Conjecture on how/why mass curves spacetime.

[md65536]

I've said before on these forums that "Why does mass curve spacetime?" was the last puzzle piece for myself having even the vaguest understanding of how gravity works.

Finally I have an idea. So I retire from science.

 

 

Assumptions:

1. Time and distance are perceptually defined. They appear different depending on how they are observed. At the speed of light, they are unobservable... they essentially disappear. I assumed that it's possible to describe a viewpoint or model in which they don't exist at all. I conjecture that they are not fundamental aspects of the universe, but only observational side-effects of a consistent, 2-dimensional universe.

2. This pretty much implies that geometry is a perceptual effect. I assume the universe can be defined topologically without geometry.

3. Earlier I posted... http://www.sciencefo...ely-impossible/

mentioning an idea that the amount of distance between everything is related to entropy.

 

I think this might be related to the way that the surface of an imaginary sphere of radius r around an observer is able to "intersect more stuff" the larger that r is.

 

If the radius of a sphere is determined by time t (ie. it grows at a fixed rate), then as it grows, the total possible entropy might be relative to the surface area of the sphere... it represents a measure of the possible states of something moving away from the observer at fixed speed. For example, if you have N photons leave a point at time 0, then at time t, the total possible locations for those photons are spread across an area of pi*t2 oops lol I mean 4pi t².

 

Blah blah blah, yada yada yada, and you have yourself a different description of the holographic principle, which to paraphrase suggests that the total entropy of a volume is proportional to the surface area around that volume.

See also:

 

4. If geometry is nothing more than a consistent 3-dimensional perception of a 2-dimensional universe, then length and time and the shape of spheres and the way things appear smaller the farther they are away are all side-effects of this.

 

 

Then you have the following principle: If the total entropy of a volume is limited by a factor of the square of its radius, yet the total perceivable entropy of a volume is a factor of the cube of its radius, then the more "stuff" you perceive in a given volume, the smaller it's radius must be perceived.

 

Thus, for consistency, more mass requires contracted space. Ie... space-time curvature.

 

 

In other words, space-time curvature is a perceptual product of a consistent universe, just like time and distance etc. The reason that everything appears as it does, is that reality is one of many (or the only?) possible consistent interpretations of the underlying universe. It may even be that any consistent mathematical consequence of the universe will be observed as a "real" aspect of it, and can be measured. Eg. even if distance is an illusion, it is consistently describable by any number of observers, and so something like our eye (which consists of a large number of individual observers working together) can perceive it.

 

 

 

 

 

Well, okay this doesn't prove anything, it's just a vague idea. Perhaps I'll figure out the math over the next 10 years, and then I'll post a follow-up.

Edited February 9, 2011 by md65536

[Mr Skeptic]

Hey, this just might be the best "crazy new theory" I've seen on the whole forums.

[Bignose]

Eg. even if distance is an illusion, it is consistently describable by any number of observers, and so something like our eye (which consists of a large number of individual observers working together) can perceive it.

 

You've really stumbled upon some good philosophical questions here. You may care to partake in some readings on the topic of Philosophy of Science. There are readings on questions like "does it really matter if what we perceive and what reality is is different?" In short, the answer really is no, because if something is unmeasurable, then it doesn't really matter if it is there or not -- its effects are unmeasurable after all.

[md65536]

Hey, this just might be the best "crazy new theory" I've seen on the whole forums.

Thanks!

 

You've really stumbled upon some good philosophical questions here. You may care to partake in some readings on the topic of Philosophy of Science. There are readings on questions like "does it really matter if what we perceive and what reality is is different?" In short, the answer really is no, because if something is unmeasurable, then it doesn't really matter if it is there or not -- its effects are unmeasurable after all.

I have some differing philosophical ideas but nothing clear enough to be worth presenting, yet. Edit: But then I went and wrote out those ideas anyway, in later posts below. :S

 

Blah blah blah, yada yada yada, and you have yourself a different description of the holographic principle, which to paraphrase suggests that the total entropy of a volume is proportional to the surface area around that volume.

To try to be a bit more precise...

 

Suppose you have a certain number of energy quanta at a single location at time 0, and then examine them at a time t.

Their max speed is c, so you should find that all the energy is contained within a sphere of radius c*t.

Assuming the quanta can interact or be accelerated, or just that they may bounce off things, we would expect that the total number of possible places for any quanta of energy would be related to the volume of the sphere (each quanta may be anywhere within the sphere).

However, the only way to get to a particular point on the surface of the sphere is to travel there at c in a straight line. Conversely, if a particle travels in a straight line (no bouncing) it will end up at the surface of the sphere at time t. Therefore, if you find a particle anywhere else inside the volume, that means it bounced (or otherwise diverted), and that means that there is some place on the surface of the sphere that can't be reached by any particle (unless we allow that 2 particles can travel the same path at the same time and diverge, which I guess we must assume is impossible. We might assume that 2 quanta at the same location after time 0 can be considered a single quantum).

 

The main thing that affects where these quanta of energy end up, is an assumption that they all travel at c (whether they consist of photons, or as matter made up of oscillating energy that might be considered "energy that bounces several many times within time t"). If the energy could travel at arbitrary speed <= c, they could end up anywhere in the volume and thus the entropy would be proportional to r cubed. But since they travel at a fixed speed, there is only one place a quanta could be at time t, depending on the direction it was traveling when it left the initial location...

 

... That part may make some assumptions about determinism that are not quite true. Regardless...

 

 

Anyway, the point of this is that each of these quanta of energy can either 1) end up on the surface of the imaginary sphere and "fill that spot" at time t, or 2) if not then the quanta is within the sphere and there is an "empty spot" on the sphere where it would be if it had traveled in a straight line. Thus, for each quanta within the sphere, no matter how many we begin with, there is a point on the surface of the sphere that maps uniquely to that quanta. If you want to end up with more quanta inside a sphere than there is room for them on the surface of the sphere, you cannot do so by having all the quanta start at the same place and the same time.

 

 

Yada yada yada Big Bang

Edited February 24, 2011 by md65536

[lemur]

Eg. even if distance is an illusion, it is consistently describable by any number of observers, and so something like our eye (which consists of a large number of individual observers working together) can perceive it.

Why not just say that distance is a "social fact," to use Durkheimian language? Is social consensus a sufficient basis to define dimensionality objectively? Or is your whole point that social consensus is due to the objective nature of the retina?

Edited February 24, 2011 by lemur

[md65536]

Why not just say that distance is a "social fact," to use Durkheimian language? Is social consensus a sufficient basis to define dimensionality objectively? Or is your whole point that social consensus is due to the objective nature of the retina?

I don't know, at least not clearly enough to make such statements. I don't think the retina or humanity has any effect on reality.

 

I might try to say instead that "distance is not fundamental in the universe".

My followup about the holographic principle seems to assume that c -- a fixed speed of all energy in the universe -- is fundamental.

Time and distance can be an illusion or a social fact or real or unreal or whatever, but the main important fact is that however they may be perceived, they are always defined by a fixed relationship between time and distance.

 

The original conjecture then goes something like this: Time and distance are perceptual effects consistent with these "fundamental aspects of the universe":

1) all energy travels at all times with a speed of c.

2) there is a limited number of possible locations within a given volume (ie. quantization of location)

3) the total entropy of a volume is limited by the surface area around the volume (consequence of 1 and 2?)

4) ???

 

Thus, you can say what you want about time and space, define them as concretely or as abstractly as you want, but in any way you do, the above fundamental aspects must hold. The conjecture referred to by the title of this thread is that if you have a definition of time and space defined by the above aspects, and it is consistent, then you have spacetime curvature due to mass energy.

 

In a sense, "what time and distance are" doesn't matter as much as the fundamental aspects matter.

Time and distance are simply an expression of the universal consensus of those aspects. So I would say more than social facts, they are universal facts, but consequential rather than fundamental ones. They are defined as a universally consistent perceptual measurement, but that definition defines a local perception that depends on the observer. Hahaha, if you are not confused then that makes one of us who isn't!

 

 

Or in other words... the nature of time and space lies somewhere between an arbitrary perceptual conceptualization of a universe, and an underlying absolute physical reality of the universe. Time and space are defined by the observer and depend on how they are observed, but only to the extent that they are consistent with the fundamental reality they represent.

 

 

 

Edit:

 

4) What is not consistent is not observable

5) What is not observable does not have a defined existence

6) Reality is consistent (consequence of 4 and 5?)

Edited February 24, 2011 by md65536

[lemur]

Time and distance are simply an expression of the universal consensus of those aspects. So I would say more than social facts, they are universal facts, but consequential rather than fundamental ones. They are defined as a universally consistent perceptual measurement, but that definition defines a local perception that depends on the observer. Hahaha, if you are not confused then that makes one of us who isn't!

 

 

Or in other words... the nature of time and space lies somewhere between an arbitrary perceptual conceptualization of a universe, and an underlying absolute physical reality of the universe. Time and space are defined by the observer and depend on how they are observed, but only to the extent that they are consistent with the fundamental reality they represent.

Ok, I misunderstood you as referring to perception as a basis for the very fact of distance. I don't think perception is defined by the speed of light as much as it is by the ocular lensing. If you change the lens on a camera, distances appear differently. Objective ideas about distance are based on extra-perceptual science. Sensual, empirical observation is one thing but measurement requires going beyond visual estimation of distance. I don't think there's any necessary consense, though, whether universal or otherwise. You can experiment with this by getting some people together to estimate the distance to various objects. You will probably get divergent estimates, proving that perception does not accurately conform to objective measurement.

[md65536]

Ok, I misunderstood you as referring to perception as a basis for the very fact of distance. I don't think perception is defined by the speed of light as much as it is by the ocular lensing. If you change the lens on a camera, distances appear differently. Objective ideas about distance are based on extra-perceptual science. Sensual, empirical observation is one thing but measurement requires going beyond visual estimation of distance. I don't think there's any necessary consense, though, whether universal or otherwise. You can experiment with this by getting some people together to estimate the distance to various objects. You will probably get divergent estimates, proving that perception does not accurately conform to objective measurement.

No you were right... I was referring to perception as a basis for the fact of distance. But not in any "imaginary, anything goes" type of way. Only in a very real way.

 

For example, if you take a wooden table, you would say that it is solid. And that is reality... it is solid. Depending on how it is perceived, it appears solid (if the wavelength of light used to observe it is blocked by it). The "underlying reality" is that it is made up of tiny particles and is mostly empty space between them, but the perceptual reality which depends on how it is perceived, is that it is solid. That your hand can't pass through the table is real, but not fundamental: It can be traced back to an effect of the fundamental forces (which of course would be considered fundamental). That stuff can't pass through a table "depends"... neutrinos can. Obviously, the impenetrability or solidity of a table is not a fundamental aspect of the universe.

 

If you change lenses on a camera, it changes the appearance of distances, but it doesn't change the actual distances. However, if you are moving relative to something, you can change its actual length (this is only noticeable at velocities approaching c). The length of something is real, but its actual value depends on how it is observed.

 

You can get different people to estimate the length of a meter stick, and due to errors in perception, they will observe 1m and think it is something else.

With perfect perception (which I'm assuming in these posts -- I'm talking about the nature of reality rather than the nature of human thought and sensing), you would perceive 1m.

However, another perfect perceiver may measure 0.5m depending on relative velocity or differing gravitational field.

 

The reality is that that meter stick actually IS 1m or 0.5m depending on the observer. Those are both "real distances". But distance isn't fundamental. The closest you can get to an absolute distance is rest distance in the absence of gravity. It could be that this actually is fundamental. I don't think it is but I can't rule it out.

 

 

Perhaps I'm not using the word "perceived" properly... Does it imply an element of human interpretation? I've been using it as if it didn't.

Edited February 24, 2011 by md65536

[lemur]

Perhaps I'm not using the word "perceived" properly... Does it imply an element of human interpretation? I've been using it as if it didn't.

You said this before:

Or in other words... the nature of time and space lies somewhere between an arbitrary perceptual conceptualization of a universe, and an underlying absolute physical reality of the universe. Time and space are defined by the observer and depend on how they are observed, but only to the extent that they are consistent with the fundamental reality they represent.

If you're going to approach objective reality as objectively defined, what is the point of even bringing up "observation-dependence," "perceptual conceptualization," etc.? If all you mean is that objective physicality determines subjective perception, why raise the issue? As far as I can tell you're not making any defensible claims about subjectivity, only objective material relations.

[md65536]

1) all energy travels at all times with a speed of c.

2) there is a limited number of possible locations within a given volume (ie. quantization of location)

But you're saying time and distance aren't fundamental, and then listing fundamental things that are related. How can you speak about speed and volume in fundamental aspects if time and distance aren't fundamental?

EXACTLY! So if we were to list all fundamental aspects of the universe, and time and distance were not defined on there, but everything else was (the definition of speed, volume etc), then I'm suggesting that you could come to any correct conclusion about time and distance, as we observe and/or understand it, based on that.

 

Then if you gave these rules to an advanced AI that had no understanding of time and space, but was able to deduce things, it could deduce things like "I get it! Things appear smaller the farther you are from them!" or, as I'm suggesting: "I get it! Spacetime must curve!"

 

Or to put it another way, my conjecture is this:

If you listed everything that is true about the universe, and then one by one removed every statement that could be logically deduced from the other statements (ie you reduced it to fundamentals), you would eventually be able to remove the definition of time and space, as their definition would be completely specified by other more fundamental truths.

 

I'm saying they need not exist, even as concepts, independent of the rest of the universe. As real as they are to us, they may just be "semblances" or something, of an underlying nature of the universe.

 

 

I think things like speed and volume would have to be definable in terms of other things (entropy maybe) for this to be correct.

 

 

 

 

Okay sorry I've rambled too long now trying to make precise the ethereal philosophical aspects of the conjecture, and my thoughts and words aren't precise enough to do this.

 

You said this before:

 

If you're going to approach objective reality as objectively defined, what is the point of even bringing up "observation-dependence," "perceptual conceptualization," etc.? If all you mean is that objective physicality determines subjective perception, why raise the issue? As far as I can tell you're not making any defensible claims about subjectivity, only objective material relations.

I'm separating "observed reality" ie "reality" (subjective, observationally dependent, relative, etc) from "underlying physical nature of the universe" (objective, absolute, ??? yet unknown or at least not yet well understood... speculative!).

This is also separate from "imaginary" (illusive ie. inconsistently observed or strictly conceptual).

 

I don't even know enough of what I'm saying to make defensible claims. The more I write to try to suss it all out, the more confusing it will probably be. It's just a vague idea that's based on conjectures about time and spacetime curvature. It's there that I should focus, where it should be possible to evaluate the conjectures mathematically if I can figure out how. I should leave the philosophy where it is: just a vague idea of the nature of existence, that will always involve flexible interpretation of the science. I can't make any claims about whether or not my philosophical outlook is right.

 

 

 

This is not related to the conjecture about spacetime curvature, but: My other conjectures, which lead to this one, also leads to an idea that the universe can be described completely as a thermodynamic system with topology but without geometry. No distance or time, possibly as little as 2 dimensions (or even less, maybe fractional), a singularity. This is usually what I'm thinking of when I speak of an "underlying physical nature of the universe". Some weird inconceivable thing that doesn't make sense in our understanding of reality, because it involves removing all the things that define perception (or result from perception), ie involves removing much of what makes up our reality as we perceive it.

Edited February 24, 2011 by md65536

[md65536]

Then you have the following principle: If the total entropy of a volume is limited by a factor of the square of its radius, yet the total perceivable entropy of a volume is a factor of the cube of its radius, then the more "stuff" you perceive in a given volume, the smaller it's radius must be perceived.

Corollary: If the apparent radius of a volume of space is determined by entropy, then the size of the universe could be determined by entropy.

The fact that the universe is expanding might be due to the way that entropy is increasing.

The fact that the expansion is accelerating, would have something to do with entropy increasing above some "nominal" rate.

 

 

As a vague guess: Normal energy interactions would increase entropy at a "normal" fixed rate, while the splitting of particles or energy would increase that rate to a new higher but also fixed rate. More particles may mean more opportunities for energy to split further, increasing not only the rate of change of entropy, but the rate at which the rate of change of entropy is changing.

Edited February 28, 2011 by md65536