the SPEED OF LIGHT and

its significance

by Sky Lee

1. The Universal Threshold

Would you believe me if I told you that the fastest speed in the vast universe is 299 792 458 ms-1, the speed of light, [1] that if something goes faster than that threshold, the universe breaks and reality collapses? The fact that the universe has a speed limit is extremely counterintuitive; it’s hard to picture something travelling at the speed of light and it’s even harder to grasp why nothing can go over that specific limit.

2. Origins

1905 was Einstein’s Annus Mirabilis, his Year of Miracles, [2] in which he published four papers: “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”, “On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat”, “On the Electrodynamics of Moving Bodies”, and “Does the Inertia of a Body Depend Upon Its Energy Content?”. These four papers have made a significant impact on the physics community, giving insights in the Quantum Theory of Light and the existence of atoms and molecules. [3] Out of the four papers, “On the Electrodynamics of Moving Bodies” is probably the one that stands out most. Why, you may ask, because it includes the most famous equation in the world, E=mc2, the embodiment of the renowned Special Relativity and is the key to understanding how this universe operates.

3. The Speed of Light as an Invariant

Einstein’s Special Relativity shows the connection between some of the most significant quantities in the universe, mass, time, and space without the complication of gravity (relativity considering gravity is known as General Relativity). [4] Special relativity is based on the fact that the speed of light is a constant for all observers when gravity is not taken into consideration (curved light gets slowed down when it is not observed from one specific local reference frame according to the Shapiro Time Delay, assuming the presence of gravity) (fig A). [5] The constant c was calculated by Scottish physicist James Clerk Maxwell with the following equation (fig B).

4. Spaceship and Planet Analogy [6]

Consider a spaceship moving relative to a hypothetically stationary planet (fig. C), according to Einstein’s First Postulate of Special Relativity, the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference [7].Thus, in this situation there is no way we can determine whether the planet is stationary, and the plane is moving or vice versa. Now imagine a ball being thrown across in the spaceship, the relative speed of the ball as observed from the planet, according to the Galilean Transformation, is the speed of impulsion of the ball combined with the speed of the spaceship itself. On the other hand, the relative speed of the ball as observed locally in the spaceship is just the speed of impulsion of the ball. With that said, the relative speed of the ball is lower if observed locally in the spaceship.

Instead of a ball being thrown in the spaceship, imagine a beam of light being shone across in the spaceship (fig. D). Intuitively, we would consider the beam of light as a travelling particle, just like the ball, and thus, assume that the relative speed of the beam of light is lower if observed locally in the spaceship. Yet, that contradicts Maxwell’s calculations of a constant speed of light c, for every observer, when gravity is not taken into consideration. So, is the speed of light c, still a constant? If it is, then classical Newtonian mechanics would simply be paradoxical. This is where special relativity comes in, a scientific principle which accommodates Maxwell’s constant speed of light and the validity of classical mechanics.

With the fact that the speed of light is constant in mind, we can move on to understanding Special Relativity with the ‘spaceship and planet’ analogy.

There are so many reasons why nothing can go faster than the speed of light. With that said, there is only one particular physical phenomenon that explains why only massless objects like photons can travel at the speed of light, that is Relativistic Kinetic Energy.

Rest mass energy is the energy (fig. E) that all matter possesses (i.e., as long as it has mass and takes up space), be it matter that is stationary or matter that has motion. Relativistic energy (fig. F) is the energy that every moving object possesses. Relativistic kinetic energy (fig. G) is the energy every object possesses strictly due to their motion (i.e., the object’s rest mass energy is excluded). What is the significance of that, you may ask. As seen in the relativistic kinetic energy equation, as the speed of the object v increases, v2 also increases, as v approaches c, the Lorentz Factor, γ tends to infinity. This implies that if an object has to travel at the speed of light, the required energy tends to infinity (fig. I). As it is impossible to supply an infinite amount of energy to anything, it is simply unfeasible for matter to travel at the speed of light.

6. Side Effect of Travelling at c: Time Dilation

Imagine a person travelling near the speed of light, Alice, and a stationary person. They experience time differently according to time dilation in Einstein’s Special Relativity.

If Alice is travelling in a spaceship at the speed of 0.9c, 90% the speed of light, then it would take her 1 second to travel a distance of 0.9c metres (ignoring the effects of relativistic kinetic energy). In this case, T, the time in Alice’s frame of reference is 1 second. Yet to stationary observer Bob, it takes Alice 2.29 seconds to travel a distance of 0.9c metres according to the Time Dilation Equation (fig. J).

What is more fascinating is that Alice or Bob could technically be the stationary observer in this case according to Einstein’s First Postulate of Special Relativity. In Alice’s frame of reference, she is stationary and Bob is moving at 0.9c, while in Bob’s frame of reference, he is stationary and Alice is moving at 0.9c. This implies that to Bob, time flows slower in his frame than in Alice’s frame. While to Alice, time flows slower in her frame than in Bob’s frame.

7. Breaking Causality and the Emergence of Time Paradoxes, a Result of Time Dilation

Cause has to come before effect in Physics. Person A would never receive a message before Person B sends it to him, your table never gets wet before you spill the water, and a person’s head wouldn’t explode before a bullet hits him. Causality governs how the Universe operates, it is that one rule which cannot be broken. Imagine your friend, Jonathan, receiving your text message before you’ve even pressed the ‘send’ button, that’s crazy!

If an object travels faster than the speed of light, causality would be broken, or in other words, the Universe goes nuts. There is not much mathematical proof on how going faster than the speed of light breaks causality, a simple analogy and example can perfectly illustrate the correlation.

Before we move on to the example, we first have to understand Spacetime Diagrams. For every object, the horizontal line represents the change in space in its frame of reference while the vertical line represents the change of time in its frame of reference. For a stationary object, a vertical line represents its activity in spacetime. fig. K Spacetime Diagram [10]

Continuing with the example of Alice and Bob [11]. Imagine in a new scenario, Alice standing stationary on planet Earth and Bob moving at 0.87c away from Earth relative to her. In Alice’s frame of reference, she can be represented by a vertical line while Bob can be represented by a line of slope magnitude greater than 1. In Bob’s frame of reference, he can be represented by a vertical line while Alice can be represented by a line of slope magnitude greater than 1. Again, Einstein’s First Postulate of Special Relativity tells us that Alice can be stationary in her own frame of reference (fig. L) while Bob can also be stationary in his (fig. M). According to the Time Dilation Equation, in Alice’s frame of reference, 2 seconds for her is 1 second for Bob while in Bob’s frame of reference, 2 seconds for him is 1 second for Alice.

Enter FTL, Faster Than Light. Imagine there was something much faster than light, something that is instantaneous. An object travelling instantaneously can be represented as a horizontal line in spacetime diagram as an object travels an infinite distance in space without travelling in time. Imagine Alice sending an instantaneous message to Bob. If she sends the message to Bob, at 4 seconds on her clock (i.e. in her frame of reference), then Bob would receive her message at 2 seconds on his clock, if we consider this situation in Alice’s frame of reference (fig. N). Things start to get weird when we look at the message from Bob’s frame of reference, we can see that the message is sent from 4 seconds on Alice’s clock to 2 seconds on Bob’s clock, in other words, the message is sent from 8 second on Bob’s clock to 2 seconds on the same clock, the message has travelled back in time (represented by a negative slope) (fig. O) in Bob’s frame of reference! Now imagine Bob taking two seconds to read the message Alice sent him, and at 4 seconds on his clock, decides to send an instantaneous reply back to Alice. She would receive it at 2 seconds on her clock, meaning that she received a reply from Bob even before she sent the message (i.e. at 4 seconds on her clock in her frame of reference). Causality has been broken (fig. P) because of special relativity and the type of messaging system that can travel faster than the speed of light, in this example, at instantaneous speed.

8. Insights

The speed of light is so much more than just a number used in calculations in physics tests, it is a value that governs how the universe operates and ensures effect comes after cause. It explains why you will never get a reply before you send a message, as there is nothing that can travel faster than the speed of light in this universe. While popular movies these days have explored the ideas of time travelling and travelling at the speed of light, the current physical laws remain unchanged, telling us concrete and undeniable facts about the universe: travelling quicker than the speed of light just isn’t feasible. ‘First comes the Physics, then comes the Engineering’, should humans endeavour on travelling at the speed of light, the fundamental laws of physics established by the great scientist, Einstein will have to be broken and overthrown.

9. Bibliography

[1] Wikipedia, “Speed of light”, accessed 2022 November 9, https://en.wikipedia.org/wiki/Speed_of_light

[2] npr, Richard Harris, “Albert Einstein’s Year of Miracles: Light Theory”, 2005, March 17, accessed 2022 November 9, https://www.npr. org/2005/03/17/4538324/albert-einsteins-year-of-miracles-light-theory#:~:text=Scientists%20call%201905%20Albert%20Einstein’s,the%20 famous%20equation%20E%3Dmc%C2%B2.

[3] Wikipedia, “Annus Mirabilis papers”, accessed 2022 November 9, https://en.wikipedia.org/wiki/Annus_mirabilis_papers#:~:text=The%20 annus%20mirabilis%20papers%20(from,the%20foundation%20of%20modern%20physics.

[4] Space, Vicky Stein, “Einstein’s Theory of Special Relativity”, 2021 September 21, accessed 2022 November 9, https://www.space. com/36273-theory-special-relativity.html#:~:text=Special%20relativity%20is%20an%20explanation,equation%20E%20%3D%20mc%5E2.

[5] Universerio@YouTube, “What is the true meaning of constant speed of light? Why is the Speed of Light Constant?”, 2022 August 22, accessed 2022 November 9, https://youtu.be/hvMAT1xeraM

[6] ScienceClic English@YouTube, “Special Relativity”, 2019 September 10, accessed 2022 November 9, https://www.youtube.com/watch?v=uTyAI1LbdgA

[7] Douglas College Physics 1207, 13.1 Einstein’s Postulates, no date, accessed 2022 November 9, https://pressbooks.bccampus.ca/introductorygeneralphysics2phys1207opticsfirst/chapter/28-1-einsteins-postulates/#:~:text=The%20first%20postulate%20of%20special,relative%20motion%20 of%20the%20source.

[8] For the Love of Physics@YouTube, “Relativistic Kinetic Energy | Answer to why nothing can travel faster than the speed of light?”, 2021 July 3, accessed 2022 November 9, https://www.youtube.com/watch?v=TwKSGVKfIXw

[9] LibreTexts Physics, “Relativistic Quantities”, 2020 November 6, accessed 2022 November 10, https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Physics_(Boundless)/27%3A__Special_Relativity/27.3%3A_Relativistic_Quantities

[10] Wikipedia, “Spacetime Diagram”, accessed 2022 November 20, https://en.wikipedia.org/wiki/Spacetime_diagram

[11] Arvin Ash@YouTube, “How Faster than Light Speed Breaks CAUSALITY and creates Paradoxes”, 2021 June 25, accessed 2022 November 20, https://www.youtube.com/watch?v=mTf4eqdQXpA&t=744s