Time is not absolute (the story of special relativity)

I know the statement “Time Is Not Absolute” may seem abstract, or maybe grandiose. But bare with me, I’d like to explain.

Up until 150 years ago, humans never had any reason to doubt our assumptions about time. Our widely accepted laws of physics (Newtons famous laws of motion) always treated it as a constant variable, reliably ticking away at a constant rate and true for all parties. We never came across a situation where that assumption required questioning. However, as humans began to discover the properties of light, electricity, and magnetism, they started to come across fundamental inconsistencies between classical mechanics and the speed of light, and for a while they chased their tails trying to make sense of it.

We owe it to Einstein and his theory of special relativity for making the above statement. The audacious, yet simple theory makes the case that it is impossible for time to be absolute, that time is indeed relative and dilates relative to the observer. This theory had groundbreaking consequences, and it eventually catapulted us into the next era of physics (the one we know today).

So I would like to explain some of the physics to you, because its pretty darn cool and its really just the tip of the iceberg. Let’s start by getting our feet wet with two important concepts: relative motion and the speed of light. And with that knowledge we can tackle Einsteins theoretical experiment which changed our perceptions of the universe forever.

  1. Velocity and relative motion

You might remember that velocity is defined as speed with a direction. We can use it to express how far something travels during a given period of time:

We can use the concept of relative velocity to express how fast object A is moving compared to object B (and vice versa) by taking the difference of their velocities.

Let’s quickly apply this concept to make sure we have a good grasp on it, because we will need it later.

Imagine Bob is driving a car at 20 m/s, and Alice is standing still (with a velocity of 0 m/s). To see how much faster or slower one person is moving, we can take the difference of their velocities. In this case, Bob moves 20 m/s faster.

If Alice hops on a bike and starts moving at 5 m/s, she is now moving 15 m/s slower than Bob, and Bob is moving 15 m/s faster.

Simple enough, right? Now let’s introduce frames of reference. We’ll add a third person (Carl) who is on a skateboard and also moving at 5 m/s (he is just super athletic, pay no mind).

Bob will observe Alice and Carl both moving 15 m/s slower than him, which makes sense. The interesting thing is, from Alice’s perspective, Carl will appear stationary to her, because their relative velocity is 0. In Alices (and Carls) frame of reference, their surroundings will appear to be speeding past, and Bob will look like he is speeding ahead, but relative to each other, they will look like they are standing still. You experience the same exact effect when you drive in your car.

So technically, we can just as easily claim that Alice and Carl are stationary, while their surroundings moving past them at 5 m/s, and Bob is speeding ahead 15 m/s. We are simply choosing to define the problem within a different frame of reference (now being 5 m/s instead of stationary at 0 m/s).

The important question I would like to pose here is: Can we confidently declare which perception (or frame of reference) is the definitive truth?

As it turns out, we cannot! One observed reality cannot be more correct than the other, and the observed experience simply depends on the frame of reference we choose.

This is more significant than you think: say you are a passenger on a moving train moving at 20 m/s. Everything in the train is also moving at 20 m/s, so it all appears stationary to you. You can even throw a ball straight into the air and see it travel ONLY vertically, and have it land directly back into your hand.

However, a stationary observer standing outside on the tracks can watch you throw the same ball and they will see it move vertically AND horizontally, because the train is moving past them at 20 m/s. In fact, the motion of the ball will appear parabolic to a stationary observer.

But the point I’m trying to make is: Is the observation of the stationary observer more valid than observation made by the observer in motion?

The first important “postulate” to draw from this is: observed reality can be different based on your frame of reference, but the laws of physics still hold true for all observers.

2. Enter: The Speed of Light

The problematic discovery was: *drum roll please* that the speed of light was theoretically and experimentally observed to always be a constant of 299,792,458 m/s. I will round up to 300 million or 3*10⁸ for brevity (10⁸ just means 8 zeros).

This concept might seem OK in isolation, but let’s put it into context of relative motion. Let’s say Alice is stationary, and Bob is now on a spaceship moving at 100 million m/s. The top of his spaceship is emitting a beam of light. Alice, from her stationary frame, will observe the light to be moving at 300 million m/s.

If we apply the above concept of relative motion, what would we expect Bob to see if he measures the speed of light from his reference frame of 100 million m/s?

You would perhaps guess the answer 200,000,000 m/s. But because the speed of light is always constant, both observers will measure the ray of light moving at 3*10⁸m/s, regardless of their reference frame. In the context of light, your reference frame doesn’t seem to matter at all.

And this was indeed an awkward elephant in the room for physicists at the the turn of the 1800s. It shook up many smart people, most famously Einstein (❤). And we have him to thank for the reconciliation of these two fundamental laws of physics, via his famous theory of special relativity.

The second “postulate”: despite the obvious validity of relative motion, the speed of light being constant busts it wide open.

3. Finally: Special Relativity and twisting our understanding of time

So let’s see how these two concepts can agree, courtesy of an example posed by Einstein. Say we have Alice, standing in the middle of a train car:

Two bolts of lightning strike on either side of the car “simultaneously”. We need to carefully define the word simultaneous, as you will see it becomes extremely important (please reread and try to visualize as many times as you need to).

Let’s define two lightning strikes occurring “simultaneously” as them striking on either the side of the car, and traveling the same distance “n” to the observer in the center. Because the light from the strikes travels the same distance n and moves at the same speed, we know that the observer will see the light from both bolts at the exact same time.

Solve for “time” in our velocity equation, and we get the time it takes for the light to travel n meters. It is indeed a very small number, but theoretically significant.

So far so good. So what if the train car is in motion (at 20 m/s), and Bob is observing this scene from a stationary reference frame along the tracks?

From Alice’s frame of reference of 20 m/s, everything remains the same. She is stationary relative to the moving train car, and when the lightning strikes, the light from the strikes can travel the distance n to Alice in the same amount of time.

Here is where it gets interesting — what about Bob? To him, the train car is moving, so the center of the train car is moving away at a constant 20 m/s. Let’s say at any instant, that additional distance is “x”.

From Bobs perspective, the lightning can strike on the left, but the center of the train car is moving away at a constant speed, so the light from the left strike will have to travel n+x meters to reach Alice as she moves away. For the right strike, the center of the car is moving towards the strike, so the light will have to travel n-x to reach Alice at the center of the car. Essentially, telling us that in Bob’s reference frame, the light will have to travel a different amount of distance, and therefore a different amount of time.

So the strikes that appear “simultaneous” for Alice will have to occur at different times for Bob!

The same concept can be applied in reverse. What if the strikes occur “simultaneously” in Bob’s perspective? In the stationary perspective, they can strike on the two sides of the train car (wherever it is at that point in time), and travel “n” meters to the center (in the stationary reference frame).

However, From Alice’s reference frame, she is moving through the stationary points where the lightning struck, so she will move closer to the right strike, and further from the left strike. So within the train, she will see the right strike, and then the left strike slightly after. So in this case, what appears simultaneous to Bob cannot appear simultaneous to Alice.

In short, for two observers moving at different speeds, the same events will occur at different times! A.K.A. time is not absolute and is dilated by your velocity.

Thank you Einstein.

Both postulates from above remain true. The brave and critical shift here was calling out the only variable that was left: time.

4. The fallout

Via a thought experiment and some elementary math, we were able to conceptualize that the velocity at which you are moving will impact the way you perceive time. In fact, the faster you move, the slower you will experience time (check out the atomic clock airplane experiment if you are curious, but I would like to address this in detail in another post).

Of course the idea was not embraced right away, especially due to the fact that the theory was based on a thought experiment and not on experimental results. The acceptance and proof of this theory paved the way for theoretical physics as a whole, opening up a serious path to derive laws of the universe from drawing connections and proving them with experimental results (rather than being limited to doing it the other way around).

You might be wondering how we could have possibly missed this crucial property for the majority of our human existence. We have to remember that even the fastest humanly capable speeds are still close to 0 when compared to speed of light. The difference in time caused by a normal speed we are used to is essentially negligible (think a 100 millionth of a second). Our tools leading up to the 1900s would have never been precise enough to measure that slight of a difference. I don’t think anyone expected we would need it. But since then, we have built the tools to verify just that!

This theoretical discovery (along with reconciling the biggest contradiction in physics at the time) also lead to innovations that transformed our classical formulas for velocity and momentum into “relativistic velocity” and “relativistic momentum”, kicking off a new era of relativistic physics, where time dilation is taken into consideration with high speeds.

And out of the development of relativistic physics, Einstein derived the most famous equation in the world:

A.K.A. the law that tells us that the energy of matter is proportional to the speed of light squared! 300 million x 300 million is ALOT of zeros, and ALOT of energy. This tells us that even in one atom we have an unimaginable amount of energy. Put that into perspective of how many atoms you have in your body. But I digress.

Of course this derivation of E=mc² was first seen as just an intriguing theoretical speculation. But scientists ran with it, and this hypothetical musing eventually birthed the Manhattan Project, and the law which at first seemed like a curious side effect of this theory was very much proven by the atomic bomb (which in essence breaks the energetic bonds of an atom and releases that energy).

All in all, as we have learned, much can be proven from a seemingly innocent thought experiment about lightning strikes.

The concept explored here is the theory of “special relativity”, which basically states that the laws of physics must hold true for all observers moving at a constant velocity. And in order for that postulate to hold true, time cannot be absolute and must change between reference frames.

This was Einsteins first monumental discovery, which would later be dwarfed by his complete theory of “general relativity”. We will get into that, I promise.

P.S. Look for a blog post on deriving E=mc² and relativistic physics, if you are curious about the math!