Myths of modern physics. Conservation laws
Continued. Start here and here :
This time we will aim at the holy: the laws of conservation, including the law of the conservation of energy. True, I do not promise a perpetual motion machine.
The law of conservation of energy has such an aura of holiness that almost every person is straining to hear that all is not well with him. Meanwhile, energy is conserved in mechanics, in quantum mechanics, and even in special relativity — the Special Theory of Relativity. But ... not in GR - the General Theory of Relativity. However, to say that energy is not conserved is also impossible. First, we will understand
')
Here we put in the bag two balls, blue and red. After some time, got them. Aha, there were two balls, and there were two balls, the balls are stored in the bag! This is the spatial - temporal picture of this experiment:
However, with the number of balls, everything is simple - all observers, no matter how they move, will agree that there are two balls. And what about energy? For example, I am standing near a house weighing 1000 tons. His kinetic energy in my reference frame is zero. Now I will go from home at a speed of 1 meter per second. In my reference system, the house has gained tremendous energy! How could I, a weak person, give such energy to a house in just one step?
If you closely followed your hands, you certainly noticed that I had done a dirty hack. He counted the energy first in one frame of reference, and then brazenly jumped to another. So you can not do. For energy, the state before and the state after must be tied to the same reference frame.
For our picture with balls, this means that the bottom and the cylinder head (in the general case, any shape) should be parallel to each other. But with this in a curved space is bad: as you remember, in a curved space there can be many parallel or not one! Worse, the space can be so crooked that it does not fit such a figure at all!
Or time is looped back - and the concepts before and after are not fully defined. Thus, in GR, it is not that energy is not conserved, but the concept of “preserved” is poorly defined.
We all know that the universe is expanding. When its linear size increases 10 times, then its volume increases 1000 times, and the density of ordinary matter (after all, atoms are balls, and all observers agree on how many of them) also drops 1000 times
But the density of radiation, in particular of the background radiation, drops 10,000 times - in addition to the fact that the photons were scattered in a larger volume, each of them also turned red. That is, the density of the substance falls as a third degree, and radiation - as a fourth.
This has an interesting consequence - if we move into the past, the radiation density will grow faster than the density of matter, and we can reach a period when the density and pressure of ordinary matter can be completely neglected. Gravity was mainly created by the pressure of a photon gas.
It should be noted that the cosmological point of view - “the whole universe at such and such time ”, despite its intuitive clarity and usefulness, for each time after the Big Bang forms a curved surface in space-time, that is, it is not a valid reference system.
Spoiler: YES . The impulse, as you guessed, is also not preserved. You can google according to Swimming in space . Here is a video of what it looks like. Of course, there is almost no practical value in this, but it’s still interesting .
This time we will aim at the holy: the laws of conservation, including the law of the conservation of energy. True, I do not promise a perpetual motion machine.
The law of conservation of energy has such an aura of holiness that almost every person is straining to hear that all is not well with him. Meanwhile, energy is conserved in mechanics, in quantum mechanics, and even in special relativity — the Special Theory of Relativity. But ... not in GR - the General Theory of Relativity. However, to say that energy is not conserved is also impossible. First, we will understand
')
What is - to persist?
Here we put in the bag two balls, blue and red. After some time, got them. Aha, there were two balls, and there were two balls, the balls are stored in the bag! This is the spatial - temporal picture of this experiment:
However, with the number of balls, everything is simple - all observers, no matter how they move, will agree that there are two balls. And what about energy? For example, I am standing near a house weighing 1000 tons. His kinetic energy in my reference frame is zero. Now I will go from home at a speed of 1 meter per second. In my reference system, the house has gained tremendous energy! How could I, a weak person, give such energy to a house in just one step?
If you closely followed your hands, you certainly noticed that I had done a dirty hack. He counted the energy first in one frame of reference, and then brazenly jumped to another. So you can not do. For energy, the state before and the state after must be tied to the same reference frame.
For our picture with balls, this means that the bottom and the cylinder head (in the general case, any shape) should be parallel to each other. But with this in a curved space is bad: as you remember, in a curved space there can be many parallel or not one! Worse, the space can be so crooked that it does not fit such a figure at all!
Or time is looped back - and the concepts before and after are not fully defined. Thus, in GR, it is not that energy is not conserved, but the concept of “preserved” is poorly defined.
Canonical example of energy conservation
We all know that the universe is expanding. When its linear size increases 10 times, then its volume increases 1000 times, and the density of ordinary matter (after all, atoms are balls, and all observers agree on how many of them) also drops 1000 times
But the density of radiation, in particular of the background radiation, drops 10,000 times - in addition to the fact that the photons were scattered in a larger volume, each of them also turned red. That is, the density of the substance falls as a third degree, and radiation - as a fourth.
This has an interesting consequence - if we move into the past, the radiation density will grow faster than the density of matter, and we can reach a period when the density and pressure of ordinary matter can be completely neglected. Gravity was mainly created by the pressure of a photon gas.
It should be noted that the cosmological point of view - “the whole universe at such and such time ”, despite its intuitive clarity and usefulness, for each time after the Big Bang forms a curved surface in space-time, that is, it is not a valid reference system.
Can I lift myself by the hair?
Spoiler: YES . The impulse, as you guessed, is also not preserved. You can google according to Swimming in space . Here is a video of what it looks like. Of course, there is almost no practical value in this, but it’s still interesting .
Source: https://habr.com/ru/post/443308/
All Articles