Some questions that human beings have grappled with for centuries still manage to boggle us with amusing answers and facts. One concept that has interested all researchers, academicians and science enthusiasts alike is light – its properties, and speed being the most riveting of them all. So, what actually happens as one approaches ‘light-speed’?

Relativity demystifies Light for us

Albert Einstein, amongst various theoretical marvels and practical scientific concepts, also gave us his Theory of Relativity. The theory determines that the laws of physics are the same for all non-accelerating observers. Einstein also proved that the speed of light within a vacuum is the same irrespective of the speed at which an observer travels. This theory of relativity helps us determine the effects experienced at the speed of light and thus will help us answer the question.

Relativity is considered to be the foundation of modern physics and is relevant at energies or speeds approaching the speed of light ‘c’ (numerically 3×10^8 m/second). The numerical value mentioned here reinforces the fact that the speed of light is a constant. Let us consider the commonly used example of two spaceships moving towards each other at speeds 99% that of light. On application of general laws of relative speeds and velocities, it should be inevitable that the astronauts in each ship should see the other ship approaching them at a speed faster than light. However, owing to the constant speed of light, one of the results is that all relative speeds are lower than the actual speed of light. For instance, in this case, the astronauts will see the other spaceship approaching them only at 99.995% of the speed of light.

Length Contraction

Consider yourself travelling in a car moving at 99% of light’s speed. If stationary observers were asked about what they see, they would notice that your vehicle is compressed in length along your direction of motion. Your body would also seem to be massless and flattened. This phenomenon is called Relativistic Length Contraction. It is important to note here that contraction is observed only in the direction of the motion of the objects. As a result of this, there would be no effect on the height of your vehicle for the stationary observers.

Length Contraction is determined by this formula, where

L = The length of the body at a speed v.

L0 = The actual length of the body at rest.

As you approach the speed of light (v -> c), the formula tells us that the length L of the body ends up at zero. Roughly speaking, this is proof enough that it is impossible for us to ever attain lightspeed – we’d cease to exist.

Time Dilation

Another interesting phenomenon that is observed at the speed of light is Time Dilation. For any object approaching the speed of light, time begins to dilate viz. turns slower for the stationary observer. In the previous example, for the people observing you from a stationary frame, your heartbeat, your clocks and every other process will appear slower. Time as a concept itself slows down. If one could actually hit the speed of light i.e. 3×10^8 m/second, time would appear to stop. Here’s a familiar example to drive home the point:

Time dilation works in ways similar to length contraction.

With T(A) configured to be the rate of time dilation, we see that as we approach light speed, the rate of time dilation would stretch to be infinite at c. Time would cease to exist.

Your moment of origin, transmission and the moment at which you reach your destination would all be the same in this case. An inevitable question that springs up is if we can travel back in time if we conquer the speed of light and travel faster than that? According to the same formula, time dilation would turn negative if we were to surpass the speed of light. Does that allow backwards time travel?

Specific and elaborate conditions must be met in order to travel backwards in time (like wormholes perhaps?). More on that, later.

The occurrence of Length Contraction and Time Dilation is not mutually exclusive. In fact, they’re easier to understand if you realize that they must work together for our speed-distance calculations to fall in place. Einstein had realised that a moving object measures shorter in its direction of motion as its velocity increases until, at the speed of light where it disappears. This was captured in the Special Theory of Relativity. The amount of time dilation and length contraction can be calculated using the Lorentz Factor.  The Lorentz Factor (Gamma) is inversely proportional to the ratio of the velocity of the object given by ‘v’ and the speed of light i.e. (v/c). This implies that the relativistic effects increase as the speed of the body approaches ‘c’.

Although time dilation is a significant result of approaching light-speed, there are several other interesting results that follow. One of them is the ‘twin’s effect’ or the twin-paradox. Given an astronaut who has a twin and has returned from a near-light-speed space voyage, he finds his twin who stayed at home, to be much older than himself. This is because the astronaut travelling at relativistic high speeds experienced only a meagre fraction of the time period elapsed on Earth. Now we know how to procrastinate ageing as well, don’t we?

Another noteworthy paradox is the ‘tunnel paradox’. The tunnel paradox is a result of length contraction where in a hypothetical train approaching a tunnel at near-light speed finds the tunnel to be shorter than what it really is. On the other hand, someone standing in the tunnel and watching the approaching train would find the length of the train to be lesser than the actual length.

Will We Ever Attain Lightspeed?

Having read about the effects that would be experienced at speed tending to that of light, we shall revisit the basics and reason out why it is impossible for us to go light-speed. A postulate of the Special Theory of Relativity says that the mass of a body increases as compared to the mass at rest as the body speeds up to relativistic speeds. The mass of the moving object can be obtained by multiplying the mass of the body at rest by the Lorentz factor. This increase in the relativistic mass reduces the effect of every extra unit of energy put into accelerating the object, on the speed of the object. Instead, as the speed of the object increases and starts to approach significant fractions of the speed of light, the portion of energy being spent into making the object more massive gets bigger. Any extra energy would thus be spent in making the object more massive instead of increasing its speed.

The formulae for calculating relativistic mass and mass-energy equivalence will show us that we will need more energy than the total energy content of the universe in order to attain such speeds. In a word – impossible. At least based on our current understanding of physics.

Having said that, it is safe to confidently state that it is impossible for any object with a mass to attain the speed of light. For time travel, we’ll need to look into exotic concepts such as wormholes.

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