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New possibility of quantum gravity


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New possibility of quantum gravity

 

Hello,

My name is Ryoji Furui.

Recently, I've done to express my idea about quantum gravity.

It took many years since I had an idea with words and images then finally I could formulate it with the simple math. Please see the attached file.

 

But I am not sure this could be the right formulation and there should be more smarter expression.

I also feel the limitation to further expand with my current knowledge.

Hopefully I could exchange any thoughts on this forum.

 

Thanks,

 

Ryoji

ei4.pdf

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I heard as in the human beings history, it has been for 100 years since Albert Einstein discovered the special relativity.

 

lol those human beings and their history! Just another reason to enslave them.

 

Seriously, there are like two or three equations copied from special relativity and then nothing. I have no idea what you even think is worth discussing about this.

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It looks like you googled any papers dealing with relativity, cut an pasted sentances and paragraphs, and strung them together in a totally random way. You then edited it to make the english unreadable;

 

"I heard as in the human beings history"

 

In conclusion, your "paper" would make a good parody of what a real paper is supposed to be, and I hope dearly that this is just a joke.

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Hi Locrian, [Tycho?] and all,

 

Thanks for your comments or reading.

I would like to discuss more about the first sentence in my paper but now please let me ask something what I was asked from someone.

 

My paper's subject is about quantum gravity but he said it needs more info like "the quantization rules"... for defining it.

I have no idea what it means. So if anyone could explain it or know any good links for reference, I would appreciate it.

 

Thank you again,

Ryoji

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CanadaAotS,

 

Actually I copied the idea of SR. Then pasted it to my vision, how I see the universe or what I see in my mind. I believe creation always comes from copy and paste. Creativity is what you choose from the flood of information.

 

By the way, here is a correction to equation (4) in my attached file of the first post as below,

 

p=ka\sqrt{1-v^{2}}.

 

Thanks,

R

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  • 2 months later...

Hi,

 

During winter holidays, I had a time to update my thesis.

Now, the first sentece is modified with other texts.

And matches to the equivalence principle of GR.

 

Any feedbacks welcome ;)

 

Ryoji

ei7.pdf

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I stopped reading somewhere in paragraph two. I had a comment here about an error I thought you had in equation 2. But now when I look at it again, I figure out that I misread it. In fact, I don´t get eq. 2 at all. Neither side of the equation is an energy. Also, if it´s supposed to be energy squared, then I don´t see how you come up with the left-hand side. It´s the energy of what, actually?

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Hi Atheist,

 

Thanks for your comment.

Indeed, I changed the explanation of eq. 2 as followed,

 

The left term represents the energy squared during the collision and the right term is the one after collision.

 

Could this be answer to your question, if it is about energy conservation?

 

Thank you again,

Ryoji

ei7a.pdf

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Hi Atheist' date='

The left term represents the energy [b']squared[/b] during the collision and the right term is the one after collision.

 

Could this be answer to your question [...] ?

It is not really an answer to my question. I can see myself that it´s an energy squared. The problem is that I don´t know which energy squared. The total enery is p+m therefore the total energy squared is p²+2pm+m², not p²+m².

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Hi Atheist,

 

I just replace graviton $p$ to $e$, so

e+m=m/\sqrt{1-v^{2}}.

 

Then the relation of $e$ and $p$ is,

e=p(1-\sqrt{1-v^{2}})/v

 

I think this would work fine?

 

Thanks

R

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Hi Atheist' date='

 

I just replace graviton $p$ to $e$, so

e+m=m/\sqrt{1-v^{2}}.

 

Then the relation of $e$ and $p$ is,

e=p(1-\sqrt{1-v^{2}})/v

 

I think this would work fine?

 

Thanks

R[/quote']

 

I think the problem here is that your paper makes absolutely no sense at all.

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Hi Atheist' date='

 

I just replace graviton $p$ to $e$, so

e+m=m/\sqrt{1-v^{2}}.

 

Then the relation of $e$ and $p$ is,

e=p(1-\sqrt{1-v^{2}})/v

 

I think this would work fine?

 

Thanks

R[/quote']

I fail to understand what you are saying. In the very lines I talked about you are speaking of a particle at rest with mass m and an incoming massless particle. Which is the graviton? If it´s the massless one, then above equations don´t seem to make any sense at all because m=0 for a massless particle. But in case you are interested: The energy of a massless particle equals the magnitude of its momentum (you actually wrote that in your equation 1). If it´s the massive one: I still try to understand at least anything you wrote so don´t expect me to instantly understand processes where massive gravitons collide with not-further-specified massless particles.

I wouldn´t want you to spend too much time trying to explain your idea to me unnessecarily so let´s be honest: I basically share [Tycho?]´s view when it comes down to judging the relevance of your work. So you should regard my remarks on it more as hints on where you are lacking knowledge about physics (until now we didn´t even get to the part where I´d tell you that the complete absorbtion of a massless particle by a massive one is forbidden by energy-momentum conservation) or simply style. The latter is what my current problem is. Besides from that you suddenly talk about a graviton, there´s one other thing that imediately caught my eye: Is it really a good idea to call the particles p and m which are also letters used for particle attributes? I think the whole thing would be way more readable if you named them A and B and talked about the mass [math] m_A [/math] and momentum [math]p_B[/math]. More readable to you, too - it´s just an imputation, but I think you don´t have an overview over what you are doing yourself.

 

Going on with the imposures (just learned that vocab from my online dictionary and I like it - hope it´s the correct one): Try to be honest to yourself: How probable is it that someone who doesn´t even know the very basics of modern physics (you mentioned that you don´t know what a quantization rule is) will publish a groundbreaking article in a forum?

I basically have no problem with people not having a solid background in physics thinking they found the sages stone. But you should be open to the thought that maybe you´re on the wrong track because you are missing some very basic things. From my experience, being wrong with an idea still provides a very personal learning experience (let´s be realisitc, that´s the way progress in physics works: You have twenty great ideas which turn up as crap and perhaps from the stuff you learned from the errors you come up with something usefull).

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Hi,

 

Thank you for your comments.

Yes, I have to remove eq. 1 from my paper, I will upgrade it when I can find the time during the job.

I was just thinking about physical meaning of new defined graviton energy.

After reading your comments, I reminded a comment on a blog at

http://www.haloscan.com/comments/59de/113631928690934653/

I hope this would be an answer for you.

So the state $E=pc$, should be applied to the flat spacetime filled with kinetic energy without mass.

 

About quantization rules, I think it would be applied from my another thesis,

http://www.ryoji.info/R118.pdf

But I cannot say much more about it.

 

I appreciate your comments.

 

Ryoji

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For example, quantising the Klein-Gordon field theory using the second quantisation method: you get yourself some commutation (or anticommutation as in the Dirac field) relations for the field and cannonical momentum and expand them as a fourier integral in terms of "ladder operators". Calculate the Hamiltonian using that expansion and find its eigenvalue spectrum.

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I'll show you part of a simple method of quantisation.

 

The Lagrangian of a free real Klein-Gordon field is

 

[math]{\cal L}=\tfrac{1}{2}\left[\left(\partial_{\mu}\phi\right)^2-m^2\phi\right][/math]

 

Define the momentum conjugate to [math]\phi[/math] as

 

[math]\pi(\vec{x})=\frac{\partial\phi}{\partial\dot{\phi}}[/math]

 

Note here that [math]\phi[/math] is still a classical field. In passing from the discrete definition of the Hamiltonian (involving a summation) to the continuous case we have

 

[math]H=\int d^3x\left[\pi\dot{\phi}-{\cal L}\right]=\int d^3x\tfrac{1}{2}\left[\pi^2+\left(\vec{\nabla}\phi\right)^2+m^2\phi^2\right][/math]

 

Then taking the field and conjugate momenta to be operators we can enforce a commutation relation analogous to the regular commutation relations between position and momentum in the continuous case

 

[math][\phi(\vec{x}), \pi(\vec{y})]=(2\pi )^3\delta^{(3)}(\vec{x}-\vec{y})[/math]

 

If we then model the Klein-Gordon field as a harmonic oscillator, drawing analogy from the quantisation of a simple harmonic oscillator with a single frequency, we can expand [math]\phi(\vec{x})[/math] and [math]\pi(\vec{x})[/math] in terms of "ladder operators" [math]a_{\vec{p}}[/math] and [math]a_{\vec{p}}^{\dag}[/math] as a fourier transform with each [math]a_{\vec{p}}[/math] etc. corresponding to a particular Fourier mode [math]\vec{p}[/math].

 

[math]\phi(\vec{x})=\int\frac{d^3p}{(2\pi )^3}\frac{1}{\sqrt{2E_{\vec{p}}}}\left(a_{\vec{p}}e^{i\vec{p}\cdot\vec{x}}+a_{\vec{p}}^{\dag}e^{-i\vec{p}\cdot\vec{x}}\right)[/math]

[math]\pi(\vec{x})=-i\int\frac{d^3p}{(2\pi )^3}\sqrt{\frac{E_{\vec{p}}}{2}}\left(a_{\vec{p}}e^{i\vec{p}\cdot\vec{x}}-a_{\vec{p}}^{\dag}e^{-i\vec{p}\cdot\vec{x}}\right)[/math]

 

Where [math]E_{\vec{p}}=\sqrt{|\vec{p}|^2+m^2}[/math] is the energy of that particular mode. The commutation relations satisfied by the ladder operators are

 

[math][a_{\vec{p}}, a_{\vec{q}}^{\dag}]=(2\pi )^3\delta^{(3)}(\vec{x}-\vec{y})[/math]

 

Then calculating the Hamiltonian using this fourier expansion we get

 

[math]H=\int\frac{d^3p}{(2\pi )^3}E_{\vec{p}}\left(a_{\vec{p}}a_{\vec{p}}^{\dag}+\tfrac{1}{2}[a_{\vec{p}}, a_{\vec{p}}^{\dag}]\right)[/math]

 

The integral of the second term is an infinite constant (as it's proportional to [math]\delta(0)[/math]) and arises as the sum over all modes of the zero point energy [math]\frac{E_{\vec{p}}}{2}[/math]. The spectrum of the first term is easily quantised using the commutation relation satisfied between H and the respective ladder operators. The state [math]|0\rangle[/math], defined by [math]a_{\vec{p}}|0\rangle=0[/math] [math]\forall\vec{p}[/math], is known as the ground state, or vacuum, of the theory and is the state with the least energy. Each eigenstate of H with momentum [math]\vec{p}+\cdots +\vec{q}[/math] can be constructed from [math]|0\rangle[/math] with a creation operator [math]a_{\vec{p}}^{\dag}[/math] by [math]a_{\vec{p}}^{\dag}\cdots a_{\vec{q}}^{\dag}|0\rangle[/math]. The Hermitian conjugate of the creation operator (i.e. [math]a_{\vec{p}}[/math]) is an anihilation operator that lowers the eingenstate, [math]a_{\vec{p}}a_{\vec{q}}^{\dag}|0\rangle=|0\rangle[/math]. Therefore we have seen that the operator [math]a_{\vec{p}}^{\dag}[/math], and thus [math]\phi[/math], is responsible for the creation of discrete amounts of energy that we can identify with a "particle", with further reasoning (quotation marks because the phenomenon is not localised in the usual sense of a particle).

 

More things can be said about this field, but I've only given it as a simple example of second quantisation. It's much more difficult to quantise other field theories, especially when interactions are involved, but the idea was to give you a taste of what it involves.

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I have of course used the Schrodinger interpretation (no time depedance of opertors), but one can easily use the Heisenberg interpretation (time dependance), by performing a time evolution on the above and using a couple of useful identities satisfied by the creation and anihilation operators, to yield the same results.

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I've missed the square on the mass term in the Lagrangian, by the way. Should be

 

[math]{\cal L}=\tfrac{1}{2}\left[\left(\partial_{\mu}\phi\right)^2-m^2\phi^2\right][/math]

 

And I missed the imaginary term from the commutation relations. That should be

 

[math][\phi(\vec{x}), \pi(\vec{y})]=i(2\pi )^3\delta^{(3)}(\vec{x}-\vec{y})[/math]

 

Conjugate momentum should be the derivative of the Lagrangian with respect to the time derivative of the field.

 

Sorry about those few mistakes, bit of a lapse in concentration there.

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hey ppl,

 

i have nothing about the paper... ( probably i'll comment after seeing the improvised version, if i have to)...

 

I am currently working on Higgs Field and Behaviour of Higgs Bosons in early universe. Just wanted to ask you people to suggest any research problem related to Quantum Mechanics, General Relativity or Electromagnetism to take up as a side-project.

 

I had been working on near-field EMT n Vaccum energy in the near past. In fact, i am still working on near-field EMT. So that gives u an idea about my interests.

 

Waiting for some suggestions

 

amruth

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Thank you for many posts,

 

I've tried to revise my paper so long time however the changes would be almost everything on this thread. Thus mathmatically, Eq. 1 should be changed to new one born here

 

e=p(1-\sqrt{1-v^{2}})/v,

 

Where $e$ is graviton's energy.

If there would be newer papers related to my thesis, it might be far from my understanding.

I have a book about the Hamiltonian but having it and understanding it are different. If I had a new idea which should be on a paper, I would like to show it. But it can't be expected soon.

 

I saved this thread on my computer once, and I would like to make this thread as the place where my graviton idea is expressed, as long as here is alive on the web.

So if anyone would like to put a link to my thesis about graviton, please link to here at this moment.

 

And in case, if anyone got Nobel prize related to my thesis, please let me know and give me money (a little bit) ;)

 

Then once again, I would like to say thanks to all joined this thread.

 

Ryoji

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  • 2 weeks later...

hi,

 

i just had an idea today.

it might be already known by some or more, or wrong.

when i consider how flat spacetime filled with kinetic energy can be described in 2d spacetime. then i drew 2d spacetime with several energy states.

if graviton, mass and kinetic energy can be described as geometry of 2d spacetime, it would be like this picture?

 

then this results that mass itself is the highest energy density.

 

any feedback welcome:-)

 

r

energystatein2dspacetime.GIF

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there should be correction in the figure of the last post.

the state, E=m should be described as the vanishment of time axis thus,

 

[math]

\eta_{00}=\eta_{01}=0, \eta_{11}=1.

[/math]

 

then there would be no light cone in it.

 

r

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