Is "Galilean gravity" a thing?

[Genady]

36 minutes ago, J.C.MacSwell said:

wouldn't "Galilean gravity" not recognize the inverse square law postulated by Newton

I don't see why not. Why?

[joigus]

Galilean gravity is Newtonian gravity.

What @geordief is proposing is redoing GR with the Galilean group as the locally inertial symmetry group (how different observers co-relate their observations). That's Galilean GR.

That's certainly possible. And as Markus pointed out, you simply wouldn't have gravitational waves, horizons, and other things. Singularities would be avoidable, as you can always assume particles to be non-pointlike. The Einstein tensor would have fewer degrees of freedom. But geometry of the distorsion of space sections of space time would be described by the inverse-square law.

[Genady]

Is "Aristotelian gravity" a thing?

[joigus]

3 minutes ago, Genady said:

Is "Aristotelian gravity" a thing?

Yes, a thing of the past.  

Aristotle thought that F=mv instead of F=ma, and that gravity was the natural tendency of things from the sub-celestial world to go back to their place. So... a thing it is. Or it was.

[Genady]

4 minutes ago, joigus said:

Yes, a thing of the past.  

Aristotle thought that F=mv instead of F=ma, and that gravity was the natural tendency of things from the sub-celestial world to go back to their place. So... a thing it is. Or it was.

We could say that his second law was F=mv, and his first law was the tendency of things to go back to their natural place. And these two laws were mutually inconsistent. So much to Aristotelian logic.

[joigus]

4 minutes ago, Genady said:

We could say that his second law was F=mv, and his first law was the tendency of things to go back to their natural place. And these two laws were mutually inconsistent. So much to Aristotelian logic.

And he didn't measure anything. Big mistake.

[J.C.MacSwell]

2 hours ago, joigus said:

Galilean gravity is Newtonian gravity.

What @geordief is proposing is redoing GR with the Galilean group as the locally inertial symmetry group (how different observers co-relate their observations). That's Galilean GR.

That's certainly possible. And as Markus pointed out, you simply wouldn't have gravitational waves, horizons, and other things. Singularities would be avoidable, as you can always assume particles to be non-pointlike. The Einstein tensor would have fewer degrees of freedom. But geometry of the distorsion of space sections of space time would be described by the inverse-square law.

So Newton is famous for coming up with something a guy who died before he was born already knew?

Galileo recognized that different masses accelerated at the same rate.

Newton went further and recognized the distance effect of the inverse square law which explained orbits.

[Lorentz Jr]

4 hours ago, joigus said:

Galilean gravity is Newtonian gravity.

Interesting! I always thought action at a distance was just an assumption that Newton made to keep his theory as simple as possible, but it was sort of forced on him by Galilean relativity. A "true" Newtonian gravity could propagate at a finite speed, but only relative to a fixed reference frame. I never thought about that before. Einstein/Lorentz relativity is the only way to have both relativity and a finite propagation speed (i.e. a finite speed without a preferred frame). 🤔

Edited December 28, 2022 by Lorentz Jr

[Mordred]

2 hours ago, Lorentz Jr said:

Interesting! I always thought action at a distance was just an assumption that Newton made to keep his theory as simple as possible, but it was sort of forced on him by Galilean relativity. A "true" Newtonian gravity could propagate at a finite speed, but only relative to a fixed reference frame. I never thought about that before. Einstein/Lorentz relativity is the only way to have both relativity and a finite propagation speed (i.e. a finite speed without a preferred frame). 🤔

The history of Eather theory is quite interesting. I have a copy of a 1918 physics textbook that described it. It didn't include anything involving relativity and the entire particle model only comprised of protons and electrons. Neutrons were discovered roughly 1935 if I recall. 

[joigus]

4 hours ago, J.C.MacSwell said:

So Newton is famous for coming up with something a guy who died before he was born already knew?

Galileo recognized that different masses accelerated at the same rate.

Newton went further and recognized the distance effect of the inverse square law which explained orbits.

"Galilean" makes reference to the space-time symmetry group of the equations of motion. All of pre-relativistic physics is "Galilean". If I come up with a model to describe certain interactions tomorrow that assumes absolute time as part of the mathematical features, it will be Galilean.

2 hours ago, Lorentz Jr said:

Interesting! I always thought action at a distance was just an assumption that Newton made to keep his theory as simple as possible, but it was sort of forced on him by Galilean relativity. A "true" Newtonian gravity could propagate at a finite speed, but only relative to a fixed reference frame. I never thought about that before. Einstein/Lorentz relativity is the only way to have both relativity and a finite propagation speed (i.e. a finite speed without a preferred frame). 🤔

You're absolutely right. Einstein's relativity and Galilean relativity are joined at the hip. One could say that, in a sense, Galilean relativity is but a particular case of Einstein's relativity with c=infinity. This forces instant interactions. If interactions were not instantaneous, inertial observers --in a Galilean world-- would be capable of telling their absolute state of motion.

[J.C.MacSwell]

5 hours ago, joigus said:

"Galilean" makes reference to the space-time symmetry group of the equations of motion. All of pre-relativistic physics is "Galilean". If I come up with a model to describe certain interactions tomorrow that assumes absolute time as part of the mathematical features, it will be Galilean.

 

So any model of gravity under investigation, correct or not, that meets those criteria is Galilean gravity?

[Genady]

35 minutes ago, J.C.MacSwell said:

So any model of gravity under investigation, correct or not, that meets those criteria is Galilean gravity?

Since Sir Isaac Newton invented gravity, "Newtonian gravity" is a well-defined notion, i.e., gravity as per Newton. Thus, we are free to talk and to mean whatever we want discussing Galilean, Aristotelian, Keplerian, Pythagorean, Copernician, etc. gravities.

What is attributed to Galileo is a notion that a constant velocity does not modify bodies' behavior. This means that in a system S' that moves with velocity v relative to a system S along x-axis,

x'=x-vt

t'=t

Any model of anything which assumes this coordinate transformation, is Galilean. Newtonian is such. GR is not.

[joigus]

1 hour ago, J.C.MacSwell said:

So any model of gravity under investigation, correct or not, that meets those criteria is Galilean gravity?

Yes. For example, a model of gravity that tried to investigate deviations from Newton's gravity only in the power law, like,

\[ \boldsymbol{F}_{12}=-G\frac{m_{1}m_{2}}{\left.r_{12}\right.^{2+\varepsilon}}\boldsymbol{u}_{12} \]

for some small \( \varepsilon \) would be "Galilean," since it complies with,

27 minutes ago, Genady said:

x'=x-vt

t'=t

for (t',x') inertial observers vs (t,x) inertial observers.

It would be perfectly Galilean, although not Newtonian, theory of gravity.

I would have problems in reconciling well-trusted conservation laws, rotational invariance, etc. though.

[J.C.MacSwell]

Fair enough. I'm satisfied that Newtonian Gravity is Galilean. Less so that Galilean gravity is the same as Newtonian Gravity.

It seems to imply that Galileo got there first, and he really didn't come close, even while making a substantial step toward it.

[Lorentz Jr]

43 minutes ago, J.C.MacSwell said:

Less so that Galilean gravity is the same as Newtonian Gravity.

To be perfectly honest, I don't think @joigus phrased that quite correctly. (I don't think he's a native English speaker.) I'm pretty sure he meant the first one, Newton's theory of gravity is a Galilean theory.

"Galilean gravity" just means any theory that's based on Galilean relativity. It's not a specific theory of gravity that Galileo had, because he didn't have one for heavenly bodies in the sky. All he had was constant acceleration near Earth's surface.

The difference between Newton and Galileo is that Newton believed there's such a thing as "absolute space" and Galileo didn't. With absolute space, gravity (and other influences) can propagate at some finite speed, but observers can tell how fast they're moving through space (and in what direction) by measuring the speed of gravity waves relative to them.

That violates (Galilean) relativity though, because relativity requires that the laws of physics are the same in all reference frames, i.e. gravity should propagate at the same speed relative to all observers.

Edited December 28, 2022 by Lorentz Jr

[joigus]

1 hour ago, Lorentz Jr said:

To be perfectly honest, I don't think @joigus phrased that quite correctly. (I don't think he's a native English speaker.) I'm pretty sure he meant the first one, Newton's theory of gravity is a Galilean theory.

I may have been not quite precise in my statement. Galilean or not is not coded in the force law though. It's almost all in the (mass)x(acceleration) of Newton's 3rd law. But not all...

To be more precise, the force law should comply with certain constraints to be compatible with the whole Galilean group (isotropic, translation-invariant). So any force law that's of the form,

\[ \boldsymbol{F}_{ij}=\boldsymbol{F}_{ij}\left(\left\Vert \boldsymbol{r}_{i}-\boldsymbol{r}_{j}\right\Vert \right) \]

for particles i and j, would be compatible with the full Galilean group,

\[ \boldsymbol{r}'=R\boldsymbol{r}-\boldsymbol{v}t+\boldsymbol{b} \]

\[ t'=t \]

where \( \boldsymbol{b} \) is a fixed translation, \( \boldsymbol{v} \) is a fixed velocity (Galilean boost), and \( R \) is a fixed rotation matrix,

\[ RR^{t}=I \]

\[ \det R=+1 \]

\( I \) being the identity matrix. The matrix \( R  \) codes a possible change of orientation between frames.

There are velocity-dependent forces (magnetic) that can be made compatible with special relativity, but not with Galilean relativity.

The whole shebang:

https://en.wikipedia.org/wiki/Galilean_transformation#Galilean_group

[Genady]

13 minutes ago, joigus said:

(mass)x(acceleration) of Newton's 3rd law

just a very tiny insignificant correction: 2nd.

[joigus]

1 minute ago, Genady said:

just a very tiny insignificant correction: 2nd.

Oh, boy. Thanks, dear islander. +1