**A colossal jerk**

The term 'jerk' has a special meaning in physics.

The rate of change of an object's position is called its

**velocity**.

The rate of change of an object's velocity is called its

**acceleration**.

Newton realized that to understand how objects move, you need to focus on their acceleration. If you push on an object, it accelerates. Knowing exactly how much it accelerates, you can work backward and figure out its velocity. Knowing that, you can work backward and figure out its position.

But why stop with acceleration?

The rate of change of an object's acceleration is called its

**jerk**.

For example, if you suddenly slam on the brakes, your car suddenly accelerates backwards - we call that 'deceleration', but it's a form of acceleration. Since the acceleration is changing, this counts as a

*jerk*. So you say to the person whose car stopped in front of you: "What a jerk!"

The universe is expanding. It's not expanding

*into*anything - the picture here is misleading - but the distance between any two faraway galaxies is increasing.

The Big Bang happened about 14 billion years ago. Since then, the universe has been expanding. For a while the expansion was slowing down, or decelerating. That's because matter in the universe attracts other matter, thanks to gravity.

But 5 billion years ago, something interesting happened. The expansion started to speed up, or

*accelerate*. We believe this is because dark energy has a repulsive effect... and while matter spreads out and becomes less dense as the universe expands, dark energy does not! So, the repulsion of dark energy eventually overwhelmed the attraction of matter.

In short, about 5 billion years ago, the acceleration of the universe's expansion changed from

*negative*(deceleration) to

*positive*. We know this from carefully looking at the redshifts of distant galaxies... and from other methods, too.

The acceleration is continuing to increase, too. So,

*we are experiencing a jerk on a colossal scale*.

But why stop there?

The rate of change of an object's jerk is called its

**snap**.

The rate of change of an object's snap is called its

**crackle**.

The rate of change of an object's crackle is called its

**pop**.

Before this week, I had never heard anyone use any of these terms except as jokes. These concepts just aren't very important. But then someone pointed out this paper to me:

• Matt Visser, Jerk, snap, and the cosmological equation of state, https://arxiv.org/abs/gr-qc/0309109.

He shows that if we know the jerk and snap of the universe, we can figure out stuff about matter and dark energy. He also brings in experimental data. According to one analysis of the data, there's a 92% chance that the jerk is positive. That is, the scenario I explained is actually right.

Unfortunately the experimental data is not good enough to measure the snap.

So we're stuck with a colossal jerk, and we may never snap out of it.

**Puzzle:**who first introduced the terms snap, crackle and pop?

Alex Klotz, who pointed out Matt Visser's paper, said:

*The earliest reference I can find is a 1996 USENET discussion in which you and Bill Jeffreys both list them as the accepted terms, and this discussion was later cited in an Am.J.Phys paper. The discussion is here:*

*https://groups.google.com/d/msg/sci.physics/eQLC6Tv_IVM/X0n8bkMc4EYJ*

*Anyway, I was wondering if you knew how those terms were initially used in physics and who used them first. Did you invent them?*

I did not invent them.

Here is another reference from 1996, written by +Philip Gibbs:

http://math.ucr.edu/home/baez/physics/General/jerk.html

It's a lot of fun to read, but I'll only quote the end:

Momentum equals mass times velocity!

Force equals mass times acceleration!

Yank equals mass times jerk!

Tug equals mass times snap!

Snatch equals mass times crackle!

Shake equals mass times pop!!

#physics

View 64 previous comments

- I still intend to answer something to your comments, but first I wanted to get a feeling for how important dark matter is for Newtonian gravity:

http://www.randform.org/blog/?p=697046w - +John Baez wrote:

.."the slight flattening would certainly not make the radius of a binary star orbit change in proportion to the cosmic scale factor as the Universe expanded."

This sounds as if you now say that the radius of a binary star may change.

Anyways there are two things here to consider separately. One is my irritation about what it means that a "galaxy does not expand" (initiated by what was written in +Sabine Hossenfelder ´s post, please see above +Noah Friedman ´s comment and my questions) and secondly what exactly is the role of the cosmological constant for galaxy formation and forms and how is it connected to dark matter.

To the first thing: I now understand that you want to simplify and say that an expansion of (spatial) distance, which is smaller than proportional to a cosmic scale factor (and where the scale factor can be attributed to the cosmological constant) is "no expansion". I find that a misleading simplification, especially if it is emphasized that it is not just non-negligable -but whatsoever.

To the second thing: Sabine Hossenfelder just blogged about an article,

backreaction.blogspot.de - Astrophysicist discovers yet another way to screw yourself over when modifying Einstein’s theory

which uses apparently some generalization of General relativity, which seems to lead amongst others to an outward acceleration, at least here

https://www.unige.ch/communication/communiques/en/2017/cdp211117/

it is written:**"In a second stage, Maeder focused on Newton’s law, a specific instance of the equations of general relativity. The law is also slightly modified when the model incorporates Maeder’s new hypothesis. Indeed, it contains a very small outward acceleration term, which is particularly significant at low densities. This amended law, when applied to clusters of galaxies, leads to masses of clusters in line with that of visible matter (contrary to what Zwicky argued in 1933): this means that no dark matter is needed to explain the high speeds of the galaxies in the clusters."**

I briefly tried to understand Sabine Hossenfelders post and even looked briefly into the article by Maeder and I don't understand neither of them. Like it would take me quite some time to figure out, what exactly is meant by this "scale invariance" (Is it multiplying a metric which is assumed to be a solution to Einsteins equation by a time-dependent factor and look what are the conditions, that such a factor gives still a solution to the vaccuum equation with cosmological constant?)

Anyways already this example shows that considerations of general relativity do play a role in the Newtonian approach to understand galaxy formation.

As already mentioned in the previous comment I thus now tried a bit to get a feeling for this Newtonian part and in particular of the implications of the Virial theorem, which use you yourself warned of (end of page at http://math.ucr.edu/home/baez/virial.html) and which is central to the dark matter question.

So I made a (maybe too simple) simulation of the Newtonian physics and in particular I found it a difficult question of how to deal with the fact that stars are no points. In the simulation I now simply assumed that below a certain distance the law of gravitation is "overuled" by inelastic collisions. If one does this then on a very first sight it actually looks as if one could find a configuration in which the movement of giant "central masses" (aka black holes?) may eventually lead to something like galaxy rotations but probably not with the right speed. I don't know how this is treated in professional simulations, but the example shows that assumptions here make quite a difference.

Anyways have a look at the simulation.46w - +Nadja Kutz wrote: "To the first thing: I now understand that you want to simplify and say that an expansion of (spatial) distance, which is smaller than proportional to a cosmic scale factor (and where the scale factor can be attributed to the cosmological constant) is "no expansion"."

Yes - if you calculate the effect of the expansion of the universe on the orbit of a binary star, you'll see it's so small that it's not worth worth worrying about: other tiny effects, like the gradual shrinking of the radius due to the emission of gravitational radiation, are probably much larger. If you want study negligible effects that have no significance for astrophysics, that's okay, but I'm not interested in them - there are lots of them, but I prefer to think about effects that actually matter.

"To the second thing: Sabine Hossenfelder just blogged about an article, "Astrophysicist discovers yet another way to screw yourself over when modifying Einstein’s theory" which uses apparently some generalization of General relativity, which seems to lead amongst others to an outward acceleration..."

Yes, she explained why Maeder's theory is stupid. I read her article and decided to read one of his papers myself. It was indeed stupid, and I left a comment on her blog summarizing my impressions. I was perhaps too polite, since a nonexpert might not notice I was saying the theory was stupid. (Now I'm going to the other extreme and being a bit too impolite.) I see that by now Maeder has joined the argument. Anyone who understands physics well will see that his arguments are confused.

I liked the look of your simulation, but since I didn't see the equations governing this system I couldn't really tell what it was simulating. (Maybe I missed those equations by accident.)46w - +Nadja Kutz
~~I'm interested in your simulation too, but I didn't see a link for it. Would you link it here?~~

Nevermind, I found it. I didn't realize the randform link was your page.46w

+John Baez wrote:

"..but since I didn't see the equations governing this system I couldn't really tell what it was simulating."

You can see the code if you look go to the menu item "view source" in your browser. It was actually good that ou asked for the equations, because I immediately spotted a mistake. Hoo. Hope there are not more...

Anyways luckily the mistake didnt change too much of the overall behaviour and since Google Plus does no latex (as I think) here the relevant parts of the code with expalanations inbetween.

Here I compute the distance from one point "d" to all others: d.yloc stands for location in y direction etc.

data.forEach(function(dd,i){

dist[i] = Math.sqrt((d.xloc-dd.xloc)**(d.xloc-dd.xloc)+(d.yloc-dd.yloc)**(d.yloc-dd.yloc)+(d.zloc-dd.zloc)**(d.zloc-dd.zloc));****Here I set the "radius of involvement" (here 8) and register the points which are within that radius:****if(dist[i]>8){distI[i]=1/dist[i];}else{distI[i]=0.0;ind[count]=i;count++;}****here I apply Newtons law and sum over all directions, if you divide dir by d.mass then this is the acceleration of the point due to Newtons law given by all points outside the radius:****dir[0] = dir[0]+(dd.mass*d.mass*GRAV*Math.pow(distI[i],3)**(d.xloc-dd.xloc));

dir[1] = dir[1]+(dd.mass*d.mass*GRAV*Math.pow(distI[i],3)**(d.yloc-dd.yloc));****dir[2] = dir[2]+(dd.mass*d.mass*GRAV*Math.pow(distI[i],3)**(d.zloc-dd.zloc));

});

Here I compute the velocity of the point using inelastic collision with all points within the radius 8:

for(i=0;i < ind.length;i++){

data[ind[i]="+data[ind[i]]);

var dc = data[ind[i]];

cloggx = cloggx+dc.mass*dc.xvel;

cloggy = cloggy+dc.mass*dc.yvel;

cloggz = cloggz+dc.mass*dc.zvel;

cloggm = cloggm+dc.mass

};

Here I add the velocity of the inelastic collision

and the acceleration computed above, there

is also a friction term but I set this to zero:

var mix = -0.5;

var fric =0.000;

if(ind.length!=1){

d.xloc += (0.5+mix)**d.xvel+(0.5-mix)*1/cloggm*cloggx;****d.yloc += (0.5+mix)**(d.yvel+(0.5-mix)*1/cloggm*cloggy);

d.zloc += (0.5+mix)*d.zvel+(0.5-mix)*1/cloggm*cloggz;}

d.xloc += d.xvel;

d.yloc += d.yvel;

d.zloc += d.zvel;

d.xvel += -1/d.mass*dir[0]+fric*d.xvel;

d.yvel += -1/d.mass*dir[1]+fric*d.yvel;

d.zvel += -1/d.mass*dir[2]+fric*d.zvel;

I actually also made a comment on +Sabine Hossenfelder `s blog on that Maeder article, but sofar it hasn't appeared.46w- I just see that the google comment software uses a couple of the "times signs" for making the text bold, so please compare with the source code. I can send it to you also if you want, then it is not in one line.

(I had to make it into one line because of the wordpress software)46w - +John Baez wrote: *"I read her article and decided to read one of his papers myself. It was indeed stupid, and I left a comment on her blog" *

Did you see my comments on her blog and the above comment, where I tried to highlight the important parts of the code?

Anyways I don't have the time to read Maeders articles I only browsed the two articles you were discussing. I also can't judge whether this is a "new theory" and of course I didn't check his equations- I do however got the impression that the equations he came up with are not just de Sitter space or a different disguise of FRW.

That is in particular equation (31) in

arxiv.org - arxiv.org/pdf/1701.03964.pdf

is not the usual Raychauthuri equation for FRW.

It would be interesting to implement a toy version of his above cited claim that a "small outward acceleration term, which is particularly significant at low densities. " more or less replaces dark matter. But unfortunately I haven't understood, what exactly is meant with "outward" . He probably means something that prevents too rapid slingshots, but I could imagine that this tremendously depends on how exactly gravity is counteracted.46w

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