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 dilation^2-10 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 T_p and the past time T_h is

   (2)                       

Where T_x is time which we want to control. We try to control T_x 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 T_x with very high velocity of the motion v.

                                                  (5)

Where t_r is the time at rest (t_r >0).

The above Eq.(5) shows that values of v, t_r and c are positive. If v<c, T_x is positive. If v>c, T_x 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 t_r to obtain a negative time T_x. From Eq(2), one can find that human being could not control T_x to make T_p become T_h. 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

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