**Question 1: Imagine a world in which c = 50 m/s. How would the every day events appear to us?**

ANSWER

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 = L_{0}. (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

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 = mc^{2} 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.

Thankyou so much for helping . This website is truly amazing. It helped me a lot during 1st year and now even in my 2nd year . The answers are explained beautifully and anyone can easily understand them . And I can’t thank you in words for how much it helped me . Thank you sir !

easy to understand elaboration !👍

In this question can we consider two situations ;

First in which when speed of light is reduced to 50m/s the speed of rest of the objects are similar to that we observe in this world . We observe relativistic effect.

Second that with decrease in speed of light the speed of rest of the object also is reduced and we do not observe relativistic effects.

Is this concept correct ???

Alishba JavedSituation 1: What when a bullet train is going with 100 m/s and light speed is 50 m/s. The relativistic factor will be negative. What will we see if we see backwards while sitting in a bullet train…. perhaps a complete darkness! So, this is true relativistic factor will be observed in

very small velocitiesand velocity greater than this limit will be impossible.Situation 2: yes, if the speeds in the universe are decreased there is a possibility. But imagine how slow the universe would be! Perhaps we will not move a step distance in the whole of our lives. By the way, the concept seems correct.

Thank you so much.

This is really a well explained answer and very helpful

Thanks.

Pingback:twin-paradox – msa

Pingback:sq-ch18-p12