Mordred

! Moderator Note Moved this thread to classical physics, as the problem is classical in nature. The wing will snap where it's mounted while the wing will want to thrust upwards it would be unable to do so as the positive pressure below the wing is pushing downward on the toroidal containment wall which in turn will try to thrust downward in response while the wing attempts to thrust upward. It would be similar to placing a plate behind a fan. The fan would push down on the plate however the plate won't move as the fan is attached to it. As far as pressure differentials your specified a vacuum outside to toroidal wind tunnel so you wouldn't have a preferred direction for the positive pressure to flow to a lower pressure potential. The containment walls themself also prevent the positive pressure flow to reach a lower pressure potential. As there is no path you wouldn't get any thrust as a result of pressure differentials. A simple experiment to validate the above. Place a water hose with a gate valve on a scale. Measure the weight with the hose filled with water but not flowing. Then measure with flow. You won't see any difference. Edit butterfly valve not gate valve lol.

As a vector gauge boson under QFT gluond are required to be massless. Vector gauge bosons are typically offshell. Experiments show less than a few Mev if they have any mass at all. One way to think of it is vector bosons on Feymann diagram are internal wavy lines. Real particles are on the external lines. All vector bosons are off shell internal lines on the Feymann diagram as the field mediator.

@Genady by the way thanks I did enjoy watching the lecture. It's nice to get a good mental challenge with a physics subject once in a while.

Well that I agree with though our universe isn't static so we will always have fluxes of mass distribution as every body is is motion and tends to clump into LSS. Anyways we both agree the Shell theorem is accurate. Which is good in so far as the FLRW metric critical density formula applies the Shell theorem as its basis. Edit Granted the scenario in the infinite case amounts to an impossibility once you consider causality. The influence of gravity also being limited to c

Ok I had to go back one lecture towards the end of lecture one to get the breadth of his statement. If you sum the masses symmetrically then Newtons Shell theorem is accurate. However if you choose a different point q off centre of point P you can get any arbitrary answer. Which highlights to ordering of how you add the mass. In the first case. The order doesn't matter as it's commutative in the second case it's non commutative I wouldn't necessarily consider Newtons Shell theorem incorrect if the mass is added symmetrically it works in that case. However I can see his argument that the Poisson equations are more accurate in all cases. I'm not sure I fully buy his argument. If I rotate q at the same radius from p and continue to sum the concentric circles I should return to sum zero

Ok I was thinking he may have incorporated the stress energy momentum tensor which he does without referring to it directly in his inflationary lecture.

No it hasn't we count is as a possibility but physicists also realize a graviton as a mediator is not required when spacetime itself is sufficient.

I think you may be referring to negative and positive pressure influences in his inflationary lecture. Where negative pressure can induce repulsive gravity.

Try it, which side would you get a net force if the mass is evenly distributed surrounding any point you choose ? Aside from a net force of zero. I also don't believe Allen Guth claimed Newtons Shell theorem as being incorrect. More likely he added some detail or scenario. If you can find the link we can examine it. Are you familiar with the Principle of least action that equates potential and kinetic energy relations ? You seem to keep wanting particle to interaction for your mechanism however you don't require this. Potential energy being the energy due to location aka field or collection of fields energy. Kinetic energy being the particles momentum.

It also describes the mechanism all particles will choose the path of least action. You do not need gravitons to mediate spacetime. Spacetime curvature is the only mechanism you require which requires the mass term as mentioned even massless particles can contribute to curvature. Try this for a thought experiment take a uniform distribution of mass where every point has the same mass. Then apply Newtons Shell theorem using any random point as the designated centre of mass. In this case you would experience no gravity at any location. You need regions of non uniform mass distribution.

It's more accurate to think of gravity as spacetime curvature. In order to understand how mass affects spacetime curvature you need a few details. 1) Mass is resistance to inertia change or acceleration. 2) spacetime curvature doesn't describe a shape per se, it describes the geodesic paths that particles will follow. If two light beams stay parallel spacetime is flat. If they converge you have positive curvature. If they diverge you have negative curvature 3) All particles and their respective fields contribute to the mass term as well as the curvature. Higgs, EM, strong and weak force included. Subjective to their respective range for each force. An everyday example that may help understand the above. A electronic conductor sending signals past an EM field may experience signal propagation delay as a result of its orientation to that field. This phenomena has remarkable similarities to how spacetime curvature affects other particles and their interactions. Also helps better understand time dilation.

Afiak which is extensive with regards to BBN and inflation all pieces of evidence for inflation are indirect in so far as predicting the correct metalicity with regards to the CMB. Hydrogen, lithium, deuterium etc. We simply cannot see far enough due to the dark ages prior to recombination

That's not quite correct the FLRW metric isn't used for the lumpiness. It is used to model the evolution history of the entire observable universe in accordance to GR and the thermodynamic ideal gas laws. The metric itself doesn't work well for non uniform distribution it is however well suited for a homogeneous and isotropic energy/mass distribution (uniform). The primary purpose of the FLRW metric is to describe how the universe expands or contracts in accordance with the above. Though it also can be used for a few other details such as the blackbody temperature history . This is the inverse of the scale factor "a" of that metric. The math I posted earlier is mostly the FLRW metric with a bit of GR and the Euler Langrangian. That demonstrates that the three methodologies are compatible with each other.

The two main energy categories used in the Langrangian including Noether is potential energy and kinetic energy. This covers mechanical and quantum energy types. Keep in mind naming energy types is simply convenient labels. The most convenient and near universal labels one can apply being the two I just named as they are used in the Lanqrangians of every gauge group of the Standard model as well as the Langrangian forms describing spacetime. This may help if we were to model the universe using the FLRW metric we tend to set the universe as a perfect fluid with adiabatic expansion. With those settings we further assume a closed system where energy is conserved. FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] The following setting describes the energy conservation statement \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] Now prior to electroweak symmetry breaking everything is in thermal equilibrium so we can describe this period as a scalar field. As I already have the workup for Higgs inflation handy from another thread I will add it here as an example. The subsequent equation does in fact work the same for chaotic inflation so its essentially identical though the derivatives to arrive to the equation of state does vary slightly. Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] This last equation is the equation of state for a scalar field for both Higgs inflation as well as chaotic inflation. The result gives w=-1 most of us are familiar with. With w=-1 this tells us Lambda (DE) is constant. In thermodynamics it also represents an incompressable fluid. If we're dealing with quintessence then we would have a value greater or lesser than w=-1. In this case DE would vary over time. Anyways what the above shows us is that in cosmology we model our universe under the following assumptions. A perfect fluid with adiabatic and isentropic process where the system is closed (causality via the speed limit of information exchange c further ensures this.) With the further assumption that due to being a closed system we can apply energy conversation. Any conserved quantity must be in a closed system that's one of the golden rules when it comes to any conservation law

That doesn't work sorry to say if a volume changes but the total energy remains constant then accordingly the energy density decreases. The only way energy density would remain constant is if energy is added to the system as the volume increases

I believe you mean total energy remains the same. As the volume increases the energy density would as well. However consider this detail. Does total energy remain the same if the cosmological constant is constant? Indeed the energy gets incredibly high along with the temperature which will correspond to the inverse of the scale factor. As to whether the conservation of mass energy applies to the universe as a whole. Well there are arguments in both corners. If your curious here is a useful formula to calculate the Hubble parameter at a given cosmological redshift \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] Here is an example argument stating why energy conservation wouldn't apply https://bigthink.com/starts-with-a-bang/expanding-universe-conserve-energy/ However one can easily find counter arguments that energy conservation does apply. For example I've read a recent paper from Allen Guth that it does apply. Needless to say its still debatable

Fair enough, one often sees different claims of our universe being in a BH or WH. The aforementioned difficulty in having a homogeneous and isotropic universe is one piece of evidence against the possibility.

More food for thought the majority of BHs rotate. So how does one arrive at a homogeneous and isotropic universe that resides in a rotating BH ? Even if the BH isn't rotating having a homogeneous and isotropic universe would be difficult.

Your welcome, a couple of Your welcome numerous articles will often state that one can use the critical density formula to calculate the energy density of Lambda. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] Which if you use the Hubble parameter value today will give an energy density of roughly \[6.0*10^{-10} joules/m^3\] However there is an interesting side note. The Hubble parameter is higher in the past than today hence I rarely call it Hubble constant. Now if this formula is used to calculate the energy density of Lambda this would then imply a far higher energy density at the pre-inflation period just after the initial moment of the BB. If this is true then it is the equation of state for Lambda that is constant and not the energy density itself. This is something I have been thinking about for some time. As I question whether the critical density formula is a valid method to calculate the critical density of Lambda. It may simply be accurate only during the Lambda dominant epoch we are currently in as a rough calculation for Lambda energy density. If one examines how the critical density formula is derived its derivative arises using matter with the corresponding equation of state. Originally its use was to define the point where the universe would switch from expansion to contraction. Which is another reason I question its validity with regards to Lambda. The main point however is that we cannot directly measure the energy density of the vacuum we can only infer its energy density from its influence.

As Phi for All mentioned is that we honestly cannot accurately define any region of spacetime as absolute nothing. For example under QM the minimum energy due to quantum fluctuations is \[E=\frac{1}{2}\hbar w\] This is referred to as zero point energy ZPE for short https://en.m.wikipedia.org/wiki/Zero-point_energy

How do you have a field excitation without a field ? One can describe any geometry as a field. Let's take an example let's toy model a hypothetical universe one that is critically flat. As spacetime is a field theory by all definitions. In this case one would measure zero curvature at all locations. The only source of uncertainty in this example would be systematic measurement errors. We quantize the amount of performed all the time. Energy is defined as the ability to perform work. Any time a force is exerted work has been done.

Your welcome you will find that this will help understand a large range of physics related topics. Examples being particle creation/annihilation virtual, real and quasi. Gravity aka spacetime curvature. (Apply Newtons Shell theorem) in essence it's an identical phenomenal. Aharom Bohm effect just to name a few related examples Quite accurate

Here is food for thought under the aforementioned QFT. What we of as particles are essentially localized field excitations. The fields themselves pervade all of spacetime. This makes sense as a field is a set of values at every geometric location even if the value is zero. So at any point in our universe is there anything we can honestly term as nothing ? Now energy is simply the ability to perform work. In essence it is simply a property much like mass being the property of resistance to inertia change or acceleration. Now ask yourself this question. If you have a perfectly uniform field where every point has precisely the same value. Are you able to measure the amount of energy at any point ? It would be much like trying to measure voltage on two points on the same conducting wire. You would read zero volts as you have no potential differences between the two points. When you think about it energy of a field results from non uniformity. Aka quantum fluctuations. Those fluctuations affect each other in constructive and destructive interference. The zero energy universe model aka universe from nothing in essence details this. You take this one step further. If every object was moving at the same direction and at the same velocity. Then you would believe every object is stationary (aka one of the statements involving relativity).

The Cosmological principle is still fully valid. Nothing I have heard or read with regards to the James Webb data counters that AFIAK. Everything I stated with regards to this thread still stands

just an fyi one under development though its been around awhile for gravity is quantum geometrodynamics. It like any quantum gravity theory is still not renormalizable