# md65536

Senior Members

2081

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## Posts posted by md65536

### Questions about spacetime curvature and geometry.

We (humans for all of history) live in a weak gravitational field, and thus in essentially "flat" space-time, correct?

And the curvature of that spacetime has been constant throughout history (to the limits of our ability to measure it, at any time in history)?

Is it possible to observe Earth from a location in a weaker gravitational field ("flatter spacetime") and observe that what we see as "flat" appears curved from that perspective?

Then, would geometry appear different? Would a unit circle on Earth appear to have a circumference other than 2Pi when measured from this "flatter" perspective? Or are we basically already so perfectly flat that there would be no difference, and Pi would be the same value because it is based on "perfect flatness" or something like that???

Or are geometrical constants such as Pi not even dependent on something like "relative flatness"?

### Question for those who post new ideas.

_I am learning all the time and i will never make an important discovery, I am afraid.

_I think my ideas are correct & important.

Yes, the poll could have been clearer and without gaps in the answers.

Part of the poll's purpose is to figure out how grandiose (not necessarily unrealistic) our expectations are. Your post sums it up, for you.

I think that having NEW ideas that are correct and important constitutes making an important discovery. So that option's good, except that it doesn't exactly express what you wrote. However, I can't think of how to perfect the wording of the poll.

However this was because it was closest to my preferred response, which was not present.

I do tend to speculate, but i do not post my own "new ideas".

It would be arrogant in the extreme to post improperly formulated ideas on the forum and expect them to be accorded any kind of attention or respect. I am continually belwildered by the psychology of those who do post such ideas with the apparently sincere belief that they are correct. I can only attribute this, in most instances, to deep rooted stupidity or simple brain damage. To say I have the utmost contempt for such individuals would be to understate the situation. I sincerely believe their approach to life and to science undermines society in a small, but significant way.

I'm more interested in where people expect their ideas to take them, rather than how realistic those expectations are.

Personally, I think that posting an idea with a sincere belief that it is correct comes from never having experienced the proper development of an idea in a way that can answer questions about it (and inevitably having those answers change the idea). I think that assuming a specific idea is correct often indicates having a limited view of the alternatives; once you see how investigating an idea can open up a tonne of alternatives that you hadn't even imagined, it's harder to take ideas for granted after that.

I like to think that ideas can be "good" and yet completely wrong, if answering questions about it refines the idea rather than eroding it to nothing. Posting a crazy idea might be just a starting point for it.

I think that unrealistic goals can be good, but they need to be balanced with realism and an acceptance of possible (maybe likely) failure.

Having a goal of winning a gold medal in the olympics is admirable. Having a goal of winning the lottery is foolish.

### Consciousness particle

Thank you DrmDoc. I believe your post essentially proves my theory.

Although some may want to believe otherwise, consciousness is a product of brain function. As a product, consciousness does not persist after or outside the cessation of brain function.

Yes, that seems correct.

However, thoughts can exist in some form without brain activity. For example, you can write out a thought.

Knowledge or information can be expressed and passed from one person to another in different forms. Not all of those are "thoughts", however surely a lot of what makes up our thoughts comes from an external source. For example, we think in a language we didn't invent (typically). So some aspects of our thoughts are not created entirely within a single brain. Similarly, if I'm pondering an idea that someone else has come up with, some part of my thoughts comes from them.

A teacher once described the brain as analogous to a computer, where not all of the thoughts we process are our own. Essentially, we can "run other people's programs" on our brain computers... this may be as simple as for example contemplating the ideas of some great philosopher.

I don't actually know anything about consciousness, but it seems that a part of it manifests thusly -- in a language that's learned, incorporating ideas that have been learned.

Say for example I wrote out all of my thoughts and ideas into a book. Then a thousand years from now, suppose someone read the book and meditated on it with such focus that they tried to think only what was written. Does their consciousness have anything to do with what came from the book? Or are the "contents of thoughts" merely data, while consciousness itself is just the state of brain: That it is switched on and operating and thinking thoughts (regardless of what they may be)?

Does consciousness require self-awareness? And does self-awareness require the learning of some set of information? If yes to both, there may be some component of consciousness that is external to our selves???

### Question for those who post new ideas.

I'm curious as to where my own beliefs and expectations are relative to my "peers".

This poll is aimed mainly at fellow speculators for which I assume the following are true:

- The topic you're speculating on is not related to your main area of work/study (unless working independently full-time on your theories).

- You're more interested in developing a new idea on a topic than understanding all existing knowledge on the topic.

### Consciousness particle

I had some ideas bouncing around in my head, when I suddenly realized this could only happen if the ideas were particles. These new particles are called "ideatons" and all consciousness is made up of them.

Yes, I know the theory sounds obvious, but science requires incontrovertible proof and also numbers, so I went and discovered the empirical evidence of ideatons!

What I did is: I weighed my head when it was empty, and then weighed it again when I was thinking some particularly "heavy" thoughts. I had to compensate for all the other "stuff" in my head (skull, hair, small amounts of air, etc), and I had to estimate the number of ideatons that made up the thoughts I was thinking. Then, dividing by the speed of thought (which obviously is c), I came up with an estimate that the mass of an ideaton is on the order of 10^27 kg. This estimate may be off by a bit, but it nevertheless satisfies the mathematical requirement of science ("There must be some math in a theory."), which proves that ideatons are REAL.

Since ideatons are heavier than most other particles, I deduced that mass is made up of thought. Therefore, the universe is made up entirely of conscious particles, thinking thought energy back and forth. And since "great minds think alike", as in "together", it is thought energy that brings things together. This completely explains gravity. As in, "when a plan comes together." Objects are thoughts, and moving objects are plans... as in, they're planning on going somewhere. Since you can think about where a thought is going, that's how science is able to make predictions. This completely explains the Future and the signs of the zodiac. (This paragraph has been edited to make more sense.)

That universal truth, "I think, therefore I am", also applies to the universe. It is a great day in history that I am able to publish this theory here in the Speculations forum, however I am a little sad that there are now no longer any mysteries in the universe.

### If men didn't exist would there be less wars?

The reality is that the line between good and evil runs through every human heart, and I don't see women any different than men.

Uh, I guess you gave some good examples linking women to war.

But it's not about good vs evil, or women vs men, or stereotypes or unfair generalization.

Men tend to have more testosterone. Testosterone levels are linked to aggression. Aggression is linked to war.

A hypothesis that (a lot) fewer men would result in less war, is a good one. I expect that it's true.

It might be false... perhaps the link between aggression and war is superficial. Perhaps war is inevitable, and any group will tend toward war as much as any other. But I don't think that's true.

I think that if you removed all the males from a group, females would naturally fill any of the necessary roles that the removed males previously had, as well as some of the unnecessary roles. I don't think war is necessary or natural (though conflict in general appears natural), and I don't see any reason why women would maintain war at the same levels that the world does now (with war currently being dominated by males).

Some possible indicators:

- Do societies predominated by women tend to be significantly more or less prone to physical conflict? (Lesbos and the Amazons being examples of either side of the argument, but I don't know what is history and what is myth).

- Do societies with female leaders tend to engage significantly more or less in war? (This may be more correlation than cause, as warring nations may prefer male leaders rather than that female leaders are better at avoiding war).

I'm fairly certain that there's a strong link between men and war that is more than coincidence or circumstance. However, I don't want to bother doing the research and it's possible I am biased due to stereotype.

### If men didn't exist would there be less wars?

I think there would be less war (fewer wars, or smaller or less destructive). I think women are less inclined toward physical aggression.

I was recently pondering an idea that matriarchies might be a more natural societal power structure in the absence of physical conflict, for humans and other animals as well. I think that if there was less war, there would be more women in power. So a decrease in the influence of men might be enough... you wouldn't have to get rid of men completely! I definitely think there is a correlation between men in power and the prevalence of war, but a causal relation between the two may go both ways. A group of animals that has more conflict may desire more male leaders, and a group that has more men may result in more conflict.

I suspect that past conflicts in human history have allowed men to gain more power, changing matriarchal societies into patriarchal ones. Then, once in power, those in power tend to want to stay there, so they may prolong or seek out additional conflict to perpetuate their "usefulness". This may be intentional (as with "war presidents") or not (aggressive leaders may simply be naturally aggressive even in the absence of conflict). That is, patriarchies perpetuate war, and wars perpetuate patriarchies.

There are probably cases to support this idea, but I don't know if it's strong enough to claim it's true in general, and certainly it's not true of all men and women as individuals.

### The sun is giving birth to planets

Well that helps. Is it the constant rotation that's made all the planets perfectly round? Like stones in an ocean? It seems like we'd have some planets that weren't round if that was the case.

This explains the true motivation for the main conjecture: lack of understanding of existing theories. If you don't understand why planets would tend to be round, it may seem like there is no existing explanation and any new idea is valuable.

You could spend a lot of time searching for evidence that your conjecture is true, and will more likely come across some contradiction that makes it impossible.

However, I think it would be a lot easier to research other answers to the questions you (and I) are guessing the answers to: Why do planets tend to be round? Why does rotating debris tend to form a disc?

Then, I suspect that you will find that things your conjecture explains have much better explanations, and there is no reason to believe in your theory. OR, perhaps you will find some problem with the existing theory that you can explain better, and if you allow yourself to rewrite your theory completely to incorporate or at least match accepted science, it could lead to something.

### The sun is giving birth to planets

The purpose of my open questions was to get the OP to think about his idea a bit more. Handwavey "I think it was dun like this because that's what I think it was dun like" is not science, it's not even very easy to analyse in anything like a scientific way, but if you can get people to think things through themselves and present them with the evidence we have then maybe they'll come to the conclusion that their idea doesn't fit reality. And maybe they'll then go on to find something that does...

Yes, and I was trying to help him out with that, but I think I've at best done a disservice. I was hoping to provide some possible ways to think through the problems with this conjecture. But my answers to your questions are nothing but a way to ignore the questions, and there's no evidence to support my answers so we're left where we started, and they "handwave" past problems that could, if properly explored, show that the conjecture is false.

I think a lot of pseudoscientists will latch on to other wild conjectures (or some very specific interpretation of other theories), that align well in some specific ways with their own beliefs, which lets them "believe it" more strongly. (Personally, I seem to be connecting all my ideas with the holographic principle, lately.) I should not be helping others make this mistake.

### The sun is giving birth to planets

[1] So why are the planets made of different % of stuff than the sun?

[2] How would the mass get out against gravity?

[3] How do you consolidate this with the evidence we have for planet formation disks observed around other planets?

[4] Why are all of the planets, pretty much, orbiting in one plane?

[5] Why are the orbits we observe not changing by the required amount for this to happen?

Also, have you been here before? If not, your idea has.

I disagree with the theory but I don't like to see an idea killed by open questions.

1. It could be that the "planet birthing" process occurs deep within the sun, involving a process that makes use of only some portion of the sun's matter. Some number of factors could influence the size and composition of each "child".

2. Births are explosive events (think Alien). Supernovae and solar winds already let stellar matter escape gravity... explosive births could too.

3. It could be possible that there are multiple means of planet formation.

4. The planet formation process might be directly related to the sun's rotation.

5. Change in planet orbits may occur in short periods due to some phenomena we haven't witnessed in our history. The births may be accompanied by a "belch" that pushes everything away from the sun.

All that said, there is no evidence that any of these answers or any of the original statements are true.

Meanwhile, other alternatives (planet formation disks) are evident, much more plausible, and have fewer unanswered questions.

I don't see any reason why someone would believe this theory. What problem does it solve or advantage does it have over other planet formation theories?

Can't find any relative posts anywhere about this. The earth was once as small as mercury, it has expanded and grown

I've seen a youtube video describing the theory that the Earth is expanding. The video argued that the continents fit together perfectly on a smaller sphere. It's an interesting idea, but it's not accepted and probably debunked and doesn't have the supporting evidence that tectonic plate theories have. But if you want to get on board with other crackpot theories, you might search for that.

Or on the other hand... you could skip youtube and instead check out some science books or even wikipedia... http://en.wikipedia....etary_formation.

Edit:

I remember at the time reading that Neal Adams is... well, let's say not reputable. When I googled this video google suggested search term "expanding earth debunked". I would suggest looking into that before getting too into this.

### gravity as surplus electrostatic attraction

Thus, I think it could be said that any body of matter will have some surplus of proton charge relative to electron charge.

Wouldn't this imply that a neutron is massless?

Neutron stars would be a problem then ("a spoonful weighs as much as a mountain"). If neutron stars are actually observed and not just predicted (I figure it's the former), how would they be explained?

Electrons have a (relatively small) mass. Does your conjecture imply that adding electrons would decrease mass, in opposition to what is observed?

### Do all functions with singularities have divergent integrals?

Sure

Consider $f(x) = \frac {1}{r}$(i.e. $\frac {1}{||x||}$) In dimension 3 0r above. Since the volume element in spherical coordinates is $r^{n-1}dr \times$ (other stuff involving angles cosines and sines) the integral converges on finite balls centered at 0. This is why random walks in dimensions 1 and 2 are recurrent but random walks in dimension 3 and above are non-recurrent. (With reasonable constraints on the probability measure).

Or if you want to stick to dimension 1 see below.

Fascinating! Thanks! No, actually I'm only interested in dimension 3 but assumed it made more sense to figure it out in one dimension first. Oops.

I don't get why the integral converges on finite balls centered at 0.

I don't get the connection with random walks. Is the integral related to the probability of eventually returning to a finite segment in 1D, or area in 2D, or volume in 3D? Does that mean that for any arbitrarily small value of epsilon, a random walk starting at location x,y will return to within a distance of epsilon away from x,y, with infinite probability (given infinite time) -- but as soon as you add in a third dimension the probability becomes finite?

What happens with $f(x) = \frac {1}{r^2}$ in 3 dimensions?

SureSure. Take $f(x)=\frac{1}{x^2}$ for $x \ge 1$ and $f(x)= \frac{1}{\sqrt x}$ for $0<x<1$

Very interesting. I may need to crack out some math books and think about these things awhile before I understand all this.

### Do all functions with singularities have divergent integrals?

I haven't done integrals for over a decade and I'm having trouble with them and my math skills are inadequate

The function f(x) = 1/x^2 has a singularity at x=0.

The definite integral of 1/x^2 is divergent, if it includes x=0.

However, the integral from 1 to infinity, of 1/x^2, is 1.

Are there examples of functions that have a singularity (where the function approaches infinity), with a convergent integral?

For example of what I'm trying to get is... 1/x^2 remains non-zero for all finite values of x.

Along the x axis, I imagine there's basically an infinitesimally tall rectangle that is infinitely wide, and yet it has 0 volume.

Yet along the y axis at x=0, 1/x^2 is undefined and a similar infinitesimally wide rectangle has infinite volume.

Is there any function, or any way, to basically "take what we have on the x axis and get it on the y axis as well", so that we have a function that stretches to infinity along both axises but has a convergent integral everywhere?

(If you know of related Sage expressions that would also be appreciated thanks!)

### The Paradoxical Nature of Black Holes

Disclaimer: I'm not a real physicist, and I haven't read all the replies, but I wanted to chip in a couple cents.

First: How can you possibly see something that's frozen in time? In the first post, you admit that you can't, but then suppose that you can -- that's just asking for problems when you assume something that's known to be unreal.

What exactly do you expect to see? If the clock is sending out a signal at frequency more than one million megahertz, yet it appears to be completely frozen for you, how much time do you think it will be between signals that you receive? Answer: Infinity much, that's how much. Similarly, if you are shining light on it and it is reflecting that light, then the light that it reflects in say a second of its own time would need to be stretched out into an infinite amount of your time. It would need to receive and reflect an infinite amount of light in its own frame, for you to see its reflection.

Second: If you do not observe that the matter of the clock has been absorbed by the BH, then you won't see the same matter evaporate out of it (you'd never know it was the same matter but you could measure its mass to be assured that it is never observed evaporating more mass than it is observed to have). However, if the BH evaporates, eventually it won't be a BH any more (it will become a normal boring dense mass?), at which point you could see the clock fall into it.

I think what you'd see is that as the BH evaporates, the event horizon shrinks???, and the clock is allowed to move closer and slowly forward through time as it follows the EH that is shrinking away from it??????

### Conjecture on the non-homogeneity of all matter

It is true that many ideas from physics have been put to good use in geometry and low dimensional topology. Now, the question of if physical ideas are enough to describe all of geometry is very much open. The trouble as I see it is that there has been so much cross-fertilisation between geometry and physics it is now hard to separate the two clearly.

I suppose for me the biggest clue would be an answer to: Is "our" geometry the only one that works?

If I am one unit of distance away from two other locations that are also one unit away from each other, that forms an equilateral triangle, with an angle of 60 degrees in "flat" geometry. Exactly 6 of these can fit around me in a circle. Why exactly 6? In curved space it could be 4, or some other number... could that curved space be transformed into a flat geometry and have everything work, only with a different value for pi, etc?

Then if you could say derive pi from c without using any of Euclid's axioms or postulates, or express geometry in terms of entropy or something, then I think you could show that geometry is the way we perceive it because of some fundamental universal constants, and not due to the fundamental nature of our particular geometry.

In other words if geometry is shown to be subjectively determined by universal constants, that would answer the question, no?

Another way might be to find a way to deduce Euclid's postulates from physics.

I need to go back to school!!!

Edit: I suppose you would also need to show that the other direction (deducing fundamental universal constants from geometry) is not valid or something.

### Conjecture on the non-homogeneity of all matter

But momentum through spacetime curvature produces acceleration, no?

No, I don't think so.

Do you mean that something moving along a geodesic changes direction? I don't think that's true either. The object might appear to curve from other viewpoints, because space itself is curved, but the geodesic is essentially a straight line in curved space. From the viewpoint of the object, the geodesic IS straight... it APPEARS always straight all along the geodesic. The object would not experience any acceleration.

> they don't follow the same path as light because they curve more than light does. Light only orbits where escape velocity is C.

I don't think this is a correct or meaningful way to describe it. "Orbiting" requires moving off of a geodesic (continuously, I suppose).

> That seems as impossible to me as the possibility that light contains infinite energy and infinite speed (instantaneity).

I don't see how that is the case.

My theory would have to have that the predicted behavior of light is no different than our accepted predicted behavior of light.

This is possible, because the singularities are inside particles, and "out of reach" of light. Light either misses the particle or is absorbed or redirected by the particle, but the light never reaches the singularity. This may in turn explain things like refraction, where to light, a "bumpy surface consisting of particles" can behave as a smooth flat surface to light which acts like a wave.

Basically, the infinite spatial curvature would have an "infinite" effect only for a radius of 0. It would quickly fall off, on the scale of subatomic particles or something like that. It would not be allowed to cause any sort of inconsistency -- if it could then the theory is wrong.

> I agree except in terms of negative gravitation. What's so implausible about repellant gravity, especially considering how electrons behave around the nucleus?

Well, for negative gravitation, you'd have to have spacetime that curves in the opposite way from "normal", so that this "repellent source" causes length expansion and time speeding up. I don't know of anything that would be explained by this, or any reason to suggest it's possible, or any aspect of reality that seems related.

It might also involve a paradox, such as "Spacetime that is flatter than perfectly flat."

> And how exactly is that "precise location" determined then?

I don't know, but experiments and observations and derivations and theories have calculated the size of various particles.

Observations of mass and light and various interactions and measurements can determine where particles are.

It's subject to the uncertainty principle, but I don't know if that relates to all this.

> I had that with you since a few posts back:) We respond where we deem our response relevant enough to share, no?

Yes, but I feel compelled to try to respond to all questions, even when my answers are just a guess! Much of what I'm saying is nonsense, I'm sure! lol

The problem with integrating 1/r^2 at r=0 makes me feel like I've hit a wall with being able to reason about this topic.

Sorry for the inline quotes... I got lazy.

### life itself, the chaos/rest dimension

The big bang is probably a result of a fractile projection formed and emulating from more original life force energies. Life itself, creating. Time and light energy are the tools of the trade. Life can only come from life and the living create all things. All life is divisions of this life force, and all things are divisions of energy and time. This "life, light, vacuum" energy is the same energy that makes up and vibrates the proton. All things together make up the body of infinity.

The seventh and final dimension in my ever evolving model of the universe. The chaos/rest dimension.

I guess now I'll have to put it all together in a book sure to blow the minds of all who laugh at me

No one would ever read or take seriously a book describing the origins of life by an eternal creative being with simplistic statements like that. The 7th D is a D of rest? No one would read something like that.

### Conjecture on the non-homogeneity of all matter

Just think about a point of net zero gravity? If you have an object at that point, that object is not being pulled in any direction by gravity, correct? So is it completely still? Probably not. If not, how is its motion/momentum different from gravitational force? I.e. think of Einstein's example of the acceleration of an elevator contributing to the net gravity inside the elevator. That elevator's momentum is thus, in effect, a contributor to net gravity no different than the planetary gravity it intersects with. Still, there is an intuitive difference to me between momentum/acceleration force and gravitation generated by mass.

Force (such as gravity) on a mass results in acceleration. Net 0 gravity means no acceleration, but it still has its velocity independent of this (v can be 0 relative to other locations).

Yes, a frame's acceleration provides a force equivalent to gravity, but not its momentum.

I thought "geodesic" just referred to any path taken by an object or particle purely due to its own inertia. Here's a quote from wikipedia:

Sure, but satellites are accelerated by gravity. If they weren't, they would fly off on their own inertia, and follow the path that light would: a geodesic that curves along spacetime.

Ok, I get it. You're basically describing the shape of a spacetime 'dent' in geometric terms I can't completely interpret because of my limited math skills. 1/r^2 is basically the weakening of a gravitational field or photon emission as you move away from the source, right? 1/r^3 would be the nuclear force, right? (at first I thought it was a magnet but you said that is 1/r). But you're just talking about a singularity where force can approach infinity as the radius becomes infinitely small.

Yes, 1/r^2 describes the magnitude of gravity and other things as well, such as the density of a fixed amount of energy stretched across a spherical surface.

The initial conjecture is that there's a mass density singularity in any mass.

This suggests that the density would taper off to fill all of space, instead of having an abrupt edge between zero mass density and some finite mass density.

I think a mass density singularity would imply a spacetime curvature singularity.

It *might* be that the mass density and the spacetime curvature could be described using the same functions. Otherwise they'd have to be discussed separately.

Yes, I think that infinite spacetime curvature could imply infinite force.

That's 3 separate but highly related things (mass, curvature, force).

Could the negative mass-energy density refer to repulsion instead of attraction? Could that be responsible for the erratic tunneling behaviors, etc. of electrons? Sorry if I'm making no sense. I'm barely able to make sense of what you're saying and why.

Negative mass makes no sense to me. All I can say is that it probably has no relation to reality, but I don't know for sure. I'd rather avoid it, but if I couldn't avoid it, it might not destroy the theory (it probably would tho).

I'm not actually making sense! I proposed a function with sin(x) in it because the integral of that is finite, but that's because sin(x) has periodically negative values. Sin(x)/x is a bad guess anyway, because the limit as x approaches 0 is not infinite, which is what I'd want for a singularity of infinite mass density.

Reality doesn't depend on how it is observed.

Sure does! Lengths, and time, depend on an observer's relative velocity and gravitational field. Quantum mechanics deals with observers differently depending on interpretation, with variations from "observing reality affects it" to "differently observable realities exist in superposition."

Invariable aspects of reality don't depend on how it is observed. I equate that with "fundamental" aspects of the universe, with observer-dependent things being "emergent". Some aspects of geometry (eg. the curvature of space) are observer-dependent. I believe that all geometry is ultimately emergent.

Our knowledge/perception of reality depends on how we perceive and know it. This discussion, to me, is about the ontology of boundaries. What constitutes a boundary and why? Is it ultimately adequate, however pragmatically useful, to define the boundaries of objects in terms of apparent surfaces visible due to light reaching a certain level of reflection or refraction/diffraction? When an object is immersed in another in a different phase, it is easy to claim that the surface of the object is its boundary, even though that may not be the case at the atomic level, right? At that level, it's the energetic motion of the particles that define them in terms of how close they can get to each other before being deflected, right? Two repellant magnets can get closer to each other before deflecting if they are moving more forcefully toward each other than if they have very little force. But yet it's the distance of deflection that defines the boundary of the repellant fields, no?

There are and may need to be different boundaries or fields for the different forces. Those would determine how it interacts with other matter or energy. I think that the precise location of mass-energy of a quantum of matter describes a boundary of mass (which may be different from interactions).

You're going into topics that are beyond my knowledge or reasoning, though.

### Conjecture on the non-homogeneity of all matter

Wait a sec... I've been on crack this whole time.

The infinite integral of 1/x is divergent.

The infinite integral of 1/x^2 is convergent, EXCEPT for the singularity at x=0.

So the "fall-off" of function f( r ) = 1/r^2 is fine... it doesn't imply an infinite mass,

unless we allow r=0. Suddenly the singularity is not so convenient :/

### Conjecture on the non-homogeneity of all matter

Right, but as you said about the moon's effect on the tides being due to the gradation of field-strength instead of absolute strength, "flat" spacetime could never really be flat insofar as there must always be some degree of "net force" acting on any object or particle above absolute zero, right? I suppose what I'm saying now is that an object's inertia is like it moving under its own gravity in the form of momentum. That sounds wrong because you think of gravity as an inherent force that emerges from mass itself whereas momentum is due to an energetic push, but I think you could view spacetime curvature (i.e. net gravitation) as including momentum, which could explain why geodesics for photons are different than those for satellites, no?

I think spacetime can be flat at a point (or over a volume of points), iff at that point the gravitational pull from all mass balances out to a net force of 0.

If the magnitude of gravitational force is directly related to curvature, then a gravitational gradient would involve the difference in curvature at different points, not the "steepness" of the curvature at those points. The main thing that affects tides is that the force of gravity from the moon at the point on Earth that is closest to the moon, is stronger from the force at the point on Earth farthest from the moon. This means a difference (gradient) in the curvature of space across the volume of the Earth.

You could have uniformly curved spacetime (ie. be in a uniform gravitational field) and tides shouldn't happen, but that doesn't mean that spacetime there is flat.

I don't think of gravity as an inherent force, but rather a kind of inertial motion in curved space.

Geodesics are "paths of zero acceleration", so satellites do not follow geodesics as they're constantly being accelerated due to gravity (inward gravitation balances outward inertia in a perfect orbit).

I'm still struggling to understand this. What kind of mass are you saying is distributed and how?

I'm speaking of any mass, specifically when viewed as a single indivisible unit (a particle, basically).

I'm saying that its distribution isn't uniform, but that it is infinitely dense at a point in its center. This describes a singularity.

Consider for example a spherical drop of water of radius R. Its mass distribution might be something like

f( r ) = { 0, r > R

1, r < R

This is a uniform distribution within its radius.

A distribution like f( r ) = 1/r^2 has a singularity at its center, but unfortunately it describes infinite mass.

So I'm not sure what type of distribution would fit what I'm proposing.

f( r ) = sin^2( r ) / r^2 would not be infinite (I think)... and it may capture a "wave nature" of matter... but unfortunately it has areas of negative mass-energy density which doesn't make sense to me, and it is not strictly decreasing which I assume matches reality.

f( r ) = 1 / C^r for some constant C might work, but I don't see how this has any connection with observations and reality).

I thought you were just saying that the force-fields of constituent particles had no defined boundary.

No... I think that's already accepted by all(?) gravitational theories. I'm talking about the uniformity of the mass that cause these gravitational fields, not the field itself.

You can't observe a magnetic field using photons, presumably, because photons don't bounce of them but you can observe it using another magnetic field. But how do you define where the magnetic fields begin to interact and where not? If two bar magnets were suspended in a perfect vacuum devoid of any other forces or energies, would their magnetism eventually draw them together? If all energy were taken out of any system with any amount of attractive force, the force would have to collapse the system into a singularity, wouldn't it, unless there was some counteracting force to prevent it?

Yes. 1/r (magnetism) and 1/r^2 (gravity) approach 0 as r approaches infinity, but they are non-zero for any finite r. They have no finite boundary, though far enough out they become negligible relative to nearer interstellar matter... or possibly even vacuum energy (dark energy?))

Yes, I think that as long as the objects didn't have inertia exceeding escape velocity, they should collapse.

But like a cloud or the sky itself, the effect is due to compound light-interference through a collection of particles that would be transparent in smaller amounts or concentrations. You can't technically define the edge of a cloud without setting an arbitrary level of relative humidity to denote the boundary, right? Otherwise a cloud is just a lump in humidity that fills the entire sky, no?

Yes, I suppose that's a good analogy. You could say that the boundary of the cloud is the volume in which all its water molecules are contained, but since the air around the cloud contains water molecules too, there's not a hard boundary. It's like a smooth transition between higher and lower humidity. You could define a precise boundary using some humidity limit.

But like you said earlier, from far away a cloud may look like a solid thing (perhaps with uniform density), but as you move into it (as with fog), the boundary of the cloud appears to change with your location. This is what I think happens with masses or particles.

In practice, I agree with you. But being "undetectable and unobservable and negligible" are relative and subjective, right? I supposed "detectable by any means" would be objective, but how can "negligible" be more than subjective?

I think the important things would be

1. It has to be consistent with all existing observations (subjective negligibility I suppose)

2. It has to be consistent with a sensible theoretical description (which might predict objective detectability)

That is interesting. Maybe that could be how photons get absorbed by electrons, i.e. due to gravitation of the electron at a very minuscule level.

I think the key to dealing with this issue would lie in how atoms and other particles maintain volume. The empty space of an atom could be viewed as making it "buoyant" and thus resistant to condensation to the point of be susceptible to collapse under the gravity of its constituent particles. Maybe the nuclear forces are not so much holding the nucleons together as they are preventing them from collapsing under their own microgravity. This is getting very speculative, though, so I don't know how unfavorable the referees will get when they read this kind of thinking.

I think we're safe in the Speculations forum as long as we're speculating and not asserting claims!

This conjecture wasn't meant as an explanation of gravity... to me it would only need to be consistent with existing gravitational theory.

The effect of infinite spacetime curvature within a particle might be related to gravity but I personally wouldn't call it gravity because it might confuse things (nuclear force is similar in ways to gravity but different enough to avoid calling it gravity).

Yeah... the issue of explaining volume of particles is key. I think the answer is that what we observe (of the subatomic world or the macroscopic world or anything), as far as volumes and empty space etc go, is not a fundamental aspect of the universe. Reality depends on how it is observed. That might open up some theoretical possibilities, but doesn't really help us figure out which are right :/

CRAZY IDEA:

- The mass distribution of a point mass is 1/r^2 but it is scaled by some infinitesimal factor, such that the mass is only apparent where the density is infinite (at the location of the singularity, though I don't know how it would then appear to have volume).

- This distribution represents "uniform mass density" throughout the entirety of a 2-dimensional universe...

1/r^2 means that a spherical shell of any radius would contain the same amount of mass as a shell of any other radius.

If we remove a dimension or 2 (time and distance, specifically), we might be able to describe a 2-D geometry in which all 3-D spheres of different radii become identical structures in the 2-D world. In this case, the mass then is uniformly distributed across the entire 2-D universe.

This is "nice" because it fits (vaguely) with the holographic principle, which among other things suggests that any point in a 3D volume maps to all points on a 2D holographic surface. This would allow a particle to be uniformly distributed across this surface.

Question: Is it possible to modify f( r ) = 1/r^2 such that an infinite 3D volume integral becomes finite? Would the "infinitesimal factor" have to be non-constant? I will try to ask in a math forum...

### Conjecture on the non-homogeneity of all matter

How can you be sure that gravitation doesn't cancel itself out to some extent, even relative to a satellite far away? E.g. supposedly the center of the planet is weightless due to gravity canceling itself out in all directions, but then are solar and lunar gravity still present as the dominant gravitational forces there? Actually, that's a bad example. The issue would be whether the cancellation of gravity in the center of the planet gradually decreases as you move away from the center, and then does it also gradually decrease from the lagrangian points between the Earth, sun, and moon. In other words, when is gravity "pure" and not "net gravitation" that results from all interacting fields? I suppose this is what "spacetime curvature" refers to.

I'm sure that gravity does cancel itself out as you suggest.

At a Lagrange point between the the Earth and moon, the overlapping spacetime curvature due to the Earth (curving in one way) and the moon (curving in the other way) combine to result in flat spacetime.

I don't think there's any distinction between "pure" and "net" gravitation: It's all net, whether you're describing a system with one atom, or a trillion stars.

I'm trying but I forgot what it means to find an integral. Is that related to taking the derivative of something to find the amount of change over time by knowing the rate?

Yes, it's the opposite of a derivative.

In this case, if you take the total mass energy of say a particle, then the derivative of that mass would represent the density of mass across space -- a mass distribution function. The integral of the mass distribution function would be the total sum of the mass.

I may not be describing that with the right terminology.

How does the rate of drop off determine the ability to observe anything? Doesn't that mix objective with subjective?

I'm not sure. However: We can make observations of mass and determine where that mass is. If I'm saying "that mass is actually spread out across all of space", that claim has to somehow match observed reality.

One way to do that is the conjecture that any such "spread out" mass somehow appears as a particle: The spread out mass appears to be only in one not-spread-out place.

Another way is if the mass density falls off at such an extreme rate that any mass energy outside of some distinct boundary is undetectable and unobservable and negligible, and thus all the mass appears to be within that hard boundary.

Edit: I think the first option is true. I think that the mass distribution of a mass depends on how it is observed. For example, from far enough a way, a table should appear to have a uniform mass density, no matter how it is measured. From closer up (or on a smaller scale), that uniform mass will separate into particles, each of which appear to have uniform mass density. If you get smaller/closer then the particles can be broken up into smaller particles. I suppose at some point there is a quantum limit to this. However, I suspect that any apparent uniform mass density that appears from any of these points of reference is not fundamental; it is only an observational side-effect.

Usually people say that gravity is negligible at the (sub)atomic level, because they're comparing it with the other forces that are relatively strong despite the minute masses involved. However, I don't know of any claims about the minimum volume of an electron and/or why it couldn't be so small that its gravity would be strong if anything could get miniscule-y close to it. I think there are supposedly other sub-electron particles that constitute it, though, and these are probably theorized as being bonded by stronger forces that gravity. Since electrons don't seem to stay in one place for any continuous amount of time, though, I don't know how they could ever maintain close enough proximity to anything to have their gravity play a determinant role.

Exactly... If we allow tiny singularities of infinite spacetime curvature inside any particle, then we may be able to model reality such that the singularities "average out" to form fairly flat spacetime on a large scale (effecting gravity), but have much stronger effects on very small scale (effecting EM and/or nuclear forces).

If we assume that spacetime curvature is actually smooth, then there's no way that I know of to make the same curvature "weak" enough to explain gravity, and "strong" enough to explain the other forces, and still maintain a gentle curvature for small masses.

### Conjecture on the non-homogeneity of all matter

With physical force-fields, I think the issue becomes more fundamental. If you are standing on the surface of the Earth, you are clearly in its gravity-well (field). But the moon is also in the Earth's gravitational field, so when you are standing on the moon are you in both fields at the same time? Likewise, are we on Earth in both the sun's gravity field AND the Earth's? What about the moon's? The tides suggest that we are. But still we can say that we're "on Earth" but not "in the Sun" or "in the moon" right?

Tides are caused by gravitational gradient, not magnitude (the sun's gravitational pull is stronger but the moon's gradient is steeper due to it being closer and thus the moon's effect on tides is greater).

Gravitational fields intersect or overlap. The gravitational pull of the sun and moon and Earth summed together would be the same as summing the gravitational pull of all of the particles that make up the 3 bodies. This is similar to the above idea that any mass can be considered a particle, from the right viewpoint. From some locations, Earth's gravitational pull is identical to treating Earth as a point mass (right?). I think that from the right locations, all physical aspects of Earth can be made indistinguishable from a point particle with the right properties.

The meaning of "on earth" or "on the moon" is semantics. I don't think it needs to be defined to precisely describe gravity. However, it does bring up a good point: We know and can measure that gravitational fields intersect, but there is no evidence that mass or energy overlaps the same way. In fact it most certainly doesn't. The mass-energy distribution of a mass probably could not be 1/r or 1/r^2 because the integral of those over all of space is infinite. Unless we attribute vacuum energy or dark matter to this theory (which wouldn't work anyway cuz neither of those are infinite), we would probably require that the total mass is finite and in fact it should be equal to existing mass measurements of whatever mass we're considering. So the speculative "influence over area" of mass energy does not have the same drop-off function as the space-time curvature drop-off function of a mass. (Does that make sense?)

So this idea certainly doesn't magically unify the forces. Mass energy and the spacetime curvature due to said mass would need different distributions. Why would that be? The distribution of the mass of a particle would have to drop off at a high enough rate that we could consistently observe that all the mass appears to be within a fixed boundary, in all observations in all of our history (whether it be planets or tables or particle experiments).

UNLESS... I'm confusing a gravitational force function (proportional to 1/r^2) with a spacetime curvature function (which I have no understanding of). Googling it, I see that "space is nearly flat for weak gravitational fields". My conjecture is that this is not true, for a very small volume within any mass: At this point, spacetime is infinitely curved.

Is it possible to "pinch" spacetime in a very small volume, such that:

1. It is infinitely curved at many points (wherever there is a mass particle), but

2. On average it is "nearly flat". On average, the curvature is exactly as GR predicts.

???

It seems that way. Physics is geometry.

I think that eventually, physics will explain all of geometry, and will also transcend it and explain things that are "more fundamental" than geometry.

Isn't this already partly true? Can (some) thermodynamic systems be described without geometry? Or the holographic principle?

Classical electromagnetism has singularities. The famous one is due to the electron self energy. This is all cured when passing to a quantum description. It is expected that the singularities in general relativity can be cured in a similar way. So, singularities probably represent our misunderstanding of the physics and our holding on to classical ideas where we should not.

Topology is very important in understanding physics and geometry. Classical gravity is very geometric, passing to a quantum description would need many ideas from topology.

I think it would make sense if singularities exist in the geometry of space (just like they do in math), but only in the geometry and are "cured" in a topological description of the universe.

Is the quantum description of electrons a geometrical one? I suppose it would also make sense if singularities disappear from the geometry with a new or more sophisticated description (this is really all over my head; I don't know what I'm saying).

But... I think that singularities in the geometry are too convenient a thing to assume they're not really there.

### Conjecture on the non-homogeneity of all matter

I am really interested in these kinds of ideas. I find that people have a hard time with them, though, because it comes more naturally to them to think of objects as external to each other and themselves as external to situations as they perceive them. I'm not sure what it would take, cognitively speaking, to enable people to be able to think in terms of internal configurations of intersecting entities, but if anything I think it would render mathematics impotent (saying this without sufficient breadth of knowledge about mathematics, btw). As far as I know, all mathematical logic relies on a boolean-type notion that a set of elements must be mutually exclusive unless they themselves are sets with their own mutually exclusive elements/contents. But otherwise, why couldn't the table be inside the chair and the chair inside the table at the same time?

Well, there's all sorts of abstract mathematics that can be used to describe real and unreal things. Singularities are simple things in math but they don't make sense given an assumption of a fundamental continuous geometry of the universe. However, if you explore some ideas that hint that geometry is not fundamental, then you can ignore geometry for awhile and imagine other things. For example, topology can be used without requiring geometry. It is still math.

If we assume that geometry is fundamental and any mathematical description of the universe must fit within that geometry, then singularities are a problem.

If we assume that geometry emerges from some other fundamental description of the universe, then whatever is consistent might be possible. Singularities might be a convenient means for simple consistency, and thus might be common.

I think math is necessary because without it, we must use other conceptual tools such as language and spatial reasoning, and I think we would then limit our understanding to what we've seen or experienced. Is it possible to figure out a universe that may exist fundamentally "underneath" 3- or 4-D geometry, using spatial reasoning that's based on that geometry?

So yes, I suppose if you remove the mathematical/geometrical restrictions that says a table can't intersect a chair etc, you can work with more abstract ideas... but we have to be careful about what we claim because words like "inside" may only have a precise definition with respect to a given geometric representation.

I would think that studying topology would be the best way to precisely contemplate junk abstractly without being confined to our habit of thinking geometrically???

### Conjecture on the non-homogeneity of all matter

In short, yes all known forces have something to do with curvature. Gravity is to do with the curvature associated with the frame bundle of a pseudo-Riemannian manifold. Alternatively, you can think about the tangent bundle as the associated vector bundle. Either way, as these bundles come for free once you have the structure of a (smooth) manifold it is customary to talk about the curvature of the manifold and not these bundles.

Way over my head but I'll have to research those topics if I ever try to develop the theory, thanks.

A smooth manifold would have no singularities? So it all works without them, and may not (or may) work with them?

Basically this would mean that the concentration of any distinct quantity of mass is greatest at its center, and tapers off to blend seamlessly into the surrounding nothingness, rather than there being a distinct boundary between mass and surrounding space.

This might mean that there are no abrupt edges to matter. The matter at a table's edge doesn't end there but carries on to exist (in a superficial form) through all of space. The hard edge that we experience might be similar in some way to an event horizon, dividing the matter into a volume where light and other matter interact with it, and a volume where they don't.

The physical presence of matter would coincide with its effect on spacetime curvature. There wouldn't need to be a distinction between things like "The matter is over here but it curves spacetime way over there." Any matter would "fill" the curvature that it causes to spacetime. Just as a single molecule has a tiny but calculable gravitational effect in a location a light year away, that molecule's tiny speculative energy density should be calculable at the same location.

This might relate to the aspect of the holographic principle that all matter in a volume maps to all points on a holographic surface. Basically: Any matter would exist everywhere at once, but it is only fully "experienced" at a small location where its concentration becomes infinite. All matter existing everywhere at once is also compatible with the idea that the universe can be fundamentally described as a singularity, with time and space being emergent observational effects.

### What happens to twin paradox if there is symmetry?

I think I figured out the answer: The symmetry of this scenario is only observed by Earth (or anyone who remains equidistant to both twins). The symmetry is observed as the twins always remaining the same age and acting in synchronization. Other observers (such as the traveling twins) would not observe the scenario occurring with synchronization, due to "lack of simultaneity", so the twins can get out of sync (different age) with each other, before eventually returning to synchronization.

For an observer to synchronize the twins' age, they'd have to become equidistant to each twin, which for the twins themselves can only occur when they're at the same place. (In general they would need to be not just equidistant but also have the same relative velocity to each???, which in this case is provided by the symmetrical motion of the twins.)

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