The answer would depend on what you mean by "the physical laws", and if you mean computational program as an analog for an algorithm (that solves decidable problems).  Giving more details on these may help researchers answer your question.

This is a good question, personally I wouldn't know, but I am definitely in the camp that thinks the Simulation Hypothesis is false (for arbitrary universes) unless you have an oracle that can determine when strings belong to undecidable languages.  Another thing to consider is if we could determine all possible laws of the universe (ours), which hasn't yet been determined (seeing as we need some idea of all of them before we can encode a machine to do it, providing we can cover them all in a finite description (i.e., algorithm)).

You are assuming that the laws of Physics are real. They might be indeed, but we don't know that. We know they work well and describe the Universe in a very competent matter. But there is no known way to answer if the laws are real (hard realism) or if we will never move beyond a softer form of realism, a la Van Fraasen, where all we can actually say is that the Universe behaves as if they were true.

Thank you for your interesting and helpful answer Daniel.

I think this is an important question, because, as I see it, there must be logical constraints on any Set of Physical Laws, whatever it happens to be, and/or the kind of universe possible.  And for that reason, theoretical physicists should take guidance from that, in their explorations.

I take your point about the language of my question.  I think it a good idea to wait to see the kind of answers I get, and the kind of answers I want to avoid, then later, I'll ask the question again, more carefully worded. 

Thank you Andre.

As Daniel already pointed out, the language of my question is ambiguous.  When I say Physical Laws (with capitals), I mean those rules The Universe obeys, whatever they happen to be.  I wasn't meaning the set of laws physicists have written down in books.

Here is your theory:

In the beginning there was the Word and the Word was with God and the Word was God. 

Don't ask is it is true, because the Truth is the Word. 

Logos rules. 

So do mean to say that whatever exists in universe also comes along with the laws it will obey and they way it will interact with other entities in universe? So an entity E in universe is not only defined by physical properties but also how it interacts with the universe and all the entities in the universe work with the "minimum acceptable agenda"? Is it a deeper abstraction than string theory?

Thank you Shalender,

Roughly yes. A logical connection between the Physical Laws and The Universe cannot be avoided. That logical connection must take some (definite) form.  And whatever that form, it must be a restriction on what Laws and what Universes are possible. 

Either:

Physical Laws precede the Universe.  Then, The Universe and its progression result from them.  My problem with this scenario is that I would be asking: Where and how do the Physical Laws originate?  Where is that information held?

Otherwise:

Physical Laws are shaped by The Universe.   And The Universe is shaped by the The Physical Laws.

This second scenario would mean that, somewhere in the Law-Universe system, there has to be self-reference or logical circularity.  This is a circular flow of information, where, no matter how hard one looks, no originating information can be found.  And the system has no definite input values.  You might be interested to know that such circularity is present in Hilbert spaces, when constructed, starting from formal, axiomatised arithemtic.

Physical Laws are nothing else as properties of the Universe. Every property comes with the object it is an attribute of, and it would be rather strange to say that it comes from outside. After seeing many things which are red, we can formulate the property "red" outside those objects, but the property came with the objects and pre-existed our definitions. However, Physical Laws are a little bit special from the following point of view: I have seen a book about six universal constants which made possible that the Universe looks as it does and life could appear: number of dimensions = 3, gravitational constant, attraction inside atomar nuclei, etc... A nice question to put is if those attributes of the universe are global or are just local. An apple can be also red only one one side! (I don't know why, but I bet they are just local...)

Inertia is 'resistance to change'. General Relativity talks about inertial entities, which have mass. An inertial entity X given 2 points A, B in space-time, has to follow the topology of space-time to travel from point A to B (in the covariant form, there exists a fibre of the bundle space-time path between A to B and X follows it). General Relativity transforms the problem of Dynamics to the general problem of topology. As per General Relativity that existence of any inertial object modifies the topology of space-time. One of the assumptions with which general relativity starts is pre-existence of space-time topology, which is a non-trivial topology. So the concept of distance and path of connection between any two points A and B pre-exists. General Relativity assumes that there already exists a space-time non-trivial topology.

String theory on the other hand says that there are no point or dimensionless entities, but all entities are a one/two dimensional topological objects and there is non absolute space-time but all the strings in the universe interact to form the space-time. For example if there are N fundamental particles represented as 1-D sets A1, A2, ..., An then the non-interacting universe of them is a cartesian product of the all set: A1 X A2 X ... X An, which is N-dimensional. The interaction between strings reduces no. of allowed states so the universe is a subset of A1 X A2 X ... An. The topology of universe depends on how A1 X ... X An interact. In string theory there is a assumption of 1-D topology for every string and the overall topology of universe is determined by rules of interaction. So the string theory splits the problem of 4-D absolute space-time topology to a more fundamental 1-D topologies and thier interactions. The string is an ordered container of some elements (may be states of string). The containership and orderedness is a information, which comes from outside of the string.

My question on all this is: Why do the non-trivial topologies exists (law of inertial is a result of non-trivial topology)? Why does a string has a non-trivial topology (or an ordered set or a 1-D structure)?

I think that we alway presume existence of topology. The presumption of existence of topology is actually derived from set-theoritical basis of 'absolute existence', which means that anything which exists must have a container.I propose that we should start from a different philosophical basis of "Relative Existence", which will not need presumption of absolute topology. I believe that this paradigm will give us deeper insights in physics. This will also allow results like replicating space-time to beat the speed of light.

The universe and physical laws are identical. Just two different names for the same fundamental concept. All matter/energy that exists "within" the universe follows directly from the laws as does the dimensional topology. I think by definition a universe is a set of laws.

The reason I am talking about inertial is because it is the inertial objects, which have to stick to the universe geodesics. Existence of universe geodesics/non-trivial imply that there is constrain on how a particle can reach from point A to point B. It has to follow a path and there is not direct connection between those points. This is presumed by assuming that the universe has non-trivial topology.

Non-trivial topology is derived from the concept of "absolute existence", which means anything which exist must exist inside a container/set. If we model the maths behind the space-time as relative existence, which seems to be more correct concept and we need not presume the topology. We always perceive things through a series of relative existence connections. We perceive only a thin envelop of sensory inputs around us, which in turn connect to next layer -- next layer --... So something far off exists for us through a series of intermediaries. That is the chain of existence.

Dear Shalender,

I have been working on quantum theory from the viewpoint of formal arithmetic.  The question I am investigating is: how does quantum mathematics look, logicly,  if it is seen as arithmetical information.  Arithmetic in this sense is a system of formulae in the complex field, the real field and the rational field.  More accurately: it is a system of formulae in none of these fields, but which may be seen as true in some of these fields but false in others.  It is an axiomatised system.  These are basicly the Field Axioms.  Collectively arithmetic's axiom-set asserts existence, because generally individual axioms assert existence of variables.

The quantum system I am looking at is the free particle.  The only assumptions I make are the arithmetic's axioms and homogeneity of space.   My findings show that the wave packet, prior to measurement is accidental.  Accidental in the sense that formation of the wave packet is not caused but relies on a certain self-reference being available in arithmetic through coincidence.  This occurs in the formation of the Fourier transform and its inverse and is the result of a cartesian product that accidentally finds itself unitary. And it looks to me there is a strong likelyhood of such self-reference occurring in all unitary vector spaces.

My reason for telling you those things is that I see no reason why your pre-existing topology cannot be accident, so long as it has some other entity to act with in a self-referential manner.  From my own findings, I would suggest that the system you are looking for is -- topology plus some other entity -- that feed off each other.  But, from the perspective of conventional physical theory, this system looks like a unitary symmetry.

If I can give you an example:  The spin-half, su(2) symmetry of the Pauli operators is a unitary symmetry.  But spin-half ultimately derives from isotropy of space. This Isotropy is a symmetry about a single arbitrary axis.  But it is not unitary.  Unitarity is drawn into the su(2) at the point of cartesian products between 3 dimensions. But careful examination of the formation of these products shows su(2) relies on a circular flow of information between the 3. So in su(2) there is self-reference.  This self-reference imposes unitarity.

I would have thought that a theory like General Relativity is a good candidate for circular flow of information. The topology gets information from local matter and the matter follows the topology.  Is there unitarity anywhere in this??  I expect this is not seen in GR, but if your string theory exhibits unitarity in this way, I'd be pleased to hear.

Thank you Lawrence.

I agree with you that the universe and laws are the same thing.  But, irrespective of whether or not you separate the causes from the existences,  the case I wish to argue is that there is a flow of information within a self-contained system with no input from outside.  And therefore, there is logical circularity inherent in The Universe.

Steve Faulkner> Let me think about it and give you a good answer.

Excellent question, and very dear to me given my line of work. Quick answer: Yes, and there are no circular flows of information. Time and causality are related. A flow of information is causal, hence when it “gets back where it started,” it does so at a later time hence a different point in causal space. We think of it as circular because we predict that what will follow is exactly the same as what has happened.

In Physics, space, time and matter are fundamental. But this is only a working hypothesis. Suppose we take "information is fundamental" as the working hypothesis. Information is always encoded the same way, as a causal set C = (S, w), where S is a finite set and w is a set of (cause, effect) pairs. In the Turing machine, S is the set of symbols on the tape and w is the transition function or algorithm, in a TV set S is the cable signal and w is the controller in the set.

Define now a functor F : C => C’. The construction of F is simple, and is published. It is an endofunctor, it is associative (in most cases), and C’ is smaller than C. F generates a groupoid G. G induces a block system S’ on S and w induces a new, smaller partial order w’ on B. Then C’ = (S’, w’), and S’ is a set of invariants with physical meaning (because we started from information as a foundation for Physics).

Functor F can be recursively reapplied to C’. The result is a fractal hierarchy H of invariants, so we get a functor E : C => H.  That’s it. The next step is, of course compare with experiment. It does, and it may explain a host of observed phenomena that no other theory of Physics can. For the sake of an example: in 2011, assuming that the brain implements functor E, I predicted that dendritic trees ought to be optimally short, power law = 2/3. At that time, 4/3 was accepted in Neuroscience. In 2012, independent confirmation was published by a team of Neuroscientists. I can expand, if I get any takers.

To the second part of the question, yes again, the causal set is the "program" and it does have to generate the physical laws. All that needs to be done is to explain space, time and matter in terms of information, and then rebuild the theories from there. Time is easy. Regarding space and matter, there are papers published but it is not resolved yet.

The question still remains, how do those mathematical microlects arise. Since we are physical, they must be explained by Physics. The problem is, then, find the law (of Physics) that answers the question. No existing theory can answer the question. Denying the problem does not help.

Good point Ellis. There are two ways at looking at reality. Either it is mind/thought that constructs the physical universe within in, or it is the physical universe which constructs minds/thoughts within it. I don't see anyway to distinguish between them using either logic or empiricism. By Occam's razor the conclusion is that they are identical. However, I'm not exactly sure what that means. All I know is that something exists (otherwise I couldn't even have the incorrect though that something exists). I have no idea what that something is, and the human race can and does argue about what that something is, but in the end the only real question is why is there something instead of nothing. That question is a fundamental mystery. It's not a mystery as in where did I put my car keys, which has an answer although we may not know it. This question does not have an answer, which means it is an ill posed question. One may pretend to answer it by postulating some unknowable untestable explanation of the mystery (for example a deity), but that is just sophistry. I'm afraid we are stuck with fundamental mystery, which is actually fine with me. The universe/reality would be a much less interesting thing to be a part of if there was a knowable explanation for it. What would we do once it was found? I'd be bored stiff (and out of a job).

Ellie> On the other hand look at another paradigm: Non-mathematical real physical system based Physics

Physicist chose to ignore the infinite nature of universe while modeling it as mathematics but it is a fact that we can never model the universe completely in terms of mathematics. Still all the physics we make is in terms of mathematics and our computation machines are also in the same form. Real universe contains many systems we cannot be modeled accurately as perfect or probabilistic input-output using finite responses. Comparing with this, let us consider another paradigm of physics computers. Let us consider a physical system, which cannot be modeled in more details because of the sheer un-predictability of its responses. But given two exactly same systems, their responses to an input are > 99% in agreement. Wouldn't it be better to create a replica of the remote system in the lab and predict the response of a remote system by giving the input to the system in lab and then model a large more complex system as a combination of the physical results? Wouldn't this be a better model than pure mathematical models?

Ellis

Why does there have to be a universe and stuff? It is possible that the only thing that exists is thought, and that the physical world is a construct of thought. By this I don't mean that thought actually constructs a physical universe in a material way, but that it constructs the concept of a physical universe to try to explain its own existence. This is a non dualistic view of reality, but equally valid as there is no way to determine the difference. I'm just taking the old brain in a jar dilemma a step further. The line between physics and meta-physics is blurry and constantly shifting. Logic is a branch of philosophy. In fact I would say that physics is a branch of philosophy as well since the empirical method came from it. It is only recently in history that we divide knowledge into increasingly more numerous separate boxes. Most likely, this is a result of the modern academic system and not a reflection of the nature of reality.

Shalender,

What makes you think physicists ignore the infinite nature of the universe? There are mathematical models for an infinite universe, both open and closed. Mathematics is perfectly capable of handling the concept of an infinite system. The concept of infinitely comes out of set theory after all. Can the universe be completely modeled by mathematics? I don't know, but just because we currently don't have a mathematical model that explains the entire universe doesn't mean that such a mathematical model doesn't exist. In fact I believe (correct me if I am wrong Steve) the question posed assumes that there does exist a mathematical set of laws that fully explains the universe. Also, what you describe with the lab experiment of a replica system is no different from how physicists model the physical world currently. It's called the scientific method. It is impossible to make a measurement of the entire universe, so we make local measurements and infer physical laws from them. These physical laws are then tested with measurements on increasingly larger portions of the universe (and by larger I also mean smaller, etc...) and modified if they are found invalid in their predictive power.

Yes I do assume the universe has a mathematical isomorphism.  But I don't see that my question needs this.  My premise is that mechanical processes in Nature suffer from the same logical anomalies as mathematics.

1. Actually the problem I have posed comes more from the measurement and automata. No model of universe can be define it in an closed analytical form and no matter how much we observe we will not be able to model it. No model can predict the future perfectly much earlier that it happens because then we can violate it. In fact no model can't even predict a finite set of possibilities. So no free willed conscious being can find a mathematical model, which can model the universe without loosing the free will itself. The existence of free will and consciousness means that there is infinite information within us. We can observe model and also counter anything which universe imposes on us.

2. There are so many other infinite entropy unpredictable systems. We have 6 billion plus of them. Prediction of human action and biological response is better done by giving inputs to a similar beings and observing them to predict the result. For example drugs are always tested on humans and not analyzed. An analytical model of drug response to body may be a NP hard problem but medicine is able to predict the response by simply giving a input and observing the output. Still an action of one drug does not imply action of another chemically slightly different drug (not same chemical action like generics) and it has to be tested on the human being. That is why I have proposed a hybrid computation paradigm.

Ellis> I disagree with your point "Brain in a jar is not just a entertaining movie", Virtual reality is reaching newer frontiers and we will in future have simulations as real as reality. The simulacrum is never that which conceals the truth—it is the truth which conceals that there is none. The simulacrum is true. --- Jean Baudrillard in "Simulacra and Simulations".

The question is how do we differentiate between the external world from the inner world created by mind? Look at my essay: https://www.researchgate.net/publication/266395784_Materialism_non-materialism_and_immaterialism . In this I show that there is a real physical space beyond us and how can we differentiate between the world created by our own mind. Here is the text of it:

"Materialism or immaterialism is a concept based on the concept of existence. The concept of existence comes along with the question: where does it exits? An idea exists in mind, an object in the space, a contradiction may exist in a proof.

If we define materialistic objects as which exist in the physical space, we have a counter-questions: what is physical space? What do you mean by an object? In my definition an object is a set of rules, which exist in our mind in response to the raw input of our senses. So a ball is a set of colored pixels as our eyes see, which seem to follow the equation of a sphere. Further it can be classified as a football, a tennis ball based on the rules our raw perceptions match with the concepts inside us.

The space is a perception of sensory variation and freedom and the time is a measure relative variation. So the space is an empty slate for your eyes, where colors and other attributes can fill up to give a perception different objects. Similarly time is the perception relative change. Let me elaborate: if in the slate of space there are many objects painted then time will allow those changes of the position and other aspects of those objects, which no dimensional aspect of space will allow. For example if there are a few balls in our space, time will allow them to hit each other, blast off breaking them or even vanish, which cannot be achieved by mere change of viewpoint in the space.

It is how your mind interprets the raw sensory inputs, which creates your interpretation of the space-time and the objects in space-time. In an ambiguous situation your mind can itself become confused. For example in the darkness you may interpret a rope like a snake. Similarly when you sleep, your dreams become your reality.

We argue that the space-time exists beyond your mind because many different people external to you will make same ‘raw’ painting of the sensory inputs as you. A counter-question is: how do you distinguish between the different people those you see as making the same painting as yourself as outside of you or a construction of your own mind? As we all understand a human mind is not a single entity, it is a mixture of many minds, conscious and sub-conscious, which generates a perception. Then how do you tell whether the other people you perceive are not the construction your own brain like what happens in the dreams?

The only decent way to test whether whom you perceive as external people are really external people is to test whether they are able to give you interpretation or ideas, which you believe that you cannot make yourself. Now what you believe as the external people because they are able to give you interpretations and ideas beyond yourself may turn out to be a hidden aspect of you. How do you resolve that?

Even if you assume that there are other parts of yourself, which give you different ideas and interpretation different than your conscious self, you have to ask, how many such people your mind can construct at a time? Can your mind paint a crowd of as many people as desired, which give different interpretations and idea from your conscious self? If your mind can paint an arbitrary size crowd, does the majority of that crowd paint the same picture of the raw data of their senses as you? If yes, then you yourself are the complete universe. If you indeed are the complete universe, what contains you? If nothing contains you, where do you exist? You have to consider yourself existing somewhere. Doesn't it mean there is a container or a space around you, which is different from yourself? This proves that there has to be space-time beyond yourself. This also means that you have to assume that there is another conscious entity external to you, which paints the raw data from the senses the same way as you.

So if you agree that there exists entities and space beyond yourself then you can define the material objects are the "raw data", which the entities external to you paint the same way as you. Non material objects are subjective, interpretations, ideas on where entities external to you can vary a lot from you and also among themselves.

By this definition all things, which are a result of raw paintings from the raw senses are the material things and rest of all is non-material. Even the interpretation of a perception of some sensory input as a rope or a snake is non-material. "

Article Materialism, non-materialism and immaterialism

Actually, DNA has nothing to do with human conscious thought. Human conscious thought developed with evolution, where matter has evolved for billions of years under its own recognizance, obeying it own dynamics and properties, and without any external director. Human conscious thought is a property of matter. It has not been stored in DNA because it doesn't fit. To explain this briefly I'll use Hofstadter's metaphor: "Suppose you see your mother and 0.5 sec later you utter `mother'. You did not see your mother" (not a literal quote). You only see 100,000,000 dots of light on your retina. In 0.5 sec, your brain converts them into thousands of carefully calibrated and synchronized signals and sends them to muscles in your lungs, through, vocal cords, chest, tongue, lips, even facial expressions, the result of all of which is the sound `mother'. The function that maps the 100M dots of light to the thousands of signals is too complicated to fit in DNA.

This argument makes the problem of consciousness a problem of Physics, not of Neuroscience or Psychology or even Cognitive Science. Some physicists, including myself, believe it might have been solved already.

Stefan.  Is what you write your opinion or is it fact?