A Crackpot Physics

[James R]

Adirian:

It looks like you're blogging here rather than having a discussion.

Moving slightly ahead, if Lorentz Contraction is a geometric change to gravity which gives rise to motion, and there is no inherent "velocity" or "inertia" property in matter, our other three forces must, like gravity, be geometric, in order to impart this geometric change.

Lorentz contraction is the apparent shortening of moving objects. How could that cause motion?

Maybe you're not saying that Lorentz contraction causes motion at all, but rather you're saying that motion is caused by changing spacetime curvature, or something like that. The problem with that view is that objects appear to move along in flat spacetimes just fine.

Examining the nuclear force, of course, this immediately implies that atoms should be black holes.

There's no evidence that atoms are black holes, as far as I am aware.

All in all, assuming my math is right, a hydrogen atom is around 2.5 meters in diameter, if measured from the inside.

Show me your math.

 

[James R]

Sin(ln(x))/x is, I think, a useful approximation for the grand unified field equation in my crackpot physics.

That's not an equation, let alone a field equation.

A slightly more mathematically accurate version of this may be sin(si(x)-si(1)), for values of x greater than 1, where x is distance divided by the radius of the particle originating the field. For large values of x, I believe this is equivalent to sin(ln(x)).

What is si(x)? I'm unfamiliar with the notation you're using.

Also, when you're doing maths, why do you need to rely on beliefs? Have you proven the equivalence you assert? If not, why do you believe it?

I know the approximate form I expect the final equation to take - a sinuisodal equation whose period is some multiple of distance, and whose amplitude also decays with x.

The equation for what? You've lost me.

And a sinuisodal wave with a period proportional to distance, and an amplitude inversely proportional to distance, exhibits a very interesting feature: The downward slope from a peak closely resembles a function whose value is inversely proportional to the square of the distance.

Show me the maths that displays this resemblance you mention.

The multiplier of the period is a problem. Right now my best guess is that the half period might be the distance times 10^6, approximately.

What distance are you talking about? The distance of what? The distance between what and what else?

If this is the case, gravity may only be accurate for distances greater than around 10^6l and less than 10^12, or greater than 10^18 and less than 10^24).

What's an "l"? What does a distance greater than 10^6l mean?

By extension (using Kaluza-Klein to extend this field to encompass electrical fields), electromagnetic fields may vanish, or behave oddly and weakly, at distances of around 10^6, and reverse apparent polarity at distances much larger than that.

Extend what field? A gravity field of some kind? Show me the maths of your field and the Kaluza-Klein extension of it.

(I am using the Kuiper Cliff as the basis of this guesswork, so it isn't evidence of anything.)

What's a Kuiper Cliff?

As for where sin(si(x) - si(1)) comes from, it is based on an abortive attempt to try to derive a proper equation...

You haven't posted a single equation yet, as far as I can tell. What equation are you talking about?

...assuming mass exhibits curvature in flat space like sin(x)/x...

Show me the maths that you used to derive this curvature? What is x?

..., assuming that this curvature is self-reinforcing...

What does "self-reinforcing" mean?

...; that is, the distance for the purposes of curvature is expected to take into account the curvature that mass produces, and integrating from 1 (the radius of the particle) to that distance.

Show me your integration. I don't understand what you're integrating, or why.

The equation I was playing with was adjusted distance n+1 = adjusted distance n + integral(sin(adjusted distance n)))[1,adjusted distance n]

Do you mean something like:

$$d_{n+1}=d_n+\int^{d_n}_1 \sin x~dx$$ ?

What are these "adjusted distances" you're talking about? And what is $d_0$ or $d_1$?

You know, all of this is pointless unless you explain to your readers what you're actually talking about. The purpose of writing is to communicate something.

It's recursive, and the equation that results includes an adjusted distance term I haven't actually figured out how to cancel out yet.

Cancel out of what? I can't even tell what you're trying to calculate here. Maybe try explaining what you're talking about.

 

[James R]

Moving up in scale from a meter, we expect protons to repel one another up to a distance of about 10^6.

10^6 what? Metres? Furlongs? Light years? Smoots?

(Recalling that the nuclear force, if relativistic, has a half period of a little over a meter).

I don't understand what you mean when you talk about the period of the nuclear force. What does that mean?

We shouldn't expect objects significantly less in size than this to exist, unless chemically bound.

Please express this in metres. You appear to be saying that your theory predicts that objects smaller than a certain size can't exist. What size, in units that are actually meaningful?

From 10^6 to 10^12 meters, gravity should behave as expected.

Metres now? Okay.

So your claim is that gravity doesn't work if things are closer together than 1000 kilometres? Is that correct?

At around 10^12, gravity drops (somewhat unexpectedly) out of existence, and orbits stop working. Kuiper belt.

But there are objects in the Kuiper belt that are observed to be orbiting the Sun, for instance.

From 10^12 to 10^18, we have a repulsive force again.

Repulsive gravity? What evidence supports this idea?

Because our force drops off with x, instead of x^2, the force at 10^18 is significantly stronger than we would expect, which means relativistic corrections are in order; we can salvage this in terms of the galactic core, if we assume gravity is strong enough that the 10^17 is actually a 10^18 after relativistic corrections.

Which 10^17 or 10^18? What are you talking about?

And as the largest chunk of mass by far, it can hold the rest of the galaxy together with the next phase of attractive force from 10^18 to 10^24. We can even arrive at the galaxy rotation curve, maybe, if everything else in the galaxy is repelling neighbors, and the core's attractive force is holding everything together; an initially stronger gravity, counterbalanced by repulsive forces, might net a flatter rotation curve. The virgo supercluster is also in this range, so all the galaxies in our local supercluster are very weakly attracted.

Show me your derivation of the galactic rotation curve, using your theory. I want to see the maths.

Okay. It almost sort of works, if you squint just right. Or rather, on a macroscopic scale, we could build a universe that looks very similar to our own using this force.

So far, we have only your assertions, backup up by some rambling text and not much else, as far as I can tell.

Well, the nuclear force straddles an inflection point.

An inflection point in what? Show me the graph.

Moving down from the nuclear force, we have a repulsive force from about 10^-6 to about 1.

In what units? Metres? Nuclear forces operate on much smaller scales than that.

Relativistic corrections imply that we will observe the 10^-6 to be significantly greater in magnitude, however.

Show me the maths.

There isn't a lot of point continuing down; I can say I expect the gluey behavior of gluons, and I do, but it doesn't even qualify as a guess at this point, but rather an intuition.

Is all of this just your fevered imaginings, or have you done at least some concrete work? Do you have anything solid you can show me in terms of mathematics or the beginnings of an actual physical theory?

The interesting thing about this model is that the universe has a finite age, but an infinite history.

That looks contradictory to me. Explain how it is possible.

The force I describe is fractal; the history of the universe is likewise fractal.

Show me the maths.

The cosmological model here is a slow collapse upwards in scale; in the first few milliseconds of the universe, tiny galaxies were born, torn apart, collapsed, and went cold, stabilizing into the building blocks of the scale we observe as the universe now.

This hypothesis is disconfirmed by actual observations.

 

[James R]

I'm going to stop and wait to see if anything concrete is posted. Most of this looks like a waste of time to me - empty speculation mixed with pseudoscientific ramblings.

 

[Adirian]

For Lorentz Contraction, I am suggesting that motion is a curvature in space-time. Assuming gravity is Lorentz-Contracted, this doesn't actually change anything as far as moving mass goes. (Gets a little weird with things without mass, though.)

As for the rest, well, the math hasn't actually worked so far. I'm still fiddling with that, trying to get a working mathematical model which is consistent with observations, but I've switched to studying tensors, because the coordinate transformations have gotten too complicated for the mathematics I am familiar with.

The short version for now is "I suspect the unified field theory will have a shape similar to sin(ln(x))/x". Si(x) was the sine integral; setting that aside as I can't solve the recursive function I got it out of anyways. X is distance.

I can force sin(ln(x))/x to match gravity with the right constants, but I can't get it to match the other forces using raw distance; the instantaneous frequency is far too low for the constants necessary such that there is both gravity on Earth's surface and also the Kuiper Belt doesn't fly off into the cosmos.

There may be a solution, in that these forces are changing distances, so using raw distances may be entirely wrong. But the coordinate transformations required there, I think, may require tensors.

So no, no equation. I could provide one of the equations that definitely isn't correct but I don't think that helps anything. If I find one that does work I will post it, though.

 

[Adirian]

For more specific responses:

The fractal is implicit in sin(ln(x))/x. Well, technically it isn't a fractal, but as a force it gives rise to fractal behavior, in that it is scale-relative; for any given stable configuration within it, there are an infinite number of configurations that are identical except for scale/size.

For hydrogen, I'd need to be at home on my laptop, but it is a fairly simple equation, just plugging the variables into the Schwarzschild metric equation and solving. (Divide the force by the metric in the equation; this is valid because there is an additional unit in the denominator, and because the metric is valid with respect to both distance and time). I get .22m, which is the radius to the peak force, giving us a .44m diameter to the peak. The other ~2m is some guesswork about the total magnitude of the rest of the potential based on integrating similar equations.

For finite age and infinite history, this is based on the fractal-like nature of the equation; as you get closer to the big bang, you are dealing with smaller and smaller configurations, with shorter and shorter distances, and shorter and shorter time intervals for given behavior. A configuration that is 10^32 smaller will evolve 10^32 faster, owing to the speed of light. Thus the closer you get to the origin, the more tightly packed events get. Finite age, infinite history, interpreting history to mean causal chain.

As for repulsive gravity, I think this is what the cosmological constant is. This might imply that blue-shifted galaxies aren't actually moving away from us; I am uncertain if we have sufficient resolution to determine whether this is the case.

As for all my exponents without units, there is a reason for these; these represent the frequency relative to the current distance. Sin(ln(x))/x has a property that the frequency is relative to distance. So a frequency of 10^6 means that the frequency is 10^6 times the distance under consideration. This particular property is determined by the coefficient of ln(x); unit conversions have to be a coefficient of x itself.

 

[Adirian]

Rereading, period, not frequency.

I'll try to reconstruct an equation that shows that sin(ln(x))/x can produce results similar to gravity later, I just don't find this that interesting; you can look at the graph and see it has a curve that looks like 1/x^2 in places. It is only interesting if I can get it to both do this, and line up with at least the nuclear force and something approximating a cosmological constant at intergalactic distances.

 

[James R]

Rereading, period, not frequency.

I'll try to reconstruct an equation that shows that sin(ln(x))/x can produce results similar to gravity later, I just don't find this that interesting

You're the one who has been going on about it. If it's not interesting, why did you bring it up?

... you can look at the graph and see it has a curve that looks like 1/x^2 in places.

What? You're judging the similarity by looking at a graph - by eye?

Do you think this is how physics is done: guess a mathematical function, try graphing it and squint a bit until you think it looks like what you want it to look like?

In my previous posts to you, I asked you several times to show me your maths. That is, I want to see the derivation of that sin(ln(x))/x function from whatever physical postulates you're putting forward.

Can you show me anything like that, or am I to take it that none of your maths has "worked so far", as you say?

It is only interesting if I can get it to both do this, and line up with at least the nuclear force and something approximating a cosmological constant at intergalactic distances.

Let's start with the basics.

What are the postulates of the model of gravity that you are putting forward?
And how do you derive a numerical model of gravity from those postulates?

 

[Adirian]

Sin(ln(x))/x arises from the side of a triangle formed from a logarithmic spiral.

The logarithmic spiral arises from my best guess at what a negative closed dimension would look like (where a negative linear dimension corresponding to X might be -1/X, with infinity at the origin; my best guess at a translation of this for a closed dimension is that the distance between equivalent points is either complex or infinite; I lean toward a logarithmic spiral as a candidate spiral because of the relationship between complex numbers and Euler's number). The x and y axes are complex dimensions.

The negative closed dimension arises from a consideration of what happens to distance as a singularity forms.

Since x and y are complex dimensions, and arc length corresponds to the original distance, sin(ln(arclength))/arclength would correspond to one of two complex components of distance. This in turn would mean this corresponds to part of curvature. The other complex component, cos(ln(arclength))/arclength, might also be part of curvature; it doesn't really affect the characteristic behavior I care about.

(Strictly speaking I can arrive at a similar-ish equation using a hyberbolic spiral, but it only "works" for arclengths less than 1. This might be valid if we multiply distance by infinity, but that isn't mathematically useful.)

 

[Adirian]

And my basic assumptions are that space-time is conserved, all forces are geometric (they are all curvature), and that there is nothing special about the scale we happen to exist at. This implies, I think, an infinite alternating series of attractive and repulsive forces/fields. Cosmological constant, gravity, what we call electricity (this description may work if protons are matter and electrons are antimatter), then both phases of the nuclear force.

This approach is merely the latest in my attempts to find a formalization for these assumptions.

 

[James R]

Sin(ln(x))/x arises from the side of a triangle formed from a logarithmic spiral.

I don't want you to tell me; that's just more of the same kind of thing you've been posting for this entire thread.

I want you to show me the steps in your derivation. If you have a relevant document somewhere online, you can link me to it, if that's easier.

I want to see your mathematical reasoning, not hear about your speculations about what might or might not "work" to get some result you think should apply.

 

[Adirian]

The steps in the mathematical reasoning are full of guesses.

My research on the question of what a negative closed dimension should be came up with nothing. Right now, for this approach, that is pretty much the most important step, and all I have is a "Uh, maybe a logarithmic spiral?". I expect one of the parameters of the spiral should fall out of actually deriving it, and it is the most important parameter to determining the viability of the approach, the coefficient of ln(x). I'm still considering ways I might derive the correct formulation of a negative closed dimension, I've tried seven or eight approaches without luck so far.

If I had all the steps, I'd be writing a paper presenting the theory of everything, not posting to Pseudoscience. (Well, maybe just a unified field theory. A theory of everything would require incorporating uncertainty in a substantive way, which would be the next step.)

 

[Adirian]

For a previous approach, I had the following recursive function:
dP = dM + integral[1,x](sin(dP)/dP + f(dP))

Where dP is proper distance, dM is Minkowski distance, and f(dP) is an unknown function, possibly just 0, corresponding to the elasticity of space-time.

It was an attempt to formalize the idea of "Force as a sine wave curvature which is self-interfering", but I couldn't simplify the recursion into anything useful. (Also the dM term was causing significant issues.). I think it converges on the same solution as my current approach, but I found the approach... intractable.

This approach seems slightly more tractable, but I have no idea how to actually bridge some of the gaps.

Like, intuitively, if a negative linear dimension has infinity at the origin, such that the distance to any other point is infinity (negative infinity for positive points, I think), what does that mean for a closed dimension, without an origin, and where the distance between two points is an infinite set? Adding the same kind of curvature that 1/x exhibits implies a spiral of some kind, except that it has to be a complex spiral, because we aren't adding an additional real dimension. So logarithmic spirals seem like a natural choice, given the relationship between e and complex numbers.

But that's all intuition and guesswork. I have no idea how to actually get there.

 

[James R]

This is really cranky.

Adirian: I think you're wasting your time, deluding yourself that you're doing physics. Surely you have better things to do than this.

I'm out of this thread.

 

[Adirian]

I'm really not sure how the crankiness could be more explicitly stated up front. What exactly is anyone expecting to find here?

As for whether I am wasting my time, that assumes that I don't get more out of this than I'd get over the next best option.