, American Journal of Physics 64, 812 (1996).
[12] S. Reinhardt, G. Saathoff, H. Buhr, et al., Nature Physics 3, 861 (2007).
[13] A. Peerally, South African Journal of Science 104, 221 (2008).
[14] S. W. Hawking, A Brief History of Time, 1988).
[15] R. Tomaschitz, Chaos Solitons & Fractals 20, 713 (2004).
[16] C. S. Unnikrishnan, Current Science 89, 2009 (2005).
[17] C. S. Unnikrishnan, Current Science 95, 707 (2008).
[18] M. A. Abramowicz, S. Bajtlik, and W. Kluzniak, Physical Review A 75 (2007).
[19] J. D. Barrow and J. Levin, Physical Review A 63 (2001).
[20] D. Boccaletti, F. Catoni, and V. Catoni, Advances in Applied Clifford Algebras 17, 611 (2007).
[21] D. Boccaletti, F. Catoni, and V. Catoni, Advances in Applied Clifford Algebras 17, 1 (2007).
[22] M. B. Cranor, E. M. Heider, and R. H. Price, American Journal of Physics 68, 1016 (2000).
[23] T. Dray, American Journal of Physics 58, 822 (1990).
[24] F. T. Falciano, Revista Brasileira De Ensino De Fisica 29, 19 (2007).
[25] S. K. Ghosal, S. Nepal, and D. Das, Foundations of Physics Letters 18, 603 (2005).
[26] T. Grandou and J. L. Rubin, International Journal of Theoretical Physics 48, 101 (2009).
[27] O. Gron, European Journal of Physics 27, 885 (2006).
[28] O. G. Gron, Current Science 92, 416 (2007).
[29] K. Hazra, Current Science 95, 706 (2008).
[30] M. Kohler, Foundations of Physics Letters 19, 537 (2006).
[31] J. X. Madarasz, I. Nemeti, and G. Szekely, Foundations of Physics 36, 681 (2006).
[32] T. Muller, A. King, and D. Adis, American Journal of Physics 76, 360 (2008).
[33] H. Nikolic, Foundations of Physics Letters 13, 595 (2000).
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[41] J. R. Weeks, American Mathematical Monthly 108, 585 (2001).
Scientific Research
The Time Dilation Factor Could Not Obtain a Negative Time
Qiao Yu Qiu*
* School of Materials Science and Engineering, University of New South Wales, Sydney,
NSW 2052, Australia
e-mail: qiaoyuqiu@gmail.com
A fundamental concept of the relativity theory is the time dilation of a transported clock. Einstein derived the Lorentz transformation to obtain the time dilation factor. The time dilation factor gives us a hope that one might find a way to go into the past. This prediction had caused the debates for more than 100 years. Can we control the time dilation to go into the past? According to the relativity theory, the time dilation can be created in between two different reference frameworks. However, one could not obtain a negative time from the dilation factor in any circumstance. In the same framework (on earth), human being could not go into the past. Therefore, the time arrow on earth is towards the future only.
Einstein predicted the time dilation of a transported clock in his relativity1. He had given two unjustifiable hypotheses and derived the Lorentz transformation to obtain the time dilation factor γ. Recently, many experts discussed the time dilation2-10 in details. Jefimenko considered that the time dilation is a dynamic cause-and-effect phenomenon and not merely a kinematic effect11. Reinhardt et al. had tested the time dilation with fast optical atomic clocks12. Saathoff et al. had done an improved test of the time dilation using laser spectroscopy on fast ions at the heavy-ion storage-ring in Heidelberg8. Petit et al. had discussed the relativistic time dilation contribute to the divergence of universal time and ephemeris10. Peerally had detected the possible occurrence of a proportionality between the time dilation effects of special and general relativity in free-fall motion in Keplerian orbits13. The time dilation factor gives us an image that one might find a way to go into the past. Stephen W. Hawking pointed out this situation in his book “a brief past
of time”14: “While this would be fine for writers of science fiction, it would mean that no one’s life would be safe: someone might go into the past and kill your father or mother before you were conceived!” Many scientists are trying to control the time dilation. Can we control the time dilation to go into the past? In this paper, we control the velocity of the motion to work out whether we can obtain a negative time from the time dilation factor or not.
How can we control the time dilation? Einstein had given two unjustifiable hypotheses in his relativity1:
1. The time-interval (time) between two events is independent of the condition of motion the body of reference.
2. The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.
Based on these two unjustifiable hypotheses, the time dilation factor γ can be derived as follows1
(1)Where v is the velocity of the motion, and c is the light speed.
The only thing we can control in Eq.(1) is the velocity of the motion “v”. The relationship between the present time Tp and the past time Th is
(2)Where Tx is time which we want to control. We try to control Tx and find a way to go into the past. Einstein first predicted the time dilation of a transported clock in his 1905 paper15. We imagine that we control the time dilation with a transported clock. From Eq.(2), one can have
(3)Based on the Lorentz transformation, the relationship between the time in motion t’ and the time at rest t is1
(4)Now, we try to control Tx with very high velocity of the motion v.
Where tr is the time at rest (tr >0).
The above Eq.(5) shows that values of v, tr and c are positive. If v<c, Tx is positive. If v>c, Tx is a complex number. When v=c, one would have
(6)The above Eq.(6) shows that the limit time one can control is zero. One could not control v and tr to obtain a negative time Tx. From Eq(2), one can find that human being could not control Tx to make Tp become Th. It means human being cannot control the time dilation to go into the past.
According to the relativity theory, the time dilation can be created only in between two different reference frameworks. Our framework is the earth. The past is the past time of the earth. We are in the present time of the earth. In the same framework (on earth), human being could not have the time dilation. We imagine that we travel in a rocket in very high speed to outer space. The rocket and the earth are two different reference frameworks. According to the relativity theory, one would have time dilation in the rocket framework. However, the past of the earth is not in the outer space. If one wants to go into the past of the earth, one must return to the earth. Once the rocket arrive the earth, the rocket and the earth become the same reference framework. Furthermore, even the rocket have time dilation, it could not obtain a negative time. From Eq.(6) one can find that one could not breakthrough the time dilation limit to obtain a negative time. Human being could not obtain a negative time in any circumstance.
It is concluded that the time dilation has been proven that it could be created in between two different reference frameworks only. The time dilation factor could not obtain a negative time. In the same framework (on earth), human being could not go into the past. Therefore, the time arrow on earth is towards the future only.
References
1. Einstein, A. Relativity The Special and the General Theory, (1916).
2. Kanai, R., Paffen, C.L.E., Hogendoorn, H. & Verstraten, F.A.J. Time dilation in dynamic visual display. Journal of Vision 6, 1421-1430 (2006).
3. Gjurchinovski, A. Relativistic addition of parallel velocities from Lorentz contraction and time dilation. Am. J. Phys. 74, 838-839 (2006).
4. Bray, J.R. From Maxwell to Einstein: Introducing the time-dilation property of special relativity in undergraduate electromagnetics. Ieee Antennas and Propagation Magazine 48, 109-114 (2006).
5. New, J.J. & Scholl, B.J. Subjective time dilation: Spatially local, object-based, or a global visual experience? Journal of Vision 9(2009).
6. Saathoff, G., et al. Toward a new test of the relativistic time dilation factor by laser spectroscopy of fast ions in a storage ring. Hyperfine Interactions 146, 71-75 (2003).
7. Saathoff, G., et al. Experimental test of time dilation by laser spectroscopy on fast ion beams. in Special Relativity: Will it Survive the Next 101 years?, Vol. 702 (eds. Ehlers, J. & Lammerzahl, C.) 479-492 (2006).
8. Saathoff, G., et al. Improved test of time dilation in special relativity. Physical Review Letters 91(2003).
9. Saathoff, G., et al. Test of time dilation by laser spectroscopy on fast ions. Canadian Journal of Physics 83, 425-434 (2005).
10. Petit, G. & Klioner, S. Does relativistic time dilation contribute to the divergence of universal time and ephemeris time? Astronomical Journal 136, 1909-1912 (2008).
11. Jefimenko, O.D. Direct calculation of time dilation. Am. J. Phys. 64, 812-814 (1996).
12. Reinhardt, S., et al. Test of relativistic time dilation with fast optical atomic clocks at different velocities. Nature Physics 3, 861-864 (2007).
13. Peerally, A. A law of time dilation proportionality in Keplerian orbits. S. Afr. J. Sci. 104, 221-224 (2008).
14. Hawking, S.W. A Brief History of Time, (1988).
15. Einstein, A. The electrodynamic moving body. Annalen Der Physik 17, 891-921 (1905).
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