### Could E=mc² be recursive?

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#### Fraktalist

• Strange Attractor
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#### Could E=mc² be recursive?

« on: June 19, 2018, 12:52:57 PM »
So I wonder, is there any way E=mc² is recursive.

energy and matter are equivalent, and nothing is ever lost, while the complexity keeps rising and (as long as energy is added - different, long topic) complex order is also rising.
matter and energy seem to interact in an eternal cycle, input-->output. old output is the new input.
to me that is obvious recursion.
in a nutshell, I see the elementary particles just like loooong trajectory chains, they all started out with the big bang, the first iteration and each particle today can be traced back to this very beginning.

but the formulas of physics, especially E=mc² aren't recursive.
so with the fractal geometry of nature in mind, the obvious question is: Can this somehow be mirrored with the basic parameters/formulas of physics?
Have there been any attempts to do so?

any thoughts?

#### RedshiftRider

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#### Re: Could E=mc² be recursive?

« Reply #1 on: June 19, 2018, 01:21:58 PM »
If it could be recursive perpetual motion would also work:

While the equation can work in both way, I would say it can't. Unless you can somehow break the laws of physics and ignore entropy you would be able to create energy.
You can for instance make it work in reverse by making matter out of light but it would take a lot of energy.

Energy will always be conserved because it transforms but it can't be used to create more energy.

#### hobold

• Fractal Phenom
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#### Re: Could E=mc² be recursive?

« Reply #2 on: June 19, 2018, 02:50:09 PM »
complexity keeps rising
(mercilessly abbreviated quote)

Are you thinking of informational complexity here? It is not clear that information and energy are strictly linked. While it is true that the concept of entropy is indeed a connection between physics and information theory, our everyday human notion of "information" is not quite what entropy can measure.

The difference is that our idea of information very strongly depends on interpretation, while information theory only really covers the parts and mechanisms that behave independently of any specific interpretation.

So, to conclude: entropy tends to increase proportionally with increasing energy. Our human concept of "information" seems to increase exponentially instead of linearly, though. Perhaps our information can even increase when energy remains constant, simply by increasing the number of interpretations?

#### RedshiftRider

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#### Re: Could E=mc² be recursive?

« Reply #3 on: June 19, 2018, 03:06:11 PM »
My previous answer might have been a bit hurried and probably misses the point.

If I remember the first topic I have ever posted on fractalforums was related to this as well. I'll see if I can find it in the broken layout.

http://www.fractalforums.com/new-theories-and-research/fractals-entropy-and-probabilities/

#### Fraktalist

• Strange Attractor
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#### Re: Could E=mc² be recursive?

« Reply #4 on: June 19, 2018, 04:07:34 PM »
hey guys!

My little introduction was strongly abbreviated too..
I understand that entropy is a crucial part of our universe and also important in relation to my fractal perspective on this, but going  into that topic would fill a loooong thread on its own. Worth starting

Leaving that discussion out should have no big impact on my initial question - at least for a start (correct me if I'm wrong)

Red, I'll read into that thread you posted again. Gotta go now..

• 3f
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#### Re: Could E=mc² be recursive?

« Reply #5 on: June 19, 2018, 06:11:10 PM »
but the formulas of physics, especially E=mc² aren't recursive.
E=mc² is not really a law of physics from a modern point of view, but a conversion of units from Joules to kg; mass and energy are not "transformed" into each other, they are one and the same thing.

Current laws of physics are recursive and chaotic and almost every physical system is chaotic and hence has fractal attractors.

Abstractly we can describe the universe by a (large) set of numbers, call them $$z(t)$$ (we don't know exactly what they are yet, but let's say all the stuff that goes into the standard model + general relativity). Laws of physics have the form
$$\frac{dz}{dt} = f(z)$$, starting from $$z(0) = "the\ big\ bang"$$. We don't know exactly what f(z) is yet, not do we know what $$z(0)$$ is.
If you consider discrete times $$t_0=0, t_1 = h, t_2=2h, ... \ etc$$ with h a small time step (say the Planck time), and call $$z(t_k) = z_k$$ we get
$$\frac{dz}{dt} \approx \frac{z_{k+1}-z_k}{h}$$ and the "laws of the universe" take the form
$$z_{k+1} = z_k +hf(z_k)$$.
If you make a toy universe where z is just a field of complex numbers in a plane with complex coordinate c and $$f(z) = (z^2-z +c)/h$$ we get the Mandelbrot equation.
The "equation of the universe" has a similar form, but a bit more complicated.

For example cosmologists have tried to figure out what the real $$z(0)$$ is by trying various things and see if they could produce the observed distribution of matter. This is like making a Julia set.

#### Fraktalist

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#### Re: Could E=mc² be recursive?

« Reply #6 on: June 20, 2018, 11:17:41 AM »
That helped me a lot already, Gerrit.
Current laws of physics are recursive and chaotic and almost every physical system is chaotic and hence has fractal attractors.
I was always sure that formulas of physics must be recursive in some way in order to unfold over time and actually produce the fractals we see all around.
But I was not aware of that this is a known fact because it's hardly ever the focus in publications and tbh I haven't seen it written so obvious like you did.
Fractals are hardly ever mentioned, just a mere uninteresting sidefact - which I really don't understand, they seem so central and important.

anyways, thanks for the explanation!
Could you give a specific example? (the simpler the better)

(My problem is; I'm not a specialist but a universalist. I know the basics of a lot of things, I love diving into new stuff, but I'm no good when it gets too deep. Fractals are the one thing that have caught me long term - probably because they're everywhere and I can just discover and connect new topics and don't have to specialize in one thing.)

So many questions pop up and I miss so many little bits of info all over the place - I'd really love to have a realtime chat with you about this, via skype or whatsapp..
would you be up for that some day?
I've had the idea of starting a "fractal friday" hangout on my mind for quite some time now.
Fractal fans meet every friday in a video chat, discussing a daily topic or whatever fractal thing comes to mind. I'd love to connect more directly with likeminded people.
« Last Edit: June 20, 2018, 02:41:58 PM by Fraktalist »

• 3f
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#### Re: Could E=mc² be recursive?

« Reply #7 on: June 21, 2018, 04:05:41 AM »
Could you give a specific example? (the simpler the better)
Simplest example is probably the double pendulum.

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