Question 1: Imagine a world in which c = 50 m/s. How would the every day events appear to us?
Decreasing the velocity of light to 50 m/s, the relativistic factor
will drastically decrease. In such a case, the difference between v and c would be less and the effect on the mass of a body and length and the time dilation would be huge.
|Mathematical Explanation: When c decreases, the term v/c increases as c is in the denominator. When v/c increases, the term (1 – v/c) will decrease, because a greater number is subtracted from 1. So the result is a decrease in the whole relativistic factor.|
Let’s consider the cases one by one.
Effect on mass
Relativistic mass is given by
|When v = c, the mass would be infinite. However, if even velocity is not equal to c, even then the mass would sufficiently increase with increase in the velocity.||Mathematical Explanation: When v = c, then v/c = c/c = 1. The denominator in the relativistic factor is 1-1 = 0. Any thing divided by zero = ∞.|
Lorentz length contraction
Relativistic length is given by
Therefore, length contraction would be observed in small velocities of our daily life.
|Mathematical Explanation: With the present large value of c, the term v/c is negligible (= 0) and the relativistic factor is 1. Therefore, L = L0. (see equation above). However, when c = 50 m/s, the term v/c becomes significant for almost all daily life velocities. Therefore, the relativistic factor would have some value less than 1 for almost all velocities. Hence, we would observe length contraction every where.|
Time dilation is given by
Time dilation would be infinite when v = c (i-e, 50 m/s). For small change (increase) in velocity a huge change in time dilation would be observed.
Einstein’s mass energy equation
The effect on Einstein’s mass-energy relation, E = mc2 would also be greater. The change in mass would be greater for a small change in velocity.
Conclusion: The world would have completely changed for c = 50 m/s. It would not be as we see it now. We would be feeling relativistic effects every where around us; in mass, in distances and in time. Similarly, it would be impossible for us to attain a speed of 50 m/s because at that speed the mass of the object would be infinite.