March 11, 2019 at 18:08Myths of modern physics. Conservation laws
To be continued. The beginning is here and here :
This time we will swing at the sacred: the conservation laws, including the law of conservation of energy. True, I do not promise you a perpetual motion machine.
The law of conservation of energy has such an aura of holiness that almost any person tenses up when they hear that not everything is good with him. Meanwhile, energy is stored in mechanics, in quantum mechanics, and even in SRT - 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. We’ll figure it out first
So we put two balls in a bag, blue and red. After some time they got them. Yeah, there were two balls, and there were two balls, the balls are stored in the bag! It looks like spatially - a temporary picture of this experiment:
However, with the number of balls everything is simple - all observers, no matter how they move, agree that there are two balls. But what about energy? For example, I’m standing near a house weighing 1,000 tons. Its kinetic energy in my reference frame is zero. Now I will go from home at a speed of 1 meter per second. In my frame of reference, the house has gained tremendous energy! How could I, a weak person, give a house such energy in just one step?
If you carefully watched your hands, then, of course, you noticed that I made a dirty hack. He considered energy at first in one reference frame, and then brazenly jumped into another. You can’t do this. For energy, the state before and the state after should be tied to the same reference frame.
For our picture with balls, this means that the bottom and the lid of the cylinder (in the general case of any figure) should be parallel to each other. But with this in a curved space it’s bad: as you remember, in a curved space there can be many parallel ones or not a single one! Worse, the space can be so crooked that it doesn’t fit such a figure at all!
Or time is looped - and concepts toand after are not well defined. Thus, in GR it is not that energy is not conserved, but the very concept of “conserved” is poorly defined.
We all know that the universe is expanding. When its linear size increases by 10 times, its volume increases by 1000 times, and the density of ordinary matter (after all, atoms are balls, and all observers agree on how many of them) also falls by 1000 times
But the radiation density, in particular relict radiation, falls 10,000 times - in addition to the fact that the photons scattered in a larger volume, each of them also turned red. That is, the density of a substance decreases as a third degree, and radiation - as a fourth.
This has an interesting consequence - if we move into the past, then the radiation density will increase 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 photon gas pressure.
It should be noted that the cosmological point of view - “the whole universe at such a time ”, despite its intuitive understandability and usefulness, forms a curved surface in space-time for each time after the Big Bang , that is, it is not a valid reference frame.
Spoiler: YES . The impulse, you guessed it, is also not preserved. You can google it according to Swimming in space . Here is a video of how it looks. Of course, this is almost no practical value, but still interesting .
This time we will swing at the sacred: the conservation laws, including the law of conservation of energy. True, I do not promise you a perpetual motion machine.
The law of conservation of energy has such an aura of holiness that almost any person tenses up when they hear that not everything is good with him. Meanwhile, energy is stored in mechanics, in quantum mechanics, and even in SRT - 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. We’ll figure it out first
What is saved?
So we put two balls in a bag, blue and red. After some time they got them. Yeah, there were two balls, and there were two balls, the balls are stored in the bag! It looks like spatially - a temporary picture of this experiment:
However, with the number of balls everything is simple - all observers, no matter how they move, agree that there are two balls. But what about energy? For example, I’m standing near a house weighing 1,000 tons. Its kinetic energy in my reference frame is zero. Now I will go from home at a speed of 1 meter per second. In my frame of reference, the house has gained tremendous energy! How could I, a weak person, give a house such energy in just one step?
If you carefully watched your hands, then, of course, you noticed that I made a dirty hack. He considered energy at first in one reference frame, and then brazenly jumped into another. You can’t do this. For energy, the state before and the state after should be tied to the same reference frame.
For our picture with balls, this means that the bottom and the lid of the cylinder (in the general case of any figure) should be parallel to each other. But with this in a curved space it’s bad: as you remember, in a curved space there can be many parallel ones or not a single one! Worse, the space can be so crooked that it doesn’t fit such a figure at all!
Or time is looped - and concepts toand after are not well defined. Thus, in GR it is not that energy is not conserved, but the very concept of “conserved” is poorly defined.
Canonical example of energy non-conservation
We all know that the universe is expanding. When its linear size increases by 10 times, its volume increases by 1000 times, and the density of ordinary matter (after all, atoms are balls, and all observers agree on how many of them) also falls by 1000 times
But the radiation density, in particular relict radiation, falls 10,000 times - in addition to the fact that the photons scattered in a larger volume, each of them also turned red. That is, the density of a substance decreases as a third degree, and radiation - as a fourth.
This has an interesting consequence - if we move into the past, then the radiation density will increase 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 photon gas pressure.
It should be noted that the cosmological point of view - “the whole universe at such a time ”, despite its intuitive understandability and usefulness, forms a curved surface in space-time for each time after the Big Bang , that is, it is not a valid reference frame.
Can I raise myself by the hair?
Spoiler: YES . The impulse, you guessed it, is also not preserved. You can google it according to Swimming in space . Here is a video of how it looks. Of course, this is almost no practical value, but still interesting .