Have you ever pondered the sheer velocity of light? It’s a common curiosity, often sparking questions like:
- Why is the speed of light, often symbolized as c, so unbelievably fast?
- In Einstein’s renowned equation, E=mc2, why does c2, a number of astronomical magnitude, feature so prominently?
It’s undeniable that light appears incredibly swift. In a mere billionth of a second, light can zip from your smartphone to your eyes. In just one and a half seconds, it covers the vast distance between Earth and the Moon.
Furthermore, the energy locked within your body is comparable to the force of Earth’s most cataclysmic volcanic eruptions and the most devastating nuclear explosions ever detonated – magnitudes greater than the energy you expend walking across a room or lifting a piece of luggage.
What principles of physics, chemistry, and biology underpin these perplexing aspects of reality? The answer is both captivating and rooted in particle physics and the fundamental structure of matter. However, it’s a layered explanation. Let’s embark on this journey step-by-step to unravel this fascinating concept.
Clarifying the Core Questions
To begin, let’s refine the initial questions for greater precision. When we refer to “c,” we’re specifically talking about the speed of light in the vacuum of space. Light does slow down when traveling through mediums like air, water, or glass. Therefore, question 1 becomes:
- Why is the speed of light in empty space, denoted as c, so astonishingly fast?
Question 2 also contains two distinct parts: a qualitative aspect and a quantitative one:
2a. In Einstein’s famous equation linking energy (E) and mass (m), why is such an enormous number involved?
2b. Why is this enormous number specifically equal to the speed of light (in empty space) squared, or c2?
We will discover that questions 1 and 2a are essentially two sides of the same coin, sharing a common answer. However, even these refined questions can be improved to truly understand the underlying physics.
The terms “fast” and “enormous” are inherently relative. A human can outrun a snail but is no match for a cheetah. Compared to a bacterium, a human is gigantic, but insignificant next to a star. To gain a deeper understanding, we need to rephrase these questions using relative terms. This shift in perspective is key to unlocking the answers.
- Why is the speed of light in empty space so much faster than the speeds we humans typically encounter in our daily lives?
2a. Why is the energy contained within the mass of everyday objects (as described by E=mc2) so vastly greater than the energy involved in our everyday experiences?
Adopting a Cosmic Perspective
Consider this perspective: “It’s widely known that light has a characteristic speed, known as c by scientists; this also represents the speed at which each individual photon travels. Centuries ago, scientists determined c to be approximately 186,000 miles per second. This is undeniably fast – our quickest spacecraft don’t even come close. To put it in perspective, even if I kept my last car for fifteen years, I drove it less than 186,000 miles. At speed c, you could circle the Earth in the blink of an eye and traverse the distance from your head to your toes in mere billionths of a second.
“And yet, c is also slow. Light takes over a second to reach the Moon, more than eight minutes to reach the Sun, and over four years to reach the nearest star beyond our Sun. If we were to launch a robotic probe at near light speed to explore the Milky Way, it would only be able to visit a few dozen stars within our lifetimes.
“From our limited human scale, light seems incredibly fast. However, the universe is immense, and from a cosmic viewpoint, light crawls at a snail’s pace.”
This highlights a crucial point: we are not the center of the universe, nor are our perspectives inherently privileged. There is nothing inherently special about Earth’s size, mass, or temperature, and certainly nothing uniquely significant about humans or even mammals. The cosmos operates independently of the scales of our everyday lives. Our human-centric viewpoints are not the only valid ones. We must recognize other perspectives, ones where the speed of light in a vacuum might be considered slow and where the energy contained within a human body is infinitesimally small.
To make our inquiries truly meaningful, we must step back and consider not just how we perceive the cosmos, but how the cosmos might perceive us. From the universe’s perspective, the questions become:
- Why are humans so remarkably slow compared to the natural speeds prevalent in the cosmos?
2a. Why are the energies involved in typical human activities so incredibly tiny compared to the natural energy scales one would expect from objects of human size?
To understand the universe’s answers, we must first define what “natural speed” and “natural energy” mean from a cosmic perspective. Let’s begin by exploring “natural speed.”
Defining Natural Speed: The Cosmic Speed Limit
It’s more accurate to refer to c as the “cosmic speed limit” rather than simply “the speed of light,” as the latter can be misleading. As mentioned, light travels slower in materials, while c itself remains constant, regardless of the medium. Furthermore, c isn’t solely the speed of light in a vacuum; it’s also the speed of gravitational waves. Most importantly, c is the ultimate speed limit for the relative motion of any physical object in the universe. This is why “cosmic speed limit” is a more descriptive term – it emphasizes that **c is a fundamental property of the universe itself, not just a characteristic of light.**
This cosmic speed limit appears to be uniform throughout the observable universe, a conclusion supported by observations of incredibly distant and ancient celestial objects. This universality makes it a fundamental constant that any intelligent civilization in the cosmos could measure. No other speed possesses this fixed and reliable nature. Consider the speed of sound, for instance. It varies with temperature and the medium it travels through, differing drastically in the atmospheres and oceans of other planets. It could never serve as a universal cosmic standard of speed.
It’s important to note that, similar to the speed of sound (though for different reasons), the speed of light does change depending on the material and temperature it travels through. However, the cosmic speed limit, **c, remains constant.** This distinction has observable consequences, such as Cherenkov radiation, which particle physicists utilize in experiments.
Nor should we consider human speeds, around 1 meter per second (roughly 2.2 miles per hour), as “normal.” If we were peregrine falcons or sloths, our perception of “normal” speed would be vastly different. Moreover, our standard units of measurement, meters for length and seconds for time, are arbitrary human constructs. A blue whale, many meters long, is considered enormous by human standards. However, a sufficiently intelligent whale species might develop a unit of length, perhaps a “whaler,” comparable to the size of a whale. By that standard, humans would be diminutive. Similarly, a sequoia tree might find “hour” a more natural unit of time than “second.”
Therefore, defining distances, times, and speeds, and judging what constitutes “large” or “small,” is species-dependent, planet-dependent, and perspective-dependent unless we ground our measurements in universal cosmic constants. When it comes to speed, the cosmos offers a clear perspective:
*”c is the natural speed, as it represents the maximum rate at which information can propagate from one point to another. No two objects can move faster than c relative to each other. No information can be transmitted faster. No other speed exhibits comparable stability or fundamental importance. Thus, typical objects in the universe should generally interact at speeds that are a reasonable fraction of c.”*
“But, WOW… you Earth-creatures are astonishingly, ridiculously slow! Look at how you crawl across your planet!”
The Emergence of c2 in E=mc2
Putting aside the question of whether c is “large,” “small,” or “normal,” we now address why c2 naturally appears in the energy-mass relation, E=mc2. This explanation aligns with the principles of dimensional analysis, a crucial tool for physicists.
Einstein’s revolutionary insight was that even a stationary object possesses intrinsic energy. He proposed that the amount of this energy is reflected in its mass – specifically its “rest mass” m, the mass measured by an observer at rest relative to the object.
Any equation relating energy and mass must involve the square of a speed (or the product of two speeds). This principle is already evident in classical physics. In pre-Einsteinian physics, the kinetic energy of a moving object was understood to be:
*Newtonian Kinetic Energy = 1/2 mv2
Replacing v2 with v3 or v99 would render the equation meaningless because the units on both sides would no longer match. It would be akin to equating the height of a tree to the color of its leaves – fundamentally different quantities cannot be equated.
Now, consider Einstein’s assertion that even stationary objects possess energy. The corresponding formula for this rest energy cannot include v, as a stationary object has v=0. Instead, some other speed or speeds must be involved.
Why should this speed be c? It would be illogical for an object’s energy-mass relation to depend on the speed of some other object. Imagine if your body’s energy were defined as your mass multiplied by the square of the speed of a distant star. Not only would this be bizarre and inconsistent with basic principles of relativity, but it would also be meaningless before that star even existed.
No, the relationship between energy and mass for stationary objects must be universal – a cosmic principle. Therefore, it can only depend on speeds that are intrinsic properties of the universe itself. As far as we know, the universe possesses only one such fundamental speed: c. In fact, it can be demonstrated that Einstein’s theory of relativity would be inconsistent if there were more than one fundamental speed. Consequently, any valid energy-mass relation must take the form: E = #mc2, where # represents a dimensionless numerical factor that needs to be determined. No other equation could logically make sense within the framework of the universe as we understand it.
Einstein recognized this necessity, as did his contemporaries. The fact that the dimensionless factor # happens to be exactly 1 is partly a historical quirk of definitions and partly a consequence of Einstein’s brilliant deduction.
Regarding whether the correct formula should be E = 1/2 mc2, E = 2 mc2, or E = 4/3 mc2, physicists benefited from a degree of historical luck. The definition of mass originated in Newton’s era, and energy was subsequently defined in a manner that, within pre-Einsteinian physics, the kinetic energy of a moving object is 1/2 mv2. There were sound reasons for these definitions, directly linked to the definition of momentum as mv (mass times velocity), without any numerical prefactor. Momentum’s definition, in turn, was motivated by Newton’s equation F=ma, which defines mass. Had Newton introduced a factor of 1/2 in his equation, the factor in Einstein’s formula would also have been different. However, with the definitions established by Newton and his successors, the equation that accurately describes nature is E=mc2, with a dimensionless factor of 1. This is a fortunate historical coincidence; any alteration in the definitions of energy or mass would have impacted the elegant simplicity of Einstein’s formula.
So, why was Einstein the one to realize that the numerical factor is 1, given the existing definitions, when his colleagues had been so close for decades? He posed the right question, while his contemporaries overlooked it.
Thus, question 2b is answered: in our universe, the only logically consistent relationship between E and m for a stationary object is E=#mc2, where # is a dimensionless factor that depends on the precise cultural definitions of energy and mass, but which, given our historical definitions, happens to be 1.
Natural Energy Scales from a Cosmic Viewpoint
From the universe’s perspective:
*”The natural energy associated with an object of rest mass m is on the order of mc2. When the object is stationary, its rest energy is precisely mc2, and when it moves, its total energy increases. If it moves at a ‘natural’ speed – a moderate fraction of c – then, as we know from pre-Einsteinian physics, its kinetic energy will be approximately 1/2 mv2, which is a substantial fraction of mc2. In essence, typical objects in the universe are expected to possess internal energy mc2 and kinetic energy that is also not drastically different from mc2.”*
“But you Earth-creatures… you behave like timid mice, keeping your activities at a whisper and a tiptoe! Are you trying to remain unnoticed? Are you cowards, afraid of any real excitement?”
The answer to the last question is, perhaps surprisingly, “yes, in a way.” But that’s a topic for further exploration.
The Intertwined Nature of Energy and Speed Questions
We’ve now touched upon why the energy question (2a) is fundamentally linked to the speed question (1). The reason the energy stored within ordinary objects appears so vast from a human perspective is directly tied to the fact that c, the speed of light (in a vacuum), seems so extraordinarily fast to us.
To reiterate:
- Einstein postulated (and experiments soon confirmed) that a stationary object possesses internal energy mc2, where m is its rest mass.
- For slow-moving objects like ourselves, where v is much smaller than c, we can use Newtonian approximations to Einstein’s equations. In this approximation, an object with rest mass m moving at speed v possesses kinetic energy 1/2 mv2.
This implies that the ratio of an object’s kinetic energy, readily observable in everyday life, to its internal energy, typically hidden from our direct experience, is:
*(Kinetic Energy) / (Internal Energy) = (1/2 mv2) / (mc2) = 1/2 (v/c)2
This ratio becomes exceedingly small when (v/c) is itself very small. Therefore, if we can understand why v is so much smaller than c in our daily lives, we will simultaneously understand why the energies involved in ordinary human activities are so minuscule compared to the internal energies of the objects around us.
In the next exploration of this topic, we will delve into how particle physics itself dictates that the speeds of our everyday lives must be slow relative to the cosmic speed limit.
