Tech UPTechnologyWhat does the equation E=mc2 mean to the man...

What does the equation E=mc2 mean to the man in the street?

If you ask the man in the street about the meaning of the most famous equation in history, E=mc2, he is likely to say that somehow a little bit of mass can be transformed into a huge amount of energy. The mass disappears giving rise to a large detonation; for example, capable of destroying a city, as happened in Hiroshima and Nagasaki. This metamorphosis is, to say the least, suspicious. How can the mass, that which gives substance to things, stop being what it is to become a kind of big push? Could we dematerialize the entire Universe with this method and transform it entirely into pure energy? In the energy of what?, one might ask…

In this article we are going to think about this matter in the most colloquial terms possible, but without sacrificing scientific rigor in any way. I want to tell you the result: no one knows what energy is, nor does anyone know what mass is, but whatever they are, they are not different things .

Let’s appeal to our experience of the world. In it, mass and energy do not seem to have anything to do with each other and in this lies the fundamental difficulty in understanding Einstein’s equation. Mass is that property of objects that makes it difficult for us to move them. If a body is at rest and we want it to reach a certain speed, this will require a greater effort the more massive the body in question. We’re not talking about friction here. We are dealing with a major issue and we are going to ignore trifles such as friction. In our world nothing rubs against anything. Note, on the other hand, that we tend to identify mass with quantity of matter, but the truth is that we do not have a better definition for quantity of matter than the one we just gave for mass, so we will not get anything clear by following that path . To be massive is to resist getting going, accelerating, period.

Now is the time to move on to talking about energy. This is going to cost us a little more. Let’s start by considering the following situation: a cube-shaped metal block of side 20 cm, for example, is at a temperature of, say, 50 degrees Celsius. Under these conditions, one of its faces comes into contact with that of another identical block, but whose temperature is lower, say about 30 degrees. Our experience tells us that something we call heat will flow from the hot block to the cold block so that the temperatures tend to equalize. We have here an example of energy in transit. The energy goes from one block to another, but it does not go anywhere else, at least approximately.

This localization of energy will allow us to carry out a very interesting experiment. Let’s push the cold block before and after it has come into contact with the hot one. This occurrence seems to have little travel. We already know what’s going to happen, right? It won’t make any difference, since heating an object won’t change its resistance to moving. This, however, turns out to be false and here is the crux of the matter. What we call the mass of the cube will change, it will increase. Little, very little, but it will. Pouring energy into a body, and who knows what that thing is, makes it more massive, less likely to be accelerated. Note that we also do not know what mass is, why objects like to be accelerated more or less, but our experiment reveals that the more energy contained in the object, the more reluctant it will be to accelerate when pushed. At this point it is completely natural to think that the entire mass of the body is energy that was poured into it at some point. We have discovered the mass dial. Turning it to the right or left; that is, by adding or subtracting energy, we can control the amount of mass at will. We see, therefore, that mass and energy are one and the same thing, or so we are invited to believe as a result of our surprising experiment. Einstein’s equation should therefore read E=m, with no ces or squares anywhere, and it would simply be telling us that mass and energy are the same thing. The “c”, by the way, is the speed of light. Its appearance is striking to say the least in this context in which there is no light anywhere and nothing is moving remotely as fast.

Let’s think about the “c”, then. I advance the conclusion again. We have been very clumsy in considering that time and space are different things. It is time to retire, many readers will doubtless think. That mass and energy can be the same happens, but that time and space are comparable goes beyond what we are willing to accept. I do not recommend it. Don’t things get more interesting?

A distance of one second is what we have always called 300,000 kilometers. If we are judicious we will choose this amount of distance as our new unit and call it a second of distance. The speed of light will be one in these units, since light will travel one second of distance in one second of time and one divided by one is one. By the way, one squared is one too. But let’s not go too fast. All this needs to be dealt with more calmly and we will dedicate ourselves to this in the following lines.

Turns out,contrary to what many might think, it is very difficult to tell if one is moving or not. The reader of these lines moves around the sun at a speed of thirty kilometers per second without realizing it, just like any anonymous Neanderthal man for whom this fact was not even part of his cultural heritage. This crazy speed does not seem to have the slightest relevance in our daily affairs. The way things move from here to there is not affected by it and everything behaves as if the Earth were standing still. Not only matters of mechanics seem insensitive to the movement of the planet; those of electricity and magnetism as well. Our mobile phones work perfectly in this cosmic fireball we live on, sending signals to repeater antennas at the speed of light. On a faster or slower planet everything would still work just as well. If not, only a few planets in the Universe, those very slow or at rest, would be “habitable”. Nature is wise and has created a world where “moving” is not a big problem. Einstein realized that this fact was crucial and allowed a kind of fusion between space and time. If we cannot detect our own movement, if the signals of our mobiles have to travel at the same speed on any planet, this speed of propagation (the speed of light) becomes a universal constant at our disposal to relate space and time. weather. It is therefore natural to define the unit of length in terms of the distance that light travels in unit time; the second, let’s say. Saying that the distance between two points is one second is perfectly understandable. We can measure distances using clocks and light rays.We just have to indicate the time it takes for light to travel that distance.We do not need tape measures, or yardsticks, or any such device. When computing the speed of light we obtain a pure number, one, the quotient between two times both equal to one second.

By making use of this fact, that is to say that c=1, in the formula E=mc2 we obtain that E=m and the insidious speed of light disappears from the equation as if by magic, revealing its true essence , namely, that mass and energy are one and the same thing.

Mission accomplished.

 

Alberto Corbi is a Ph.D. in Physics and Director of the Degree in Physics at the International University of La Rioja (UNIR).

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