# Eli5, Is the relationship between speed and time directly proportional?

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I’ve been going down a physics rabbit hole with the speed of light on this sub and am honestly blown away. I understand now that the faster you move the slower you experience time.

Is this relationship directly proportional?
i.e. moving at half the speed of light makes you observe time at half the normal speed.

In: 2 It may help you to view gravity as time also. Now you are in the slow motion of our gravity but feels Normal to you. Now you are moving away from the gravity hole which is our sun and going faster and faster. Time would be going faster for you as there is less gravity plus your speed. You should read a book called Hail Marry it explains this is more of a physics way. First of all its important to note that all of this is relative, and in your own frame you always experience time as moving at the same rate.

Time dilation is the change in the interval between events between you and another reference frame moving relative to you, e.g half the speed of light.

To answer the question, it’s not linear. The equation for time dilation is t’ = γt, where γ (gamma) is the Lorentz factor

γ = 1/sqrt(1-v^2/c^2).

This doesn’t vary linearly, for small values of v this is effectively just equal to 1 and there is no time dilation, as the velocity approaches the speed of light this equation approaches infinity. [This graph](https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Lorentz_factor.svg/2019px-Lorentz_factor.svg.png) shows how gamma changes as you approach the speed of light. For v=0.5c, gamma is about 1.15 so there would be about 15% time dilation. not directly proportional at all. The relationship is given by the Lorentz factor

γ = 1/√ (1-(v²/c²))

At half light speed time is about 15% slower. No, it’s not linear. We describe the change in measurements of length, time, and other properties that change with velocity using something called the Lorentz factor. The math is beyond the scope of this question, but take a look at [this graph](https://en.wikipedia.org/wiki/Lorentz_factor#/media/File:Lorentz_factor.svg). Velocity is on the x axis, with 0 on the right and c (the speed of light in a vacuum) on the left, and the Lorentz factor is on the right. You can see that it’s not linear – it doesn’t increase very much until you get to a significant fraction of c and then it rapidly increases as you get closer to c.