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Everything posted by Mordred
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Yes I did as Strange mentioned the Uncertainty doesn't require observer effects. I replied to the OP your response is a thread hijack so I didn't respond to it.
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Well I know the OP won't be able to answer this one so I will Ghost fields arise in perturbation theories such as QFT. They refer to unphysical states or left over degrees of freedom in gauge groups. Through gauge invariance where the field degrees of freedom exceed the degrees of freedom of the particle such as the photon the ghosts are the mechanism to account for the unused degrees of freedom. A commonly used example is [latex]A_\mu(x)[/latex] the photon that is normalized from this field only has two polarity states. The left over states will be goiter rid of through the ghost field. The other condition is the negative modes of a Fourier transform when we induce a positive norm. The negative norm states violate unity. It's not really a state of no energy but the energy would correlate to those of field fluctuations that don't induce localized action. They would reside in internal lines of a Feynman diagram. A physical state being measurable by definition an unphysical state would not be measurable.
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Gravity as the curvature of the wave function of the universe.
Mordred replied to Kuyukov Vitaly's topic in Speculations
I wasn't expecting a particle wavefunction however you are connecting the wavefunction to gravity which would lead to a quadrupole wavefunction. Where as you have Dipolar wavefunctions. Look at the proofs of how GW waves were derived and you will see what I mean. The GW waves takes spacetime itself through the EFE to derive a quadrupole wave. The gravity formulas your using are anistropic. They describe a Centre of mass distribution. -
Lol one of my three rules of life. Tomorrow I will be a better man than I am today (always strive for self improvement ) Treat others as I wish to to treated If I'm not having fun pretend. ( learn to enjoy every moment no matter how daunting)
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Pair production (Electron, positron)
Mordred replied to Lizwi's topic in Modern and Theoretical Physics
Your not wrong -
OK so you want particles and and antiparticles popping in and put. So let's use the field treatment of QFT. Now the positive frequency modes form the annihilation operators for particles with the negative frequency modes for the creation operators of anti particles. [latex]\hat{a}^\dagger (\vec{k}) \hat{a}(\vec{k})[/latex] the former is creation the latter annihilation operators for particles For antiparticles [latex]\hat{b}^\dagger (\vec{k}) \hat{b}(\vec{k})[/latex] Hence [latex]\hat{a}^\dagger (\vec{k})[/latex] creates a particle of energy [math]\hbar\omega[/math] and momentum [latex]\hbar k [/latex] same applies to the antiparticles Now with the above you sum up the positive frequency parts with the negative frequency parts. [latex]\hat{\psi}(x)=\int\frac {d^3k}{(2\pi)^{\frac {3}{2}}\sqrt{2\omega_k}}[/latex][latex]\hat{a}(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}[/latex][latex]+\vec {b}^\dagger(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}[/latex] How's that for a start to your model you now have the a scalar spacetime complex field of particles and antiparticles. Now accepting that baryogenesis leaves a slight higher density of positive frequency parts (cause unknown) I will let you think about this in terms of the energy density values for different observers for the Unruh effect in your link above. Naturally the mass density valued will vary accordingly to field potential which will affect the path integrals described by the Feynman lines you referred to. (I am going to up vote you +1 for coming up with a viable speculation model though we can improve your descriptive as we go ) Now continuing from above a complex field has an adjoint. [latex]\hat{\psi}^\dagger(x)=\int\frac {d^3k}{(2\pi)^{\frac {3}{2}}\sqrt{2\omega_k}}[/latex][latex]\hat{a}(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}[/latex][latex]+\vec {b}^\dagger(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}[/latex] Now assuming you want bosons for an uncharged field. We can incorporate the Pauli exclusion symmetry to the Bose Einstein statistics So first we have normalize the vacuum to unity. In Dirac notation [latex]\langle 0|0\rangle=1[/latex]. The ket [latex]|\rangle [/latex] is the initial state the bra [latex]\langle | [/latex] is the final state. So we need to compute the normalization to an arbitrary state. [math]|\vec{k}\rangle[/math] for that we need the inner product [math]\langle\vec{k}|\acute{\vec{k}}\rangle[/math] So [latex]\hat{a}^\dagger (\vec{k})|0\rangle=|\vec{k}\rangle[/latex] with adjoint [math]\langle 0|=\langle\vec{k}|\hat{a}(\vec{k})[/math] Without going through all the steps [math]\langle\vec{k}|\acute{\vec{k}}\rangle=\delta(\vec{k}-\acute{\vec{k}})[/math] Now each k state represents the momentum of a single particle. If they are bosons then the following relation holds [latex]|\vec{k_1},\vec{k_2}\rangle=|\vec{k_2},\vec{k_1}\rangle[/latex] Now you have a complex spin zero boson field in momentum space. Next lesson we apply thus to the four momentum of GR. As we're dealing with a complex scalar boson field of particles/antiparticles let's start with the Minkowskii metric [latex]ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex] Apply coordinate notation [latex] (x^0,x^1,x^2,x^3x^4)=(ct,x,y,z)=x^\mu[/latex] Where the indice range is 0 to 3. Four momentum is given here https://en.m.wikipedia.org/wiki/Four-momentum In the format I have provided using a particle number operator I will just latex the positive frequency modes as the negative frequency modes simply switch a to b. [latex]\hat{N}=\hat{a}^\dagger (\vec{k})\hat{a}(\vec{k})[/latex] The Hamilton is [latex]\hat{H}=\int d^3k\omega_k [\hat {N}(\vec{k})+\frac{1}{2}][/latex] includes the harmonic oscillator. The field momentum [latex]\hat{P}=\int k\vec{k}[\hat {N}(\vec{k})+\frac{1}{2}][/latex] Now there is an interesting consequence of this when you compute the energy of the field...it is related to the energy of the harmonic oscillator. Can you guess what it is ? I will show the answer tomorrow. PS to OP I hope your descriptive above needs considerable work however you have several details with accuracy that although poorly described are applicable. So I hope you don't mind if I run the modelling gauntlet with the basis of particle/antiparticle creation and annihilation and it's effects. I will get to your network analogy later on as I can employ that analogy
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Try not to think about expansion as expanding into something. Expansion is simply the average density decreasing. This mathematically can be described as the expansion of the metric coordinate system. Now the other thing is to not think of space as a substance. Space is simply a volume. It is the volume filled with the SM particles. The average mass/energy density decreases as expansion occurs as per the ideal gas laws of thermodynamics. Now spacetime adds time as a coordinate. To give time a coordinate we must give it an equal footing with length we do this by using the interval ct. So our coordinates become ct,x,y,z
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OK here is a hint learn how to apply the four momentum to the Klein Gordon equations. What you need will end up being QFT instead of QM. Now here is the tricky part you will end up having to deal with symmetry and rotation groups. Unfortunately this will take considerable study. Both QFT and GR use the same four momentum methodology the rotation groups are essentially identical PS there is in physics a ghost field. It arises in certain group theories Fadeev Popup ghosts is variation https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1406.4550&ved=2ahUKEwju85rWsvfjAhUrxVQKHbkZA-wQFjAAegQIBRAB&usg=AOvVaw0U_1b1iR1IQ7CQYR5DnqEJ
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Well you have fun because honestly I have seen some very foolish papers get peer reviewed before. The most amusing one was using a nuclear bomb on an EH to peek inside. Peer review doesn't mean right. If you think that just because you got peer reviewed your article will make a difference all on its lonesome. Without substantially more work guess again.
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Your word salad Captcass isn't completing anything. How many times have I asked you to show a galaxy rotation curve ? Complete you couldn't do it how is that possibly complete ??? How many times have I asked you to show how you apply your NOT tensors ? Complete ??? I don't think so... Then when I address you on expansion and you account for observational data. Your response is "please no expansion". How is that complete when you cannot account for measured data.??? You haven't shown a single solution to any of your claims. You have a total of what three miniscule first order formulas that suddenly solves DM DE and the singularity problems ? I don't think so
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Well have fun with those reviewers. It matters not to me if you choose to stay blind to other data. What you believe won't affect me. I never ignore valid data, I have worked on dozens of personal models. When I find data that counters them I trash the model attempt. However I believe in the proper scientific method.
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As Strange mentioned the HUP is fundamental in our universe.
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If you ignore expansion altogether that's been my point you refuse to accept expansion on any terms. Even though expansion doesn't require DE. The thermodynamic data you chose to ignore. The changes in metalicity you ignore the Lyman alpha forest you ignore. The CMB data you ignore. You ignore baryogenesis you ignore anything that relates to expansion. With expansion the Hubble sphere is roughly z= 2.1 well below z=11.1 The types of stars at z=2.1 is different than 11.1 but you will ignore that too.
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This wave equation is for a two dimensional Hilbert space it only applies in the x y coordinates with the wave propagation along the x axis. [latex]\psi = e^{i \phi}[/latex] you can immediately recognize that detail by the indices. Ie your measuring it on a screen. See the plot here https://m.wolframalpha.com/input/?i=plot+\psi+%3D+e^{i+\phi} That plot does not represent a photon or any particle. There are no finite boundaries.
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Do you honestly believe that last word play means anything any idiot can declare what he believes. Show the math on his you account for redshift 1100. Which observational data has measured. I know all about how light ones function. Go ahead use your Lorentz transforms of course your going to obviously state it's c at the Hubble horizon but that still doesn't account for the higher redshift data. It's fairly typical that you arbitrarily ignore other observational data when it counters your pet theory. It's a very common tactic but one that doesn't work. Good example is the number of times you state my model and please stop mentioning the current theories. As it's not your model. A good example was your response to the metalicity data at different redshift in terms of the element percentages present at those redshifts. Aka that Lyman alpha Forest paper I posted earlier. In laymen terms the types of stars don't match.
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The circles is due to you not making sense. The redshift value that has been measured at the various telescopes has a detection range up to z=1100 How does your equations account for that when the Hubble horizon is roughly redshift 5 ? You have to account for why the telescopes measure those far higher redshifts the non linear portion of the redshift curve. Simply stating there is no need to because it competes with your model is not sufficient. Of course Heading toward any horizon and it will recede. The Hubble horizon isn't the only horizon. There is also the particle horizon and the cosmological horizon.