# Dubbelosix

Senior Members

518

1. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

Also this equation $\dot{s} \equiv \sqrt{<\dot{\psi}|\dot{\psi}>} = \sqrt{<\psi|\frac{\hbar^2}{4m^2}\nabla^4|\psi>} + \frac{1}{\hbar} \sqrt{<\psi|V^2|\psi>} + \sqrt{<\psi|\frac{m^2\phi^2}{\hbar^2}|\psi>}$ might be confusing, it can be seen as, without any of the simplifications I made as $\sqrt{<\dot{\psi}|\dot{\psi}>} = \sqrt{<\psi|\frac{1}{\hbar^2}\frac{\hbar^4}{4m^2}\nabla^4|\psi>} + \sqrt{<\psi|\frac{1}{\hbar^2}V^2|\psi>} + \sqrt{<\psi|\frac{1}{\hbar^2}m^2\phi^2|\psi>}$
2. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

I have noticed myself the term $<\psi|\frac{m^2\phi^2}{\hbar^2}|\psi>$ Is very similar to the term you find in the Klein-Gorden equation $\frac{m^2c^2}{\hbar^2}\psi$ Remember the gravitational potential $\phi = -\frac{Gm}{R}$ has units of velocity squared - you can know this from the definition of the standard gravitational parameter $c^2R = Gm \rightarrow \frac{Gm}{R}$ This is why when calculating powers of the gravitational parameter you often encounter the form $\frac{\phi}{c^2}$ (and is almost the metric of GR save an additional two constants). To make sure a Schrodinger equation can have appropriate boundary conditions so that the physical nature of the model can be studied, requires a model for this non-linear wave equation in terms of the Green function which is usually attached to the ordinary potential $\mathbf{G}_FV$. It will create a propagator in the model. I will try and do this and write it up soon.
3. ## Vacuum Fluctuations can Become Real

Well, there are intuitive reasons why the universe is expanding at an ever increasing rate - its because it has became too large so that gravity can not ever pull it back. Think about it in terms of Newtons laws - A system unless affected by a force, will tend to stay in motion, if it is accelerating, will tend to continue accelerating. The universe is definitely in such a situation today, the mass content is no where near the required amount for collapse. The question is, what pushed the universe out of the dense Planck phase - what led up to a universe to become as big as it is so that the expansion overwhelms its own gravitational attraction? I have suggested we need to look at new alternatives to the inflation model, since this now has reasonable scientific objections in literature. I have suggested if the early universe had a spin, then it could have pushed the universe outwards, an effect known as the centrifugal force. The spin is even allowed to decay as shown by Hoyle and Narlikar - and this is important because we would want to know why the universe shows no background axis today. There is some evidence maybe dark flow is a residual primordial spin - this leftover spin is so slow, people have even disputed its existence.
4. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

So, I had a look at what this non-linear Schrodinger equation may look like when considering the metric curve and the metric itself. The metric curve with the non-linear Scrodinger-Newton equation is (without any inequalities imposed), $\dot{s} \equiv \sqrt{<\dot{\psi}|\dot{\psi}>} = \sqrt{<\psi|\frac{\hbar^2}{4m^2}\nabla^4|\psi>} + \frac{1}{\hbar} \sqrt{<\psi|V^2|\psi>} + \sqrt{<\psi|\frac{m^2\phi^2}{\hbar^2}|\psi>}$ The metric of the theory is $ds \equiv (t_1 - t_2)\sqrt{<\dot{\psi}|\dot{\psi}>} = (t_1 - t_2)\sqrt{<\psi|\frac{\hbar^2}{4m^2}\nabla^4|\psi>} + (t_1 - t_2)\frac{1}{\hbar} \sqrt{<\psi|V^2|\psi>} + (t_1 - t_2)\sqrt{<\psi|\frac{m^2\phi^2}{\hbar^2}|\psi>}$ There is also the idea of the Langrangian encoded in all this $\mathcal{L} = <\psi|\frac{\hbar^2}{2m}\nabla^2|\psi> - <\psi|V|\psi> + <\psi|m\phi|\psi>$ where the potential energy is simply the sum of an ordinary potential and the mass of the system which in turn interacts with its own gravitational field $\phi$ $PE = <\psi|V|\psi> + <\psi|m\phi|\psi>$
5. ## Vacuum Fluctuations can Become Real

This is my understanding as well, however my own investigations have ruled out the effects of virtual particles over cosmological distances. This is because the forth power over their momentum is generally considered zero. However, it has been shown by Sakharov this may not be the case when the background curvature is taken into consideration. For this reason, I find significant contribution for virtual particles for early cosmology when the universe was young and consequently, small, possessing a large curvature. That early contribution may be what we call, the observable matter and energy in the universe. (Maybe).
6. ## Vacuum Fluctuations can Become Real

Maybe? I remember reading the explanation by its creator. at the time, I actually thought it made sense. You might find that original explanation on youtube.
7. ## Vacuum Fluctuations can Become Real

I'll need to read the experiment more carefully before I really say anything, didn't have much time yesterday.
8. ## Vacuum Fluctuations can Become Real

In a recent discussion here at science forums, in a thread related to a similar discussion I explained how some scientists consider all observable matter as just ''longer lived'' fluctuations of the vacuum. This article seems to be related to these kinds of discussions. Scientific American is no stranger to the discussion of virtual particles. https://www.scientificamerican.com/article/something-from-nothing-vacuum-can-yield-flashes-of-light/?utm_content=bufferbfd4d&utm_medium=social&utm_source=facebook.com&utm_campaign=buffer
9. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

A while back I did find an author who wrote the curvature tensor in the phase space similar to mine, except they wrote it in a more appropriate form: I had the notes reference this https://arxiv.org/pdf/hep-th/0007181v2.pdf but cannot find where it is, so thinking I have referenced the wrong paper. They find for the equality term ~And they identify an inequalityWhich is a very useful construction to remember and I wish I could remember who the author is - maybe I can find it? In the paper they identified $\theta^{ij}$ as an antisymmetric tensor. When you consider the tensor $R_{ij}$ which is antisymmetric in the two indices, then the spacetime relationship they gave in the paper is identical to mine.
10. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

The whole point of this, exists on whether in principle the physics holds up. I want people to consider geometry as an observable (which it is under the treatment of general relativity) and for a full transition into quantum theory would require the requite that geometry be described by Hermitian matrices. There appears to be slight change in notation when considering the Hermitian Ricci Curvature and you can follow that in the first reference. You don't need to do anything fancy, we just impose there exists a Hermitian manifold - which is the complex definition of a Riemannian manifold and so you can also have the complex definition of the Ricci curvature. This means at least in princple, the space time non-commutivity can still remain since it is known that two Hermitian operators may not do this. It also means geometry can in principle be described as an observable which I feel is important for the unification theories that involve ''measureable lengths.'' Moving on, we now have a possible application of the spacetime uncertainty principle, in a new kind of form. We showed at the very start of these investigations, how you might interpret it as two connections of the gravitational field, one with spatial derivatives and another with time. For the non-commuting Hermitian operators (since space and time are treated as observables $[x, ct] \ne 0$ - also keep in mind, the fourth dimension is manifested in observable three dimensions as the curvature path of a moving infinitesimal (test) particle), we showed how to calculate them. The mean square uncertainty of both the spatial and time connections are $\Delta <\nabla_i>^2 =\ <\psi|(\nabla_i - <\nabla_i>)^2|\psi> =\ <\psi|A^2|\psi>$ $\Delta <\nabla_j>^2 =\ <\psi|(\nabla_j - <\nabla_j>)^2|\psi> =\ <\psi|B^2|\psi>$ The scalar product of $A|\psi> + i \lambda B|\psi>$ - as a modulus, the scalar product must be greater or equal to zero. Expanding you get $<\psi|A^2|\psi> + \lambda^2<\psi|B^2|\psi> + i \lambda <A\psi|B\psi>\ \geq 0$ After reorganizing the inequalitis in terms of uncertainties you can find the following identity: $\Delta <\nabla_i>^2 \Delta <\nabla_j>^2\ \geq - \frac{1}{4}<\psi|[A,B]|\psi>$ The operators $A$ and $B$ are given as $A = (\nabla_i - <\nabla_i>)^2$ $B = (\nabla_j - <\nabla_j>)^2$ (This is all pretty standard) it does show an application of the physics we have encountered so far, in a neat way. Just for clarity, the connections follow the non-commutation: $[\nabla_i, \nabla_j] = (\partial_i + \Gamma_i)(\partial_j + \Gamma_j) - (\partial_j + \Gamma_j)(\partial_i + \Gamma_i) = (\partial_i \partial_j + \Gamma_i \partial_j + \partial_i \Gamma_j + \Gamma_i\Gamma_j) - (\partial_j \partial_i + \partial_j\Gamma_i + \Gamma_j \partial_i + \Gamma_j \Gamma_i)= -[\partial_j, \Gamma_i] + [\partial_i, \Gamma_j] + [\Gamma_i, \Gamma_j]$ Before this post is over, I want to draw our attentions back to what I called the Hilbert-Wigner Distribution Inequality: $\sqrt{<\dot{\psi}|\dot{\psi}>} = |W(q,p)| \sqrt{<\psi|R_{ij}^2|\psi>} \geq \frac{1}{\hbar}\sqrt{<\psi|H^2|\psi>}$ The Schrodinger equation as I have already noted can satisfy this $H|\psi> = i \hbar |\dot{\psi}>$. A new question arises, can we use a non-linear (takes into account gravity) Schrodinger equation? Yes, it seems we might be able to think this way: http://sci-hub.bz/10.1063/1.1301592 A simple way to form a non-linear wave equation is through using the Schrodinger-Newton equation: $i \hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m}\nabla^2 \psi + V\psi + m\phi\psi$ If applying a non-linear version of the Schrodinger equation, we might be able to talk about gravity in the Hilbert vector space. http://sci-hub.bz/10.1063/1.1301592 http://sci-hub.bz/10.1142/S0219887814500662 https://arxiv.org/pdf/1011.0207.pdf fixed typos
11. ## Quantum Entanglement ?

The only thing I can think of is that some theorists have suggested all particles could be quantum entangled (in some way) because they have the same source/origin. How the entangled does not become destroyed over time, is some immediate problem I can think of - I wonder if I can find that paper now?
12. ## Matter/Antimatter Asymmetry

We have measured differences in the Kaon particle. The charge-parity was found to be violated, suggesting asymmetries exist within our understanding of their relationships with each other.
13. ## Are there no discontinuities in Nature ?

If I can find the relevant source for the discontinuities of the electromagnetic field I certainly will. I should know where the source is located so will be back later. In a system that is static, only spatial derivatives contribute to the electromagnetic tensor $\partial_0 T^{ij}_0 = -\partial_{0j}T^{ij}_0 = - \rho_0E^{i}_{0}$ The charge density is the same as the surface charge where in the rest frame is simply $\sigma = \frac{e}{4 \pi R^2}$ which satifies $\rho_0 = \sigma \delta(R - \tau_0)$ at the surface of the electron, there is a discontinuity at least in principle, in which the electric field is said to jump from $\frac{e}{4 \pi \epsilon_0R^2}$ $E^{i}_{0}$ is satisfied by $r_0 < R: 0$ and $r_0 > R: \frac{e}{4 \pi \epsilon_0 R^2} \frac{x^i}{r_0}$ I have this written as a reference below my notes, no idea if it is related to the source of this information. http://philsci-archive.pitt.edu/1990/1/electron-10-2004.pdf
14. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

Wrote up a lot more so if I find time tomorrow, will update
15. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

Well that's very kind but honestly, it won't be an issue. I can understand most posters I encounter, no matter how bad your English.
16. ## What is inner-peace?

To me inner peace is defined by many things I think.. how do you define it, we all mature at different rates?
17. ## What's the opposite of entropy?

Unless one thinks about breaking the laws of therrnodynamics (negative entropy) then no such thing exists in nature. It exists within the second law the entropy can never be negative. Except for the ''exceptions'' of physics, like negentropy. wiki~ ''Research concerning the relationship between the thermodynamic quantity entropy and the evolution of life began around the turn of the 20th century. In 1910, American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of thermodynamics and on the principle of entropy.[1][2] The 1944 book What is Life? by Nobel-laureate physicist Erwin Schrödinger stimulated research in the field. In his book, Schrödinger originally stated that life feeds on negative entropy, or negentropy as it is sometimes called, but in a later edition corrected himself in response to complaints and stated the true source is free energy. More recent work has restricted the discussion to Gibbs free energy because biological processes on Earth normally occur at a constant temperature and pressure, such as in the atmosphere or at the bottom of an ocean, but not across both over short periods of time for individual organisms.''
18. ## Theoretical form of acquiring energy from stellar collisions

Everything should make curvature so long as it has a stress self energy.
19. ## Theoretical form of acquiring energy from stellar collisions

Sure it does.... Curvature even happens around Pluto. Think about curvature as the response of mass to spacetime as a phenomenon of curvature, always. curvature should even be a response of particles to the background curvature. oh sorry different earlier? I didn't read it all properly. There are situations in which no observer can agree when something happens, based on the relativity of simultaneity.
20. ## Theoretical form of acquiring energy from stellar collisions

I believe the early universe has all the conditions necessary for the creation of particles in an irreversible way. Even fluctuations are effected by the curvature of spacetime according to Sakhrarov.
21. ## How many in bed?

Is it possible to love more than one person at a time? I experienced it when I was younger yet was not the reason that tore my relationship apart. It was something else. Have you ever been in a situation where you have found yourself loving two people? You might not even intend it, but I think it is always possible. But it's taboo. Not sure why the post has repeated three times.
22. ## Theoretical form of acquiring energy from stellar collisions

The conservation is only a local feature, there is no explicit conservation of energy at this time, under the framework of relativity, this is because that time evolution is generated as a symmetry of the theory - so energy is not always conserved globally in our theories. Under strong gravitational fields you, can in theory create irreversible particle creation processes as well. I find it significant for early cosmology, Think about our inability to think of a global time, inherently tied to our inability to find a global description of time. Noethers theorem applies to every conserved system.

lol
24. ## The Irony of Randomness

But they have, you were the one making an issue of inserting words were they couldn't even make sense. It is offensive, sorry you don't like this. BUT remarking on my ability to speak English, while being born English, is an offensive remark. It just adds to your stupidity when you insert the word ''slow'' and it doesn't even make grammatical sense. I saw it, I saw what word you crossed out and you replaced it with ''slow''. Then tell me who speaks English? And I told you more than once, the word I chose was right and you continued with your rhetoric. I saw it, maybe others did as well. Can I ask you a personal question? Strange, would I be stressing too much now, for that answer that physicists are supposed to be well known in, that the collapse has an entirely deterministic process?
25. ## Looking at the Spacetime Uncertainty Relation as an Approach to Unify Gravity

I better make sure I speak in my first language - it has been commented I do not speak good English. Sorry if anyone has had this impression here, I have not had reason to think it. I thought up until tonight, I understood and other posters understood me in the process.
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