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).
[34] J. N. Percival, Physics Essays 13, 555 (2000).
[35] P. Pesic, European Journal of Physics 24, 585 (2003).
[36] C. Renshaw, Ieee Aerospace and Electronic Systems Magazine 11, 27 (1996).
[37] B. F. Roukema and S. Bajtlik, Monthly Notices of the Royal Astronomical Society 390, 655 (2008).
[38] M. Schon, Foundations of Physics 28, 185 (1998).
[39] W. S. Soni, European Journal of Physics 23, 225 (2002).
[40] J. P. Uzan, J. P. Luminet, R. Lehoucq, et al., European Journal of Physics 23, 277 (2002).
[41] J. R. Weeks, American Mathematical Monthly 108, 585 (2001).
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