Hello, and welcome back to MPC! Last week, we analyzed the relationship between *spacetime diagrams*, *light cones*, and *causality*. This week, we will take a step back and think about *special relativity* as a whole.

What is *special relativity*? Recall that we initially defined *special relativity* with two principles:

- The laws of physics are the same in all inertial frames of reference.
- The speed of light is constant in all inertial frames of reference.

Beyond those principles, though, let’s just think about its name: “*special relativity*.” Why is it called that? Well, we know what *relativity *is from a previous post, and it is rather clear how *special relativity* incorporates our definition of *relativity*. For example, when we spoke about *time dilation*, we discussed how one person’s clock would appear slower to you if he were moving **relative** to you. Moreover, the exact sluggishness of that person’s clock would be dependent on how fast he was moving **relative** to you. Overall, this idea of *relative motion* played a huge role in *special relativity* and our definition of *space *and *time*.

Alright, so the “*relativity*” part of *special relativity* makes sense, but what about the “*special*” part? Yes, *special relativity* is exciting and mind-blowing, but *special*? Electricity is pretty exciting too, but we don’t call it “special electricity.”

The truth is, *special relativity* is *special* because it can only model *space *and *time *in a very specific, or *special*, scenario. Recall the scenario we used to derive the *time dilation* formula (in this post): we had a person inside of a rocket ship that was zooming off at a speed of *v*:

**Figure 1:** The scenario we used to derive the *time dilation* formula

From this simple scenario, we were able to derive a powerful formula:

However, in deriving this formula, we made a rather large assumption: the rocket ship was moving at a constant speed. *How so?* We explicitly stated that the rocket ship was traveling at a speed of *v*! This is okay, but it does present a “small” problem: our derivation does not account for the scenario where the rocket ship’s *speed *is continuously increasing throughout its journey. Recall that *acceleration *is the change in *velocity *per unit *time* (see this post). *Acceleration* is not a foreign concept to us — we are used to acceleration when driving. When you are stopped at a traffic light and the signal turns green, you step on the gas pedal to *accelerate *your car to the speed limit. Let’s imagine our rocket ship does something similar: it starts at a speed of *0*, and accelerates to a higher speed, say *0.98c*. How slow does the person inside of the rocket ship’s clock seem to the person on the ground? Well, let’s just calculate the *relativistic factor* (see this post):

But wait, what is *v*? The rocket ship’s speed is constantly changing: at one point it isn’t moving, later it is traveling at *0.1c*, later it is traveling at *0.2c*, etc. Which *speed *do we plug in?

This is why *special relativity *is so *special*: it only works for objects moving at *constant**velocity* (not *accelerating*). *Special relativity* cannot handle *acceleration*!

So what do we do if we have objects that are *accelerating*?

*Who cares about objects that are *accelerating*? Is *acceleration *even that common in nature?*

Yes, it is! *Acceleration *is everywhere! Drop a book and it *accelerates *to the ground, roll a ball on the floor and it *decelerates *to a stop! If we want to understand our universe, we need some way of analyzing *space *and *time *when *acceleration* is involved.

Einstein, the father of* special relativity*, realized this limitation of his theory and worked hard to make *special relativity* more “*general*” (account for all types of motion, with or without *acceleration*). The result of his efforts, *general relativity*, took many years to develop and is much more complicated than *special relativity* (as we will soon see; do not worry though, it is nothing we cannot handle!).

Next week, we will be diving into *general relativity*. We will be sticking to conceptual discussions rather than mathematical discussions (because of *general relativity*‘s mathematical complexity). I hope you are excited — I certainly am! See you then!

(featured image: https://www.walldevil.com/wallpapers/a55/background-computer-apples-desktop-theme-wallpapers-food.jpg)