An Accidental Universe

Tom / Rob

We are arguing in circles! So let me try to 'square the circle'. I will again take it one idea at a time, listed and numbered, and you can pick and choose and agree or disagree (True / False). With well reasoned arguments of course!

1)Physical laws are different from mathematical identities.

2)Physical laws depend on certain physical assumptions for their derivation, or on empirical evidence for their validation. They are simply assumed to always be true as long as their premises are true. In this sense, they could be thought as "identities" but that's NOT what I do. A "postulate" for me is NOT an "identity". A=A is logically very different from assuming F=ma is always true when m is constant.

3)Mathematical identities do not depend on any physical assumptions, unlike physical laws.

4)Both physical laws and mathematical identities can only be applied to situations where all their premises are known to be true.

5)Newton's Laws are considered to be physical laws. I do not call these mathematical identities "true by definition". That's sophistic play on words. They are not! Since these depend on empirical validity.

6)Planck's Law for blackbody radiation is also considered to be a physical law, since in its derivation the physical assumption of "energy quanta" is used.

7)I have shown (through my derivation of it) Planck's Formula to be a mathematical identity and not a physical law per se. This mathematical identity is a functional relationship between the incremental change of a quantity E(t) over an interval of t, the average of the quantity E over the same interval and the value of E(t) at the beginning (or end, if we reverse t) of that interval. When E(t) is a simple exponential of t, then this relationship is exact. For any other integrable E(t), this relationship is a limit. (See my chapter, The Thermodynamics in Planck's Law).

8)All physical laws contain physical assumptions. All physical assumptions presuppose a physical view. All physical views are descriptions of "what is" the Universe (Nature). Any description of "what is" is metaphysical in essence. Basing Physics on mathematical identities instead of physical laws (assumed to be true) keeps physics from 'morphing into metaphysics'. I argue we can have Physics without assuming 'physical laws'.

Tom you write:

"Your claim that physical laws are mathematical tautologies is either falsified ... or trivial"

Physical laws are different from mathematical identities. What I am arguing is that we can and should formulate Physics in such a way that what otherwise would have been physical laws are instead derived as mathematical identities without any physical assumptions.

"There are any number of mathematical tautologies that have nothing to do with physics." True! But so what!

"you neglect that Planck's law applies only in the case of blackbody radiation. To take this special case -- (albeit an important case, since it is the limiting case of a body's heat content, which is why it is a "law") -- and declare that it is general, ignores, e.g., radiation effects in out of equilibrium conditions, such as LASER, which do depend on the quantization hypothesis."

Nothing changes about Planck's Law but its derivation using no physical assumptions. Planck's law as was derived by Planck applies only to ideal blackbody conditions. But the same result can be obtained as a mathematical identity and without the "quantization of energy hypothesis". If E(t) is a simple exponential of time, than Planck's Formula is exact. For any other integrable E(t), Planck's Formula is a limit. There are no other premises to my derivation. Just a very simple mathematical identity I am using. I fail to see how you conclude I "declare that it [Planck's Law] is general". Unless you mean this Formula generally applies whenever we want to express the quantity E(t) knowing its incremental change and average value over a duration of t. Which it does! And this is pure math with no physical assumptions made.

"If you are just saying that the mathematics describes a limiting case in every instance of physical law, how is that nontrivial?"

I am not saying or doing anything of the sort! I am only suggesting Physics can be so formulated that Basic Law of Physics can equivalently be derived as mathematical identities. The advantage would be that no physical assumptions are made which could ultimately lead to metaphysics.

Rob, you write:

"force is the first derivative of linear momentum, with respect to time."

That is also how I am considering force. No problem here!

Constantinos

Paul,

A person is not a "Body". It is a "Being".

Constantinos

Constantinos

No, a person is a physical entity. So too is a brick. But a person has certain qualities, such as temperament, which whilst not physically existent of themselves are a function of something physical. Probably to do with brain structure and 'wiring'. Indeed, we attribute different qualities to different bricks, say hardness, but we know immediately that this is a function of the materials used and the method of construction.

Paul

Anonymousse

"To you that ageing process of matter is just part of the world, you accept it"

What do you mean "just", both in the sense:

-it is just part of physical existence, what else is it? It is an example of alteration in physical existence. The rate at which this sequence of alteration occurred is what timing is measuring

-I do not just "accept" it, ie and then want to do nothing more, which is apparently, according to you, what "modern physics" does. What have I said that implies that?

Incidentally, what is this question you refer to, which, by virtue of the way you make the point, I apparently have not addressed?

It would also be useful in this exchange, ie would not take up so much of the ageing process, if you addressed the points I make, rather than posting new ones and/or just saying 'no it isn't'

Paul

Constantinos

I have picked and chosen.

"Physical laws depend on certain physical assumptions for their derivation, or on empirical evidence for their validation. They are simply assumed to always be true as long as their premises are true"

Obviously. But if the premises are true, then that is not an assumption.

"Mathematical identities do not depend on any physical assumptions, unlike physical laws"

Not so. Because, by definition, any statement is, if the reference is absolute, an assumption. Your mathematical identity must be based on presumptions in order to invoke it. If A, there is always the possibility of not-A.

And herein is an illustration of the flaw in your thinking which I keep pointing out. There is a 'correct' form of physical existence, ie the one we can know, which is based on a definitive and identifiable physical process, not philosophy. So assuming any law/theory/representation is proven to correspond with that, then it is correct. That is, within the existentially closed system of which we are a part. It may be rubbish 'really', but we cannot externalise ourselves from our own existence. We can only know what it is potentially possible for us to know, so that is irrelevant. This is science not mysticism. The reference for validity is that, not some unattainable absolute.

Paul

Rob

Going back to your original point(!)

Exactly. The only 'choice' is the degree of differentiation in the timing reference, ie the faster the rate of alteration referenced, the better. There is no choice over what timing is.

The other major flaw in the thinking is that what we see is existence, whereas it is a photon based representation thereof, the degree to which it provides an accurate and comprehensive representation is something which needs to be examined.

Paul

Sorry, will try to explain, but briefly, because I really do suggest you do some background reading. Time is an area where some people feel they can get away with being vague, because there's so little accepted physics on the map about time, and the well-known physicists are rather quiet about it for that reason. But although it's less talked about, everyone knows the situation, and you can't just throw vague staements around.

When I say you accept the process of change that modern physics doesn't accept, I mean for instance where you say "physical existence is an existential sequence". You've said several things about the process of alteration that boil down to "That's just the way it is".

The question you don't seem to understand is - how can that process of alteration we seem to observe be real, when the Rietdijk-Putnam argument proves beyond any doubt that if the standard view of SR is right, then this flow of time is in the perception of the observer only? It proves this by showing that different observers moving differently have the past and future in different places for objects seen across a distance. This seems to put the difference between past and future squarely in human perception, and it seems to rule out the idea of a present moment moving along through time, other than in human perception. I'm not going into this further, you need to read up on it. I'll wish you luck with that - hope you reach a clearer understanding of these things, which we're all trying to do.

Rob,

You write, "two sides of a coin -- and equally likely initial conditions (1) the cosmos had a beginning, and (2) the cosmos had no beginning; it has always existed, it just changes form."

That's what Einstein originally believed as well, and the reason he inserted the cosmological constant term into his equations.

It was more than the physical expansion of the universe that he didn't foresee, however; his physics of continuous functions also forbids probabilistic equally likely outcomes. An initial condition that includes an infinity of equally likely universes solves that problem -- trading the singularity for random fluctuations.

Tom

Tom,

I know you are "done" with me, but Einstein inserted the cosmological constant to balance the contraction of gravity from causing "the universe" to collapse to a point. What Hubble discovered is that the space between galaxies appears to expand. This doesn't change Einstein's observation that gravity causes the measure of space to contract and that according to both observation and theory, these two effects balance out, resulting in overall flat space. What is expanding between galaxies, is collapsing into them. Hubble discovered Einstein's cosmological constant. Further measurements of this effect have only seemed to confirm that it is the cosmological constant. So if there is a balanced cycle of expanding(energy) and contracting(mass), there is no need for a singularity. On an infinite scale, galaxies are just random fluctuations.

Would an "initial condition" would be a singularity, or a vacuum? You say it obviates the need for a singularity, so the only remaining description would seem to be the void; infinite, inert space. The fluctuations in which being what we see. Mathematically, an infinity of equally likely frames and points.

For the mathematical explanation of my last, see my ICCS 2006 conference paper. I've been in the process for several years, of making it more accessible.

Key points related to post above: 1) a physical definition of time: "n-dimension infnitely orientable metric on random, self-avoiding walk." The exchange of a continuous curve for a discrete point on the 3-manifold (Poincare Conjecture).

Tom

Paul,

Just to clarify your blatant misunderstands ... not that it will make any difference to you.

You write,

"if the premises [to a physical law] are true, then that [the physical law?] is not an assumption". A statement can be totally false yet the premises to that statement be true. A simple example: "if the sun comes up today, then I will win the lottery". Clearly the premise "the sun comes up today" is true. Yet the conclusion "I will win the lottery" is probably false! Were we to assume this statement (as a physical law) true, then we would wrongly conclude I will be a rich man at the end of the day!

You write,

"Not so[to 'Mathematical identities do not depend on any physical assumptions, unlike physical laws']. Because, by definition, any statement is, if the reference is absolute, an assumption. Your mathematical identity must be based on presumptions in order to invoke it."

Certainly any mathematical identity can only be invoked if all of its premises (presumptions) are known to be true. What I am arguing here is the premises to mathematical identities are NOT 'physical assumptions'. Such is the nature of mathematical reasoning as contrasted to Physics.

You conclude, "We can only know what it is potentially possible for us to know". This is certainly true in more ways than you realize.

Constantinos

Constantinos,

Rob and I aren't arguing at all, much less in circles. If the F = ma explanation isn't acceptable to you, consider the unreduced equation of special relativity: E^2 = m^2c^4 (pc)^2

These terms explain that a relativistic particle of nonzero mass and zero momentum possesses negative energy. Does that make physical sense? -- certainly not within the context of local measurement results. Another example:

The very same mathematics that describes energy entropy applies to communication entropy. Are these the same thing? -- that's a deep and open question.

Point is -- equations that apply to physical phenomena are always ambiguous unless considered in the context of certain assumptions about the physical world, which are dervied from physical experience. So to try and characterize physical laws by mathematical formulations that are not derived from physical experience, contradicts both the rules of physics and the rules of mathematics. It will always be possible to find a counterexample to your argument.

Tom

Tom,

Regarding "That's what Einstein originally believed as well"

I did not say that I believed it, rather, I know it.

I know there is no proof for the existence of a creator God, and I know there is no disproof either. I know I have no information, so flip a coin.

But I believe, along with Laplace, "That god is an unnecessary hypothesis." It is a hypothesis, that explains nothing, that needs to be explained.

Now if there were some great "Cosmic Coincidence", that needed to be explained, regarding creation, then I could easily change my belief. For example, if the estimated age of the universe turned out to be exactly pi billions years before the birth of Christ, if every better estimate of the age yielded one more digit for pi, then I and any other rational being would be very hard pressed to argue, that it is just a "Cosmic Coincidence". But no such unexplainable initial condition has been observed. There is nothing like that, that needs to be explained.

The universe does not appear accidental to me, but neither does it appear to be designed. It appears to have resulted from the process of natural selection, operating at many different scales, spatially, temporally and logically.

Natural Selection is a process that transforms equally likely initial conditions, into exceeding unequally likely final conditions. The point is, that the likelihood of the observable, final conditions provides no information about the likelihood of the initial conditions. Consequently, observing that the final conditions seem to be "finally tuned for human life", need not imply anything at all about the initial conditions. Natural Selection can, and will, transform even the most mundane initial conditions into something unusual and interesting.

Rob McEachern

Rob,

You write: "Regarding 'That's what Einstein originally believed as well'

I did not say that I believed it, rather, I know it."

No, actually. There's no objective knowledge there. You only assume that the choices between a static universe and an exploding one are equally likely and the only choices available.

"I know there is no proof for the existence of a creator God, and I know there is no disproof either. I know I have no information, so flip a coin."

I didn't mean a creator god, and neither did Einstein. "God" here is a metaphor for nature -- Spinoza's god.

For some time now, I have been studying the implications of Leslie Lamport's paper, "Buridan's Principle" and one such implication is that a single coin toss does not decide the tipping point of an ensemble of individual events from a continuous range of random variables: "(Charles Seife) proposed that elections (in a NYT article) be decided by a coin toss if the voting is very close, thereby avoiding litiginous disputes over the exact vote count. While the problem of counting votes is not exactly an instance of Buridan's Principle, the flaw in his scheme will be obvious to anyone familiar with the principle and the futile attempts to circumvent it. I submitted a letter to the Times explaining the problem and sent email to (Seife), but I received no response."

Not surprising. I have also met with silent opposition from Richard Gill over this misapplication of the law of large numbers. In any case, though, one should be able to see that -- just as in the case of an uncollapsed wave function -- "equally likely" choice are independent of one another, a fair outcome not predictable by a single Bernoulli trial.

"But I believe, along with Laplace, 'That god is an unnecessary hypothesis.' It is a hypothesis, that explains nothing, that needs to be explained."

Laplace didn't say that. He said (to Napoleon IIRC), "I had no need of that hypothesis." The difference is that dropping an assumption -- common in physics and mathematics -- is to be preferred to "multiplying superfluous assumptions"(Newton). The god hypothesis actually explains a lot -- if one wishes to invoke it, however, be prepared to multiply superfluous explanations to make it work. Obviously, that happens a lot here on FQXi.

"Now if there were some great 'Cosmic Coincidence', that needed to be explained, regarding creation, then I could easily change my belief. For example, if the estimated age of the universe turned out to be exactly pi billions years before the birth of Christ, if every better estimate of the age yielded one more digit for pi, then I and any other rational being would be very hard pressed to argue, that it is just a 'Cosmic Coincidence'. But no such unexplainable initial condition has been observed. There is nothing like that, that needs to be explained."

Apply the equally likely hypothesis to the multiverse, though, and it is explained -- with probability 1 -- that there exists at least one trajectory within the history of the universe from among random choices of initial condition, that results in the physical laws as we know them.

"The universe does not appear accidental to me, but neither does it appear to be designed. It appears to have resulted from the process of natural selection, operating at many different scales, spatially, temporally and logically."

Albrecht's hypothesis doesn't dispute that. *The* process, however, is one among infinite results of evolution from differing cosmoloigcal initial conditions.

"Natural Selection is a process that transforms equally likely initial conditions, into exceeding unequally likely final conditions. The point is, that the likelihood of the observable, final conditions provides no information about the likelihood of the initial conditions."

Sez who? What gives you the idea that final conditions are observables? May I borrow your crystal ball? :-)

"Consequently, observing that the final conditions seem to be 'finally tuned for human life', need not imply anything at all about the initial conditions. Natural Selection can, and will, transform even the most mundane initial conditions into something unusual and interesting."

Only in the context of equally likely universes -- from a continuous range of infinite independent variables of a multiverse, each choice of which results in a distinct cosmological initial condition.

Tom

Tom,

"Apply the equally likely hypothesis to the multiverse, though, and it is explained -- with probability 1"

The probability that I see the world that I actually live in, is also 1. The probability of me seeing some other universe, at least in my life-time seems indistinguishable from 0. There are many versions of the Anthropic Principle, and many interpretations of it. But I believe the correct version/interpretation is more or less equivalent to the "reduction to an absurdity" argument: Given that my life exists, with probability 1, any hypothetical history of the universe, that predicts any other result, is self-evidently absurd. All such hypotheses must be employing either bad assumptions, bad statistics, or bad logic. Other interpretations are possible. But they are not probable. It is not random, independent probability that matters. As in the "Monty Hall Problem", it is conditional probability that matters. Given the condition that the probability of my existence = 1, it is inevitable the I must be able to look back upon my history, and observe all the conditions conducive to my existence. Looking forward, from the beginning, my existence might seem wildly improbable. But looking backward from the present, it is inevitable. Unlike the laws of physics, the "law" of natural selection is NOT time-reversable. That is why the perspective is so alien to the physicist.

The concept of "Determinism" means different things to different people. To me, in order to be compatible with my free-will, and the laws of physics, it must mean that, after the fact, I can, at least in principle, determine how things came to be; hind-sight is 20-20. But forward-sight is not; not all things can be "determined", in the sense of being predicted before-hand; the problem is, that the entire "computing resources" of the entire universe, are only sufficient to perform some predictions in real-time - making the prediction takes just as long as performing the action, because they are one and the same thing.

"Sez who? What gives you the idea that final conditions are observables"

Sez me. For me, my life is my final condition. I do not believe I will observe any other.

Rob McEachern

One further thought about the multiverse:

If all possible laws (which are not self-contradictory) exist somewhere in the multiverse, then there must exist at least one universe in which that universe's initial conditions and laws, including those of Natural Selection, are such that it is *Necessary*, rather than contingent, that things be as they are in this universe.

I merely point out that this *is* the universe we live in. All other universes within the multiverse are thus *unnecessary* to the existence of this one special universe, which is *necessary*.

Thus, following Laplace, I may state the multiverse itself is such that "I had no need of that hypothesis." - namely, the hypothetical existence of an infinite number of *unnecessary* universes in addition to the one *necessary* universe.

Rob McEachern

Jim:

Just because I don't want to repeat myself continuosly I do invite you to read my post of january 16th,.This it's not all we can say about the so called "time" but it is the basement. later I would read what is your tought about it.

Hector

Rob,

It is a conundrum for those who view math as foundational, that after distilling reality down to its mathematical essence, that the result is effectively meaningless. By eliminating infinities from reality, in order to limit it, they end up with an infinity of realities.

Nature has the last laugh.

I appreciate your sensibility.

Tom,

I appreciate the sentiments in your last comment. And I will try to respond as clearly as I can to the best of my ability.

Let me respond directly to your comments in order:

You write, "These terms explain that a relativistic particle of nonzero mass and zero momentum possesses negative energy. Does that make physical sense?" No! This does not make physical sense to me! But the problem, imho, arises because we consider the mathematical construction of SR and GR as describing "what is" physically real. Were we not to make such assumption this (meta)physical mystery goes away. That is what I am arguing is possible.

You write, "The very same mathematics that describes energy entropy applies to communication entropy. Are these the same thing? -- that's a deep and open question." Yes, I do believe the two ideas (thermodynamic entropy and communication entropy) are the same. One of the results that comes out of my derivation of Planck's Law is to show that link. What 'thermodynamic entropy' and 'information entropy' have in common is that they are both 'amounts of evolution' (in one case energy in the other case information) over a given period of time. This is how 'entropy and time' are mathematically linked. And thus, the Second Law of Thermodynamics is not really about 'entropy' but about 'time'. This Law should really state that "a positive duration of time is needed for any physical event to evolve".

You write, "to try and characterize physical laws by mathematical formulations that are not derived from physical experience, contradicts both the rules of physics and the rules of mathematics". I am not sure I understand your reasoning here. Are you saying that unless a 'physical law' is discovered in the heap of experimental data it cannot apply to Physics? What gives validity to a 'physical law' is empirical evidence only? I disagree. And point to the Pythagorean Theorem as a counterexample. Certainly, this formula can be discovered in the measurements of physical distances. As the ancient Egyptians did! But what gives validity to this 'physical law' is the mathematical necessity which deduces its truth. Thus making it a 'mathematical identity' rather than a 'physical law' per se. Something analogous to this is true of Planck's Formula. I have shown this Formula is also a 'mathematical identity' rather than a 'physical law'. And based on this experience (and others as well) I argue that Basic Law of Physics can and should be derivable as mathematical identities. See The Thermodynamics in Planck's Law

Constantinos