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Eureka

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Corman

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Please notice that this journal entry has been edited since its orginal posting.

I have always had the curious scientist like mind from a young age as my parents remind from time to time and I remember it too. I had glorious dreams of becoming a famous inventor or physicists some day. Then came computers and video games and my goals changed. Instead of trying to figure out the real world I would create my own that had their own rules but mimicked the real one. You can see many examples of this fact all through my journal entries here. But I still go back to my armchair mathimatian and physicists roots from time to time and muse around. Even if what I come up with is not real it can still be used for some interesting aspect or even as a good plot device for a story. But last night in a eurka moment involving a bathroom incident like Doc Brown had I realized that one of my current musings could actually meen something. I will evolve my ideas and findings here over time by starting with known values and working from there. This journal entry may end up showing that etheir I am on to something or that I am just dangerous with math but I will let you decide.



For some time now I have been obsessed with the above equation that I found searching the web one day. I became fixated on this equation not only because the units worked out but because I felt it described matter as a 3D volume of energy among other interesting things. The site that I found this at also has a lot of interesting views on space and time even if it is psuedo physics and in the end turns out to be wrong. So I wanted to know if I could derive and explain this equation or something close by using already known values and equations.











This brings us to a similar looking and very familiar equation (the above mass equation) with the reduced Planck Constant instead of just the orginal Planck Constant by deriving it.

So given Einstein's equation:


And my derived equation:


So with this:


Since I am doing this just for my own amusment and nothing else I am going to be making some assumptions here. I am going to pretend for now my equation stands on its own, losses meaning and reason if reduced, and actually has some deep secret that I need to find. From what it seems my equation is the Celsius to Einstein's Fahrenheit scale but a little bit more complicated than that. If this is real I believe that this is something very profoundly amazing. I think one equation is for particles and one for waves. Just like all the Planck units and equations show, this is telling us the limit where the particle and wave nature of mater is equivalent and indistinguishable from each other. I am believing if this is true that our current systems does not take into account for two types of mass and energy (two different but related mass and energy types for the particle and wave structures of matter). Now for different mass values in increments of one Planck Mass (the smallest mass increment that I will be using and treating as indivisible) the equations do not equal each other anymore and need a conversion factor. Now lets look at some ratios for different mass values to see what is going on.

The ratio is:


Expressed below as:










Looking at the above examples the ratios end up being:


So with this:



I gather from this that not only does light have a particle/wave duality but matter as well. I also believe from this we can see matter and energy come in very discreet amounts. This leads me to believe that space and time must also do so. Besides all of this I have more equations and ideas that I will continue to develope as I go along. I will continue to work on this journal entry little by little to help clear things up. Questions, comments, and suggestions are welcome as usual.
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YAyy!! Cool post. but its nearly 8AM here, Ill have to read it later...Time for bed now :D.

P.S. I am the opposite of you, I originally wanted to be a game developer and now am studying pure maths and heading for an outlook that will place me as a philosopher of mathematical and physical foundations. Yeesh.

P.P.S. Yes, images.

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This certainly took more time than i expected. Spent too long working then making pictures...

I couldnt sleep. Hmm it seems journals are broked.

So the main equation here is



But if we go back to:



That equation is basically a tautology. Essentially, it says that the energy of a planck mass or planck energy is the product of: planck energy cubed, the reciprocal of the speed of light quadruprled and the reciprocal of a planck mass squared. There is already a hint that there is some circularity going on.

In the equation:



the m on the left and the E on the right are the same thing in terms of natural units, thus you cannot know E^3 without knowing m. It seems that you are treating energies at relativistic speed as those that are at rest.To put it another way, E = m * c ^2 <> mγc^2 = En with n not 0. Hence:



Some definitions are at hand. Planck mass is by definition more or less the maximum mass an elementary particle can take. This follows from the fact that the planck length is the minimum length at which an object can be observed. This minimum exists because a mass must have a lower value of mass than a black hole of the same size else it would simply not be observable due to it absorbing all particles that are scattered off it in order to measure it. In addition in order to be observable the crossectional length of our object must be greater than its effective wavelength.



Since d must be greater than both hbar/mc and mG/c2 then



An elementary particle must be smaller than its compton wavelength while being larger than the planck length limit, with m < hbar/c *planck_length, from there we can state:




Note that this proves that the notion of a point particle is impossible. In reality, points do not exist. The planck mass or planck energy are as I noted earlier basically equivallent and such macroscopic elementary particles signal the breakdown of stuffs. There as you note, one ceases to be able to tell matter from the space-time itself. Space time and matter are sprung for the same source and indistinguishable at that level. This is what we are currently trying to unravel. What is going on at the boundaries?

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Hi Im back. I realize that you have reasoned this far more thoroughly than I assumed. My statement, "It seems that you are treating energies at relativistic speed as those that are at rest", is incorrect. In fact everything before "Some definitions are at hand" is irrelevant. There, I was unsure what it is you were doing and assumed without following your arguments in their totality.

Reasoning further, I thought your error was might be that you treat planck energy as all energy but that was not the case. Nonetheless there lies a subtle point that is being overlooked.

First it is important to note that your derivation is equivallent to that i gave above:

.

This is not readily evident but can be proven:




But I do not understand what it is you are doing with A,B,C etc. It seems you are trying a method to link speed of light or energy with planck mass? There are masses whose values fall between those of any two planck masses. I am confused because there seems to be results gotten in a roundabout manner. I am quite tired though.

What you do is equivallent to stating that, with P sa planck energy:

((P^3)^(1/3))P^-1
((2P^3)^(1/3))2P^-1
((3P^3)^(1/3))3P^-1
...
((NP^3)^(1/3))NP^-1

Which is equivallent to saying the cube root of the rest energy of N fleas cubed divided by their rest energy.

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Now that the journal system seems to be fixed I will be hopefuly editing this entry soon to clear up some logic and spelling errors. Also please keep in mind that this is all just for fun and good laughs at math's expense.

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Corman, I believe you might just be insane.

But if not, please mention me in your nobel prize acceptance speech.

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They say there is a fine line between genius and insanity. My only problem is I waddle side to side when I walk.

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