Special Relativity and Time Dialation

Question

I have trouble understanding why time dilation occurs for objects moving towards you at no angle.

There are two example in my physics textbook:

1. A woman is on a moving train holding two light bulbs in her hands. As she moves across the platform, they flash. To her, the flashes are simultaneous. To an observer on the platform, the closest one flashes first. This makes sense to me as one flash has less distance to travel.

2. An observer on Earth sees a meteor travelling directly toward Earth. Classically, to calculate how long it takes the meteor to hit Earth, divide the distance between Earth and the meteor by velocity. Makes sense.

But why does special relativity tell you to multiply the time it takes for impact by $\gamma$? Why is the time longer for the person when the distance in both classical and special relativity is the same?

Answer 1

Answer:

1. According to Special Relativity, the Lorentz factor γ applies equally to the two examples. However, for classical systems, the relative velocity of the moving object with respect to the observer is much smaller than the velocity of light (v << c), implying γ ≈ 1.

2. Note that Special Relativity is insensitive to the direction of relative motion. This means that an observer on Earth will measure time dilation relative to the proper time on the meteor, regardless of whether the meteor in your example travels towards Earth or away from Earth with equal velocity.

3. Due to the insensitivity of Special Relativity to the direction of motion, the theory predicts that the proper time of an event taking place on an object traveling back and forth relative to an observer on Earth, will suffer time dilation twice. Thus, for the famous Twin Paradox, Special Relativity predicts that the traveling twin will return to Earth younger than the staying twin.

4. Studies on the Sagnac effect sharply contradict Special Relativity by showing: 1. That the measured velocity of light depends on the velocity of the detector relative to the light source, 2. That the direction of relative motion matters. Instead of a constant c, you have c ± v (the + sign applies to approaching objects, the - to departing object). Thus you get time dilation only for departing objects, but time contraction for approaching objects.

References:

1. Wang, R, Zheng, Y., Yao, A., & Langley, D. Modified Sagnac experiment for measuring traveltime difference between counter-propagating light beams in a uniformly moving fiber. Physics Letters A, 312 7–10, 2003.

2. Wang, R., Zheng, Yi, & Yao, A. Generalized Sagnac effect. Phys. Rev. Lett., 93 (14), 143901 (3 pages), 2004.

I hope that you find my answer helpful. Ramzi suleiman

Answer 2

Why is the time longer for the person when the distance in both classical and special relativity is the same?

This is where you will find your resolution because the distances are frame dependent in special relativity and not the same.

In the Earth frame lets say the meteor has a velocity v and is at a distance d. The meteor will strike the Earth at time t=vd, nothing special here yet. In the frame of the meteor the distance between it and the Earth will be contracted by a factor of γ. For the meteor this distance is d/γ. With a shorter distance to travel but going the same speed v it will arrive at Earth in time γv/d or γt.

Note that this is assuming that the meteor was at rest in the Earth's frame then accelerated up to a constant velocity toward Earth before reaching distance d. This assures the meteor has proper time.

Answer 3

I downloaded the article in the link. Now I just browsed in it, but I shall read more carefully in due time. There is one essential remark that I can say before reading the article is that the Sagnac effect, whether rotational, translational, or other, is a special case of the general rule of adding and subtracting velocities. If an observer moves with constant velocity v1 towards an object, and the object sends a signal in the direction of the observer, which travels with velocity v2 (v2 > v1) relative to its source, then the velocity of the signal relative to the observer is v2 + v1. If the observer is moving away from the object, then the velocity of the signal relative to the observer is v2-v1. Note that the "signal" can be any information carrier, not necessarily light, and not even a wave.

The Sagnac effect is the special case in which the signal is light, or another electromagnetic wave.

Do you agree with the rule stated above? If not, please explain why. Yours,

Ramzi