Joy Christian's colourful exploding balls experiment

[gill1109]

Fred: charities: excellent suggestions. My favourite charity is Médecins Sans Frontières (MSF).

Michel: apples and oranges: let's also distinguish the *experiment* and the *bet*.

The result of the experiment will be a big computer file containing a lot of numbers which will be publicly archived on internet. Anyone will be able to do just whatever they like with it. No doubt, the experimenter and Joy will be publishing scientific papers about the experiment and its results. Other peope too. Maybe the experiment gets repeated by other groups. Science.

The bet is determined by one particular computation on those numbers with just one outcome, which is the designation of a winner. The computation to be performed has been agreed on in advance and the procedure will be public and reproducible. The outcome of the bet is announced by a team of adjudicators and their judgement is binding.

As just said, the numbers come from an experiment. The experiment has been described by Joy in a paper on arXiv and in his book.

The experiment involves filming two objects which fly apart from one another, both rotating. The rotating objects are filmed by a battery of video cameras. The video films are analyzed in order to reconstruct the motions of the two objects. Software is going to determine the directions in which each object is rotating at a particular point in their path. All the details of this will be worked out by the experimenter and Joy together. The image reconstruction work is all part of the experiment.

The two objects are distinguishable from one another. One run of the experiment results in two measured directions, call them u and v for the moment. The image processing and numerical analysis of the observed paths is part of the laboratory work. It may use assumptions and theoretical knowledge of any kind. Joy and the experimenter decide on all this. But in particular, the experiment is set up so that the total angular momentum of the system is zero and the numerical analysis will actually impose the constraint that v = - u.

We have to agree on how we represent directions. Think of them as points on the unit sphere S^2. We need to agree on some reference directions, e.g. an x, y and z axis. We haved to agree on a coordinate system, e.g. we might decide to use some kind of spherical coordinate system. For instance, polar coordinates, so that finally the direction u is represented by two numbers theta and phi, polar angle and azimuthal angle.

In that case, one run of the experiment results after a huge amount of hard laboratory work (including computer laboratory work) in just two numbers theta and phi.

The experiment is repeated N times and this results in N pairs of numbers theta_k, phi_k, k=1, ..., N. These numbers are saved in a computer file in agreed format and the file is made available to anyone interesting on internet.

Now Joy and I have a bet between the two of us, and it will be settled by doing certain calculations on those N directions. Our bet involves just four particular correlations E(a, b), i.e., four particular choices of a pair of directions (a, b). We are going to use Joy's published instructions to compute those correlations. Everything we do will be open, transparent, reproducible. The computer code implementing Joy's instructions and determining the outcome of the bet will be published, we have a committee of adjudicators who ensure fair play and resolve any unforseen difficulties, and who announce the outcome, which is that either Joy has won the bet or I have won the bet.

[minkwe]

Since the experimental data is going to be publicly available to all, everyone can analyse that data any way they like.

Absolutely, everyone is free do anoint themselves with their own droppings too. That doesn't mean it won't stink.

[gill1109]

Michel, do you have a problem with the experiment? if so, please let us know what your problem is.

The bet is between Joy and me, and the adjudicators are Andrei Khrennikov, Hans de Raedt, and Gregor Weihs.

Please distinguish apples from oranges.

Apples: an experiment described in a paper by Joy. Read it carefully and comment on it, if you like. Joy's paper describes the data coming from the experiment. What that data is, how it is created, is all part of the experiment.

Pears: a personal bet between Joy and me, to be determined by one particular computation based on the data coming from the experiment.

Perhaps we should have separate threads on the two topics. The data coming from the experiment is the bridge between the topics.

[FrediFizzx]

Absolutely, everyone is free do anoint themselves with their own droppings too. That doesn't mean it won't stink.

LOL! Okay, dokay.

[gill1109]

Absolutely, everyone is free do anoint themselves with their own droppings too. That doesn't mean it won't stink.

LOL! Okay, dokay.

Fred, do you have a problem with the experiment? If so, please let us know.

I think we need a new thread to discuss the bet.

I am going to discuss with Joy a protocol for the bet, and the starting point of the protocol will be a data-set containing N measured directions, represented in spherical coordinates, https://en.wikipedia.org/wiki/Spherical_coordinate_system. Actually my protocol will be a little program written in the R language but I'll try to write a Mathematica version too.

[FrediFizzx]

Fred, do you have a problem with the experiment? If so, please let us know.

I have no problem with the experiment. It needs to be done so that we will know for sure.

[gill1109]

Fred, do you have a problem with the experiment? If so, please let us know.

I have no problem with the experiment. It needs to be done so that we will know for sure.

Joy and I use the word "run" and sometimes "trial" for just one explosion, two hemispheres flying about, spinning wildly in opposite directions to one another, filmed on video. A heap of computer processing generates one direction per run. The "experiment" consists of N runs. I don't know how big N will be yet.

Basicly, N times we will get to actually observe the hidden variable lambda. We get to see lambda_1, lambda_2, ..., lambda_N. (At least: a good experimental approximation thereof).

For the purpose of the bet, we *compute* correlations like this: E(a, b) = 1/N sum_k sign(a . lambda_k) sign(b . - lambda_k)

If anyone wants to draw graphs or calculate other things by taking small subsamples from the N observed directions lambda_k, a different one for each pair of directions a and b, they are welcome to, but I don't see the point, since the average of a random sample will be close to the average of the population we are sampling from, if the sample is large enough; and if it is small, it is useless!

The population I am talking about here is of size N. It will be right there on the table in front of all of us. There is no need to sample from it at all!

Of course, the "population" lambda_1, ..., lambda_N can itself be thought of as a sample - where each observation is moreover perturbed by hopefully only small measurement error - taken from an infinite ensemble.

[FrediFizzx]

Actually my protocol will be a little program written in the R language but I'll try to write a Mathematica version too.

You don't need to do Mathematica. It has Rlink which will link R into it. I will get that going one of these days.

[gill1109]

Actually my protocol will be a little program written in the R language but I'll try to write a Mathematica version too.

You don't need to do Mathematica. It has Rlink which will link R into it. I will get that going one of these days.

Nice! Steve Wolfram is very smart. He's aware of the competition.

This is the way of the future. All these different fourth generation languages become hidden behind a very high level interface which wisely chooses the right tool for each job. Sage http://www.sagemath.org is based on this concept. And it's going into the cloud so you can do whatever you like whenever and where-ever you like.

Sage's mission: creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Built on Python. Incorporates NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R, M2 and many more.

[Joy Christian]

I thought a little more about the squashy ball version of the experiment, which I think is the best version so far, because it removes all the moments of inertia of the spinning balls. The remaining and unavoidable sources of error are the air and gravity effects. Much analysis of these effects will be needed to be sure that they are not contributing adversely.

In any case, here are my thoughts so far. Take a pair of colourful squashy balls, preferably striped, so we can see clearly the directions of their spins. Now take one of the balls and make a tiny notch, no more than a millimetre in width and depth, making sure that the notch is not too deep to puncture the ball (we want them to be air tight). Now fill up the notch with lead, like filling gold on a tooth. This will make the ball spin more likely in a specific direction. Now make N such pairs of balls and we are almost ready for the experiment.

In the lab, install two laser screens at the two ends of a long table, perpendicular to the horizontal direction of the supposed flights of the balls. Now squeeze a pair of balls together and release them, hoping that they would fly forcefully towards the laser screens. We must make sure that the balls on the two sides pass through their respective laser screens simultaneously. It is at the moment when the laser screens are right at the centre of the passing balls that the respective videos would record the directions of their spins with respect to a fixed coordinate system of the laboratory. Note that, although the laser screens are 2D, the directions of the spins form a 3D map on each side (they would form points on S^2). And that is it. No need to choose a or b until all the N runs are accomplished.

The rest is just analysis of the two 3D maps of data from the two sides. When the analysis is done, you will see E(a, b) = -a.b.

[gill1109]

I thought a little more about the squashy ball version of the experiment, which I think is the best version so far, because it removes all the moments of inertia of the spinning balls. The remaining and unavoidable sources of error are the air and gravity effects. Much analysis of these effects will be needed to be sure that they are not contributing adversely.

In any case, here are my thoughts so far. Take a pair of colourful squashy balls, preferably stripped, so we can see clearly the directions of their spins. Now take one of the balls and make a tiny notch, no more than a millimetre in width and depth, making sure that the notch is not too deep to puncture the ball (we want them to be air tight). Now fill up the notch with lead, like filling gold on a tooth. This will make the ball spin more likely in a specific direction. Now make N such pairs of balls and we are almost ready for the experiment.

In the lab, install two laser screens at the two ends of a long table, perpendicular to the horizontal direction of the supposed flights of the balls. Now squeeze a pair of balls together and release them, hoping that they would fly forcefully towards the laser screens. We must make sure that the balls on the two sides pass through their respective laser screens simultaneously. It is at the moment when the laser screens are right at the centre of the passing balls that the respective videos would record the directions of their spins with respect to a fixed coordinate system of the laboratory. Note that, although the laser screens are 2D, the directions of the spins form a 3D map on each side (they would form points on S^2). And that is it. No need to choose a or b until all the N runs are accomplished.

The rest is just analysis of the two 3D maps of data from the two sides. When the analysis is done, you will see E(a, b) = -a.b.

Cool!

Spelling: the balls should be striped, not stripped, don't you think?

[Joy Christian]

Spelling: the balls should be striped, not stripped, don't you think?

Corrected!

[Heinera]

Richard believes Apples are really Oranges due to some kind of statistical tricks. If he has confidence in his work, he shouldn't mind if you guys bet to do an Orange experiment. But he appears to mind because he keeps insisting on calculating everything on the same set.

Uuuuhh...? Keeps insisting? I guess the situation is exactly the opposite: When Richard explained he was perfectly happy with calculating the correlations on four different, random subsets (provided N was sufficiently large), he got this reply:

We leave nothing to chance. We follow the first procedure. All the other variants with the data will be tried later by many people if the strong correlations are seen.

[Mikko]

I thought a little more about the squashy ball version of the experiment, which I think is the best version so far, because it removes all the moments of inertia of the spinning balls. The remaining and unavoidable sources of error are the air and gravity effects. Much analysis of these effects will be needed to be sure that they are not contributing adversely.

Gravity effects are not a problem. They affect the motion of the bodies but not their rotation. The real problem is aerodynamic effects. There are basically two ways to handle them: either eliminate them or compute the initial spin as a backwards extrapolation of observations. The extrapolation requires more observations than would be needed without aerodynamic effects. Aerodynamic effects can be reduced to neglible by using dense materials (but such materials tend to be too rigid for squashy balls) or vacuum (but some materials do not behave well in vacuum).

[Heinera]

Gravity effects are not a problem. They affect the motion of the bodies but not their rotation. The real problem is aerodynamic effects

Yes, and fortunately, creating a vacuum in a closed box is much cheaper than performing the experiment in outer space. On the other hand, the latter scenario would take crowdfunding to a whole new level.

[Joy Christian]

I thought a little more about the squashy ball version of the experiment, which I think is the best version so far, because it removes all the moments of inertia of the spinning balls. The remaining and unavoidable sources of error are the air and gravity effects. Much analysis of these effects will be needed to be sure that they are not contributing adversely.

Gravity effects are not a problem. They affect the motion of the bodies but not their rotation. The real problem is aerodynamic effects. There are basically two ways to handle them: either eliminate them or compute the initial spin as a backwards extrapolation of observations. The extrapolation requires more observations than would be needed without aerodynamic effects. Aerodynamic effects can be reduced to neglible by using dense materials (but such materials tend to be too rigid for squashy balls) or vacuum (but some materials do not behave well in vacuum).

Good thoughts on aerodynamics. Of course both problems would go away if we do the experiment in vacuum on the space-station with zero gravity. Gravity is actually a problem because the balls would fall towards the ground in a parabolic motion when they fly from the centre of the "explosion" towards the laser screens. Although the spins will not be affected significantly, they would be tilted differently towards the ground for each run. One can treat this as a systematic effect if the tilt is the same in each run, but we can't tell until it is tried out in the actual experiment.

Another problem would be to ensure that the balls emerge in a singlet state: s_1 + s_2 = 0. This would be difficult to tell for two independent balls squeezed together.

[gill1109]

ld be to ensure that the balls emerge in a singlet state: s_1 + s_2 = 0. This would be difficult to tell for two independent balls squeezed together.

One way out of this is to do without the balls altogether. Simply use a pseudo random generator to generate a point s_1 uniformly at random on the unit sphere, and then define s_2 = - s_1. (Without loss of generality, the absolute value of the angular momenta can be taken to be 1). Do this N times. Save the N values of the spin direction of the first particle in a computer file.

It would make the experiment a whole lot cheaper! No exploding balls, no battery of video cameras, no expensive image reconstruction.

We could do it tonight, and settle our bet tomorrow.

A bit less heroic, but very effective.

[Joy Christian]

ld be to ensure that the balls emerge in a singlet state: s_1 + s_2 = 0. This would be difficult to tell for two independent balls squeezed together.

One way out of this is to do without the balls altogether. Simply use a pseudo random generator to generate a point s_1 uniformly at random on the unit sphere, and then define s_2 = - s_1. (Without loss of generality, the absolute value of the angular momenta can be taken to be 1). Do this N times. Save the N values of the spin direction of the first particle in a computer file.

It would make the experiment a whole lot cheaper! No exploding balls, no battery of video cameras, no expensive image reconstruction.

We could do it tonight, and settle our bet tomorrow.

A bit less heroic, but very effective.

Nice try.

[gill1109]

ld be to ensure that the balls emerge in a singlet state: s_1 + s_2 = 0. This would be difficult to tell for two independent balls squeezed together.

One way out of this is to do without the balls altogether. Simply use a pseudo random generator to generate a point s_1 uniformly at random on the unit sphere, and then define s_2 = - s_1. (Without loss of generality, the absolute value of the angular momenta can be taken to be 1). Do this N times. Save the N values of the spin direction of the first particle in a computer file.

It would make the experiment a whole lot cheaper! No exploding balls, no battery of video cameras, no expensive image reconstruction.

We could do it tonight, and settle our bet tomorrow.

A bit less heroic, but very effective.

Nice try.

I wonder why there should be any difference. Both versions result in a computer file containing N directions s_k, k=1,...,N. You were worried that with the squishy balls, we might not have a singlet state. And with all that image analysis software, there will be measurement errors as well. But with my computer generated directions, we certainly do have the singlet state: zero total angular momentum; each particle separately has completely random angular momentum.

[Joy Christian]

I wonder why there should be any difference. Both versions result in a computer file containing N directions s_k, k=1,...,N. You were worried that with the squishy balls, we might not have a singlet state. And with all that image analysis software, there will be measurement errors as well. But with my computer generated directions, we certainly do have the singlet state: zero total angular momentum; each particle separately has completely random angular momentum.

Again, nice try.