Mordred

There have been numerous estimates using a wide variety of methods generally involved in measuring the total mass and factoring out all known baryonic mass sources. This article for example estimates 90% the total mass be dark. However the values I have come across are fairly varied. the link is more the textbook answer than a research paper. I don't know the mass estimate bounds are https://sites.astro.caltech.edu/~george/ay20/eaa-darkmatter-obs.pdf

Fermi's Golden Rule \[\Gamma=\frac{2\pi}{\hbar}|V_{fi}|^2\frac{dN}{DE_f}\] density of states \[\langle x|\psi\rangle\propto exp(ik\cdot x)\] with periodic boundary condition as "a"\[k_x=2\pi n/a\] number of momentum states \[dN=\frac{d^3p}{(2\pi)^2}V\] decay rate \[\Gamma\] Hamilton coupling matrix element between initial and final state \[V_{fi}\] density of final state \[\frac{dN}{dE_f}\] number of particles remaining at time t (decay law) \[\frac{dN}{dt}=-\Gamma N\] average proper lifetime probability \[p(t)\delta t=-\frac{1}{N}\frac{dN}{dt}\delta t=\Gamma\exp-(\Gamma t)\delta t\] mean lifetime \[\tau=<t>=\frac{\int_0^\infty tp (t) dt}{\int_0^\infty p (t) dt}=\frac{1}{\Gamma}\] relativistic decay rate set \[L_o=\beta\gamma c\tau\] average number after some distance x \[N=N_0\exp(-x/l_0)\]

While both answers provided are good the QFT viewpoint may help. As Lorentz Jr and Exchemist mentioned you have the fields involved. The EM field being a composite field as per Maxwell. As that field becomes perturbed the anisotropic disturbances generate potential energy differences. This in turn generates an increase in the particle number density of gauge photons for the EM field as per the momentum force mediator. So in essence a light beam generates its own medium comprised of gauge bosons the gauge photon however it will be offshell in this case. The photon becomes real as per the quanta of action terms. So in essence one could view it as the photon generates its own localized medium via the EM field permutations. In QFT that's done via the creation/annihilation operators via the Lorentz invariant Klein_Gordon equations.

I wouldn't know about most instances. Its enough to be aware that as both modelling and interpretations lead to testing they both are useful tools in model development QM as well others.

I would have to say a combination of both. Sometimes the tests developed to test an interpretation has led to QM development. Other times its the tests of a mathematical model that led to QM development.

If your applying the QM mathematical method then yes that follows the Copenhagen interpretation. However QM isn't the only methodology other methodologies can have their own subsequent interpretations. In essence the choice breaks down to which mathematical method best describes the state or evolution of states. If you don't religiously apply one theory over another but apply the aspects that best suit the situation you will invariably gain a far better understanding of how physics describe physical processes. However QM in an of itself has several different interpretations as to the deterministic and stochastic aspects. I lost track of the numerous QM based interpretations there are years ago lol

Well as I typically choose to ignore any interpretation aspects in any article or video. I found the paper useful in so far as the mathematics being applied. Which essentially breaks down an examination of error margin elimination to the weak limit. The paper examines the method of using a combination of preselection and post selection without causality violation as its not involving any causation signal sent from post selection to the past. Rather its making predictions of the past events based on the post selection results, as well as making predictions of the future events from the preselection correlations. the paper suggests this dual methodology will eliminate errors and minimize the error margin to improve the error margin to better understand the evolutionary history of the entangled particle pair.

Do what I do ignore interpretations stick to the numbers. Its too easy to for a choice of interpretation to be followed with religious like zeal

I'll have to study the article in greater detail however if you recall above I described how non locality vs local defined in regards to Bell type experiments. You happened to find an article that clearly states that post. "2.5. Dynamical nonlocality and the whole-part dialogue Dynamical nonlocality [37] impacts the dialogue concerning the relationship between parts and wholes. Motivated by the AB non-locality and by weak measurements, we look for new manifestations of the dynamics of QM which are not predicted by the dynamics of classical mechanics. The key difference is that the equation of motion of QM exhibits a new kind of non-locality, which is best described by using modular variables." equations are 2.32 and 2.33 for this examination for the local (classical) vs non local (quantum). As I have time tomorrow will read it in more detail thanks for sharing

Its amazing at the amount of output a star like our sun emits per second. Our sun outputs roughly \[3.8*10^{26}\] watts per second. 1 watt per second equals 1 joule per second The Earth receives roughly 1400 watts/m^3 of that energy. At peak emission given by wiki the peak wavelength of our sun is approx 883 nm convert to joules per second gives roughly 2.25 *10^{-19} joules . A quick back of envelope calculation gives roughly 10^{46} photons but that's a very rough estimate (granted I also only applied the peak wavelength not the entire ensemble of wavelengths) the total photons radiated is far far higher. So yes a star emits an incredible amount of EM radiation. However I wouldn't advise thinking of light in the fashion of a stream of bullet like photons. Instead your better off understanding light as a superposition of EM waves. Where the sum of energy levels of the waves at a given volume correspond to a probable number density of photons as per Bose Einstein statistics. The photons themselves of that wave do not necessarily have to originate from the star but can be generated on route as well as interfered with on route. The number density will still correspond with the mean energy density or blackbody temperature

your welcome

One of the things about mathematics is the symbology often takes a second place to the relations ( I could literlly hand someone 10 different articles covering precisely the same thing and no two papers apply the same symbology) outside of common standardized forms) However P is simply the entangled particle state with the A and B identifying each particle state whether is spin up, down, left, right, etc. M is simply the probability density matrix of each. with rho \[\rho\] being the density of the operator from that matrix. ie the momentum, position operator. the trace of matrix M can best be covered here https://en.wikipedia.org/wiki/Trace_(linear_algebra) however the above was simply an FYI in so far as one has to take care on how the term local vs non local applies for a given examination the usage can often vary

You can't really separate the two gravity is spacetime curvature the time dilation itself results from that curvature where inertial mass and gravitational mass have equivalency ( m_i=m_g). As I mentioned they did test the weak equivalence principle on the moon "Lunar Laser Ranging Tests of the Equivalence Principle with the Earth and Moon" https://arxiv.org/abs/gr-qc/0507083 the strong equivalence principle is also inclusive, however as the test involves laser ranging you are in actuality also testing time dilation via the rate of signals. it might help to further understand that with spacetime curvature you get distortions in light rays from an object. Take two lasers fie them in parallel. If the beams stay parallel you have a flat geometry with no time dilation. If the beams converge you have positive curvature aka gravity with time dilation. So its quite possible to test for time dilation without having to place a clock on the moon. You can literally use lasers or other EM signals.

Thanks there are aspects I like in that model however I will still tend to use QFT over that lol mainly as I'm more familiar with QFT. What appeals to me in the cellular autonoma is that it helps ease numerous calculations to reasonable approximation. This is more an FYI than in regards to the opening post. However as were onto interpretations vs correlation functions. Some of the interpretations I will actually follow without conclusion as to which is the best interpretation are those that apply mathematics with the subsequent tests of those mathematics. This falls into the Bell inequalities as well as CHSH inequalities how CHSH works is in itself a lengthy topic but the essence of it is that it further tests the probability vs the determinable aspects of the various correlation functions via the density matrix that is often employed... without going into the mathematics itself one should be aware that this methodology has some ramifications into the terms locality and non locality. We tend to think this is applying the relativity definition however this isn't necessarily true in the inequality case. The inequality essentially separates the classical probability (local) part vs the quantum interference term (non local). So what are they truly saying here ? Well as I've come to understand it the local in essence means that all the variables to describe a particles evolution is local to the particle state itself. However in the quantum case for example the quantum harmonic oscillator interferes as the quantum harmonic oscillator is part of the field outside the boundary of the well defined particle then then it is non local to the potential boundary we define as the localized excitation. this further ties into the :hidden variable aspects: Is all the information to describe the evolution history of the particle state inclusive in that particle state. (local to the particle state) though hidden. Or non local do we need to further include the field interactions (key note though those field interactions must still follow causality and speed of information exchange. I point this out as it is another commonly used descriptive of local vs non local commonly used in Bells type experiments. a simplified version of the mathematics is as follows. \[P_{all} (+a,+b)=Tr[M_{a}^{+ }\otimes M_{b}^{+ }](\rho_{c}+\rho_{q})\] \[ =(+a,+b)=P_c(+a,+b)+P_q(+a,+b)\] where M is the probability density matrix where the average values of a and b in the classical vs quantum mechanical part is \[\langle ab\rangle=P_c(+a,+b)-P_c(a-,-b)-P_c(a+b)+P_c(-a,-b)=\cos\theta_a\cos\theta_b\] \[\langle ab\rangle=P_q(+a,+b)-P_q(a-,-b)-P_q(a+b)+P_q(-a,-b)=\sin\theta_a \sin\theta_b] sin 2\xi\cos(\phi_a+\phi_b=2\eta)\]

If I recall he applied this to his cellular autonoma model but its been a while since I studied cellular autonoma

I fully agree with the above its literally the same as I have come to understand what is involved in entanglement and the nature of the correlation function Though when you get right down to it QM is entirely probabilistic

lol you have no idea how often I have stated this detail.

lmao well if you think about it the Greens correlations is a good example with regards to creation and annihilation operators however I think you should instead refer to this for starters https://en.wikipedia.org/wiki/Correlation_function note the specifications of autocorrelation https://en.wikipedia.org/wiki/Autocorrelation

The correlation function is determined at the preparedness of the entangled states and the experimental apparatus. Before I go further you do know how a correlation function applies is statistical math correct. ? Any two variables can be tested for a correlation those two variables can be 100% unrelated to the other. It could be the number of accidents in Japan vs population growth in the US if one value increases and so does the other then you a positive correlation. If one goes down while the other up then a negative correlation if one value changes while the other randomly goes up and down them no correlation. Regardless of the correlation results no communication hidden variable or cause and effect or in this case shared causality need exist. Here is a simple two possible analogy take a bag of apples and a bag of oranges. You have a statistical chance of getting either oranges or apples. Alice opens her bag she has determined she has apples the probability becomes zero as she determined the physical state (apples) Bob knowing Alice got apples will automatically know he has oranges. The states of what were in the bag were not changed to get the results. The same applies to particle entanglement measuring the (I will stress this the physical state) of one particle does not change the physical state of the other particle) the measurement only affects the probability states. Ignoring the quantum uncertainty when applied to observational interference for the moment

Well quite frankly I never liked any metaphysical interpretation but block has always been one I found lacking. Yes there is a fundamental difference on time to space.

Yes to all the above I really don't see where your coming from with this. You know as well as I do that temperature for example is part of the EM field a field itself requires space. I really don't see a purpose arguing validity of any form of state that does not involve space. If that state changes you obviously require time. Even if it doesn't can apply duration to that state

No I'm not your still applying space via a point in space for temperature that literally equates to my statement on measurement doesn't it? even if you define a space its still involves space. Interesting thought but I rather doubt the conclusion by A. Zee but would have to read the analysis myself to truly understanding where he is coming from.

Phase space equations applications to Bolztmann. \[q_i=ap_i\] commoving coordinate of particle as r^i. proper momenta as p_i \[P_i=\frac{m_a dx_i}{\sqrt{-ds^s}=(1-\psi}q_i\] particle density in canonical phase space distribution \[(f^a,P_j,\tau)\] \[dNa=f_a(r_i,P_j \tau)d^3 r_id^3P_j\] for every particle species and their polarizations (a) the energy momentum is given in the Newtonian gauge by the expression (first order) by \[T_{a\nu}^{\mu}=\int d^3 p_i \frac{p^\mu p_\nu}{p^0}f_a\] with \[p^0=-p^0=\sqrt{(q/a)^2+m_a^2}\] \[p^i=p_i=q_i/a\] obeys Boltzmann equation of the form \[\dot{f}+\dot{r}^i\frac{\partial f}{\partial r^i}+\dot{q}\frac{\partial f}{\partial q}+\frac{\partial f}{\partial \tau}_c\] Relativistic Wigner Function Approach to Neutrino Propagation in Matter. https://arxiv.org/pdf/hep-ph/9810347.pdf Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering https://arxiv.org/pdf/astro-ph/0310198.pdf

The question is more fundamental than that. its literally how can anything physically exist without taking up space. Physics describe physical processes and quantities

how do you have existence of any form without space?