The Tao of Physics -- and the Zen of Zero

[zoro]

I'd be grateful for help from knowledgeable physicists. Maybe I could even stimulate your assistance by reminding you of the many admonitions to you (from leading physicists and from various scientific organizations) to share your knowledge with the public.

A brief sketch of the background for my request is the following. As you can find at http://zenofzero.net, I'm adding a chapter per week to a (free!) on-line book, which I explicitly wrote for my (now) 16-year-old granddaughter but which I hope will be useful for other teenagers (and maybe even some adults!) throughout the world. When she was four, my granddaughter asked me why I didn't believe in god; I responded that I would tell her when she was older; thus, the book. As you can see from glancing even at the book's first chapter (of about 40 chapters now posted), one of the important topics, which I want to stimulate kids to consider, is possible ways that the universe might have come into existence.

Let me also provide a little personal information, for a reason that I'll mention at the end of this paragraph. Way back in '61, I earned by bachelor's in engineering physics; my master's in nuclear physics in '62, and in '69, my Ph.D. -- which I started in astrophysics, but for financial reasons, switched to (and earned) in aerospace engineering with minors in plasma physics and applied math. Subsequently, I taught such subjects at four West Coast (U.S.) universities and (again for financial reasons) engaged in mostly atmospheric research for about 30 years. After taking an early retirement offer, for the past 12 years I've been writing the above mentioned book for teenagers. All of which I mention to say the following: if you would be willing to share some of your knowledge, please try to convey it as you would to a teenager! I know some basic physics, but readily admit that I'm now an "old fogey", behind the times.

With that out of the way, I'll now turn to some questions.

1. As you can see from the book's first chapter (at http://zenofzero.net/docs/Awareness.pdf), starting at p. 4 (after the "stanza") and continuing through p.12 (until before the "poem"), I suggest that this universe of ours still sums to "totally nothing", but it separated itself into positive and negative components. My questions are: Does that seem reasonable to you? Have I made some major misstatements?

2. If our universe were "created" by some "symmetry-breaking fluctuation in a total void" (resulting in the Big Bang), then what would you suggest are reasonable candidates for such a symmetry-breaking event? And let me add: a) I doubt it was parity, which I learned a little about working on my M.S., b) What do you think about the possibility that "the event" was the formation of some particle (or a string of energy)? and c) In your response, please convey it so that a teenager would understand you -- because I readily admit that I had great difficulty trying to understand group theory and I never studied elementary particle physics.

3. Although the following isn't yet posted, it's in a later chapter (now in draft form) and a little of it is already posted in Chapters Ia and Ic. I'll summarize by asking the question (which follows from Q#1): Does it then seem reasonable to state that "existence" isn't a scalar but is actually a higher-order tensor, say T, so that the universe could be described as 0 = T - T ?

[And I hope you don't dismiss this third question as trivial. Let me put it this way: even after teaching complex variables for years, it took me decades to finally see that all the textbooks (at least, in those day) neglected to mention the obvious point that once one starts talking about negative numbers, one is no longer talking about scalars but the components of a vector. With that realization, I finally saw that the EE's were the only ones who were teaching complex numbers in a reasonable way (with their phasors, i.e., as components of 2D vectors), that imaginary numbers weren't "imaginary", and that the source of them was proposing that although normally we consider "existence" to be represented by positive numbers, we can work with the idea that another type of "existence" can be represented with negative numbers. Thus, although I recall that Dirac wrote (in his original paper) that he didn't understand the meaning of "negative energy", perhaps he later saw (I didn't follow his later work) that just as "real" as "positive existence" are various types of "negative existences", such as "space" or "the vacuum". And thus my 0 = T - T, with the components of T including "everything" (electrical charge, momentum, spin, energy, charm, color,…). And I probably should add that, in later (as yet not-posted) chapters, I do try to explain the above ideas about complex numbers in a way that I hope teenagers will understand.]

I have three other questions that I want to ask you [dealing with 1) the possibility that gravity is actually not a force of attraction between two masses but a repulsion of mass (or better, "positive energy") by "space" (or better, "negative energy"), which seems to lead to the same expression for Newton's law and is consistent with "gravitational" bending of light, 2) that within Black Holes, the "positives" and "negatives" of "existence" might "reassemble", once again creating "total nothing", and 3) the possibility that time "flows" in the opposite direction in the "negative-energy vacuum", that the entropy of the vacuum is negative, and that the total entropy of the universe is exactly zero)], but I think that it would be best to see what sort of response I get to my first three questions (listed above) before I get way-way out on these three other limbs!

Again, I'd be most grateful for your help, in turn, to help kids -- I hope throughout the world. [Incidentally, with Google having my web pages indexed (and not completely!) for only about a month, already the site has about 40,000 hits, including some from Egypt and Saudi Arabia.] Also, please notice that my efforts have been (and will continue to be) entirely "gratis": I'll leave the book on the web (anonymously, to protect my grandchildren from religious extremists, and with my paying for the website) and I certainly don't plan ever to try to sell the book. Besides, what publisher would be dumb enough to take on such a monstrosity?!

[editor]

The link didn't work for me.
Q1. In a strictly materialistic way the positive energy of mass and energy is exactly balanced by the negative potential energy of gravitation. So that the total energy of the cosmos is zero.
Q2. We have no idea. If we accept that billions of virtual particle pairs can pop in and out of our universe all the time, and virtual EM can do the same, then it's not too big a stretch to accept a bubble of energy that expands to become the universe.

[nox]

We have no idea. If we accept that billions of virtual particle pairs can pop in and out of our universe all the time, and virtual EM can do the same, then it's not too big a stretch to accept a bubble of energy that expands to become the universe.

Interestingly, summing up the virtual particle pairs' energies will ( without frequency boundaries ) lead to an infinite amount of energy. But obviously no spaciotemporal curvature can be observed. Consequently something must cancel their energy at the time of creation or the concept of quantum fluctuations is wrong or my understanding is simply too limited to contribute to this topic.

Two questions -

1. Does an alternative mainstream interpretation of the 'Casimir Effect' exist, which does not involve quantum vacuum fluctuations ?
2. Doesn't the flatness of space-time far from massive objects imply that the universe's average energy is negative if the fluctuations are not present ?

[zoro]

Editor:

Sorry about the link -- demonstrating my incompetence, also, with "computerese". The last ")" seems to have done me in. That chapter is at http://zenofzero.net/docs/Awareness.pdf .

Re. your responses (gratefully received) to:

Q1. Yes, in the poorly linked chapter (!), I do reference the statement of "exactly balanced" from Hawking's 1988 "time book" (p.129) -- although in the chapter, I also question (a little) why he made the claim of energy conservation for the entire cosmos quite so boldly (I would have preferred a conditional statement such as "if we can extrapolate the first law to the entire cosmos, then…"). Also, I do reference Tryon's 1973 Nature article (v.246, p.396), where the first estimate from data seems to have been made, but then I wonder about any need to modify his estimate with the new "results" for dark matter.

Q2. And yes, I agree "we have no idea" (about what might have broken the symmetry). In the chapter, I suggest (also) that it's "not too big a stretch" to accept that [in my words] the key is energy, but I was wondering if physicists were beginning to focus on some specific "symmetry breaker" (the "god particle"?, a string of energy?…).

[zoro]

nox:

Well, your comments illustrate to me why I need help -- and also, the difficulty of communicating ideas to teenagers! I can't knowledgeably respond to your post, but it's not clear to me if we're addressing the same issue. What I address (in the poorly referenced chapter!) is the (assumed) "first symmetry-breaking fluctuation" in a "total void" (or "total nothingness" or "the original zero"), leading to the Big Bang, not fluctuations in what we normally call "space" (or "the vacuum"), which I understand Dirac would have us consider to be "brim-full" with negative energy. Thus, I don't understand why you used the plural "pairs" in "virtual particle pairs' energies". Instead, I was wondering about just the first, single, "symmetry breaker". Also, I'm afraid I don't understand even why any such fluctuation would possess energy: wouldn't the positive-energy component of any fluctuation be exactly balanced by its negative-energy component -- until some symmetry is broken?

[zoro]

I'm somewhat surprised at the lack of response to my question #3. Of the many options available, let me temporarily proceed with the assumption that the cause is that the question was poorly posed. Here, therefore, I'll try to reframe the question -- and with your requested indulgence, I'll begin by boring you with some fundamentals.

Fish, monkeys, and eventually people established the two fundamental principles that things exist and are distinct. Those principles provided the bases for logic, which in turn, provided the bases for (positive) numbers, with zero meaning "nothing" (exists) and unity meaning "something" (exists and is distinct). The rest of the numbers then followed (with agreed-upon definitions for numerals), as did fractions and simple arithmetic operations.

Upon learning arithmetic, little Johnny (at the back of the room) objected when his teacher first introduced negative numbers. He agreed that it was sensible for her to write 3 - 2 = 1, but when she wrote 2 - 3 = -1, he scoffed: "If you only have 2 buckets of water in the well, how in hell can you take 3 buckets out?!"

After reprimanding him for his language, she explained that it was just convention: an arbitrary zero was defined, and if the water in the well fell below that level, then those values were to be called "negative numbers", by convention.

"But," Johnny objected, "zero was supposed to mean 'nothing'!"

"And so it does," responded his teacher: "It means nothing -- it, too, was just a convention."

Tricked by the teacher's faulty logic (the fallacy of amphiboly), Johnny gave in, learned what he had to learn about negative numbers (so he could pass exams), later ran into even sillier teachers who wanted to take square and other roots of negative numbers, spent years learning all there was to learn about complex variables, and eventually earned credentials as a physicist. As a physicist and as a result of all his experiences, he could then fully appreciate Dirac's comment that he [Dirac] didn't understand what "negative energy" meant.

What I was trying to get at with my question is something along the following. I'm wondering if others agree (or disagree) that we've caused ourselves serious problems by abandoning the original definition that zero was to mean "nothing". In my view, it seems that we've introduced substantial confusion by adopting 'zero', by convention, as any convenient reference level (e.g., of water in a well). By doing so, both +1 and -1 can mean "something exists and is distinct".

Instead, suppose we returned to the original meaning for zero (and unity). Then, in answer to the question "How did the universe come into existence?" or, equivalently, "How can you get something (normalized to, say, unity) from nothing (i.e., zero)?", the answer seems obvious: 0 = 1 - 1. But in that answer, -1 has a new meaning: it's not derived (by convention) from choosing an arbitrary zero, but means that "-1" is a "different kind of existence".

Put differently, the suggestion is that "existence" isn't a scalar (a zeroth-order tensor) but (as a minimum) it's a vector (first-order tensor) -- and a rather strange vector at that, since (at least to this far in the consideration) it can have only two components: +1 or -1. For example, there is what we are pleased to call "positive" energy (e.g., of mass) as well as Dirac's negative energy of "the vacuum" (or space). And with that, I'm suggesting that the negative energy of space isn't just a conventional way of describing gravitational energy, but that the negative energy represents a "different kind of reality", i.e., a "negative reality", as opposed to the usual reality (in which we're pleased to call most things "positive").

But that example is only for energy (a scalar), and there's a lot of other "weird stuff" going on. Somehow, in our "positive-energy side of reality", we can have both positive and negative values of electrical charge (usually considered to be another scalar -- but because it, too, can have positive and negative values, it must be at least a vector); presumably the same can occur with electrical charge in the "negative-side of reality" (i.e., in the vacuum).

Being an obvious vector (at least in space or in space-time) momentum (p) is more complicated: certainly we can have both a +p and a -p on this side of reality (where mass is considered positive), but maybe "on the other side", there could correspond a -p, differing by some +p on "our side", only because "the mass", there, would be negative. Presumably, also, the case of spin (a second-order tensor) would be similar -- but more complicated.

In addition, still more "weird stuff" seems to be going on. That is, whatever the "other side of existence" is, it (which we call "space" or "the vacuum") behaves very strangely. For example, when on "this side of reality" a positron appears (e.g., in decay of some krypton isotopes), then usually quite rapidly, the positron finds a way to "snuggle" into "the other side of existence", throwing away excess energy and momentum in the process (as gamma radiation). It's as if krypton's decay ripped a hole open in the other side of existence -- a hole that an electron from "our side of reality" soon plugs.

And thus my original question (#3): Does it then seem reasonable to state that "existence" isn't a scalar but is actually a higher-order tensor, say T, so that the universe could be described as 0 = T - T?

Now, assuming the above eliminates one possible reason for the lack of responses, I'll wait results for other possibilities. I agree that many possibilities exist. For example, you might respond: "Of course that's so -- why do you waste our time with such trivial stuff?" [To which I'll note (to myself): "Well, good; then what I've written in the book isn't so stupid!"]. Another possibility is the response: "For cryin' out loud: how can you be so stupid? It's obvious that..." [To which I'll note (to myself): "Ouch, I'd better get busy on some revisions."] And so on. In any event, thank you in advance for any advice.

[editor]

Nox. The virtual pairs that pop in and out are governed by the rules of the Heisenberg Uncertainty, and the conjugate pair in this instance are energy and time. So you can 'borrow' the energy from the vacuum provided it is done for a short enough time that the universe doesn't notice.

[editor]

Zoro. I'm not comfortable with the philosophical stuff. I just don't know. But your electricity example may just be a red herring. After all neg. is an excess of electrons and pos. is a lack of electrons. So here is an underlying simple explanation, just count the electrons.

[zoro]

Editor: Thank you for your reply. I like your explanation for charge.

[zoro]

Again I'm surprised by the lack of responses -- and again I thank "editor" for donating so much of his or her valuable time. After spending a lifetime on practical science, I certainly understand editor's discomfort with "philosophical stuff", but for the book, I felt forced to broach the boundary, to try to show kids alternative ways to try to comprehend the universe.

I'm also sensitive to two other criticisms, which haven't (yet) been raised -- and I have responses ready! First is criticism along the line: if an idea doesn't provide testable predictions, what's the point in raising it? My response would be similar to: it seems reasonable to pursue an idea as far as one can (subject to the constraints that it's consistent with data and with well established principles); after that, maybe one can see what new predictions can be made.

The second criticism is similar to the one against which John Cramer erected a defense for his "Transactional Interpretation of Quantum Mechanics" (Rev. Mod. Phys. 58, 647-688, 1986, available at http://www.npl.washington.edu/TI/TI_toc.html and see also his 2004 "slide show" available at http://faculty.washington.edu/jcrame...skone_0402.ppt ). My paraphrase of his defense is that, should one find that available interpretations of some well established mathematical description of some process lead to conceptual difficulties (as occurs so commonly in QM!), then we should seek alternative interpretations -- that are still consistent with the accepted mathematical description.

With those preliminaries out of the way and given that apparently I haven't yet been totally "shot down", I'll move on to the other three questions in my original post.

Q4. Does anyone see anything wrong with the interpretation of gravity as a force of repulsion between any mass and (the negative-energy) "space" or "vacuum"? The only additional assumption that seems to be needed is that each material body "excludes" a volume of space proportional to the body's mass (suggesting that it's as if "elementary particles", within each body, displace "space").

As some illustrations: (i) an isolated body would experience no net force, repulsed uniformly by all space, (ii) two, otherwise-isolated masses would experience a net force as if of attraction between them, because each body would experience a decrease in the repulsive force resulting from the absence of some "space" at the location of the other body, (iii) with the assumption that the volume of excluded space is proportional to a body's mass and simply from geometrical considerations, then the apparent force of attraction would be as given by Newton's law of gravity, (iv) if space (negative energy) also repels EM radiation (positive energy), then rather than saying that mass warps space-time, one could interpret the bending of light in the neighborhood of mass simply, again, as resulting from the absence of space within the body and therefore a net repulsive force by space on the radiation.

Q5. Would those physicists who know more about Black Holes than I do (and that probably includes essentially all physicists!) please suggest reasons (that would be obvious to a teenager) why, within Black Holes, the negative energy of space and the collected positive energy couldn't once again merge to form "total nothing"? And yes, I am wondering about the possiblity that Nature isn't "going about her business", trying to obliterate this universe -- so she can start making other "verses", e.g., within Black Holes!

Q6. This question deals with the total entropy of the universe, will be more difficult to pose, and from the particular perspective that I'm "coming from", is the most important of these three questions. The bottom line is to ask opinions about the suggestion that the total entropy of the universe is zero (just as is the total electrical charge, linear and angular momentum, and energy). I'll approach the question rather slowly, with questions en route.

My first subquestion is: if Cramer's idea (referenced above -- and as I understand it!) about time flowing in the opposite direction in space (i.e., its "past" is our "future") hasn't been "shot down" (and actually, that's another question!), then would a "reasonable definition" for the entropy of space show that it's negative? I'll now amplify that question.

In such a "reasonable definition", I assume that entropy would continue to be an extensive property (of space). And although it seems inappropriate to relate space's entropy to any heat transfer, I assume it can be related to "information content" (a la Shannon). But with (I presume) space being "perfectly ordered", then its entropy would seem to be at the minimum value permitted by QM (i.e., space is as far from "equilibrium" as possible).

Next, if the current interpretation of the red-shift evidence is correct, then with the expansion of space, its entropy (an extensive quantity) would seem to be increasing (using our time). But if Cramer's idea is correct that time goes in the opposite direction in space, then for it, it's as if the entropy is decreasing in time (using its time). I'm wondering if the resolution to that quandary is (i) that the entropy of space is negative, and (ii) that, from our point of view (with our time), the entropy of space becomes progressively more negative as the universe expands.

And if I can get by with all those "ifs", then if (in addition) the universe's expansion is driven by the universe's EM radiation "pushing" the expansion of the universe into the "total nothingness" that's "outside" our universe (and recall that "the Tao that can be spoken about is not the true Tao"!) -- with this EM radiation, in turn, being the product of all the dissipative processes within our universe -- then since it's that same expansion that makes the entropy of space increasingly more negative (from our viewpoint), is it too big a stretch to suggest that the two increases might cancel?

That would lead to what I unfortunately seek ("unfortunate" in the sense that my desire may be making it harder for me to see my errors), namely, that the entropy of the total universe (i.e., on both the positive and negative side of "zero") would be exactly zero (along with the usual conserved quantities -- and save for fluctuations in the entropy, including delays caused by the system's response time).

Let me put it this way: unless it seems reasonable to say that the total entropy of the universe is zero (or unless I have a fundamental misconception about entropy), then it would seem that I'd need to abandon my suggestion that "In this universe, there's nothing here, exactly as before the Big Bang" -- because, otherwise, there is something "here", namely, entropy. Thereby, perhaps you then see why I would definitely appreciate response to the above questions about entropy.

And I'll close with the hope that I won't end up using even more of "editor's" valuable time -- but I'd certainly be grateful for any additional generosity.

[Larne]

Originally Posted by zoro

Q4. Does anyone see anything wrong with the interpretation of gravity as a force of repulsion between any mass and (the negative-energy) "space" or "vacuum"?

Yes. Such an interpretation would be at odds with a lot of experimentally verified facts including:

1) Gravitational time dilation
2) The loss of energy through gravitational radiation
3) The fact that gravity couples to energy as well as mass
3a) The fact that gravity couples to massless particles (gravitational lensing)
4) Frame dragging
5) Lorentz invariance
6) The equivalence principle (which also kind of goes back to point 3)

I am not, in principle, opposed to alternative interpretations of established theories. Personally I think any attempt to describe general relativity in a way that avoids curvature is doomed from the start, but you're welcome to try. However before you embark on such a program it would probably behoove you to have a really solid understanding of GR. You could start with Baez' Relativity on the World Wide Web

[zoro]

Larne Planet: Thank you.

In particular, thank you for the Baez reference, which I'll look at now -- but it sure wasn't my plan ever to "attempt to describe general relativity"!

I wonder if you would take the time to explain, in just a brief sentence, your including Lorentz invariance. My training in that (almost 50 years ago!) was back with just special relativity, so I don't understand how gravity enters.

Also, re. your point 6), do you mean the equivalence of gravitational and inertial mass?

[Larne]

Originally Posted by zoro

Larne Planet: Thank you.

You're welcome! But the "planet" isn't part of my name, it's just a title the forum assigns me based on the number of posts I've made

but it sure wasn't my plan ever to "attempt to describe general relativity"!

You offered an interpretation of gravity and general relativity is the definitive theory of gravity, at least at the moment. So, as far as I can see, you were either attempting to reinterpret GR or offer an alternative to it.

The later, by the way, would violate this forum's policies unless your alternative has appeared in a peer-reviewed journal.

I wonder if you would take the time to explain, in just a brief sentence, your including Lorentz invariance.

The measured volume of space excluded by an object would not be the same for all observers (think Lorentz contraction). Therefore different observers would measure different gravitational forces between such objects.

Now that's a somewhat naive take, and possibly if you wrote out full tensor equations for your interpretation it would work out. But as it's your model the burden of proof that it is Lorentz invariant rests on you.

Also, re. your point 6), do you mean the equivalence of gravitational and inertial mass?

That's one way to put it, yes. It can also be expressed by saying "no experiment in a sufficiently small region can distinguish between gravity and acceleration" or "in sufficiently small regions the laws of physics reduce to those of special relativity." These are all equivalent.

[zoro]

Larne: Thank you again. Sorry about the "Planet". Maybe one of these days I'll get the hang of this newfangled stuff!

Re. any reinterpretation of GR: In my developing book (referenced in an earlier post), I was "just" trying to explain to kids (explicitly, my 16-year-old granddaughter) some basic ideas about gravity (in a chapter that isn't posted yet; it's still in draft form). While trying to do that, I had great difficulty trying to explain to her why two masses would attract, with the difficulty following because I couldn't understand it myself -- and still can't! [I tried the standard, simple model of two people on ice skates, on very smooth ice, tossing a medicine-ball back and forth. That model works great for repulsive forces -- and thus my wondering about a repulsion between "space" and mass.] But since understanding gravity isn't critical to one of the book's central themes (all of which deal with "the god idea" in which she and so many kids throughout the world have been indoctrinated), specifically, the possibility that this universe may have created itself from "nothing" and that there's still "nothing" here (but now the "original zero" has been separated into "positive" and "negative" components), then if my suggestion about gravity is wrong, there's no problem if I just omit the idea.

Thank you for your explaining the potential Lorentz invariance more completely. I'm afraid I'll need to leave it to someone more competent to investigate the matter in the manner you suggested. Thank you, also, for your additional explanations of the equivalence principle.

[Larne]

Originally Posted by zoro

Sorry about the "Planet". Maybe one of these days I'll get the hang of this newfangled stuff!

No apology needed. I actually wish there were a Larne Planet. You could probably get some great pasta there.

Re. any reinterpretation of GR: In my developing book (referenced in an earlier post), I was "just" trying to explain to kids (explicitly, my 16-year-old granddaughter) some basic ideas about gravity (in a chapter that isn't posted yet; it's still in draft form).

Ah, okay. If your goal is just to convey a sense that there are natural, scientific explanations for everything we see around us you could try the standard bowling ball and rubber sheet analogy. I'm not crazy about this analogy myself, but it does convey the essential idea that what we experience as gravity is really just a manifestation of the geometry of spacetime.

Possibly some of the pages linked to from Baez's site have some better metaphors, I haven't investigated all of them.

I tried the standard, simple model of two people on ice skates, on very smooth ice, tossing a medicine-ball back and forth.

That analogy comes from a picturesque view of the "virtual particles" that arise in quantum field theory. Again it's OK at conveying a general sense of how things work, which may be good enough for your purposes. But as you've seen it doesn't even work for the attraction between electrons and protons, and it really doesn't work for gravity, for which we do not yet have a quantum theory.

Good luck with the book! I'm sure you're aware of the numerous books on atheism that have hit the shelves lately, but personally I'm always happy to see more.