"I don't have any special talents, but I like to investigate the root of the problem." ——Einstein

The problem I want to talk about today is A question that is easily confused by everyone is the speed of light! Is there any phenomenon in the universe faster than the speed of light? If so, why don't they violate the theory of relativity? What does relativity really prohibit?

The speed of light c is an absolute physical constant. No matter where we are in the universe or how fast we are moving relative to other objects, the speed of light in a vacuum is always the same. This means that nothing can travel faster than the speed of light, but the real situation is not that simple. It turns out that there are several ways to make an object travel faster than the speed of light!

Superluminal speed in the medium

We know that the speed of light is constant only for light in vacuum. When light passes through a material, its effective speed is reduced. Usually affected by the refractive index n of the medium, where the effective speed of light is c/n (n is always greater than 1). For example, when light travels through water, its speed is about 0.75c. Because of this, it is possible for particles to "break the barrier of light" in matter while still moving at speeds below c.

For example, in a nuclear reactor, electrons are fired at close to the speed of light. As these electrons travel through the coolant (water) surrounding the reactor, they travel faster than light can travel through the water, breaking the light barrier. We know that a sonic boom occurs when an airplane flies faster than the speed of sound, which is caused by a shock wave in the air. A similar effect occurs when electrons break through a light barrier. The electrons create an optical "shock wave" called Cherenkov radiation, which makes nuclear reactors glow faintly blue.

The random path of photons through the sun

Photons travel extremely slowly in the sun

Another phenomenon that travels faster than light in a medium is sound waves in stars. In the sun (as in any star), light is produced in its core by nuclear fusion, travels at the speed of light, and takes only 2 to 3 seconds to reach the sun's surface. But the Sun's interior is filled with such a dense concentration of charged particles that scatter photons so that they can't simply travel in a straight line. On average, a photon in the sun's coreIt travels less than a centimeter before colliding with an ion. The photons are then scattered in random directions. Now imagine a photon trying to leave the sun, but being randomly bounced every centimeter it travels. The random walk of photons in the Sun means that light actually takes 20,000 to 150,000 years to travel from the Sun's core to its surface.

But sound waves travel differently. They are pressure waves that transfer energy through the material rather than the material itself. Therefore, they are not hindered by core ions. Sound waves can travel through the sun at thousands of kilometers per second, and they vibrate the sun as a whole. The study of these sonic vibrations is called helioseismology, and the study of other stars is called asteroseismology. By analyzing these sounds, we can determine things like the density and pressure inside the sun.

But neither phenomenon is actually faster than the speed of light in a vacuum. So is there anything faster than the speed of light in a vacuum? This is also possible to some extent thanks to general relativity.

Space expands faster than the speed of light

Since the 1920s, we have known that the farther a galaxy is from us, the greater the redshift of the emitted light, so the galaxy The farther away from us, the faster away from us. This relationship between redshift and distance is known as Hubble's law. Over time, we've come to realize that this relationship is not due to what we think of as an explosion, where galaxies are speeding away from a point, but due to the expansion of space itself.

The rate at which the universe expands is determined by what is known as the Hubble constant. Our best current measurement of the Hubble constant is 20 km/s per million light-years. This means that two points in space that are 1 million light-years apart are moving away from each other at 20 kilometers per second. Since all space is expanding, the greater the distance between two points in space, the faster they will separate. Because of this, if the two points we consider are far enough apart, they can move away from each other faster than the speed of light. Since the speed of light is about 300,000 km/s, according to our current Hubble constant, this means that the critical distance beyond the speed of light is about 15 billion light years.

A galaxy 16 billion light-years away is moving away from us faster than light, but this distant galaxy does not violate the theory of relativity. from thisFrom the perspective of the distant galaxy, we are moving away from it faster than light, because speed is relative. But the key point to remember is that this relative motion is due to cosmic expansion, not galactic motion. The theory of relativity requires that nothing can move faster than light in a vacuum, but it does not constrain the expansion of space itself.

Faster-than-light quantum entanglement

The strangest faster-than-light interaction is quantum entanglement. Let’s say you and I have a mutual friend who decides to give us both a pair of gloves. She puts the gloves in two boxes and sends us one each. So we all know we're getting one of a pair of gloves. But until we opened our respective boxes, we didn't know which glove we were holding, it could be the right hand or the left hand. When you open the box, you find that the glove sent to you is left-handed. Then at this moment, you will know in an instant that my glove must be the right hand.

This is the basic idea behind the so-called Einstein-Podolsky-Rosen (EPR) experiment. In quantum theory, things can be in an indeterminate state until you observe them. It's like having a glove in your box, but it's impossible to know whether it's left or right until you measure it.

In quantum theory, we would say that the things contained in the box are in a state of superposition, and the result becomes deterministic only when observed. That means the results are tangled until we even open the box. When we know what's in one box we immediately know what's in the other. We've actually done this experiment with two entangled photon pairs, and determined that it works.

If we use the standard Copenhagen interpretation of quantum theory, the observation of a state collapses the "wave function of the entangled system". This collapse occurs instantaneously, so apparently faster than the speed of light. But that doesn't violate relativity, because information about the system doesn't travel faster than the speed of light. In other words, the information you measure on the quantum system will not be transmitted to others faster than the speed of light. The observations you make don't change the uncertainty of others until they get information about the entangled system from you.

Let’s also talk about gloves. When you receive the gloves, the left and right of the gloves are in a superimposed state, you open the box and know that yours is left handed and ours is right handed. But your observation of the glove does not change the indeterminate state of my receipt of the glove, and if you want to tell us about the measurement results, you will also be limited by the speed of light.

What this all means is that there is no way to send information faster than light.

Summary: What is the limitation of the theory of relativity?

So lots of things travel faster than light, and it's simple to make such a device, because relativity doesn't prevent faster-than-light travel. What it really forbids is information or objects traveling through space faster than the speed of light in a vacuum. So unless we master extreme space-time bending and can send objects through wormholes, it will still be years, hundreds or thousands of years before we get to any star other than our sun.