Tom,
Isn't the assumption of an observer-created reality at variance with the original notion of reality as something assumed to exist objectively? For instance, a wave can be observed at effectively the same location by different observers moving relative to the medium with different velocities. It is nonetheless just one wave with one velocity re medium.
What about singularities, see Fig. 3 of my essay.
Eckard
Hi Tom,
I have put a new paper on the arXiv. I thought you might find it interesting.
I am also attaching a PDF file below for your convenience.
Best,
Thanks, Joy! I haven't time to do more than scan it right now. I know I'm going to enjoy it, though. Years ago, I tried to follow the periodic newsletter on spinors/twistors that Roger Penrose published (perhaps still does)-- like so much of Sir Roger's work, for me, I found it tough going.
I have found your approach to classical orientation entanglement, geometry and topology much closer to my own understanding of the subjects.
Best,
Tom
I'm not ignoring you, Eckard. It's just that I don't have LaTex installed on my work computer and I want to use mathematical symbols. Time at my home computer has been very limited lately.
In the interim:
Yes, of course, I agree that reality is objective and local. I'll deal with the question of observer-wave correlation in my formal reply later. (Much of the answer is informally addressed in my essay.)
In re your figure 3: I think one has to see Dedekind's "pebble like" notion of number in the context of Dedekind Cuts. In that, for example, there do exist two numbers that when multiplied together produce sqrt2. We don't know what these numbers are, and we are unlikely to ever know what they are -- but we can know, by explicit construction, that they exist.
Dedekind's and Weyl's work on the Continuum is some of the deepest in mathematics (and something I have studied extensively), and I can't do justice to it here. I will venture to say, however, that I don't think that there is a *real* distinction between mathematical structures and physical reality, although in experimental science there is a very sharp and practical demarcation. So in this respect, I agree with Max Tegmark in the reality of mathematical continuity with physical phenomena -- though at the same time I am compelled to address all the nonsense written that identifies Tegmark's view as Platonic. True Platonism posits an ideal world independent of our physical reality (consider Plato's allegory of the cave). Tegmark's hypothesis is of a mathematical world identical to our physical reality.
If we speak simply of mathematical realism and leave Plato out of it -- we get a constructivist philosophy supported by eminent 20th century mathematicians whose work either strongly relates to, or is based in, physics. Not only Dedekind and Weyl, but Brouwer, Weierstrass, Poincare and others. Not a bad club to belong to.
Tom
Tom,
While I agree with you on that reality isn't observer-created, I would like to more elaborate Robert McEachern's view. Concerning the uncertainty relation between time and frequency I gave results of MATLAB simulations in my previous essays.
You know, my understanding of reality differs from yours. To me the reality is a belief in objective relationships including causality and the possibility to be influenced or to influence in principle. It is not necessarily a belief in something constructed that can be reduced to binary pairs.
What about your trust in mathematics as basic to anything, please look at my Fig. 4 that illustrates how modern (introduced by Weierstrass, Dedekind, and G. Cantor) mathematics differs from logic.
Eckard
"You know, my understanding of reality differs from yours. To me the reality is a belief in objective relationships including causality and the possibility to be influenced or to influence in principle. It is not necessarily a belief in something constructed that can be reduced to binary pairs."
You're right, Eckard -- objective science doesn't have anything to do with personal belief in my world. The binary relation (bit) is that which constructs, not that which is derived from a construction necessitating the axiom of choice (Zorn's lemma); it's the most fundamental relation, as Wheeler allows, in nature as well as in mathematics. As a general law, I find (as my essay instructs) that the irreducible binary relation is exactly equivalent to the relation between a pair of odd primes of any magnitude. In other words, a pair (P_1, P_2) are inequivalent in any respect except mod 2.
The whole story follows in the attachment.
TomAttachment #1: Buridans_Principle_and_the_point_at_infinity.pdf
Tom,
I see your arguments presented in a horribly confusing manner and also most likely wrong.
In your "Buridan's Principle and the point at infinity" you wrote: t goes to infinity. You introduced "(x,y) variables are either fixed or fluctuating values of a continuous range. In other words, the car (x) at time t and the tree (y) at time t..." This is not understandably explained to me.
You referred to Wheeler: "The binary relation (bit) is that which constructs, not that which is derived from a construction necessitating the axiom of choice (Zorn's lemma); it's the most fundamental relation, as Wheeler allows, in nature as well as in mathematics."
I consider this idea wrong, no matter whether or not you accepts AC. I see Euclid's abstraction to the notion unity the basis of mathematics and any repetition of this operation already belonging to the level of abstraction in my Fig. 1. Accordingly there is obviously no exact equality in reality, and trichotomy is something artificial that decouples mathematics from logics.
What about Planck's constant h, I don't see it necessarily related to the uncertainty principle which is also valid for time and frequency. Plank's constant is just a factor of proportionality that relates position to momentum.
Eckard
Fine, Eckard. Then perhaps you'll take your questions to a source that gives you answers you want to hear.
Tom
Tom,
"Do you know what you mean by that? I don't. In the conservation of angular momentum in a spinning object, the central point is fixed -- the speed of points equidistant from that point vary evenly from the origin to the extremus. That is, like an ice skater drawing her arms in to spin faster and extending them to slow -- the difference between fast and slow is conserved as a unitary function. It isn't the inertial motion outward that increases local energy (and therefore temperature), but the true centrepital force inward that does so. When I was 12, I had an old Cushman motor scooter to deliver my paper route, which had a centrifugal clutch -- I must have taken that old scooter apart and reassembled it a dozen times in this short carefree part of my life -- the clutch works by expanding its spring-attached pads to the drum lining. When the pads are spinning fast enough -- driven by the energy input from the motor controlled by my hand operating the accelerator -- they contact the lining and transfer part of the force from the heat-generating friction of the lining to the wheel connected to the clutch, and the scooter ... scoots. It should be easy to see that it's not the centrifugal momentum that powers the scooter; it's the energy of the friction lining, stored and then transferred to produce what we call work, with the greater part of the energy content dissipated. Were the lining frictionless, no energy could be directed, no temperature created."
I did grow up on a farm, I do understand the physical effect.
The point is what is the spin in relation too? Is it in relation to other points of reference? For one thing, it's not about energy conserved as diameter of the object changes. This would just be a stable system. The energy is in the spin. Say that object is out in normal interstellar space. We can tell it is spinning relative to the other stars, that give us a fixed background. A piece breaks loose and is thrown out in the direction of momentum at the point it breaks free. Is this due to those other stars giving a stable frame, or is there a stable frame anyway? If those stars were not visible, didn't exist, so there would be NO point of OUTSIDE reference to determine the spin, would this affect whether the object is spinning and thus the velocity and direction of the piece that came loose?
Tom,
Ok. Let's not call it space, let's call it an unbounded frame of reference. It has no physical markers. You are on a merry-go-round, or rather the spacestation from 2001 A Space Odyssey. Presumably you would be able to tell how fast it is spinning relative to that frame, by the G forces, not by any reference to outside points.
So what is that frame, if it has virtually no other physical property than what the spin is relative to? What is this frame derived from? Algebra? Geometry? Space?
John,
"Let's not call it space, let's call it an unbounded frame of reference."
I'm afraid that's what space is. Add boundary conditions and you can call it geometry.
"It has no physical markers. You are on a merry-go-round, or rather the spacestation from 2001 A Space Odyssey. Presumably you would be able to tell how fast it is spinning relative to that frame, by the G forces, not by any reference to outside points."
No you couldn't. This was the whole point of Einstein's elevator gedanken experiment -- that one cannot determine whether one, colloquially speaking, is being pulled up or pushed down, in the absence of an external reference.
"So what is that frame, if it has virtually no other physical property than what the spin is relative to? What is this frame derived from? Algebra? Geometry? Space?"
Pick one, or all three. Or a method yet to be invented. What is clear though, John, is that you are innocent of how classical physics works. I promise that if you study it, you will be rewarded with insights that not only answer your questions, but lead you right to the edge of the cliff overlooking the truly deep questions.
Tom
Tom,
"Pick one, or all three."
So we agree space is an equilibrium state.
"So we agree space is an equilibrium state."
WHA ....?
Tom,
""So what is that frame, if it has virtually no other physical property than what the spin is relative to? What is this frame derived from? Algebra? Geometry? Space?""
"Pick one, or all three."
I picked the third.
Having been engaged in a long dialogue with James Putnam on his essay site -- though we strongly disagree, I think it worthwhile to reproduce this post on my own site, because I think it adds to the argument in favor of abandoning nonlocality for a topological limit in the generalized Euclidean space.
James,
Thinking about your contention that "mass varies" reminded me that I constructed a mathematical picture of what a continuum of mass would look like, in my 2008 preprint "On Breaking the Time Barrier."
I have done more sophisticated (yet unpublished) work from this basis since. The gist is, though, that such a continuum demands negative mass in the n-dimension Hilbert space, and some criteria for nonlocal measure to make it viable. I wrote it before being exposed to Joy Christian's framework, by which I became convinced that the topological 8-dimension limit (7-sphere) is more physically realistic than the Hilbert space. I haven't taken it down from my site, however, because I think that it shows why a physical limit -- and not nonlocality in the n-dimension Hilbert space -- makes the generalization of Euclidean space up to S^7 (limit of the division algebras) a better bet for a real and complete description of reality.
I have extracted and attached the relevant pages from the paper.
Tom
The only problem being that e does not =mc2 , in the same way that other similar assertions are wrong. You discount c, but the real point here is that c cannot have any influence on physical existence. c is one of a number of physical attributes which has an influence on the physically existent entity known as light. Which is a representation of what physically occurred, not what occurred. c, etc, has an impact on the physically existent representation, not what was physically existent which it is representing.
The other underlying problem is that whatever is occurring is only spatial. It alters, to something else. And what was in existence ceases. The rate at which that occurs, ie the changeover from one state to another, is what time is about. There is no duration in physical existence, duration is associated with alteration thereto.
If one sorts out first, generically, what is happening, then it becomes much easier to identify what all these concepts can relate to.
Paul
"The only problem being that e does not =mc2"
The empirical data disagrees with you.
Tom
Tom
Oh, and what 'empirical' data is this? Hopefully not something that is self fulfilling, ie start with a false premise, sort out facts accordingly, prove start point.
What I want to see is something which proves that the speed at which a physical effect in photons which, if received by the right entity, can be subsequently processed, has an influence in the physical characteristics, known as energy and mass, of physically existent entities. Or indeed, in the wider sense, how this physical effect, known as light, has any physical influence on physical existence. Because, just for a start, the light is created AFTER that physical existence has occurred! Which sounds to me like something of a showstopper, before disappearing any further into the trees and leaving complete sight of the forest.
Paul
