Special Relativity: “We’re All Special”

Posts by Alex

WARNING: Ahead is a very long-winded and text heavy post. Proceed with free time. You have been warned.

As some of you know, I’m a physics teacher! So I figured I would be remiss if I didn’t talk about some cool science on here! I know most people have probably taken an intro physics class at some point in their lives, but as someone who teaches those classes, I know they don’t always cover the most interesting topics. Therefore, I’m going to do my best to talk about something that a lot of people hear about, but nobody learns unless they study more advanced physics: Special Relativity!


In case you’re wondering, Einstein’s Special Theory of Relativity is the thing that says that time and space do funny things when an object travels close to the speed of light. Not to be confused with his theory of General Relativity which has to do with gravity and is much more confusing. I don’t pretend to be anywhere near as knowledgeable about that one.
According to General Relativity, planets like to have picnics together on big, groovy space-blankets (Source)
So, in order to talk about Special Relativity, we need to define what relativity means.
Let’s begin with a fairly simple thought experiment:
Imagine you are in a featureless white room. There are no distinguishable features on the walls or floor, so you really can’t tell if you’re moving (I think they have those in photography studios?) If you begin walking forward and throw a ball straight up, it would come back to your hand. It would appear that you and the ball did not move forward at all. Now, if someone were to observe you doing this, they would tell you that you and the object BOTH moved forward, which is why it landed in your hand. So both of you have very different versions of what just happened. This is because of the concept of reference frames.You and the ball share a reference frame, and so it seems that you are in one position the whole time. The observer is their own reference frame, in which you and the ball both moved forward while they stood still.
This is the case for all systems in the universe, and they will behave similarly. If you throw a ball from a moving car, the ball will have the speed you threw it with, plus the speed of the car it originated in. This isn’t so with light. As it turns out, the speed of light is the same no matter what, and everything we can see in the world is actually just the light particles from an object hitting our eyes. This means that when things start moving close to the speed of the light we observe coming off of them, things get very interesting.
Consider an object moving towards you from very far away (like a spaceship). The light from this object travels at a finite pace, so when we see it, we are actually seeing it in the past. Now if this object is moving towards you at some large fraction of light (let’s say 90%), that means that by the time you saw that object very far away, it would be much closer.
No, that’s not why they put these warnings there. (Source)
But the universe can’t be inconsistent like this. If you think about it, this means you would always see the object lagging behind where it actually was at all points, and that would mean that if something moving fast were to hit you, you would perceive it as being very far away but still quite clearly causing you pain! If this seems to go against your intuition, it should. This is not what happens. If possible, the truth is even stranger.

Put on your thinking caps kiddos, it’s about to get abstract in here!

What happens in this situation is different for each reference frame involved. When discussing relativity, we have a saying you may have heard: “Moving clocks run slow”. For you, standing here on Earth, it would seem that everyone on board that spaceship is moving in slow motion. To see why, let’s do another thought experiment:

Let’s assume that on board the spaceship is a clock. But this is no ordinary clock, this clock measures time by sending out a pulse of light straight up to a mirror and receiving it back every second. Now, to the observer on the ship, the pulse of light goes straight up and down, and so nothing is wrong with their perception of time, just like the ball and white room experiment. However, to the observer looking at the ship from outside (not moving with it), they see something different. We know the light hits the mirror and comes back down to the sensor but as it does so, the ship is moving. This means that the light no longer goes up and down, but rather diagonally. Basic geometry tells us that the path the light takes is longer in this frame than in the spaceship frame. Since the speed of the light has to be the same, that means that to the observer outside the ship, their clock takes longer than one second to tick. If you’re confused, here’s an illustration:

(Source)

There’s an additional consequence to this weirdness. For this to work, that means that the distances these frames believe themselves to be travelling have to change in order to keep the time difference consistent. The result is a weird spacial “smooshing”. But I suppose if you want to sound smart when you talk about this stuff you could call these phenomena “time dilation” and “length contraction”.

An example of relativistic “smooshing” (Source)
Now I know, this sounds all made up, so I’m going to try and explain it with a common phenomena that we have actually observed here on Earth.
There is a particle that is well known to physics called the muon. Muons travel at about 99.8% the speed of light and they originate in our upper atmosphere, thousands of meters above sea level. It’s a well established fact in physics that muons decay in about 2 microseconds (that’s 0.000002 seconds). In that time with the speed they travel, muons can only make it about 600 m before they decay. So how could we possibly observe them thousands of meters from where they come into existence????
You guessed it, relativity. These particles move damn close to the speed of light. That means to us on Earth, their “clock” runs slow. We know that they decay in 2 microseconds in their own reference frame, yet we observe them to be in existence for about 30 microseconds because of time dilation. Likewise, the muon experiences its travel in 2 microseconds, but because of length contraction, it appears that the Earth’s surface is only about 600 m away, instead of several thousand.

This is an example of how time and space both have to distort as a consequence of each other. If only time dilation occurred, the muon would reach Earth in our frame, but not in its own frame, which is a serious causal dilemma. Because we know that time does dilate, and I believe I’ve made a strong case that it does, length then must contract or else causality is broken. A nonexistent muon would reach Earth!

So there you have it. There are a ton of other strange paradoxes that arise from relativity like the twin paradox and the pole-barn paradox that are worth looking into if you’re interested. Who knows, they may even be cause for a future post! The universe is a strangely beautiful place, and its a shame that we don’t get a chance to teach the cool stuff in grade school!
This has been an incredibly quick and very imperfect lesson on Special Relativity. I tried to leave out all the math, which does not lend itself well to this kind of discussion so if you have questions, I’m not surprised. I’d be more than happy to discuss things in the comments!

(function(i,s,o,g,r,a,m){i[‘GoogleAnalyticsObject’]=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,’script’,’//www.google-analytics.com/analytics.js’,’ga’);

ga(‘create’, ‘UA-44399366-1’, ‘auto’);
ga(‘send’, ‘pageview’);

By Jess

A bookworm since the tender age of whenever I stopped chewing on books and started actually reading them. A cat-mom, graphic designer, and introvert originally from Pittsburgh, but now resides in the humid, hot, state of Texas. Cheers!

  • Katherine Koba

    Ahh, I love stuff like this~~. Unsurprising that I inadvertently introduced time dilation/contraction and frames of reference in my YA fantasy novel by making time a proper physical element magicians can manipulate.

    The question is though: is it possible for there to be *some point* in the universe that isn't in motion, where one could theoretically observe "true" time?

  • Alex

    The short answer to your question would be "no". But fear not! I have a longer, more satisfying answer!

    I am kicking myself re-reading this post because I realize that I left out a very fundamental idea. In his paper on Special Relativity, Einstein lays out two postulates that actually guarantee the effects of the theory. First, the speed of light is the same in all inertial (non-accelerating) reference frames. This is where we get that time dilation example from. Second, the laws of physics hold in ALL inertial reference frames, and therefore no inertial frame can be considered more "true" than any other.

    The implications here are huge, because it means that their is no part of the universe that is any more fundamental to the laws of physics than any other, provided it is in an inertial frame. The reason why comes from my first example. Say that you are in a frame that you consider to be completely stationary and therefore, are experiencing "true" time. Someone moving toward you at constant speed (aka inertial) would think of themselves as stationary while you are moving toward them. To this person, THEY experience true time and you do not.

    So to reiterate, my answer is no, but that is because everyone experiences the universe and "true time" all the time. It is the only way to experience the universe. However, your true time and my true time are theoretically different, and it is impossible to say which is better. Hence my subtitle, "We're all special"

  • thedailymiacis

    You know, it's my inner wish that I could really understand physics but there is something that my mind just can't understand, and for that, on my degree, biology, I had biophysics, and it was so hard for me to do it. But damn, I would love to understand because I believe like math, it's one of the great sciences, and it's the base to a lot of things that I study for example. This theory I loved specially the Cosmos episode where he talks about light, and light speed and wormholes 🙂

  • Alex

    If it is a problem with math, I recommend you pick some physics books up that are non-textbooks. So many physicists and theorists are publishing books now meant to present the interesting topics in a way that tries not to rely on math (much like I attempted here). With a science background you should have no problem reading through books like this and coming out the other side feeling like you learned something! Browse the physics and astronomy section at your local bookstore and see what you can find!

  • thedailymiacis

    Math is not a problem, I love math! And I need to understand due to my backgroud, I need to understand the basics and Biostatistics. My problems is with laws and applying them. For example last year I was a teacher on a center to help kids that have difficulties in school or want better grades, I was giving Biology, Chemestry-Physics and Math lessons. I reviewed the things that they learned on college and a lot of things I understood better then when I was a student but still somethings I I just dont get why is like that. What books do you recomend? Know I want to read 🙂

  • SCIENCE! This is seriously so cool, and I love learning something new. Yay, teachers! (P.S. How's it going!?)

  • Alex

    "For the Love of Physics" by Walter Lewin would be a good place to start (the man is a legend among educators).
    "A Tear at the Edge of Creation" by Marcelo Glieser if you're more interested in cosmology or just want to have your emotions tugged on by a scientist.
    "Death By Black Hole" by Neil Degrasse Tyson for astronomy and in general all things related.
    "The Dancing Wu Li Masters" by Gary Zukav for all things Modern, like relativity, quantum mechanics, and the wave-particle duality of light. Also very philosophical in terms of the nature of experience etc.

    Almost all of these are written for the understanding of people without a science brain, yet all of them are certainly leagues better if you are a science person.

  • Alex

    I'll try and work some more science in here somewhere in the future if I can!

    Teaching is going well. I was considering doing a post detailing all the lessons I've learned this year, but thought better of it. I completely obliterated my internet presence prior to this year in hopes of anonymity(this blog is probably the largest part of my internet footprint, and its not even mine!). I figure I probably shouldn't discuss the exact thing I want to stay hidden from. Talk about counterproductive! Maybe I'll write about it a year from now when I am in a different environment. Suffice to say, I'm still loving what I'm doing!

  • thedailymiacis

    Thank you! 🙂

  • I don't talk about it much for the same reasons, but at this point, disconnecting myself from my blog and tech just isn't an option. As an English teacher, I probably have a little more "academic" justification for my online presence, as I post a lot of writing tips and it serves more or less as my portfolio, but still. I'm one of the few bloggers with my social media on lockdown because of students. Not like I post anything questionable (maybe I just get really ranty when the Pens make the playoffs), but it's still a privacy/professional barrier I'd rather not break. I'm glad to hear you're enjoying it though!