The speed of light is often considered the ultimate speed limit in the universe, as established by Einstein’s special theory of relativity. According to this theory, nothing can move through space faster than light. Despite this, many people have come up with creative ideas to try and surpass this cosmic speed limit.
One interesting example involves shining a laser at the moon. If you can move the laser beam across the moon’s surface in less than a hundredth of a second, the spot of light seems to move faster than the speed of light. However, this is just an illusion. The individual photons from the laser still travel to the moon at the speed of light; they just land side by side very quickly, making it look like the spot is moving faster. Importantly, this method cannot send information faster than light because no actual object is moving that fast.
Another idea involves using a long, rigid stick. The thought is that if you flick your wrist, the tip of the stick could move across the moon’s surface faster than light. Unfortunately, this doesn’t work. As shown in the slinky drop experiment, the fastest a force can travel through an object is the speed of sound. Each atom in the stick must bump into its neighbor to pass on the force, which is a slow process. So, the tip of the stick wouldn’t move at all, let alone faster than the speed of light.
A more advanced idea involves designing a futuristic engine that spins at over 10,000 RPM while using two long tethers made from carbon nanotubes. The idea is that the end of the tether could eventually reach the speed of light. However, several problems arise with this concept.
Any object moving in a circle needs centripetal force to stay on that path. This force depends on the square of the object’s speed. For example, if a one-gram mass were to rotate at 99% of the speed of light, the required centripetal force would be equivalent to the weight of $6,000$ African elephants. While carbon nanotubes are very strong, the tether would need to be thicker to handle the extra force, making it impractical.
As an object speeds up, its inertia increases, meaning it needs even more force to keep accelerating. To push a one-gram mass to 99% of the speed of light would require seven times the previously calculated force. This means the tether would need to be even thicker, adding to the problem.
Trying to accelerate the tip of the tether to the speed of light presents a huge challenge. The object’s inertia increases so much that it would need an infinite amount of energy to reach the speed of light.
Even if we could build an incredibly powerful motor and use a material stronger than carbon nanotubes, there’s one last hurdle: the tether’s structure is held together by electromagnetic interactions, which are carried by photons. Since photons themselves travel at the speed of light, no matter how advanced the technology, the tether cannot exceed the speed of light.
While nothing can travel through space faster than light, there are situations in the universe where objects seem to be moving away faster than light. Some distant galaxies are moving away from us so quickly that their light will never reach us. This doesn’t break Einstein’s theory of relativity because these galaxies aren’t moving through space faster than light; instead, the space between us and them is expanding.
In summary, the speed of light remains the ultimate speed limit in the universe. Various ideas to exceed this limit, whether through lasers, sticks, or theoretical engines, ultimately face insurmountable challenges based on the laws of physics. The quest to understand and explore the boundaries of our universe continues, but the speed of light stands firm as a fundamental principle.
Try to recreate the laser illusion by using a laser pointer and a distant wall. Move the laser across the wall quickly and observe how the spot seems to move faster than the speed of light. Discuss why this is an illusion and how it relates to the concept of information transfer.
Use a long stick or a slinky to demonstrate how force travels through a medium. Flick one end and observe the delay before the other end moves. Discuss how this relates to the speed of sound and why it prevents the stick from moving faster than light.
Calculate the centripetal force required to spin a one-gram mass at 99% of the speed of light. Use the formula $$F = frac{mv^2}{r}$$ and discuss the implications of needing the force equivalent to the weight of $6,000$ African elephants. Explore why this makes the theoretical space age engine impractical.
Explore the concept of increasing inertia as an object approaches the speed of light. Calculate the energy required to accelerate a one-gram mass to 99% of the speed of light using $$E = gamma mc^2$$, where $$gamma = frac{1}{sqrt{1 – frac{v^2}{c^2}}}$$. Discuss why infinite energy is needed to reach the speed of light.
Simulate cosmic expansion using a balloon and small stickers to represent galaxies. Inflate the balloon and observe how the stickers move apart. Discuss how this demonstrates the concept of space expanding and why it doesn’t violate the speed of light limit.
Speed – The rate at which an object covers distance, typically measured in meters per second (m/s). – The speed of light in a vacuum is approximately $3 times 10^8 text{ m/s}$.
Light – Electromagnetic radiation that is visible to the human eye, typically with wavelengths between 400 and 700 nanometers. – When light passes through a prism, it is dispersed into its constituent colors.
Photons – Elementary particles that are the quantum of the electromagnetic field, including electromagnetic radiation such as light. – Photons have no mass and travel at the speed of light.
Inertia – The tendency of an object to resist changes in its state of motion, described by Newton’s first law of motion. – Due to inertia, a spacecraft will continue to move in a straight line at constant speed unless acted upon by an external force.
Force – An interaction that changes the motion of an object, typically measured in newtons (N). – According to Newton’s second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration: $F = ma$.
Energy – The capacity to do work or produce change, often measured in joules (J). – The total energy of an isolated system remains constant, as stated by the law of conservation of energy.
Expansion – The increase in distance between objects in the universe over time, as described by the Big Bang theory. – The expansion of the universe is evidenced by the redshift of light from distant galaxies.
Galaxies – Massive systems consisting of stars, stellar remnants, interstellar gas, dust, and dark matter, bound together by gravity. – The Milky Way and Andromeda are two of the largest galaxies in our local group.
Relativity – A theory formulated by Albert Einstein that describes the laws of physics in the presence of gravitational fields and high velocities. – According to the theory of relativity, time dilation occurs when an object approaches the speed of light.
Universe – The totality of space, time, matter, and energy that exists. – The observable universe is estimated to be about 93 billion light-years in diameter.
