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Tag: Mathematical Construction

To achieve interstellar travel, the Kline Directive instructs us to be bold, to explore what others have not, to seek what others will not, to change what others dare not. To extend the boundaries of our knowledge, to advocate new methods, techniques and research, to sponsor change not status quo, on 5 fronts, Legal Standing, Safety Awareness, Economic Viability, Theoretical-Empirical Relationships, and Technological Feasibility.

In this post on technological feasibility, I point to some more mistakes in physics, so that we are aware of the type of mistakes we are making. This I hope will facilitate the changes required of our understanding of the physics of the Universe and thereby speed up the discovery of new physics required for interstellar travel.

The scientific community recognizes two alternative models for force. Note I use the term recognizes because that is how science progresses. This is necessarily different from the concept how Nature operates or Nature’s method of operation. Nature has a method of operating that is consistent with all Nature’s phenomena, known and unknown.

If we are willing to admit, that we don’t know all of Nature’s phenomena — our knowledge is incomplete — then it is only logical that our recognition of Nature’s method of operation is always incomplete. Therefore, scientists propose theories on Nature’s methods, and as science progresses we revise our theories. This leads to the inference that our theories can never be the exact presentation of Nature’s methods, because our knowledge is incomplete. However, we can come close but we can never be sure ‘we got it’.

With this understanding that our knowledge is incomplete, we can now proceed. The scientific community recognizes two alternative models for force, Einstein’s spacetime continuum, and quantum mechanics exchange of virtual particles. String theory borrows from quantum mechanics and therefore requires that force be carried by some form of particle.

Einstein’s spacetime continuum requires only 4 dimensions, though other physicists have add more to attempt a unification of forces. String theories have required up to 23 dimensions to solve equations.

However, the discovery of the empirically validated g=τc2 proves once and for all, that gravity and gravitational acceleration is a 4-dimensional problem. Therefore, any hypothesis or theory that requires more than 4 dimensions to explain gravitational force is wrong.

Further, I have been able to do a priori what no other theories have been able to do; to unify gravity and electromagnetism. Again only working with 4 dimensions, using a spacetime continuum-like empirically verified Non Inertia (Ni) Fields proves that non-nuclear forces are not carried by the exchange of virtual particles. And therefore, if non-nuclear forces are not carried by the exchange of virtual particles, why should Nature suddenly change her method of operation and be different for nuclear forces? Virtual particles are mathematical conjectures that were a convenient mathematical approach in the context of a Standard Model.

Sure there is always that ‘smart’ theoretical physicist who will convert a continuum-like field into a particle-based field, but a particle-continuum duality does not answer the question, what is Nature’s method? So we come back to a previous question, is the particle-continuum duality a mathematical conjecture or a mathematical construction? Also note, now that we know of g=τc2, it is not a discovery by other hypotheses or theories, if these hypotheses/theories claim to be able to show or reconstruct a posteriori, g=τc2, as this is also known as back fitting.

Our theoretical physicists have to ask themselves many questions. Are they trying to show how smart they are? Or are they trying to figure out Nature’s methods? How much back fitting can they keep doing before they acknowledge that enough is enough? Could there be a different theoretical effort that could be more fruitful?

The other problem with string theories is that these theories don’t converge to a single set of descriptions about the Universe, they diverge. The more they are studied the more variation and versions that are discovered. The reason for this is very clear. String theories are based on incorrect axioms. The primary incorrect axiom is that particles expand when their energy is increased.

The empirical Lorentz-Fitzgerald transformations require that length contracts as velocity increases. However, the eminent Roger Penrose, in the 1950s showed that macro objects elongate as they fall into a gravitational field. The portion of the macro body closer to the gravitational source is falling at just a little bit faster velocity than the portion of the macro body further away from the gravitational source, and therefore the macro body elongates. This effect is termed tidal gravity.

In reality as particles contract in their length, per Lorentz-Fitzgerald, the distance between these particles elongates due to tidal gravity. This macro expansion has been carried into theoretical physics at the elementary level of string particles, that particles elongate, which is incorrect. That is, even theoretical physicists make mistakes.

Expect string theories to be dead by 2017.

Previous post in the Kline Directive series.

Next post in the Kline Directive series.

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Benjamin T Solomon is the author & principal investigator of the 12-year study into the theoretical & technological feasibility of gravitation modification, titled An Introduction to Gravity Modification, to achieve interstellar travel in our lifetimes. For more information visit iSETI LLC, Interstellar Space Exploration Technology Initiative.

Solomon is inviting all serious participants to his LinkedIn Group Interstellar Travel & Gravity Modification.

To achieve interstellar travel, the Kline Directive instructs us to be bold, to explore what others have not, to seek what others will not, to change what others dare not. To extend the boundaries of our knowledge, to advocate new methods, techniques and research, to sponsor change not status quo, on 5 fronts, Legal Standing, Safety Awareness, Economic Viability, Theoretical-Empirical Relationships, and Technological Feasibility.

In this post I discuss three concepts, that if implemented should speed up the rate of innovation and discovery so that we can achieve interstellar travel within a time frame of decades, not centuries.

Okay, what I’m going to say will upset some physicists, but I need to say it because we need to resolve some issues in physics to distinguish between mathematical construction and conjecture. Once we are on the road to mathematical construction, there is hope that this will eventually lead to technological feasibility. This post is taken from my published paper “Gravitational Acceleration Without Mass And Noninertia Fields” in the peer reviewed AIP journal, Physics Essays, and from my book An Introduction to Gravity Modification.

The Universe is much more consistent than most of us (even physicists) suspect. Therefore, we can use this consistency to weed out mathematical conjecture from our collection of physical hypotheses. There are two set of transformations that are observable. The first, in a gravitational field at a point where acceleration is a compared to a location at 0 an infinite distance from the gravitational source, there exists Non-Linear transformations Γ(a) which states that time dilation ta/t0, length contraction x0/xa, and mass increase ma/m0, behave in a consistent manner such that:

(1)

.

The second consistency is Lorentz-Fitzgerald transformations Γ(v) which states that at a velocity v compared to rest at 0, time dilation tv/t0, length contraction x0/xv, and mass increase mv/m0, behave in a consistent manner such that:

(2)

.

Now here is the surprise. The Universe is so consistent that if we use the Non-Linear transformation, equation (1) to calculate the free fall velocity (from infinity) to a certain height above the planet’s or star’s surface, and it’s corresponding time dilation, we find that it is exactly what the Lorentz-Fitzgerald transformation, equation (2) requires. That there is this previously undiscovered second level of consistency!

You won’t find this discovery in any physics text book. Not yet anyway. I published this in my 2011 AIP peer reviewed Physics Essays paper, “Gravitational Acceleration Without Mass And Noninertia Fields”.

Now let us think about this for a moment. What this says is that the Universe is so consistent that the linear velocity-time dilation relationship must be observable where ever velocity and time dilation is present, even in non-linear spacetime relationships where acceleration is present and altering the velocity and therefore the time dilation present.

Or to put it differently, where ever Γ(a) is present the space, time, velocity and acceleration relationship must allow for Γ(v) to be present in a correct and consistent manner. When I discovered this I said, wow! Why? Because we now have a means of differentiating hypothetical-theoretical gravitational fields, and therefore mathematical conjectures, from natural-theoretical gravitational fields, which are correct mathematical constructions.

That is, we can test the various quantum gravity & string hypotheses and any of the tensor metrics! Einstein’s tensor metrics should be correct, but from a propulsion perspective there is something more interesting, Alcubierre tensor metrics. Alcubierre was the first, using General Relativity, to propose the theoretical possibility of warp speed (note, not how to engineer it). Alcubierre’s work is very sophisticated. However, the concept is elegantly simple. That one can wrap a space craft in gravitational-type deformed spacetime to get it to ‘fall’ in the direction of travel.

The concept suggest that both equations (1) and (2) are no longer valid as the relative velocity between the outer edges of the spacetime wrap and an external observer is either at c, the velocity of light or greater – one needs to do the math to get the correct answer. Even at an acceleration of 1g, and assuming that this craft has eventually reached c, equation (1) and (2) are no longer consistent. Therefore, my inference is that Alcubierre metrics allows for zero time dilation within the wrap but not velocities greater than the velocity of light. Therefore, it is also doubtful that Dr. Richard Obousy hypothesis that it is possible to achieve velocities of 1E30c with a quantum string version of Alcubierre warp drive is correct.

Previous post in the Kline Directive series.

Next post in the Kline Directive series.

—————————————————————————————————

Benjamin T Solomon is the author & principal investigator of the 12-year study into the theoretical & technological feasibility of gravitation modification, titled An Introduction to Gravity Modification, to achieve interstellar travel in our lifetimes. For more information visit iSETI LLC, Interstellar Space Exploration Technology Initiative.

Solomon is inviting all serious participants to his LinkedIn Group Interstellar Travel & Gravity Modification.

To achieve interstellar travel, the Kline Directive instructs us to be bold, to explore what others have not, to seek what others will not, to change what others dare not. To extend the boundaries of our knowledge, to advocate new methods, techniques and research, to sponsor change not status quo, on 5 fronts, Legal Standing, Safety Awareness, Economic Viability, Theoretical-Empirical Relationships, and Technological Feasibility.

In this post I discuss part 2 of 3, Mathematical Construction versus Mathematical Conjecture, of how to read or write a journal paper that is not taught in colleges.

I did my Master of Arts in Operations Research (OR) at the best OR school in the United Kingdom, University of Lancaster, in the 1980s. We were always reminded that models have limits to their use. There is an operating range within which a model will provide good and reliable results. But outside that operating range, a model will provide unreliable, incorrect and even strange results.

Doesn’t that sound a lot like what the late Prof. Morris Kline was saying? We can extrapolate this further, and ask our community of theoretical physicists the question, what is the operating range of your theoretical model? We can turn the question around and require our community of theoretical physicists to inform us or suggest boundaries of where their models fail “ … to provide reasonability in guidance and correctness in answers to our questions in the sciences …”

A theoretical physics model is a mathematical construction that is not necessarily connected to the real world until it is empirically verified or falsified, until then these mathematical constructions are in limbo. Search the term ‘retrocausality’ for example. The Wikipedia article Retrocausality says a lot about how and why of the origins of theoretical physics models that are not within the range of our informed common sense. Let me quote,

“The Wheeler–Feynman absorber theory, proposed by John Archibald Wheeler and Richard Feynman, uses retrocausality and a temporal form of destructive interference to explain the absence of a type of converging concentric wave suggested by certain solutions to Maxwell’s equations. These advanced waves don’t have anything to do with cause and effect, they are just a different mathematical way to describe normal waves. The reason they were proposed is so that a charged particle would not have to act on itself, which, in normal classical electromagnetism leads to an infinite self-force.”

John Archibald Wheeler and Richard Feynman are giants in the physics community, and these esteemed physicists used retrocausality to solve a mathematical construction problem. Could they not have asked the different questions? What is the operating range of this model? How do we rethink this model so as not to require retrocausality?

This unfortunate leadership in retrocausality has led to a whole body of ‘knowledge’ by the name of ‘retrocausality’ that is in a state of empirical limbo and thus, the term mathematical conjecture applies.

Now, do you get an idea of how mathematical construction leads to mathematical conjecture? Someone wants to solve a problem, which is a legitimate quest because that is how science progresses, but the solution causes more problems (not questions) than previously, which leads to more physicists trying to answer those new problems, and so forth .… and so forth .… and so forth .…

In Hong Kong, the Cantonese have an expression “chasing the dragon”.

Disclaimer: I am originally from that part of the world, and enjoyed tremendously watching how the Indian and Chinese cultures collided, merged, and separated, repeatedly. Sometimes like water and oil, and sometimes like water and alcohol. These two nations share a common heritage, the Buddhist monks, and if they could put aside their nationalistic and cultural pride, who knows what could happen?

Chasing the dragon in the Chinese cultural context “refers to inhaling the vapor from heated morphine, heroin, oxycodone or opium that has been placed on a piece of foil. The ‘chasing’ occurs as the user gingerly keeps the liquid moving in order to keep it from coalescing into a single, unmanageable mass. Another more metaphorical use of the term ‘chasing the dragon’ refers to the elusive pursuit of the ultimate high in the usage of some particular drug.”

Solving a mathematical equation always gives a high, and discovering a new equation gives a greater high. So when we write a paper, we have to ask ourselves, are we chasing the dragon of mathematical conjecture or chasing the dragon of mathematical construction? I hope it is the latter.

Previous post in the Kline Directive series.

—————————————————————————————————

Benjamin T Solomon is the author & principal investigator of the 12-year study into the theoretical & technological feasibility of gravitation modification, titled An Introduction to Gravity Modification, to achieve interstellar travel in our lifetimes. For more information visit iSETI LLC, Interstellar Space Exploration Technology Initiative.

Solomon is inviting all serious participants to his LinkedIn Group Interstellar Travel & Gravity Modification.