The constant rhythmic beating of time dictates everything that goes on in our lives, from the moment we are born to the moment when our eyes close for the last time. The way our planet is set up seems to indicate that time is static – however, this couldn’t be further from the truth. Time is as fluid and dynamic as water! But this seems to go against everything we’ve ever learned. After all, if time wasn’t constant, then it seems like our world would fall into chaos. The answer to this mysterious property of time lies within the realm of special relativity.
At the mention of “special relativity”, the first image to come to mind is that of Albert Einstein. We can picture him working away at his job in the patent office while simultaneously daydreaming about the speed of light, and time travel, and a multitude of other complex ideas. If we examine what the theory of special relativity states, then this “dynamic” paradox of time explains itself. It seems counter-intuitive at first, but give it some *time*, and it’ll make perfect sense.
The first part of special relativity states that the laws of physics apply regardless of your ‘frame of reference’. This is the simpler and intuitive part of special relativity. For example, say that you have a block of wood that’s 5 feet in length. If you place it on the ground and measure it with a ruler, you would obtain 5 feet. If you were to measure it in a moving car (constant speed*), then you would obtain 5 feet once again. Seems pretty basic right? That’s exactly the point! No matter what your ‘frame of reference’ (a fancy way to say ‘point of view’) is, the laws of physics still apply.
Using this as a foundation, we can jump into the second part of special relativity which deals directly with the speed of light. High school has taught us that light (or in our perspective, visible light) is a small section on something known as the electromagnetic spectrum. This spectrum essentially diagrams the different electromagnetic waves (simply put, electromagnetic waves are electric and magnetic fields that work together to transport energy) that are possible. Now according to the first part of special relativity, the laws of physics that govern electromagnetic waves must be the same for every frame of reference. One of the fundamental properties of electromagnetic waves is that they all travel at the speed of light (186,282 miles/second). From this, we can infer that regardless of the frame of reference, the speed of an electromagnetic wave (such as light) will not change.
Let me give you an example to show why this specific point is so crucial. Suppose that you were standing at one end of the football field and your friend was at the other. Your friend (the super-human athlete that he is) starts running towards you at a speed of 40 mph. While still in motion, he throws the ball directly towards you (as soon as he reaches a specified position, A) at a speed of 30 mph. Intuition tells use that, from your frame of reference, the ball is coming at you with a speed of 70 mph. Well your intuition would be absolutely correct in this case.
Now let’s use the same example when looking at the speed of light. This time, your friend carries a flashlight instead of a football. He takes off at a speed of 40 mph and turns on the flashlight (at position A) while still in motion. Intuition tells us that from your frame of reference, the light is coming at you with a speed of 186,322 mps (speed of light + 40 mph). Well in this case, intuition is wrong. The light you see would be coming at you with a speed of 186,282 mps (its original speed).
Remember, the speed of an electromagnetic wave will not change according to the frame of reference because the laws of physics do not change between different frames of reference! So why does the difference originate between the football and the light? Well, the football’s speed is not bound by the laws of physics. Its speed can increase depending on factors such as force or wind. However, this is not so in the case of light. The laws of physics dictate that nothing can travel faster than light, not even light itself!
So how does this relate to the concept that time is ever-changing? Well, special relativity explain a curious phenomenon known as time dilation. This is where we truly see the dynamic nature of time.
Let’s imagine that you’re sitting in a car that’s moving at 100 mph (to the right). If you throw a baseball up in the air, it comes straight back down and falls into your hand, right? The up-down movement is what you perceive it as in your frame of reference. However, to an outsider, the ball has horizontal movement as well. When that car is moving at 100 mph, every single object in that car (including you) is moving at 100 mph. Thus, when the ball is throw upwards in the air, you supply the vertical movement but the car supplies the horizontal movement. Combining these two forces gives us a slanted direction of the balls movement (as shown below).
If we complete this movement on the way down, the outsider will see that the ball has traveled in an upside-down V shape. However, from your frame of reference within the car, the ball simply travels up and down into your hand because everything in that car is moving at the same horizontal speed. To put it simply, the perception of the horizontal movement is cancelled because relative to you, there is no horizontal movement of the ball (since you’re moving “with” the ball horizontally). Now let’s extend this analogy to apply to light.
Picture yourself in a car moving at 0.5C (C is the general notation for the speed of light) to the right – in this case, it means half of the speed of light. The ceiling of the car has a reflective surface while the floor of the car has a light detector. When you’re moving at 0.5C, you turn the flashlight on and see the beam of light bounce off the top and hit the detector on the bottom. Let’s say that (somehow), an observer was also looking into your car when it was moving and measured that it took the light 5 seconds to hit the reflective surface at the top.
186,282 (miles/sec) x 5 (sec) = 931,410 miles.
Using this same information, we can calculate the length of V1 (which represents the distance traveled by the car) after 5 seconds.. Since the car is moving at 0.5c, it’s speed in mps is 93,141.
93,141 (miles/sec) x 5 (sec) = 465,705 miles. **
From these two pieces of information, we can calculate the height of the car (be patient with me here – it might seem like we’re gathering arbitrary pieces of information, but we’re getting to the main revelation soon!) using the Pythagorean theorem.
V12 + h2 = U2. We can manipulate the variables to obtain h2 = U2 – V12.
Substituting in the values we just calculated, we get h2 = (931,410)2 – (465,705)2. After doing the math, we figure out that the height of the car is about 806,624 miles (so don’t try this experiment at home). Now here’s the fun part – we get to see the dynamic nature of time in action.
So let’s switch back to your perspective from within the car. We formulated an experiment based on the idea that the observer notices it takes light 5 seconds to hit the ceiling. If you measure it from within the car, how much time do you think the beam of light will take? Common sense tells us 5 seconds, but common sense fails miserably when it comes to this aspect of special relativity.
We know that Speed = Distance/Time. From this, we get that Time = Distance/Speed. Well we know the distance from you to the ceiling (it’s h because from your perspective, the “light” will simply shine upwards and not at the upside-down V shape). We also know that the speed of light never changes.
Time = 806,624 (miles) / 186,282 (miles/sec).
From this, we obtain a value of 4.33 seconds! Thus, relative to the observer, the very essence of time inside the car has slowed down! However, when you’re sitting inside the car, you won’t notice this at all because every object inside the car with you is experiencing this same “slow-time” state. If you happen to look outside, you would notice that time seems to be moving faster. I encourage you to try this same experiment again, but with higher values for the speed of the car (if you try 0.99C, then you’ll see a drastic difference between the observer’s time and your time).
The principle we just explored above is the reasoning behind time dilation. It goes to show how time itself can be dynamic! However, this is not the only paradox that we see with time. Read the next installment in the “Time” series – The Paradox of Time.
*Don’t confuse this with length contraction. This only occurs (from the perspective of the observer) when you’re moving relative to an observer who isn’t moving. Length contraction will be covered in greater detail in an upcoming article!
**This is simply half the distance of U since we’re cutting the speed-factor by 1/2 – the calculation was done to demonstrate the ideas behind the “magic”.
