Mordred

Using what I mentioned above and the graph A of the article posted by Studiot. on the Y axis assign \(\sigma^\ast\) excited quantum state of an atom. The Y axis on the graph assign \(\phi(E)\) on the x axis E. The vertical center line of the amplitude peak assign \(E_R\) for peak energy of the amplitude. The width of the amplitude 2/3 up determines the the lifetime of the resonance. Resonance is used for all particles under Breit-Wigner. further details here. ( a simplified treatment for ease of understanding ) https://web2.ph.utexas.edu/~vadim/Classes/2019f/resonances.pdf a cross section being the entire graph rather than the localized highest peak resonance. In terms of sound this would apply to the phonon. (keep in mind by the statement extremely simplified even though the later parts gets complex a full cross section of an interaction would look like below (as I already have this in latex in another thread my Nucleosynthesis thread) I will simply copy and paste from there. It includes further details on Breit Wigner Breit Wigner cross section \[\sigma(E)=\frac{2J+1}{2s_1+1)(2S_2+1)}\frac{4\pi}{k^2}[\frac{\Gamma^2/4}{(E-E_0)^2+\Gamma/4)}]B_{in}B_{out}\] E=c.m energy, J is spin of resonance, (2S_1+1)(2s_2+1) is the #of polarization states of the two incident particles, the c.m., initial momentum k E_0 is the energy c.m. at resonance, \Gamma is full width at half max amplitude, B_[in} B_{out] are the initial and final state for narrow resonance the [] can be replaced by \[\pi\Gamma\delta(E-E_0)^2/2\] The production of point-like, spin-1/2 fermions in e+e− annihilation through a virtual photon at c.m. \[e^+,e^-\longrightarrow\gamma^\ast\longrightarrow f\bar{f}\] \[\frac{d\sigma}{d\Omega}=N_c{\alpha^2}{4S}\beta[1+\cos^2\theta+(1-\beta^2)\sin^2\theta]Q^2_f\] where \[\beta=v/c\] c/m frame scattering angle \[\theta\] fermion charge \[Q_f\] if factor [N_c=1=charged leptons if N_c=3 for quarks. if v=c then (ultrarelativistic particles) \[\sigma=N_cQ^2_f\frac{4\pi\alpha^2}{3s}=N_cQ^2_f\frac{86.8 nb}{s (GeV^2)}\] 2 pair quark to 2 pair quark \[\frac{d\sigma}{d\Omega}(q\bar{q}\rightarrow \acute{q}\acute{\bar{q}})=\frac{\alpha^2_s}{9s}\frac{t^2+u^2}{s^2}\] cross pair symmetry gives \[\frac{d\sigma}{d\Omega}(q\bar{q}\rightarrow \acute{q}\acute{\bar{q}})=\frac{\alpha^2_s}{9s}\frac{t^2+u^2}{t^2}\]

It may be best to add some important details as it goes beyond the good example provided by Swansont. As dealing with this gets lengthy I will include an article to supply the details behind eugenstates which has no uncertainty. The article opens with the following key statement. "As we know, observables are associated to Hermitian operators. Given one such operator A we can use it to measure some property of the physical system, as represented by a state Ψ. If the state is in an eigenstate of the operator A, we have no uncertainty in the value of the observable, which coincides with the eigenvalue corresponding to the eigenstate. We only have uncertainty in the value of the observable if the physical state is not an eigenstate of A, but rather a superposition of various eigenstates with different eigenvalues. https://ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/005979fa741c3ea2e0430456b70caf93_MIT8_05F13_Chap_05.pdf In essence eugenstates has no uncertainty however this gets into the measurement axiom of QM. Where the act of measurement produces a state however any further measurement will produce a new state. Better described below https://www.britannica.com/science/quantum-mechanics-physics/Axiomatic-approach For the OP this deals specifically with "observation" measurement where the superposition of state's is lost due to observation. However I will leave that to a mental exercise with the article Studiot posted. Side note graph A is a delta function that is localizable you can readily determine the boundaries from graph a. Whereas a sine wave is not localizable. In terms of a particle the mean lifetime can be determined by graph a) using Breit Wigner distributions. The outside amplitudes not the primary amplitude would be considered resonance however as the width is equal or greater than the amplitude would not be considered a resonant particle. (Just a little side note and taking advantage of the graph provided by Studiot.

Any Fourier transformation will inherently have uncertainty in position, momentum and time +1 for mentioning that Cross posted with Swansont. Here is a decent article involving Fourier transform uncertainty http://math.uchicago.edu/~may/REU2021/REUPapers/Dubey.pdf

Fairly common on forums particularly those that allow Speculation. You see the same thing of FB as well.

How about simply thinking of observer effect as any measurement ? That is how QM describes observer effect.

I seem to to recall that so your likely right on that.

After running into the problem numerous times of my latex getting changed to rich text format. I noticed a couple of repeatable and consistent causes. For example if you have latex in your post and try to insert an image or hyperlink to another website this will more often than not cause the latex instructions to drop and the post entirety seems from my end to switch the post to RTF. Do not know if this is repairable but I mention it for everyone's awareness. (010) The last switch occurred simply due to thread merge. The latex was placed in a separate post but the merge operation switched it to rtf. This was what I had actually typed minus the latex command brackets. (010) Lol that activated without \[ command brackets on merge. Both lines were using pmatrix latex format.

One idea I was considering suggesting is simply dropping negative rep points but keep the positive side. The negative rep tends to get a members hackles up which rather defeats the intent behind the rep system being a recognition for good post quality.

Hence the usage of supercomputers like Illustrus Millenium simulation which when they zoom in produced each galaxy type. https://wwwmpa.mpa-garching.mpg.de/galform/virgo/millennium/ Even the NFW profile though requires using a PC as its formula is a power law though in that case one can factor that into a natural log function in the same manner as the scale factor for the FLRW metric.

I was thinking more in lines of bulging occurring during cooling but that would require an early tidal locking prior to completely cooling. However I agree with the rest we have to see if the OP returns or not but still a good topic discussion

Yeah one of the hassles of how to describe something outside of the math lol. Leave that one for the metaphysics arguments give them something useful lol

Sounds like what's being described is the CNN blackbody temperature decrease due to expansion which means the mean average kinetic energy is reduced due to reduction in number density of neutrinos. That makes sense now the current CNB temperature from calculation is 1.97 Kelvin however in the past much higher. Yes even with 3 generations of sterile neutrinos to replace DM you would need more than the baryonic particles. As you recall there is more DM than baryonic matter. That's the essential clincher against a sterile neutrino solution. One can show sterile neutrinos has a good match in mean lifetime and weakly interactive with the non relativistic (cold) characteristics. It's the sheer number required that's the main issue.

Actually redshift applies to all particles but I understand your referring to photons being the meansof how we measure an objects redshift. Yes neutrinos does have a high momentum term however due to its weak interactions any scattering collisions is greatly reduced. Were both trying to get DanP to clarify to which class of observer. Ie applying the four momentum but recognizing observer effects to the particles four momentum term.

The FLRW metric is often described using the symbol \(\chi\). It occurred to me that many of our viewers would not recognize this angle. The metric can be expressed as a 3d hypersphere for its spatial part \[dl^2=R^2(d\chi^2+sin^2\chi d\phi^2\] the 3d hyper sphere is an embedding in 4d space using (x,y,z,w) in the following manner below For some reason trying to insert images messes up latex instructions in the above but in this case its still readable. anyways the above is from the following reference https://jila.colorado.edu/~ajsh/astr3740_14/flrw.pdf see section 10.1 I am considering adding this diagram to the pinned threads above for easy reference. Thoughts ?

Forgot to add the velocity equation \[v(t)=\frac{\dot{a}(t)}{a(t)}d(t)=H(t)d(t)=H_0d(t)\]

Velocity in cosmology via the FLRW metric is to a commoving observer which in essence is tying that observer to the scale factor a(t) for proper velocity as opposed to peculiar velocity such as from an observer on Earth measuring the cosmological event horizon which is based on Hubbles law v=HD. Hope that helps.

R2D2 8 track cassette player. https://www.ebay.ca/itm/264286734720 Though the one I owned being much earlier

Yes research agrees with this Maria if I recall is due to asteroid collisions evident of its impact characteristics however those impacts could be the result of debris returning home as you put it. If I recall the studies also show that the lunar crust is thinner on one side than the other which if I recall it's thicker on the Maria side. You might want to look into that detail as it's a piece of evidence in regards to which side struck the Earth. Edit forgot to add tidal locking isn't a result of impacts but a result of gravitational influence between the moon and Earth. All orbiting bodies gradually become tidal locked unless they are gaining momentum via other influences such as impacts. This statement is incorrect see above.

I'm not the one giving negative rep points. I never do regardless of what I think of the post quality or of the posters attitude. I found that pointless long ago. I only hand out positive rep points. Never negative. Does nothing to alter my view of a posters mannerism or post quality. So take the advise or not. Matters not to me. However one of the rules you agreed to for membership is civility. Too many uncivil posts will eventually lead to account banning but that's your choice. Makes no difference to me

As expansion allows electroweak symmetry breaking to occur in that manner it's accurate that includes cosmological redshift however one must also recognize that cosmological redshift affects how we measure the kinetic energy in the same manner as it effects how we measure its mass term. However the particle itself has an invariant mass and kinetic energy term (momentum) which defines the particle. (If either changes its no longer the same particle type) One must take into account observer effects as per GR when measuring either quantity. So it's likely Swansont was describing observer effects due to expansion

Your welcome reputation points are always an indication of post quality. Usually one receives positive votes by stating something informative and well mannered.

That's fine I recall the reply GR can be applied to MOND even though MOND modifies f=ma. The change simply needs to carry over when you run calculations using GR. In essence it's own class of GR solution. For the record I would not be surprised if there isn't a paper out on how to use GR with MOND. Rather in this case I would expect there would be.

Yeah I'm sure that's what it is. The manner of your posts couldn't possibly have anything to do with it. Yes that's sarcasm Maybe improving the quality of your posts and less attitude might actually solve the problem?

No expansion doesn't affect a particles momentum terms. The relic neutrinos need to be slow (cold/non relativistic) to begin with. Edit rather slow once they acquire mass from electroweak symmetry breaking.

Could be I was hoping for something more profound or a stronger argument. However that's your choice of course. There's nothing new to relying on how we interpret our senses.