If you have an idea for a blog post or a new forum thread, then please contact us at forums@fqxi.org, with a summary of the topic and its source (e.g., an academic paper, conference talk, external blog post or news item).

Contests Home

Previous Contests

**Trick or Truth: the Mysterious Connection Between Physics and Mathematics**

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

read/discuss • winners

**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

*Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American*

read/discuss • winners

**It From Bit or Bit From It**

*March 25 - June 28, 2013*

*Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American*

read/discuss • winners

**Questioning the Foundations**

Which of Our Basic Physical Assumptions Are Wrong?

*May 24 - August 31, 2012*

*Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American*

read/discuss • winners

**Is Reality Digital or Analog?**

*November 2010 - February 2011*

*Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American*

read/discuss • winners

**What's Ultimately Possible in Physics?**

*May - October 2009*

*Contest Partners: Astrid and Bruce McWilliams*

read/discuss • winners

**The Nature of Time**

*August - December 2008*

read/discuss • winners

Previous Contests

Media Partner: Scientific American

read/discuss • winners

read/discuss • winners

read/discuss • winners

Which of Our Basic Physical Assumptions Are Wrong?

read/discuss • winners

read/discuss • winners

read/discuss • winners

read/discuss • winners

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Tobias Fritz**: *on* 2/19/15 at 1:18am UTC, wrote Although it's been a few years since this essay has been written, it seems...

**Tobias Fritz**: *on* 11/2/09 at 17:29pm UTC, wrote Dear Andreas Martin, unfortunately I'm having trouble retrieving the paper...

**Eckard Blumschein**: *on* 10/31/09 at 21:45pm UTC, wrote Dear Tobias, John Baez is a prolific writer. I am sorry. I did not...

**Tobias Fritz**: *on* 10/29/09 at 14:45pm UTC, wrote Dear Eckard, thank you for your comment. Although I'm aware of John Baez'...

**Eckard Blumschein**: *on* 10/28/09 at 18:06pm UTC, wrote Dear Tobias, Let me mention with a grin that John Baetz could probably if...

**Andreas Martin Lisewski**: *on* 10/28/09 at 16:43pm UTC, wrote Interesting answer from Spekkens. However, I do not see why modal logic...

**Tobias Fritz**: *on* 10/28/09 at 11:06am UTC, wrote Third, I don't interpret the probabilities in the toy theory as subjective...

**Tobias Fritz**: *on* 10/28/09 at 11:06am UTC, wrote Here are some comments by Robert Spekkens on my essay, divided into two...

RECENT FORUM POSTS

**Robert McEachern**: "Tom, Your essay concludes with: "If reality is objective and not..."
*in* Quantum Coherence =...

**Zeeya Merali**: "This month’s podcast is jam-packed, thanks to all the huge physics..."
*in* New Podcast: Pluto,...

**Thomas Ray**: "It's verifiable, although not falsifiable. This is the point of my essay..."
*in* Quantum Coherence =...

**John Cox**: "Gary, You are correct. More then that, the much publicized hype about the..."
*in* Inferring the Limits on...

**Georgina Woodward**: "Dear Eckard, thank you for your comments. I don't see it as an attack on..."
*in* Alternative Models of...

**Eckard Blumschein**: "Dear Georgina, Should RCIP RIP? I feel guilty because RCIP mentioned me,..."
*in* Alternative Models of...

**Gary Simpson**: "I'm thinking that the time line might contradict your hypothesis. SR dates..."
*in* Inferring the Limits on...

**Zeeya Merali**: "Dear Steve, I have just read your post, and I wanted to say that I am..."
*in* In Praise of Physics...

RECENT ARTICLES

*click titles to read articles*

**Conjuring a Neutron Star from a Nanowire**

Using tiny mechanical devices to create accelerations equivalent to 100 million times the Earth’s gravitational field—mimicking the arena of quantum gravity in the lab.

**Inferring the Limits on Reality (that Even the Gods Must Obey)**

The fuzziness of the quantum realm could arise from mathematical restrictions on what can ever be known.

**The Quantum Thermodynamic Revolution**

Combining theories of quantum information with the science of heat and energy transfer could lead to new technologies.

**Face Off: Building a Toy Universe to Pit Quantum Theory Against Gravity**

Using superconducting circuits to create a curved-spacetime analog with stronger gravity than our cosmos.

**Is Gravity Time's Archer?**

A new model argues the forces between particles in the early universe loosed time's arrow, creating temporal order from chaos.

RECENT FORUM POSTS

RECENT ARTICLES

Using tiny mechanical devices to create accelerations equivalent to 100 million times the Earth’s gravitational field—mimicking the arena of quantum gravity in the lab.

The fuzziness of the quantum realm could arise from mathematical restrictions on what can ever be known.

Combining theories of quantum information with the science of heat and energy transfer could lead to new technologies.

Using superconducting circuits to create a curved-spacetime analog with stronger gravity than our cosmos.

A new model argues the forces between particles in the early universe loosed time's arrow, creating temporal order from chaos.

FQXi FORUM

July 29, 2015

CATEGORY:
What's Ultimately Possible in Physics? Essay Contest
[back]

TOPIC: Possibilistic Physics by Tobias Fritz [refresh]

TOPIC: Possibilistic Physics by Tobias Fritz [refresh]

I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels "possible to occur" or "impossible to occur" to each outcome of each measurement. It is found that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The essay ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one.

Tobias Fritz is a graduate student at the Max Planck Institute for Mathematics in Bonn, Germany. He works mainly on the foundations of quantum mechanics.

I like this essay. However, I am not at all convinced why giving up probabilities in favor of possibilities will do any good. After all, the very basis of quantitative science (including physics) comprises the natural numbers. Natural numbers are intrinsically and fundamentally probabilistic, which is due to the random nature of the primes. What would be the fundamental counterpart of possibilities? Why giving up something fundamental and specific (probabilities) for something that lacks both a fundamental basis and specificity (your possibilities)?

Anyway--nice job.

report post as inappropriate

Anyway--nice job.

report post as inappropriate

Andreas Martin,

thank you for your feedback. You've made a very interesting point.

I agree that most theories of physics are based on the natural numbers. There are a few exceptions, though, for example the causal set approach to quantum gravity. I do not agree, though, that the natural numbers are instrinsically and fundamentally probabilistic. Let me explain why.

First of all, certainly the primes are a very interesting subset of the natural numbers &ndash mathematically. But how are they relevant for fundamental physics?

Then, yes, it seems that the probabilistic Cramér model accurately captures many aspects of the primes. But, as Terry Tao mentions in his structure and randomness in the primes, there are some problems with this model like "most primes are not divisible by 5". If the primes were totally pseudo-randomly probabilistic, exactly 1/5 of them should be divisible by 5. This aspect can indeed better be captured in a possibilistic model. Consider the following possibilities:

So a natural number is considered to be a possible prime if and only if it is not divisible by 2, 3 and 5. This yields the sieve of Eratosthenes.

These are the reasons why I don't believe that the natural numbers are enough justification for the use of probabilities. This, together with the arguments given in the essay, is everything that I can say right now in the favor of possibility. Personally, I don't believe that the concept of possibility is necessarily superior. But I do believe that the concept of probability shouldn't be taken for granted.

thank you for your feedback. You've made a very interesting point.

I agree that most theories of physics are based on the natural numbers. There are a few exceptions, though, for example the causal set approach to quantum gravity. I do not agree, though, that the natural numbers are instrinsically and fundamentally probabilistic. Let me explain why.

First of all, certainly the primes are a very interesting subset of the natural numbers &ndash mathematically. But how are they relevant for fundamental physics?

Then, yes, it seems that the probabilistic Cramér model accurately captures many aspects of the primes. But, as Terry Tao mentions in his structure and randomness in the primes, there are some problems with this model like "most primes are not divisible by 5". If the primes were totally pseudo-randomly probabilistic, exactly 1/5 of them should be divisible by 5. This aspect can indeed better be captured in a possibilistic model. Consider the following possibilities:

So a natural number is considered to be a possible prime if and only if it is not divisible by 2, 3 and 5. This yields the sieve of Eratosthenes.

These are the reasons why I don't believe that the natural numbers are enough justification for the use of probabilities. This, together with the arguments given in the essay, is everything that I can say right now in the favor of possibility. Personally, I don't believe that the concept of possibility is necessarily superior. But I do believe that the concept of probability shouldn't be taken for granted.

Hello dear Tobias Fritz,

Very interesting essay and discussions about numbers .Congratulations.

They are fascinatings these numbers indeed.

I think what these numbers have a correlation ,a pure correlation,with the physicality and their specific fractals .

The serie and its oscillations si specific .

The pairs are relevant .

I think rerally what the primes are finites like a specific number .

For me the same what our quantum entanglement of spheres and our universal spheres with its cosmological spheres .

The number of spheres is specific ,finite .

If our fundamental mathematics are physicals ,the synchronization is possible .

I have always thought that the infinty ,the zero ,the imaginaries are just a human extrapolation ,the physicality ,rational is finite ,

thus in our serie too we must insert the limits .

Of course the naturals ,reals, there ,are a multiplication or addition of primes .

Thus a finite system with primes and inside an infinite systems of naturals ,products ....for the complexification .The closed system is evidently a spherical system with the center ,the volume ....we can insert the thermodynamic ,the evolution too the mass .....

Best Regards

Steve

report post as inappropriate

Very interesting essay and discussions about numbers .Congratulations.

They are fascinatings these numbers indeed.

I think what these numbers have a correlation ,a pure correlation,with the physicality and their specific fractals .

The serie and its oscillations si specific .

The pairs are relevant .

I think rerally what the primes are finites like a specific number .

For me the same what our quantum entanglement of spheres and our universal spheres with its cosmological spheres .

The number of spheres is specific ,finite .

If our fundamental mathematics are physicals ,the synchronization is possible .

I have always thought that the infinty ,the zero ,the imaginaries are just a human extrapolation ,the physicality ,rational is finite ,

thus in our serie too we must insert the limits .

Of course the naturals ,reals, there ,are a multiplication or addition of primes .

Thus a finite system with primes and inside an infinite systems of naturals ,products ....for the complexification .The closed system is evidently a spherical system with the center ,the volume ....we can insert the thermodynamic ,the evolution too the mass .....

Best Regards

Steve

report post as inappropriate

The link with the uniqueness and the unity vector is relevant .

The serie in a kind of physical fractal beginning with the number 1 is relevant .if the serie goes....... thus the thermodynamic link about the volume of the sphere is important,the serie increases in the numbers of primes but the volume prortionally decreases in its specific fractal in the two senses,quant. and cosm. 1 2 3 is fascinating it's the ultim begining even correlated with the Big Bang which is for me a kind of multiplication .If I had the volume of the main central sphere and the volume of our Universal sphere and the numbers of cosmological spheres ,it d be better and easier to calculate .

Regards

Steve

report post as inappropriate

The serie in a kind of physical fractal beginning with the number 1 is relevant .if the serie goes....... thus the thermodynamic link about the volume of the sphere is important,the serie increases in the numbers of primes but the volume prortionally decreases in its specific fractal in the two senses,quant. and cosm. 1 2 3 is fascinating it's the ultim begining even correlated with the Big Bang which is for me a kind of multiplication .If I had the volume of the main central sphere and the volume of our Universal sphere and the numbers of cosmological spheres ,it d be better and easier to calculate .

Regards

Steve

report post as inappropriate

Here are some comments by Robert Spekkens on my essay, divided into two posts for length reasons:

Dear Tobias,

Thank you for directing me to your paper. I largely agree withyour perspective. I am also of the opinion that it is best *not* toconsider the toy theory as a probabilistic theory. I have often saidthat all that is required for this theory is modal logic, that is,...

view entire post

Dear Tobias,

Thank you for directing me to your paper. I largely agree withyour perspective. I am also of the opinion that it is best *not* toconsider the toy theory as a probabilistic theory. I have often saidthat all that is required for this theory is modal logic, that is,...

view entire post

Third, I don't interpret the probabilities in the toy theory as subjective degrees of belief nor as objective propensities but rather as relative frequencies. My epistemic states describe the relative frequencies of ontic states in an ensemble of similarly preparedsystems, or, equivalently, what an agent knows about the ontic state of a single system drawn from this ensemble. Unlike the subjective...

view entire post

view entire post

Interesting answer from Spekkens. However, I do not see why modal logic automatically implies the binary, possibilistic view. Any model (or actual representation as a Kripke structure) of modal logic is equipped with a truth assignment function over all possible worlds. This function naturally leads to probabilities or, at the least, to beliefs in the sense of Dempster-Shafer theory.

See, e.g., "Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic"

Resconi, Germano; Klir, George J.; Pessa, Eliano

International Journal of Modern Physics C, Volume 10, Issue 01, pp. 29-62 (1999).

Also, my own essay, "The Ultimate Physics of Number Counting", which too starts from a modal logic perspective.

report post as inappropriate

See, e.g., "Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic"

Resconi, Germano; Klir, George J.; Pessa, Eliano

International Journal of Modern Physics C, Volume 10, Issue 01, pp. 29-62 (1999).

Also, my own essay, "The Ultimate Physics of Number Counting", which too starts from a modal logic perspective.

report post as inappropriate

Dear Tobias,

Let me mention with a grin that John Baetz could probably if possibly have trouble with replacement of his negative probability by negative possibility.

Regards,

Eckard

report post as inappropriate

Let me mention with a grin that John Baetz could probably if possibly have trouble with replacement of his negative probability by negative possibility.

Regards,

Eckard

report post as inappropriate

Dear Eckard,

thank you for your comment. Although I'm aware of John Baez' work, I don't know what "his negative probability" is. Could you point me to a reference?

Obviously, probabilities in the sense of asymptotic frequencies are always non-negative. And asymptotic frequencies are what the Born predicts. No negative probabilities here.

best, Tobias

thank you for your comment. Although I'm aware of John Baez' work, I don't know what "his negative probability" is. Could you point me to a reference?

Obviously, probabilities in the sense of asymptotic frequencies are always non-negative. And asymptotic frequencies are what the Born predicts. No negative probabilities here.

best, Tobias

Dear Tobias,

John Baez is a prolific writer. I am sorry. I did not consider it worth to note where I read claimed negative energy and even most nonsensical negative probability, maybe in sci.physics.research, maybe via his home. While I did not find physical items without a natural zero, experts like Baez are claiming that virtually anything can be positive as well as negative.

I understand that e.g. negative pressure is reasonable for instance:

- if we consider an instantaneous value of the alternating component

- if we measure sound pressure re 20 microPascal in dB.

In general, application of formal mathematics needs obedience of common sense if necessary in the aftermath. Joke: Just 3 people are sitting in a room, then 5 of them leave it. Consequently 2 have to come in as to make the room empty.

If you have humor, read the longish lesson in two parts just written to me by Anton Biermans at my 527. I feel sick.

Regards,

Eckard

report post as inappropriate

John Baez is a prolific writer. I am sorry. I did not consider it worth to note where I read claimed negative energy and even most nonsensical negative probability, maybe in sci.physics.research, maybe via his home. While I did not find physical items without a natural zero, experts like Baez are claiming that virtually anything can be positive as well as negative.

I understand that e.g. negative pressure is reasonable for instance:

- if we consider an instantaneous value of the alternating component

- if we measure sound pressure re 20 microPascal in dB.

In general, application of formal mathematics needs obedience of common sense if necessary in the aftermath. Joke: Just 3 people are sitting in a room, then 5 of them leave it. Consequently 2 have to come in as to make the room empty.

If you have humor, read the longish lesson in two parts just written to me by Anton Biermans at my 527. I feel sick.

Regards,

Eckard

report post as inappropriate

Dear Andreas Martin,

unfortunately I'm having trouble retrieving the paper you mentioned... no online access and not in our library.

But I am currently reading your essay, which seems to contain some intriguing observations, and I will need a little more time to fully grasp it.

So do you mean that probability emerges from a Kripke model of modal logic, just as it emerges in many-worlds interpretations of quantum mechanics? If yes, then that implies that -- in modal logic -- probability is not a fundamental concept, but merely a derived quantity. If this is what you mean when you write "this function naturally leads to probabilities", then we agree: probabilities then are an extremely useful, but non-fundamental, concept.

Also remember that I'm not claiming possibilistic physics to be realistic in any sense; I'm just trying to question established concepts and see what one can do without them.

(By the way, both the long delay in posting Spekkens' email and the missing spaces therein are completely my bad.)

unfortunately I'm having trouble retrieving the paper you mentioned... no online access and not in our library.

But I am currently reading your essay, which seems to contain some intriguing observations, and I will need a little more time to fully grasp it.

So do you mean that probability emerges from a Kripke model of modal logic, just as it emerges in many-worlds interpretations of quantum mechanics? If yes, then that implies that -- in modal logic -- probability is not a fundamental concept, but merely a derived quantity. If this is what you mean when you write "this function naturally leads to probabilities", then we agree: probabilities then are an extremely useful, but non-fundamental, concept.

Also remember that I'm not claiming possibilistic physics to be realistic in any sense; I'm just trying to question established concepts and see what one can do without them.

(By the way, both the long delay in posting Spekkens' email and the missing spaces therein are completely my bad.)

Although it's been a few years since this essay has been written, it seems that there is still some interest in it and it is being read. So I would like to mention a few additional things about the possibilistic Bell inequality of the essay.

It turns out that this possibilistic Bell inequality had been well-known before and is actually due to Lucien Hardy. Nowadays it is known as "Hardy's paradox", and many papers have been written about it.

On the general idea of possibilistic Bell inequalities, there are also notes of a talk "Horn Formulas as Linear Inequalities and Nonlocality Paradoxes" on my webpage,

http://perimeterinstitute.ca/personal/tfritz/2011/ho

rn_formulas.pdf

and a paper that I coauthored,

http://arxiv.org/abs/1105.1819

On a related note, Abramsky and Hardy have subsequently explored "logical" Bell inequalities,

http://arxiv.org/abs/1203.1352

It turns out that this possibilistic Bell inequality had been well-known before and is actually due to Lucien Hardy. Nowadays it is known as "Hardy's paradox", and many papers have been written about it.

On the general idea of possibilistic Bell inequalities, there are also notes of a talk "Horn Formulas as Linear Inequalities and Nonlocality Paradoxes" on my webpage,

http://perimeterinstitute.ca/personal/tfritz/2011/ho

rn_formulas.pdf

and a paper that I coauthored,

http://arxiv.org/abs/1105.1819

On a related note, Abramsky and Hardy have subsequently explored "logical" Bell inequalities,

http://arxiv.org/abs/1203.1352

Login or create account to post reply or comment.