Dubbelosix

I never said you did, my question was remarked, remarkably, with a question mark

Yes it was aimed at your post, I wondered if you were hinting that time is not an obervable, and I WOULD like to challenge this contention, especially the poster boy Julian Barbour, who is convinced time does not exist and holds that time is not an observable in physics. What he actually fails to tell you it has to be under the treatment of relativity and actually, his timeless universe makes no sense in relativity. In fact, time in relativity is* relative, not absent, from first principles. These laws cannot fundamentally change unless you have a Lorentz symmetry breakdown. is* fixed

''Recent observations of gravitational waves have put an upper bound of 1.2×10−22 eV/c2 on the graviton's mass.'' https://en.wikipedia.org/wiki/Graviton#Gravitons_in_speculative_theories Can I play mod for once, and say, ''please contain yourself within mainstream physics?'' Certainly, quantization of gravitational waves have been considered. But I like how you think, I don't think they are gravitational fluctuations either... but that wouldn't be mainstream, eh? To be fair all options appear to be open, that would be more mainstream. Maybe it might be fairer if we establish what we are allowed to talk about in the speculations section. If it is published, is it good enough? Or is experimental evidence required? In which case, why are these topics reserved for speculation? certainly, if quantization of gravity is certain, which it isn't, but let's imagine it was, if gravitational waves were not composed of gravitons, they could not be gravitational waves under any quantization, (which), suspiciously enough) indicates two different aspects of a single theory and it certainly wouldn't make sense to me. But I tell you, you don't even need a graviton, to understand gravitation in physics, and whilst that might be a surprise, it's been a glaring fact since relativity was first formulated.

It's a good question, ... and yes, we live in all four dimensions. Always. We go through the time dimension at different rates, depending on how fast you are moving through space. For this reason, we call them relative. We realize the relative nature is not trivial, or some magic mathematical set up, it seems to be a clear description of reality since, through time we come to notions of spacetime curvature. In the general treatment, time is manifested observable through the curvature of space. Without time, we could not describe the gravitational interactions properly. Also, we always move through time. We are always time travelling. It's just that curvature will deal you different circumstances in which the rate at which you move through that dimension, changes. Then there is Kaluza Klein and then String Theory. I have heard convincing elements of the Kaluza Klein in respects to a ''physical need'' for a fifth dimension, whilst for string theory, I find it more like a needle in a haystack since it probably represents all of reality, melded into a crazy dimensional manifold. This is why string theory predicts all possible things, it has more degree's of freedom, more chance of getting it right somewhere down its long sad murky path. A time observable? I challenge this with my most recent investigations, all of which conclude that time is an observable manifest of three dimensional space in the form of curvature. You cannot understand curvature in Einstein's theory properly without the definition of time. Time strictly is not an observable from first principles of QM, but equally, nothing from first principles forbids it. Only a naive attempt of quantization called the WDW equation drives this crazy notion time does not exist.

What does it serve as a conscious being sits in the most recent Japanese self-drive automobile? There is some evidence now that the body follows deterministic laws and that actually we are bound by the deterministic laws happening inside our brains. Why we act like puppets like this is not entirely clear. But what I can say is this... consciousness is more than the sum of its parts (according to some neurobiologists), and when you take this into consideration, there is something more than the deterministic processes going on inside your head. There are many things we still can't explain, many of them still classed as ''Hard Problems'' of consciousness. Like... how does the retina collect a two dimensional image and recast it perfectly to create the three dimensional experience of consciousness? Some have likened consciousness to the holographic principle, but I am not too convinced at all with this idea.

He doesn't even understand the material he is reading. Then when he has no material to read from, steals from other peoples material or regurgitates material he has already memorised. And even when he is wrong, he is right. Actually, Trump is a classical psychopath. And I don't say that lightly. I know of one good case he regurgitated material he had memorised, there was an easter egg hunt going on at the white house, and his speech somehow turned into how it was going to make america better. America has made several steps back, in several pressing topics, two of those include racism and climate control Now maybe stupidity control has to be factored in to the next generation after all... Trump is not the only disappointment right now. Neo Nazi far right agenda parties have won votes in Germany recently. Can anyone say fourth Reich? But then , I say took several steps back in racism, but it could be argued, what we have seen with Trump acting as the far right poster boy for America, has given incentive for racists to come out of the woodworks. My black friend in america was called a Nigger three times within the three weeks after his election. Whether this has continued. is not known to me, but this is the issue and Americans are allowing it to happen, some of them reluctantly. Psychopaths are not honest people. In fact, high functioning psychopaths do very well, by such manipulation of people around them. Many of them hold very respectable jobs, such as judges, lawyers, police officers... but do you see a pattern emerging? Psychopaths thrive on power. Such as the case with Trump. And he hates being challenged and your constitutional rights are being challenged every day. America is not what it once was and it is not great. What makes me laugh is that Trump once said no one understands the ''amendments like he does'' in his own words, yet, the only one he seems to be upholding is your right to bare arms and even that speaks platitudes for Trump and his agenda, because he is a demagogue. Yes, guns are an issue, but when he is in office, he is the first issue. Life is about its shades, let's not forget this. Life is about doing right over evil, since the majority appear complicit in this way. So.... what I am saying is, things are actually not too late for America to become great again. But it won't happen under him... not much happens under him. If you recall all his promises, hardly any where fulfilled.

No problem.

[math]Tr(R_{ij} \rho) = Tr(R_{ij} \sum_i p_i|\psi_i><\psi_i|)[/math] [math]= \sum_i p_i\ Tr(R_{ij}|\psi_i><\psi_i|) = \sum_i p_i\ Tr(<\psi|R_{ij}|\psi>) = \sum_i p_i<\psi_i|R_{ij}|\psi>[/math] [math]\mathbf{P} = \frac{(\mathbf{I} + n \cdot \sigma )}{2} = |\psi_n><\psi_n|[/math] Now, we have traceless Pauli spin matrices in second equation, this posits investigation. I know there are traces for the products of Paul matrices.

It is mainstream. Matter actually is a condensed form of energy, sorry you don't like that Swansont. I know you like making these public declarations, but I don't need to put in my effort here. Read a very nice book by David Bodanis called E=mc^2. He explains why energy is a diffused mass and why matter is a condensed form of energy. wrote that wrong fixed it Now in what context we think it is a condensed form of energy is unclear, only that in physics, mass translates as a lot of energy through a conversion factor. It is in effect, a condensed form of energy - the atom itself, harbours a great deal of what could otherwise be free energy. But its trapped there and by simply splitting the atom, we can in effect release all the energy inside of it - a funny thing is, Einstein once considered this impossible to do. I find it ironic because his own theory predicts the convertibility.

Mass can be thought of as a condensed form of energy yes. Just as energy can be often be taken as a diffusion of mass. Presence means local vicinity of. So if you have a bunch of particles in local vicinity, they will exert a spacetime disturbance. Hell, even a particle should disturb the vacuum in some way albeit, very small. It is a ''response'' mechanism to how matter should travel in space - a curve in space may conserve energy making it the most plausible geodesic (principle of least action). In relativity, we call the method to calculate those curvatures as Parallel Transport. How is energy affecting spacetime? Because spacetime is not nothing, it is dynamical. This is why famously people have said, the Einstein field equations explain how one side states matter tells space how to curve, whereas the other side space (geometry) tells matter how to move. My typos are bad today, sorry, fixed.

Sorry, that equation should be [math]n \cdot \sigma |n \cdot \sigma>[/math] just posted this and cannot edit.

The projector in 2 dimensions can be written in the form [math]\mathbf{P} = \frac{(\mathbf{I} + n \cdot \sigma )}{2} = |\psi_n><\psi_n|[/math] This does introduce the traceless Pauli spin matrices where [math]n \in \mathbf{R}^3[/math] which is known as the Bloch sphere. So [math]n[/math] has to be the real unit three vector [math](n_x,n_y,n_z)[/math]. We have been speculating in the Hilbert space which deals with the projective space so here is one avenue to incorporate spin into the model. I'm familiar with some of this algebra so I can understand this. I'll get to work see what I can do with it. This approach though seems to be good for pure states only? Seems right. But I have already wrote down the relationships that ties the inner and outer products as you know, so will write it up later Mordred. [math]\mathbf{P} = \frac{(\mathbf{I} + n \cdot \sigma )}{2} = |\psi_n><\psi_n|[/math] This does introduce the traceless Pauli spin matrices where [math]n \in \mathbf{R}^3[/math] which is known as the Bloch sphere. So [math]n[/math] has to be the real unit three vector [math](n_x,n_y,n_z)[/math]. We have been speculating in the Hilbert space which deals with the projective space so here is one avenue to incorporate spin into the model. [math]\mathbf{P} = \frac{(\mathbf{I} + n \cdot \sigma )}{2} = |\psi_n><\psi_n|[/math] https://physics.stackexchange.com/questions/70436/differences-between-pure-mixed-entangled-separable-superposed-states [math]\sigma_3 = \begin{pmatrix} 1 & 0 \\0 & -1 \end{pmatrix}[/math] (it has eignevalues of +1 or -1) [math]\sigma_1 = \begin{pmatrix} 0 & 1 \\1 & 0 \end{pmatrix}[/math] A property of these two matrices is that if you square them, you just get the identity back. The last one is [math]\sigma_2 = \begin{pmatrix} 0 & -i \\i & 0 \end{pmatrix}[/math] [math]| n \cdot \sigma>\ = |1>[/math] [math]|n \cdot \sigma>\ = 1[/math] [math]n \cdot n\sigma|n \cdot \sigma>\ = 1| n \cdot \sigma>\ = |1>[/math] These are eigenstates of [math]|\sigma \cdot n>[/math] and I use the notation of 1 to denote identity. Same for another definition of the vector for [math]|m \cdot \sigma>\ = 1[/math] and so a probability amplitude is [math]|n \cdot \sigma>\ = 1[/math] The probability is [math]|<m \cdot \sigma |n \cdot \sigma>|^2[/math] and [math]n \cdot \sigma = \begin{pmatrix} n_3 & n_{-} \\ n_{+} & -n_3 \end{pmatrix}[/math] Which explains one component of this projective space.

It's indistinguishable in relativity, curvature and gravity. They tend to be saying the same thing, two sides of a different coin if you will. Gravity is a pseudo force, so we'll need to be clear about what we mean when we ask questions like ''what is pulling down on and around spacetime to cause the curvature?'' A simple case of a planet like ours with mass, it is pretty much near spherical because of spacetime curvature. Curvature is the presence of mass and energy and the curvature is more significant the denser the object. So it is mass that is affecting the spacetime structure giving rise to gravity and further, in fact all types of energy distorts the fabric of spacetime. Curvature also doesn't make much sense without a concept of four dimensional space.

I am reading back and I spoke about say a correlated system as [math]S(\rho_A \otimes \rho_B)[/math] and there are some things I need to be clear about, I didn't write that very well before. Compared to the object above, a separable state is one that can be written like [math]|\psi> = \psi_A \otimes \psi_B[/math] for any states [math]|\psi_A>[/math] and [math]|\psi_B>[/math] in which (and now here comes the important part) then the trace over the system will pick the terms in the system such that [math]|\psi_{AB}>[/math] When there is no statistical mixing (pure state) then you write the system as outer product [math]\rho_{AB} = |\psi><\psi|[/math]

Just to add to Mordred, the density parameter from the Friedmann equations measures the ratio of the observed vacuum density to the critical density. Only when these two quantities are [exactly] the same does the Friedmann equation allow a geometry which would fit Euclidean flat spacetime. It's not difficult mathematics, consider an equation of state [math]\dot{\rho} = \frac{\dot{R}}{R}(\rho + P)[/math] I have left a constant out of the equation. Ordinary density goes down in an expanding universe and the critical density is when [math]\rho \rightarrow \frac{\Lambda c^2}{8 \pi G}[/math] and that results in the equation [math](\frac{\dot{a}}{a})^2 = \frac{8 \pi G}{3}\rho + \frac{kc^2}{a} \rightarrow \frac{8 \pi G}{3}\frac{\Lambda c^2}{8 \pi G} + \frac{kc^2}{a}[/math] Note, there appears to be something wrong with the equation since, in absence of any non-luminous matter, the critical energy (a tool used to explain possible collapse models) is worked out to be five atoms of hydrogen per cubic metre of space which is (actually) far denser than what is observed. Our universe appears to be well under the critical energy. Notice when you plug in the critical density, a factor of [math]\frac{\Lambda c^2}{3}[/math] appears - this is just the standard definition of how the cosmological constant which drives acceleration enters the equation for critical density - the cosmological constant is believed to only get significant when a universe get's large enough. It seems strange that we might measure a different measure of density for the vacuum than that predicted by the Friedmann equation. Of course, things like vacuum density becomes obscured under relativity anyway since moving observers will not agree on things like density, but I feel like this is a different issue entirely. Personally, I have likened this lack of density being linked to acceleration of the universe. Something rings true about the prediction, just not the model we are using..

Yes I have so far as well, quite a bit of reading.

I will certainly look into it, familiar with the Levi cevita from general relativity. Thanks for the link.

The Fubini-Study metric was, [math]d(\psi,\psi) = \arccos\ (|<\psi|\psi>|)[/math] If [math]|\psi>[/math] is separable, then it can be written as [math]|\psi> = |\psi_A> \otimes\ |\psi_B>[/math] Then the metric is [math]ds^2 = ds^2_A + ds^2_B[/math] Then a curve in the metric may be taken as [math]\frac{ds}{dt} = \sqrt{ \dot{s}^2_A + \dot{s}^2_B}[/math] Keep in mind, a curve in a Hilbert space may take on the following appearance, with an understanding of geometry - the following equation also makes use of the Wigner function which allowed me to write it as an inequality (as was shown previously) [math]\frac{ds}{dt} \equiv \sqrt{<\dot{\psi}|\dot{\psi}>} = \int \int\ |W(q,p)^2|\ \sqrt{<\psi|R_{ij}^2|\psi>}\ dqdp\ \geq \frac{1}{\hbar} \sqrt{<\psi|H^2|\psi>}[/math] If you are interested in the correlations (entanglement) then here is some notes I wrote down: In terms of probability density, the separable state also looks like [math]\rho_{AB} = \rho_A \otimes \rho_B[/math] Correlated entropy is [math]S(\rho_A \otimes \rho_B) = S(\rho_A) + S(\rho_B)[/math] so long as [math]S(\rho_A|\rho_B) < 0[/math] and [math]S(\rho_A \otimes \rho_B) = S(\rho_A) + S(\rho_B)[/math] Note also that the upper bound of correlation is found as (from Carrols paper) [math]S(\rho_A \otimes \rho_B|\rho_{AB}) = S(\rho_A) + S(\rho_B) - S(\rho_{AB}) \geq \frac{1}{2}| \rho_A \otimes \rho_B - \rho_{AB}|^2[/math] [math]\geq \frac{(Tr(\mathcal{O}_A \mathcal{O}_B)( \rho_A \otimes \rho_B - \rho_{AB} ))^2}{2|\mathcal{O}_A|^2|\mathcal{O}_B|^2}[/math] [math]= \frac{( <\mathcal{O}_A><\mathcal{O}_B> - <\mathcal{O}_A\mathcal{O}_B>)^2}{2|\mathcal{O}_A|^2|\mathcal{O}_B|^2}[/math] https://en.wikipedia.org/wiki/Separable_state https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Feragen_Geodesic_Exponential_Kernels_2015_CVPR_paper.pdf

Well written. Good points as well.

On Misunderstandings of the Role of Observables in QM It was stated to me that ''No, position is not an operator at the relativistic level; and Nature is relativistic. Time not an operator at any level.'' You could say if you wanted that the relativistic version of QM is by definition a QFT, where position and momentum are no longer operators on a Hilbert space. It's not that quantum mechanics does not describe them as operators, it is just that one treatment of melding relativity with quantum mechanics resulted in a modern QFT which did not treat them as operators fundamentally. Though, some have argued in literature that it ''may be the only way'' to go forwards, but I don't think this is the case. Again, classical gravity may extend into the phase space. Classical gravity may have a definition in the Hilbert space (albeit) you have to modify your model. For instance, the Hilbert space is a vector space, it doesn't naturally induce curvilinear coordinates. To do that, you have to literally invent notions of curvature in the Hilbert space - is it so strange we come to do this? Absolutely not, the Hilbert space is after all an abstract space, but one that seems to work very well with quantum mechanics. Equally in an abstract space you can invent abstract tools. Gravity is a pseudo force in relativity, its not a real force by definition - so field theories that have quantized it may also be wrong from first principles. This may also be a reason not to expect any quantum corrections to gravity. I have chosen a model in which classical gravity extends even to the phase space of quantum particles. This idea that an understanding of gravity at the fundamental level remains classical is not entirely a new idea and in similar idea's, was studied earlier - as wiki puts it: ''Later on it was proposed as a model to explain the quantum wave function collapse by Diósi[4] and Penrose,[5][6][7] from whom the name "Schrödinger–Newton equation" originates. In this context, matter has quantum properties while gravity remains classical even at the fundamental level. '' Certainly, one main foundation of the QFT approach is a direct quantization of gravity - I have been vocal about this as well. Relativity was clear about gravity - it is like the centrifugal force, it doesn't need a mediator to be explained. It can be understood perfectly in terms of geometry only. Continued failure to quantize gravity has made scientists skeptical of the QFT approach. Some have taken the divergence problems as evidence that gravity cannot, and by default the theory of relativity, be quantized. And of course, attempts have been made to find relativistic versions of our phase space https://en.wikipedia.org/wiki/Newton–Wigner_localization

Based on the Langrangian, the Hamiltonian of the theory with an interaction would look like and allow the Hamiltonian to have eigenstates [math]H_0[/math] which gives [math](\mathcal{H}_0 + V + m\phi)|\psi>\ =\frac{\hbar^2}{2m} \nabla^2|\psi>[/math] and allow [math]\frac{\hbar^2}{2m} \nabla^2 = E[/math] allows us to write it more simply as [math](\mathcal{H}_0 + V + m\phi)|\psi>\ = E |\psi>[/math] As noted before we must try and construct a Lippmann-Schwinger-like equation from this - the general idea is that the continuity of the eigenvalues would make [math]|\psi> \rightarrow |\phi>[/math] as the potential [math]V[/math] goes to zerp. But our situation is a bit more complicated, we don't just have one potential. We have two interaction terms in this theory (making it non-linear essentially). (Presumably) the solution we seek would take the form [math]|\psi>\ = |\phi> + \frac{1}{E - H_0}(V + m\phi)|\psi>[/math] And since I know not much about this equation, I've had to read literature. [math]E - H_0[/math] though is singular of course, and it has been suggested that making the denominator slightly complex removes it - [math]|\psi>\ = |\phi> + \frac{1}{E - H_0 \pm i \epsilon}(V + m\phi)|\psi>[/math] I have a feeling the denominator does not need to be complex but will need to look into it. Also note, I've simplified the notation a bit, a popular notation is to write the wave function with ingoing and outgoing wave solutions [math]|\psi^{\pm}>[/math]. This approach above brings us into some new physics, because the Lippmann Schwinger equation is a free particle solution where the interaction terms do not vary, whereas it can be assumed when you have a non-linear equation, parameters will almost certainly vary. And all that is an indication this needs to be considered carefully. I know you haven't replied Mordred, but this was kind of the idea I had in mind above.

True. I didn't. But these are things that go through my mind.

Just because I experience it doesn't make it right. It becomes a moral question of whether your love for one person is greater than loving two people or whether it means more.

Don't worry Mordred, I haven't forgotten about this either, I have just been taken with the toy model of gravity right now over the toy model of rotation. I also want to study my primordial fluctuation hypothesis as well again. But I've not really had more idea's (as of yet) in which way I would like to continue with this.

Been trying to understand my physics clearly before continuing making some Hamiltonian with an interaction which would result in a Lippmann Schwinger equation. Inside of it, I can create the propagator. I want the solution to satisfy not just outgoing waves but also those incoming wave solutions. Generally, such an equation is used in scattering theory - from such an equation though, I could describe the scattering, or S-matrix. It's certainly not impossible, I just redefine the Langrangian as a Hamiltonian and the Lippmann Schwinger equation becomes non-linear because of the extra interaction term of the mass with its own gravitational field. Mordred, does the Lippmann Schwinger equation, automatically have solutions for both outgoing and ingoing waves?