The Velocity Conundrum: Why Near-Light Travel Defies Addition

The speed of light is constant in all reference frames. This is a fundamental principle of special relativity, which states that the speed of light is the same for all observers, regardless of their relative velocity. This means that velocities do not simply add together as they do in classical physics. Instead, the relativistic velocity addition formula must be used, which takes into account the relative velocity between two observers, the velocity of an object relative to one observer, and the velocity relative to the other observer. This formula ensures that velocities cannot add up to be greater than the speed of light, as this would violate causality and imply time travel.

The speed of light is not just a speed limit but an intrinsic property of light. Light travels at this speed because it has zero rest mass, and according to special relativity, only particles with zero rest mass may travel at the speed of light. This is why the speed of light cannot be influenced by the velocity of its source.

The speed of light is constant in all reference frames

The speed of light is not augmented or reduced by the motion of its source or observer. For example, if you are in a car moving at night, and you flash your lights at another car travelling in the opposite direction, the total speed of the electromagnetic disturbance is the same, and is not affected by your motion.

The only thing that affects the speed of light is the refractive index of the medium through which it moves. For empty space, this number is 1.0000000, and gives you the maximum possible speed of light. In glass, it is 1.3333 times smaller.

The speed of light is just the most obvious example of the covariance of all the physical laws. The physical laws do not change even when gravity produces different rates of time or motion gives different frames of reference. For example, energy, force, inertia, mass, etc. all must undergo coordinated changes in order to keep the physical laws (including the constant speed of light) the same in all frames of reference and all gravitational potentials.

The speed of light in a vacuum is, of course, not the speed in an imaginary absolutely empty space. There is no such space in the physical world. But there is a physical vacuum in which the speed of light can be a universal constant only if the motion of a photon is a sequence of acts of absorption and re-emission.

Velocities don't add directly when things move close to the speed of light

The relativistic velocity addition formula is:

> v' = (u + v) / (1 + uv/c^2)

Where v' is the final velocity, u is the velocity of an object relative to one observer, and v is the relative velocity between two observers.

This formula is the correct formula that applies for velocity addition in general. As you can see, if uv/c^2 is negligible, then this formula is approximately equal to the classical one. But whenever uv/c^2 is big enough to notice, this is the correct formula, even if neither u nor v is equal to c.

In classical physics, velocities add as vectors. For example, if a girl is riding in a sled at a speed of 1.0 m/s relative to an observer and she throws a snowball first forward, then backward at a speed of 1.5 m/s relative to the sled, the velocity of the snowball relative to the observer is 2.5 m/s when thrown forward, and -0.5 m/s when thrown backward.

However, this classical addition of velocities does not apply to light. Imagine a car traveling at night with its headlights on. If classical velocity addition applied to light, then the light from the headlights would approach an observer on the sidewalk at a speed of u = v + c, where v is the velocity of the car. But we know that light will move away from the car at speed c relative to the driver and towards the observer on the sidewalk at speed c too.

Therefore, light is either an exception, or the classical velocity addition formula only works at low velocities. It turns out that the latter is the case.

The speed of light is always constant and nothing can travel faster than it. Velocities cannot add to be greater than the speed of light.

For example, suppose a spaceship is heading towards Earth at half the speed of light and sends a signal on a laser beam of light. Given that the light leaves the ship at speed c as observed from the ship, what is the speed at which it approaches Earth?

Using the relativistic velocity addition formula, we find that the speed of light approaching Earth is also c.

As another example, suppose the spaceship in the previous example shoots a canister at a speed of 0.750c directly towards Earth. What velocity will an Earth-bound observer see the canister at?

Using the relativistic velocity addition formula, we find that the velocity of the canister relative to Earth is 0.909c.

Now, suppose the canister is shot directly away from Earth instead.

Using the relativzjih velocity addition formula, we find that the velocity of the canister relative to Earth is -0.400c, which means it is heading towards Earth.

As you can see, relativistic velocities do not add as simply as they do classically. In the first part, the canister approaches Earth faster, but not at the simple sum of 1.250c. The total velocity is less than you would get classically. And in the second part, the canister moves away from Earth at a velocity of -0.400c, which is faster than the -0.250c you would expect classically. The velocities are not even symmetric.

In conclusion, velocities don't add directly when things move close to the speed of light. Instead, the relativistic velocity addition formula must be used.

The speed of light is not about light, it's the speed of causality

The speed of light is not about light; it's the speed of causality.

The speed of light is a constant, and nothing can travel faster than it. This is because the speed of light is tied to causality. If something could travel faster than the speed of light, it would violate causality and imply time travel.

For example, imagine a speeding fire truck coming towards you with its warning lights on. In between you and the truck is a slow-moving car that is on a collision course with the fire truck. The driver of the truck swerves to miss the car. If the speed of the truck's lights added to the speed of the truck, you would see the lights swerve before the car had entered the intersection. This would mean that you would see the effect (the swerving) before the cause (the car entering the intersection).

In the context of special relativity, velocities do not add up as in classical mechanics. The classical velocity addition formula does not apply to light or anything else. The relativistic velocity addition formula is:

> v' = (u + v) / (1 + uv/c^2)

Where v is the relative velocity between two observers, u is the velocity of an object relative to one observer, and u' is the velocity relative to the other observer.

The speed of light is always constant. Light will move away from a car at speed c relative to the driver of the car, and light will move towards an observer on the sidewalk at speed c, too.

The second postulate of relativity says that classical velocity addition does not apply to light. If it did, then the light from a car's headlights would approach an observer on the sidewalk at speed u = v + c. However, we know that light will move towards the observer on the sidewalk at speed c, and this speed is independent of the relative motion of the source and observer.

The speed of light is about more than just light—it's about the speed limit of the universe and the speed of causality.

Light doesn't exist until it's emitted

The second postulate of relativity states that the classical velocity addition formula does not apply to light. This means that light does not exist until it is emitted. Light travels at a constant speed of 299,792,458 m/s (approximately 186,282.397 miles per hour) in a vacuum. This speed is the same for all observers, regardless of their relative velocity.

In classical physics, velocities add like regular numbers in one-dimensional motion. For example, if a girl on a sled moving at 1.0 m/s throws a snowball forward at 1.5 m/s relative to the sled, the velocity of the snowball relative to an observer on the ground will be 2.5 m/s. However, this classical velocity addition formula does not hold for light.

Imagine a car traveling at night with its headlights on. If classical velocity addition applied to light, then the light from the headlights would approach an observer on the sidewalk at a speed equal to the sum of the car's velocity and the speed of light. However, this is not the case. Light will always move away from the car at the speed of light relative to the driver and towards the observer on the sidewalk at the speed of light. This is because light always travels at the speed of light, regardless of the relative motion of its source and observer.

The correct formula for one-dimensional relativistic velocity addition is:

> u = (v + u') / (1 + (vu' / c^2)>

Where v is the relative velocity between two observers, u is the velocity of an object relative to one observer, and u' is the velocity relative to the other observer. This formula ensures that velocities cannot add up to be greater than the speed of light.

To illustrate this, consider a spaceship heading towards Earth at half the speed of light. If the spaceship sends a signal to Earth using a laser beam, the speed of the light beam as it approaches Earth will still be the speed of light, even though the spaceship is moving at relativistic speeds. This is because the speed of light is independent of the relative motion of its source and observer.

In summary, light does not exist at a specific velocity until it is emitted from its source. Once emitted, it always travels at the speed of light, regardless of the velocity of its source or observer. This is a fundamental principle of special relativity and has far-reaching implications in physics and our understanding of the universe.

The speed of light is an intrinsic property of light

The speed of light is a fundamental physical constant. It is independent of the motion of the source of light or the inertial frame of reference of the observer. This means that all observers, regardless of their relative motion, will measure the speed of light to be exactly the same.

The speed of light in a vacuum is exactly 299,792,458 metres per second (approximately 300,000 kilometres per second, 186,000 miles per second, or 671 million miles per hour). This is denoted by a lowercase c and is used as a way to define the metre.

The speed at which light travels through transparent materials, such as glass or air, is less than c. The speed of light in air is about 90 kilometres per second slower than c, and the speed of light in glass is about two-thirds of c.

The finite speed of light has many practical effects. For example, much of the starlight we see on Earth is from the distant past, allowing us to study the history of the universe. The speed of light also imposes a limit on how quickly data can be sent between computer processors.

The speed of light is also of great theoretical importance. Einstein's theory of special relativity explores the consequences of the invariance of c. One consequence is that c is the speed at which all massless particles and waves, including light, must travel in a vacuum. Another is that the energy of an object with rest mass m travelling at a speed v is given by γmc^2, where γ is the Lorentz factor. As v approaches c, γ approaches infinity, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light.

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