Simple Math for Questions to Physicists by Lee Bloomquist

Good question! It's going to take me a while to think about this.

In the mean time please tell us what you think about the final question of the essay--

Is action more basic than space?

L

"Are the objects of the model mathematical objects?"

I imagine these streams as "robotic petri nets."

Petri nets that can re-write themselves-- in fact, re-diagram themselves-- on the fly, in real time.

It's a kind of Category Theory. There's lots about it on John Baez's blog about the climate anomaly.Attachment #1: 4_image.jpg

Thank you for commenting on my submission, Mr. Fisher.

Like words, all types of mathematics mean language. But whatever the language, I do agree that reality is more than just words.

I read your FXQI submission and perhaps of interest to you may be an ancient, one-sentence fragment from Parmenides. Parmenides was the person Zeno was defending by means of his story about the race between Achilles and the tortoise.

The fragment, only partially translated, is this: "'Auto' is for thinking and being." I leave "auto" untranslated because the ancient meaning of the word depended on context. Compared to other possibilities (e.g. auto = the same thing), I prefer a translation of the word that we rarely see analyzed these days--

"The self is for thinking and being."

I can think about the self.

And, I can Be the self.

If the former is occurring, at that time it seems to me that I would have also to Be the self, because otherwise, how could I think?

And also, I experience thinking as a stream of thoughts.

Putting these together might look like equation 1 in my submission--

being = (thinking, being)

which, like equation 2, would expand out to this--

being = thinking, thinking, thinking...

(forgetting about the parentheses for the moment)

But the self is for thinking AND being.

So Parmenides also seems to be saying that this is a possibility--

being_self = (being_self)

In this case thinking has disappeared! Parmenides seems to imply that in some way, I can stop my thoughts and just-- Be the self.

From other fragments of text from Parmenides there is a "way of believing" to which we fall victim; and compared to that, a "way of knowing." Although it can involve inference, for example inference in mathematics or physics, thinking frequently does involve beliefs. For example--

stream of thinking = belief, belief, inference, belief, inference, and so on.

On the other hand, consciously Being the self seems like basic knowledge to me, with no belief and no thinking involved.

So Parmenides may also agree with you. There is more to reality than just thinking-- even if the thinking involves a lot of inference, as in the case of math and physics.

L

...and therefore:

regarding *dark energy*

Does anyone really believe that it requires no thermodynamic work to run the Universe?

Thermodynamics is very common sense.

First law of thermodynamics:

You can't win, you can only break even.

Second law of thermodynamics:

You can't break even unless you reach the state of absolute zero.

Third law of thermodynamics:

You can't reach the state of absolute zero.

(Because,

you are only a finite machine.)

Following the theory of these laws. engines running the Universe must produce waste streams.

Next consider the Probability Learning Game.

The experimenter throws loaded dice to determine a varying escape route for one after another of prey animals.

Each time, the subject predator guesses where.

Some always do escape.

Constituting a thermodynamic waste stream.

Which

expands the Universe

proper time

Proper time

Greetings Joe and Vladimir,

Thank you for requesting my comments!

To better understand what you are saying is there a diagram you could show me? I think you could upload it as a file in order to accompany any explanatory text you may want to post.

Best Regards,

L

Vladimir, if there were a diagram of what you wrote I believe it would assist thinking about your ideas-- especially (for me at least) if the diagram were based on a language of objects and arrows.

Georgina-- I now see that the paper I submitted to this contest is too terse. More words are needed to clarify. So I will make the attempt. I also hope the result will be a useful example of a diagram written in the language of objects and arrows. To begin:

By expanding the model of proper time discovered by Minkowski (now basic to General Relativity) the paper shows a mathematical connection between General Relativity and Quantum Mechanics, specifically by linking the Born rule of Quantum Mechanics to proper time of General Relativity.

However this is not a link written in the language of Quantum Field Theory. Rather, it is a link between GR and QM that involves multiple mathematical languages-- non-wellfounded sets, nonstandard analysis, situation theory, channel theory, informationalism, game theory-- and then, the resulting, expanded model of time can be diagrammed using objects and arrows. It turns out to be compatible with something Einstein said:

"The only reason for time is so that everything doesn't happen at once"

Here's how I found this model of time:

Years ago, I used the programming language Smalltalk80 and a diagram based on objects and arrows to simulate a complex and expensive automated manufacturing system-- before it was built. The engineers in charge wanted to know from a simulation whether or not the system would work in all anticipated situations. The answer was not obvious by looking at the layout of machine drawings, because the system had to process a complex schedule of parts.

The objects in the diagram I used to model this system were of two types: (a) places, each drawn with something like a circle, and (b) transitions, each drawn with a rectangle. Hundreds of these objects had to be drawn and connected by arrows in order to model the system.

The result looked like a board for playing a game. There were rules for drawing this game board. There were also rules for moving the tokens on the game board. (The tokens represented the parts and information conveyed between the elements of the system).

Here are the rules for drawing the game board:

(1) Every arrow starting from a place must end at a transition.

(2) Every arrow starting from a transition must end at a place.

Here are the rules for moving tokens on the game board:

(1) When the places "upstream" from a particular transition (as determined by the direction of its attached arrows) become filled with tokens, remove one token from each upstream place.

(2) After the code written for that transition is completed, place a token into each of its downstream places.

Smalltalk (today, the programming language Pharo) allows objects to spawn blocks of parallel code that wait for signals from "semaphores." The block of code will only run when the semaphore signals it. The result is Not lines of code that run one after another exactly as they are written in the source text. Instead the sequence of executing the blocks of code depends on when the semaphores trigger the code-- in "real time." The semaphores look at upstream places from the transition object which, by means of the attached arrows in the diagram, own them. So instead of a sequence following how the source code was written down, in the simulation the sequence of running the blocks of code was determined by the tokens placed on the game board.

This worked-- except when the parts entering the system according to the simulated schedule backed up. I found that in this case, when a transition had "fired" (by means of its underlying semaphore), another token in an upstream place could fire yet another copy of the transition object. So instead of just one of that particular transition existing in the simulation, as a result there could be more than one. The transition was no longer unique. There existed multiple copies of it in the simulation. To anthropomorphize a bit, the transition had no unique self identity. It had multiple identities-- which is an oxymoron except in spy circles and psychotherapy.

In this sense things could "happen all at once." As in Einstein's quote I had to add something to the simulation in order to prevent "everything from happening at once."

The solution is in the attached diagram. I drew one of these kinds of places for just the transition itself for each transition where it was possible for "everything happening at once." To characterize this feature in words, each transition with the possibility for "everything happening at once" needed a place to itself and only for itself, to keep it from firing when it was already firing, and prevent "everything happening at once." I realized that I had to simulate time itself in order to make the simulation work properly.

When running the simulation, these places for each transition's "self" use looked like they were constant-- as if they were always constantly filled with a token. But each of these "self identity" tokens was really, according to the rules, being taken off and put back into its place faster than the eye could see. It was this mechanism, where each transition had a place for itself so that only one instance of itself existed, that kept "everything from happening at once."

Years later at a workshop at Stanford called "The Business Applications of Situation Theory," I learned from Jon Barwise about non-wellfounded sets.

It struck me that the "place for self" I had used years before in the simulation had a structure which looked like a non-wellfounded set:

Eq. 1: unique_constant_identity = (changes, unique_constant_identity).

"Unique_constant_identity" in eq.1 produces the stream of "changes" evident in all of the downstream places from the transition that owns the unique place.

This perspective on proper time is not new. In fact it's ancient. Parmenides, whom Zeno was defending with his story about the race between Achilles and the tortoise, had described the same situation in the fragments left to us of his poem titled "On Nature." The poem tells of a journey from the domain of belief into the domain of knowledge . The person making this journey must be carried in a chariot.

In eq. 1 the chariot is "unique_constant_identity"-- the constant presence of a unique self existing in the present, which is always constantly supporting and evident to a conscious person for as long as that person is alive. The unique constant self that's experienced, and the time in which this self is experienced-- i.e. the present-- are always the same to that person as long as the person is conscious and lives, just as for the place reserved for "self" in the above diagram, and just as for "unique_constant_identity" in eq. 1. The road on which the chariot travels is "changes." Like the old saying, wherever you go, there you are!

Although Minkowski discovered the modern representation of proper time which has become the basis of General Relativity, as far as I'm aware the ancient representation of proper time is due to Parmenides. The ticking of the clocks Einstein imagined to obtain relativity are like the trees and changes along the path travelled by Parmenides' chariot. But Einstein left the constant chariot itself implicit, and not explicit, in his mathematics of relativity. Eq. 1 make this constant chariot, "unique_constant_identity," explicit in the mathematics.

Even if not supportive of numerical calculation, this mathematical connection between General Relativity and Quantum Mechanics supports logical models of dark matter and dark energy.

Reference:

The diagrams in the following paper show the origin of this idea.

https://docs.google.com/file/d/0B9LMgeIAqlIET3B2NEE2MmxDOWM/edit?usp=docslist_apiAttachment #1: Petri_net.pdf

Georgina wrote: "Re.your question, I think it depends on what you mean by basic. Does it mean most simple, or most foundational or of primary importance"

"Yes" would be way too cute, of course. I should be able to answer you by examples.

In the context of the paper, I mean using equations without space variables would be more basic than using equations with space variables. Existing classical formulae for action involve moving from one set of space variables to another (possibly the same) for example. Then would moving in a game be more basic action than action based on space variables? Would it be action at all?

In another sense it's the vacuum state, as Roger Penrose uses it in this paragraph from his book The Road to Reality (p 657):

"The shadowy state-vector

[math]|0 \rangle[/math]

over on the extreme right is normally taken to be the 'vacuum state', representing the complete absence of particles of any kind. A succession of these creation operators then creates a succession of particles, added one by one into the vacuum, so that

[math]\Psi\Phi\ldots\Theta |0\rangle[/math]

is the state that results from introducing particles successively with wave-functions

[math]\theta , \ldots , \phi ,\psi.[/math]"

The formula looks like the product of factors of powerful numbers, like octonions or something like that. The basic idea being that in a product of factors like this, if any factor is zero, the whole product gets zeroed. So the vacuum state-vector, from which the sequence of products starts, can't be zero.

Probably in QFT there is too much basic stuff-- way too much, 120 orders of magnitude too much stuff. Which leads to the vacuum catastrophe.

If instead the sequence of products like this begins with the Born infomorphism, there is far less basic stuff to begin with.

John Baez found "Quantropy" (it's on his Azimuth blog) which means to me the sum of complex numbers representing possibility must add to one.

In the case of multiple particles with Born infomorphisms-- in the nonstandard future, where the only "words" available involve possibilities, and particles do not yet exist, the state (previous comment here) "unique_constant_identity" is such a state of possibility in the nonstandard future. Using complex numbers to represent possibility and impossibility (as in the paper), information about a particle in this situation can be conveyed in terms of possibilities by saying that the particle on which we're focused has a possibility (complex number) of 1 for its particular "unique_constant_identity" and zero for every other "unique_constant_identity" in the universe of particles considered.

In terms of quantropy, this looks OK. Because at this level of inquiry-- before space is introduced into the equations-- the 1 we have assigned conforms to the rule of quantropy, and, of course, adds to 1.

That's compatible with the way complex numbers are concluded to represent possibility according to informationalism, as in the paper. 1 means it's possible with value 1.

0 for all the other states of "unique-constant_identity" means all those other states are impossible for the particle.

OK, now we start with a 1 in Penrose's equation.

There is far less basic stuff to begin with. And the 1 can be ignored when later we introduce space as a possibility.

[math] \Theta\times 1 =\Theta[/math]

"...over my head." Actually me too.

On the equation in previous post--

There's a horrible mistake in physics.

It's somewhere in that equation.

And, it's not a *calculational* error.

It's a *logical error.*

First let me show you how big this mistake is.

Then you can say whether or not you think it really is horrible.

That shadowy vacuum state vector in previous post is the source of dark energy.

Astoundingly brilliant physicists have calculated how much energy this equation puts into the universe. And the result is horribly and logically wrong.

Calculations say that the amount of dark energy there should be in the universe is 120 orders of magnitude greater than the actual dark energy in the universe, according to the expansion of the universe as measured by instruments.

That amount of error signals a *logical* mistake somewhere in the equation.

First I'll try to write it down. Then after that huge number, I'll return say why it's a *logical* mistake in physics.

[math]\bold 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[/math]

OK, with that much dark energy expanding the universe, the universe would have to expand at very close to the speed of light if the vacuum energy is massive.

But if the vacuum is massless, then the Universe would expand faster than the speed of light.

There's a *logical* error here.

But now, because I said this, I have to give a concrete example in the history of physics of a *logical* error in physics.

It's Einstein's thought experiment.

Say that Einstein dreamed that he was riding a wave away from an electromagnet.

But he was riding a normal magnet.

The electromagnet held him back by pulling on the normal magnet that he was riding.

So he applied more speed. He went faster than the speed of the waves of electromagnetism pulling backward on his normal magnet.

But as soon as he went faster than the waves, from his perspective the electrons he was looking at in the electromagnet switched direction and began cycling around the core of the electromagnet in the opposite direction from which they had been turning.

He was outpacing the waves, and seeing into the past of the electromagnet.

Following the laws of electromagnetism, as soon as the elections were seen to change rotation, the force from the electromagnet on the normal magnet changed direction. Instead of pulling back on the normal magnet, because of the change in direction of rotation, the electromagnet then pushed the normal magnet in the direction it was already going.

With no limit on the speed of light, this process could continue without end. And the faster the speed of the normal magnet, the more force exerted on it from the electromagnet. There could even be infinite force, if this kept up forever.

It's a logical violation of the laws of thermodynamics.

You can't have a force that can increase itself by pushing something away from itself.

It's beyond being a perpetual motion machine. It's like wall street.

That's what I mean by a *logical* mistake in the physics.

But since physics is logical, you can't go faster than the speed of light.

Once in a while there comes a time when new logic, instead of new method of calculation, has to introduced in order to fix up a logical mistake in physics.

In previous post I tried to correct this logical mistake in physics by writing the final equation in the post.

To get to that equation, I had to adopt the role of being an *informationalist*. It's in the references for the paper.

I had to apply an "informationalist inquiry" in order to deduce what kinds of numbers represent the possibilities that exist in the nonstandard future.

The science required to write that equation down is Not a science of calculational method.

It's a science of information.

Again, it's in the references.

The same science is required to understand the mysterious connection between mathematics and physics.

Where the mysterious connection occurs, it's an infomorphism.

But you need a science of information to say that.

Update:

Interacting dark matter:

http://arstechnica.com/science/2015/04/new-evidence-that-dark-matter-could-be-self-interacting/

If Born infomorphisms are ordered commutative monoids, here's how they can be assembled into resources--

https://johncarlosbaez.wordpress.com/2015/04/07/resource-convertibility-part-1/

E.g.,

[math]BornInfomorphism_1 \newline BornInfomorphism_2 \newline BornInfomorphism_3 = \newline BornInfomorphism_{cartesianProductOf123}[/math]

On the right hand side of the equation is the core of an information channel, from Channel Theory (in the references for the paper).

On the left hand side of the equation might be quarks.