A Self-Gravitational Upper Bound on Localized Energy

John,

Math is unlike religious belief. But it is also unlike science.

Aristotle is often viewed as the father of formal logic. Math employs this logic as follows:

State some "starting points", such as axioms or postulates.

Use "deduction" to derive some logical consequences of those axioms.

The axioms, as such, are neither true nor false. They are merely "interesting" or "uninteresting", depending upon whether or not they lead to interesting deductions.

Science, for Aristotle, was much the same:

State some assumptions, like "the cosmos is perfect", "the most perfect form is a perfect sphere", then deduce that the moon etc. must be a perfect sphere.

Unfortunately for Aristotle, and modern physicists that make the same mistake, in science, unlike math, the "truth" or "false" of the "starting points", are of interest. That is the most important distinction between math and science.

The truth/false question about the starting points cannot be resolved, ever, via deduction. So attempts to demonstrate their truth via induction, were made. But all such attempts failed.

Consequently, the "scientific method" rejects all such assumptions, axioms etc., as valid "starting points". In their place, it simply uses observations as the "starting points".

Observations are what they are, and like the "starting points" in math, they are neither true nor false.

But unlike math "starting points", the "starting points" of science, have other problems; they might be "repeatable" or not. They might be subject to misinterpretation or not. And attempting to use them, in science, is impossible, without dealing with the "Problem of Induction", as described by David Hume, a couple of centuries ago; "repeatable" observations necessarily assumes that the future will resemble the past.

From these scientific "starting points", theory merely "fits" mathematical equations to the observations, to create a concise, quantitative description of those observations. Then, as Karl Popper noted, good science, as opposed to pseudo science, makes risky predictions about yet-to-be made-additional-observations, collected under different circumstances (in the distant future, at very different temperatures, pressures, energies etc.), that can be falsified, or not, by future observations.

A major problem in modern physics, is that many physicists have reverted to using "starting points", other than observations (as in mathematics), and/or fail to make risky predictions (as in pseudo science).

As George Santayana said "Progress, far from consisting in change, depends on retentiveness... Those who cannot remember the past are condemned to fulfill it."

Rob McEachern

Rob,

As one might expect, I don't agree with you on what is "wrong" with physics, because my philosophy of science is conventional. Yours, I claim, is not.

For example, you say, "Science must be based only on observations, not assumptions about what is being observed."

In fact, assumptions about what is being observed is *exactly* the basis of theoretical science, which becomes successful as a scientific theory when what those assumptions predict are tested against the outcome of physical measurements. The whole content of science is theory and result. Your view of the scientific enterprise is entirely inductive.

"But as Socrates noted 25 centuries ago, observations are deceptive; 'what is actually observed' is never quite the same as 'what actually exists'.

Fine, but that isn't science.

You write, "Physics has sought for 'Theories of Measurement', but neglected 'Theories of Inferences derived from those Measurements."

This isn't true. We don't infer anything from measurements -- we infer by correspondence of *theory* to measurement results. This is exceedingly easy to see, when one considers data in the absence of theory -- the best example I know, is that of the cosmic microwave background radiation, a precisely measured value. Unless explanation is supplied -- most popularly, at the moment, by big bang theory -- the data are absolutely meaningless.

Tom

Rob,

Keep in mind monotheism is just one religious sub-set and a logically flawed one at that, since a spiritual absolute would be the essence of being from which life rises, not an ideal form from which it fell. It is politically convenient though, as it validates top down authority.

Religion is a society's vision of itself and nature, as government is how it manages itself within nature. This is a very old dichotomy. Think Chieftains and Shamans. Of the three monotheistic religions, Christianity was an undergound movement long before being co-opted by an empire in decline and thus has a significant split between religious vision and government management. On the other hand, Islam was a very successful social movement for the first seven hundred years and coasted the next six hundred, before being eclipsed by the industrial west in the last hundred. Thus has an integrated vision of and management of society. Not that it always works in practice. Judaism has had two thousand years of developing ideal social views and now has to incorporate them into the actual governance of a country.

So what you are saying is that math is the vision of what knowledge should be, while science is how it is actually acquired.

Tom,

You have to have induction before you can have deduction. We are mortals, not Gods.

Tom,

"my philosophy of science is conventional. Yours, I claim, is not." I agree. I merely point out the recent essay contest was about "Which of Our Basic Physical Assumptions Are Wrong?" To which I respond, your current, perverse, philosophy of science that has become conventional.

"the data are absolutely meaningless"

Regardless of whether or not data is "meaningless", it may be useful.

Consider the distinction between "precision" and "accuracy", as those terms are used in engineering.

"Precise" means that repeating the measurement will yield precisely the same result. It has nothing to do with how closely the measurement approximates some supposed "true" value.

"Accurate", on the other hand, is concerned with how closely the measurement approximates the "true" value.

"False-Color" visual perception is *always* precise. But it is only accurate under special circumstance. Its usefulness is *entirely* due to its precision, not its occasional, startling accuracy.

Now consider:

What is more important to an observer's continued survival, "accurate" measurements of the solar spectrum, or "precise" measurements of the manner in which the solar radiation is "modulated" when it is reflected off other entities in the observer's environment?

In this situation, as in most situations, Accurate measurements are about the source, but precise measurements are about the modulator.

Now here is the catch-22. Precise measurements can be made with little or no a priori information about what is being measured, But accurate measurements cannot; How would you know whether or not it even is "accurate", if you do not already know the "true" answer?

Physicists frequently confuse these two types of measurements.

Consider the double slit experiment. Does it measure anything you do not already know about the "emitted" signal? Or does it merely measure the manner in which that signal is spatially modulated by the two slits?

In other words, what are these measurements even about, the source or the modulator? Physicists have assumed they are about the source, even though they already know, by experimental design, what the source is doing. The measurements are *actually* about the modulator, not the "carrier" emitted by the source.

"We don't infer anything from measurements -- we infer by correspondence of *theory* to measurement results."

How then, does the color-vision system, infer the existence of non-existent yellow light, given that it has no theory whatsoever? You are confusing precision with accuracy, in which the "theory" is assumed to yield the "true" value.

Rob McEachern

John,

"So what you are saying is that math is the vision of what knowledge should be,while science is how it is actually acquired"

No, they are both knowledge. But they are about different things. Science is about knowledge of the world.

Math is about knowledge about math.

Rob McEachern

Rob,

I made my point that your view of science is nonstandard. I think I will leave it at that, since it's off topic in this blog. Just a parting observation:

You write, "How then, does the color-vision system, infer the existence of non-existent yellow light, given that it has no theory whatsoever?"

It certainly does have a theory. It's only that *theory* -- not the mere data which the system records -- by which we structure the meaning that we assign to the symbol "yellow." Otherwise, you deny the existence of objective knowledge altogether.

"You are confusing precision with accuracy, in which the 'theory' is assumed to yield the 'true' value."

I'm not the one confused here. I spoke only of the *correspondence* -- as did Popper, and as did Tarski from whom Popper borrowed the correspondence theory of truth -- between the theoretical expectation and the physical measurement.

Tom

Rob,

And math is?

Tom's "objective knowledge?"

Rob

"When you "receive" an image..."

This is not what I said.

To my left there is a waste basket, and a chair with a dog on it. A photon based representation of whatever constitutes the physically existent state which we are referring to as waste basket is currently being received by the chair, and vice versa. In just the same way as the dog and I are receiving such physical input. The physics is the same. The dog and I can subsequently process what is received, indeed, we do it differently. But that is irrelevant to the physics. The processes certainly need to be known, so that we can understand how the output from that processing relates to the input.

But that input was an independent physically existent entity. However, it was not the existential reality (ie what is usually referred to as reality), it was created as a result of an interaction with that. And systems have evolved so, if received, that can be utilised in sentient organisms in order to invoke awareness of the physical existence they are in, including themselves. That is, it is, of itself, a representation of what occurred.

Paul

Tom

"Paul's Aristotle-like observation that "existence exists" doesn't have any technical meaning"

Again, this is not what I am saying. We are part of existence, so whatever it 'really' is we can never know. We are trapped in a form of existence, a closed system, which is dependent on the ability of sentient organisms to detect. Detection includes directly received and hypothesised. But the latter is only valid if it abides by the rules of direct detection, ie it does not have the form of a belief. This existence which we can potentially know is a function of a physical process, not philosophy. The twist in the tale being that what we receive is not it, but a representation of it. It being the physical existence which we can know (either directly or indirectly).

This failure to understand what is being investigated in physics is the crux of its problems.

Paul

Tom,

FYI:

Math is not "objective knowledge." It is extreme abstract reductionism. Simplistic clarity, not anywhere near objective completeness. To go back to our cutoff point, how do multiples of zero add up to something, ie, infinite numbers of dimensionless points equal a line?

When you distill reality down to the most abstract concepts, then try to reconstitute it, you end up with the current Frankenstein's monster of multiverses, etc.

Math is a tool. Nothing more and nothing less.

A further thought,

While Math can be an exercise in extreme reductionism, it is a fairly broad subject that allows expansion in the opposite direction too. The way I see it; there are telescoping levels of abstraction that allow one to work toward specificity or generalities, using Category Theory as an example of a discipline working toward the latter.

But your Frankenstein comment is slightly off base. I think that things have been remarkably skewed toward the reductionist approach in Physics, when what is needed is a more balanced and holistic way to learn about reality. I'd continue to entertain the possibility of multiple timelines or universes, rather than prematurely toss it out as nonsense, but only in a certain context.

We should continue to ask 'what if?' questions, as long as there are things we don't understand. However; it's better not to use our 'answers' as a crutch.

Regards,

Jonathan

Jonathan,

Where would humanity be without tools? Sets can be like a telescope and project far beyond what we could otherwise consider. They can be misused though, when particular formulations start getting treated as canonistic. The current banking crisis is a function of projections far beyond reality, based on the misconception that money is a commodity, rather than a contract.

I realize I am really taking on the orthodoxy, when I keep arguing time is effect, like temperature and thus the entire mathematical structure(from expanding space to wormholes) arising out of spacetime as causal, is based on such a misconception, but no one actually refutes this point. They only question my credentials, or ignore it. This impulse isn't logic, but the power of collective belief. So I keep coming back to this point. Right now, physics is in a quandary and looking for ways to fix the current model. My guess is this will take years to realize just how far down the fractures go. Fortunately my income isn't dependent on being taken seriously.

Jonathan,

It is interesting you should seem to equate multiple timelines with multiple universes. According to relativity, it would seem clocks operating at different rates travel different timelines. Now presumably a clock on a GPS satellite and one on the ground exist in the same universe, yet do run at different rates. So it would seem the multiverse option is unnecessary in this context. That it is a projection far, far beyond what is necessary to understanding the nature of the variability of time. Where has Ockham's razor been relegated to, in all this extreme theorizing?How do we get back to more conservative thinking? Sensationalism sells, but it does not provide a solid foundation.

John,

It is apparent that Planck action is a fundamental aspect of reality, in my opinion perhaps THE fundamental aspect. The dimensional units of action are MLL/T (M=mass, L=length, T=time). I don't believe this fact is consistent with your 'time as temperature' perspective, and it has nothing to do with your credentials. You can be correct about the very serious problems with current physics, and yet be wrong in all of your individual prescriptions. I believe you are both.

Best,

Edwin Eugene Klingman

Jonathan,

You said, "With the "Upper Bound" paper we are discussing, the question naturally arises of whether the result is some artifact of the Math, where the Math in question may well be an idealized notion, or an approximation of what's factual in reality. -- However; I argue that Steven has simply used the Maths to probe the Physics in a way that is not often examined. By adding the self-gravitation term back in, and running the equations back to the Planck scale, he has used the next higher-order approximation - and found there is a natural limit we bump into."

As I've remarked above, I was and am very much impressed with Steven's paper(s). My original impression was that the idea was novel with him. But, like Geometric Algebra, the idea has been around for a very long time, I just had never heard of it. As I pursued the idea I found where Arnowitt, Deser, and Misner , in "Dynamics of General Relativity", in 1962, state: "The gravitational field, of course, also has aspects not found elsewhere. In particular, its sources are the total energies of *all* other fields. The attractive, static interaction, part of the total energy provided the possibility of a compensating effect on the flat-space self-energies of other fields."

Then I found Sivaram in "Planck length as a cosmological constraint" speaks of "...the old suggestion (cf. Landau, 1955; Klein, 1956) that gravitation might provide a natural cut-off to the virtual photon energies at wavelengths on the order of L-sub-p."

Where have I been?

But to top it off, the 8 March 2013 issue of Phys Rev Letters (which I haven't even received yet) has an article "Ultrarelativistic Black Hole Formation" in which they say: "According to general relativity, kinetic energy, like all forms of energy, gravitates. This implies that [...] the gravitational force will eventually dominate any interaction." They simulate the collision of 'perfect fluid' collisions at high gamma with fascinating results!

I was first interested in this because it is inherently interesting, but now I am looking at a potential mechanism whereby the C-field [gravitomagnetic field] can reach the significant levels that I have postulated in several essays. I find this a most exciting topic in a very exciting time.

Have Fun,

Edwin Eugene Klingman

I guess I have a lot of reading too Ed..

Fred mentioned the work of Schiller, but there are some papers by Gibbons that bear mentioning. Steven forwarded me one such paper earlier today, that I have not had a chance to look at yet. But there are indeed other examples. As Michael Goodband pointed out in private correspondence, the essay by Weiser from the last FQXi contest speaks to the upper bound issue, and his work also, but perhaps they do not make some of the same strong points clear - that Steven elucidates.

The PRL article sounds very interesting, and I'll have to check that out; but a text from 1962 huh? Yes that's a long while, but I guess people who want to ignore important things have to start somewhere. Nice they get rediscovered though.

All the Best,

Jonathan

Edwin,

You may well be right. I admit I'm little more than a casual observer and the nitty gritty is far beyond my basic views. Out of general curiosity though, one of my sources for the current state of the discussion is Peter Woit's blog, in which there is this current discussion of the ramifications of no susy:

"The scales of various observed physics have some explanation in terms of our understanding of the astrophysics/physics (except I guess the size of the universe, the time back to the big bang is just an historical fact).

Very roughly, the idea of naturalness is that if even if you don't know how to compute something, you expect it to be "naturally" of order 1 in the appropriate units. If it's exponentially smaller, there should be some reason. People try and apply this to particle physics at scales such that we don't have experimental evidence.

Then the question arises as to why the Higgs mass (or W, or Z, etc) is so small in units of the GUT or Planck scale. The answer may just be that there is no GUT scale and the Planck scale is irrelevant. The SUSY explanation is that fermionic superpartners 0f the Higgs have zero masses (before SUSY breaking), and this keeps the Higgs small small. You then expect the SUSY breaking scale to be what determines the mass. Thus the problem arising now, since the LHC has shown that the SUSY breaking scale must be quite a bit higher than the electroweak breaking scale.

This argument is made in various forms at the beginning of just about every review paper or talk on SUSY, and I'm just giving a crude version of it. Best I not go on about the details, but look for a more detailed version that might be readable."

There is a lot to sort out and it will likely take a long time.

Edwin,

Then there was this from some years ago:

"Dr Laurent and colleagues searched for differences in the polarisation at different energies, but found none to the accuracy limits of the data. Some theories suggest that the quantum nature of space should manifest itself at the 'Planck scale': the minuscule 10-35 of a metre, where a millimetre is 10-3 m. However, Integral's observations are about 10 000 times more accurate than any previous and show that any quantum graininess must be at a level of 10-48 m or smaller."

John,

In the movie "Dances with Wolves," when Kevin Costner's character is "rescued" by the cavalry after having gone over to the native Indian tribe, his carefully recorded diary of the events since his arrival at the abandoned desert fort is seized by an illiterate soldier who uses it for toilet paper.

Yes, mathematics, and any variety of symbolic language is "a form of extreme reductionism." Which is not only an obvious, but quite meaningless statement. As are your repeated inferences that if you can't wipe your behind with it, what good is it?

You do yourself the disservice -- by not having learned to read -- of attacking what you call the "fantastic patches" in theoretical physics (such as dark energy) while having not the slightest notion that serious researchers are filling those gaps with narrative that obviates your concerns. Really, what intellectual satisfaction can you possibly derive from baseless skepticism? -- you must have convinced yourself that it has some value, yet I fail to see it.

Did you even try to understand from Kauffmann's article that it the quantum field does not collapse, the universal wavefunction, which is continuous (Kauffmann concludes, " ... only the universe itself, with its cosmological redshift, is actually capable of 'containing' the arbitrarily high frequencies of a quantum field") is physically real and dark energy isn't?

Tom