# Myths of Popular Physics, continued: Gravity

The first part of the article is here . In the meantime, we will analyze other myths that these two guys will not tell you about:

Once I had a book on the theory of relativity, published back in the USSR. As I remember now, there was an illustration drawn: a rocket flies (at light speed) and monstrous gravity pulls planets, stars, galaxies toward itself ... All this grows from this formula:

Where big M is the “relativistic” mass. This concept was very popular at the beginning of the 20th century, but then Einstein himself buried it . Actually, up to the “ce” factor, this value coincides with the total energy of the body, so it makes no sense to have two different physical quantities that differ only by the factor (and in the “natural” system of units, where c = 1, these quantities are generally identical) . By default, the word “mass” means a

However, the popularizers of science read many of the early works of physicists - because they wanted to describe how it all began. So they~~dug up the stewardess~~ pulled the relativistic mass on the pages of their books. This, in general, is not so scary, it is only important to understand that this quantity has no relation to gravity. Here is an example:

In picture A, we have two balls of the same mass at rest relative to the observer. Thanks to gravity, in a minute the balls are attracted to each other. Now option B - the balls fly close to the speed of light. Let Lorentz factor 2 (slowing down the time by half, reducing the length by half, the “relativistic mass” is twice as large as the rest mass). How long do these two balls attract each other?

The task is solved simply. From the point of view of the observer sitting on the ball, the balls will collide anyway in a minute (equivalence principle). But time in the system of balls is slow for an observer who looks at them from the side. This means that this will happen

Not. Here the only thing that can be said is see above.

But this is true. Here it is worth stopping at what actually creates gravity:

This is a tensor, a 4 by 4 matrix. Where does the number 4 come from? Three spatial dimensions and one temporary. On the diagonal we have: in the upper left corner is the energy density (for matter, it’s simplistic to think about the rest mass times the tse-squared). Then comes the pressure (in three dimensions). The remaining cells are important for bubbling plasmas with fluxes close to the speed of light. By heating the body, we increase the pressure inside it (for simplicity, it is better to consider gas)

Here it is appropriate to ask an interesting question. But gas pressure is the movement of molecules! That is, instead of one body with a pressure inside, one can consider many separate moving molecules, and the pressure is zero? Right. Moreover, this can be done even for a “gas” consisting of stars - you can calculate the motion of all stars individually, or you can say that a galaxy contains “gas” from stars under a certain pressure. And the result will be the same!

Here, such a property of GR helps a lot: in the coordinate system, where the total momentum of the system is zero, we can replace all this tensor with just a certain mass value (that is, leave one cell) (if we do not take into account the radiation losses of gravitational waves). Thus, we can simply say that a heated body is heavier and not be interested in what is going on inside. You know what this reminds me of from the IT world?

Everyone knows that light is deflected by stars. But does the light itself attract other objects? Many people think that it’s not, because “the rest mass of a photon is equal to zero”. Returning to our tensor, the photon energy is not zero, and they also have momentum and create pressure - almost all cells are nonzero! A photon gas enclosed in an ideal mirror shell will create gravity.

Light is attracted to each other, and from the light you can make a black hole. Two rays of flashlights directed towards each other will bend, attracted to each other. Interestingly, two rays traveling in the same direction do not interact (you can imagine this as an extreme case of the first example with balls). In particular, a ray of light cannot “focus itself” due to gravity.

If we have many interacting bodies, then what is the mass of the system? We cannot, as in classical mechanics, take and sum the masses. Observers sitting on different stars will have different opinions about the simultaneity of events, about the mass of different bodies, about the center of mass of the system. For a number of special cases, the concepts of Komar’s mass (not an insect, but a scientist with that name!), ADM mass, Bondi mass — have been developed in detail here . But these are all special cases. In the general case, it is not clear what mass is in GR. By the way, in the general case, the concept of “potential energy of the gravitational field” does not exist either.

Thanks for the comments on the first part. There were so many that I could not physically answer everything. The question was often repeated - here you are saying something, and why you should believe you, this is your word against ours. The purpose of this article is not to prove anything to you, but only to provide you with starting points for googling.

## The mass of fast flying bodies increases

Once I had a book on the theory of relativity, published back in the USSR. As I remember now, there was an illustration drawn: a rocket flies (at light speed) and monstrous gravity pulls planets, stars, galaxies toward itself ... All this grows from this formula:

Where big M is the “relativistic” mass. This concept was very popular at the beginning of the 20th century, but then Einstein himself buried it . Actually, up to the “ce” factor, this value coincides with the total energy of the body, so it makes no sense to have two different physical quantities that differ only by the factor (and in the “natural” system of units, where c = 1, these quantities are generally identical) . By default, the word “mass” means a

*rest mass*(it’s more correct to say -*invariant mass*).However, the popularizers of science read many of the early works of physicists - because they wanted to describe how it all began. So they

In picture A, we have two balls of the same mass at rest relative to the observer. Thanks to gravity, in a minute the balls are attracted to each other. Now option B - the balls fly close to the speed of light. Let Lorentz factor 2 (slowing down the time by half, reducing the length by half, the “relativistic mass” is twice as large as the rest mass). How long do these two balls attract each other?

The task is solved simply. From the point of view of the observer sitting on the ball, the balls will collide anyway in a minute (equivalence principle). But time in the system of balls is slow for an observer who looks at them from the side. This means that this will happen

*more slowly*, and not*faster*, as many people think (because, they say, the relativistic mass has increased)## If the star is accelerated to high speed, then it can become a black hole

Not. Here the only thing that can be said is see above.

## If the body is heated, then it weighs more.

But this is true. Here it is worth stopping at what actually creates gravity:

This is a tensor, a 4 by 4 matrix. Where does the number 4 come from? Three spatial dimensions and one temporary. On the diagonal we have: in the upper left corner is the energy density (for matter, it’s simplistic to think about the rest mass times the tse-squared). Then comes the pressure (in three dimensions). The remaining cells are important for bubbling plasmas with fluxes close to the speed of light. By heating the body, we increase the pressure inside it (for simplicity, it is better to consider gas)

Here it is appropriate to ask an interesting question. But gas pressure is the movement of molecules! That is, instead of one body with a pressure inside, one can consider many separate moving molecules, and the pressure is zero? Right. Moreover, this can be done even for a “gas” consisting of stars - you can calculate the motion of all stars individually, or you can say that a galaxy contains “gas” from stars under a certain pressure. And the result will be the same!

Here, such a property of GR helps a lot: in the coordinate system, where the total momentum of the system is zero, we can replace all this tensor with just a certain mass value (that is, leave one cell) (if we do not take into account the radiation losses of gravitational waves). Thus, we can simply say that a heated body is heavier and not be interested in what is going on inside. You know what this reminds me of from the IT world?

**Encapsulation**!## Does light attract other objects?

Everyone knows that light is deflected by stars. But does the light itself attract other objects? Many people think that it’s not, because “the rest mass of a photon is equal to zero”. Returning to our tensor, the photon energy is not zero, and they also have momentum and create pressure - almost all cells are nonzero! A photon gas enclosed in an ideal mirror shell will create gravity.

Light is attracted to each other, and from the light you can make a black hole. Two rays of flashlights directed towards each other will bend, attracted to each other. Interestingly, two rays traveling in the same direction do not interact (you can imagine this as an extreme case of the first example with balls). In particular, a ray of light cannot “focus itself” due to gravity.

## But in general, everything is very bad

If we have many interacting bodies, then what is the mass of the system? We cannot, as in classical mechanics, take and sum the masses. Observers sitting on different stars will have different opinions about the simultaneity of events, about the mass of different bodies, about the center of mass of the system. For a number of special cases, the concepts of Komar’s mass (not an insect, but a scientist with that name!), ADM mass, Bondi mass — have been developed in detail here . But these are all special cases. In the general case, it is not clear what mass is in GR. By the way, in the general case, the concept of “potential energy of the gravitational field” does not exist either.

**PS**Thanks for the comments on the first part. There were so many that I could not physically answer everything. The question was often repeated - here you are saying something, and why you should believe you, this is your word against ours. The purpose of this article is not to prove anything to you, but only to provide you with starting points for googling.

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