However, this formula is like this. A few simple characters explain the relationship between mass and energy in the universe. They are actually different expressions of the same thing. But many friends don't understand why how much energy a mass object contains is related to the cosmic constant of the speed of light, and why is it the square of the speed of light? Not a cube? Or what? Simply put, the reason why the mass-energy equation is what we see now is actually the result of the conservation of momentum and energy. Let's analyze it in detail.
Let's start with m in e = MC 2. You see, the scales of the universe are big and small, and there are macroscopic and microscopic points, but whether it is galaxies, stars, the earth, molecules, atoms or elementary particles, they all have an inherent essential attribute, that is, mass, that is, even if we remove all the internal energy of a mass object, that is, cool it to absolute zero, stop the random motion of molecules and atoms, and then stop the object itself.
In other words, quality is a manifestation of energy. Even if an object has no internal energy and kinetic energy, it will carry static energy. This kind of energy will have an impact on the space-time of the universe, causing the space to bend, and the bent space will change the motion mode of another energetic object. This is what we call gravity.
The opposite of mass objects, objects without mass exist in our universe. Besides particles with mass, there are some particles without mass but carrying energy, such as photons. Photons can interact electromagnetically with charged particles and be absorbed by objects. When photons are absorbed by atoms of an object, the internal energy of the object will increase, and the random motion of molecules and atoms will gain additional kinetic energy, so that the object will be heated. At the same time, after atoms absorb photons with corresponding energy, the base electrons will be excited to a higher energy state, and even the photons with higher energy can ionize neutral atoms into charged particles.
The energy carried by light depends on its wavelength and frequency. The longer the wavelength, the lower the frequency and the lower the energy of light. The shorter the wavelength of light, the higher the frequency and the higher the energy. The product of wavelength and frequency is always equal to the speed of light and will not change. We can reduce the energy carried by a mass particle by reducing its speed, but we can't reduce its speed by reducing the energy carried by light, which will only increase the wavelength of light.
These are objects with mass and photons without mass. Now let's consider that when we annihilate two positive and negative particles, such as positrons and electrons, we will emit two high-energy photons with energy. According to the mass-energy equation, the energy of these two photons is equal to the sum of the masses of two electrons multiplied by the square of the speed of light. Let's talk about a thought experiment to understand why there is the square of the speed of light in the mass-energy equation!
Einstein's thought experiment is like this. Imagine a static box, which is in a vacuum space and is an isolated heat insulation system. There are two perfectly emitting mirrors on both sides of the box, and a photon is moving towards a mirror in the box.
This photon first emanates from the left side of the box and then moves to the right. Because the momentum of the whole system is conserved, the box will move to the left at the moment when the photon is emitted, and the box will stop moving when the photon moves to the right and is absorbed by the box.
Here's a problem. The whole system has no external force. It is reasonable to say that the center of mass of the box will not shift, but the box has moved to the left after the photon is emitted. So how to solve this paradox? How can I keep the center of mass or gravity of the box in its original position?
Einstein solved this paradox. He proposed that the energy carried by photons must be equal to the mass. That is to say, the photon emitted from the left side brings some mass to the right side of the box. Even if the box moves a little to the left, the mass on the right side increases, so the center of gravity of the whole box system remains in the original position. This is actually a thought experiment with equivalent quality and energy.
Let's deduce this conclusion mathematically. The momentum of photons can be written as: p (light) = e/c.
Where e is the energy of photons and c is the speed of light.
If the mass of the box is m and the speed of moving to the left is v, then the momentum of the box is: p (box) =Mv.
How long does it take for a photon to leave from left to right? T, how far has the box moved during this time? X, then the speed of the box v=? X/？ t .
Due to the conservation of momentum of box and photon, m (? X/？ t)=E/c
Suppose the length of this box is l, then the time spent by photons is:? T=L/c, substitute the above formula to get:
m？ X = El/c^2
According to Einstein's idea, we think that the energy and mass of photons are equivalent, that is, photons bring some mass from the left to the right. Assuming this mass is m, we know that the mass of the box is m, the displacement of the box is x 1, and the displacement of the photon is x2, so the center of mass of the whole system is:
We require the center of mass of the box to remain unchanged before and after the experiment, so:
Since the photon has no displacement before the experiment, that is, x2=0, the above formula can be simplified as: mL= M? X
Next we will M (? X/？ T)=E/c and mL= M? X
Got: ml = El/c 2
Final equation: E = MC 2
Summarizing Einstein's thought experiment, it is found that the energy and mass of photons are equivalent, and E = MC 2 is obtained by the law of conservation of momentum.