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I beg to differ on this score the FLRW metric is a GR solution and in GR time has dimensionality of length via the Interval (ct). It is that relation that includes length contraction and time dilation. Whether or not its required depends on the spacetime geometry. The simple reason you only really need the spatial component is that observational evidence shows a flat spacetime geometry. That's not some arbitrary choice of the metric. That the findings of all observational evidence. We have very useful methods for seeking spacetime curvature terms at our disposal. One example is distortions curvature causes light paths to bend this leads to distortions. Those distortions are constantly looked for. They can also be useful such as boosting viewing distance by gravitational lensing. That's just one method of detecting spacetime curvature there are others. The point being the metric does factor in the time component simply by being a GR solution. It's simply not needed due to all observational evidence. As far as observer effects, we do indeed need to take those into consideration. The dipole anistrophy due to Earths motion through spacetime in relation to the object we are observing must be factored in. A clear example was the findings of the first Planck dataset that had a dipole anistrophy in its first dataset. That dataset didn't have the correct calibration. That led to all kinds of pop media and scrambling. The next dataset had eliminated that dipole as we then had a better understanding of Earths momentum. As well as other localized effects. There isn't any arbitrary choice made the FLRW metric is quite capable of dealing with curvature. It's simply not needed beyond the weak field limit. You really only need the Minkowsii metric for the weak field limit. In a flat curvature parallel beams will remain parallel. If you have positive curvature those beams will converge. They will diverge for negative curvature. The converging or diverging is detectable and quite apparent in spectography in particular....which makes hydrogen a particularly useful test for distortions in its spectrographic readings. In particular the 21 cm line. That is what spacetime geometry ddescribes. All major findings show miniscule at best curvature best fit of a global geometry is flat. So the FLRW metric follows GR in the appropriate manner described by GR for a flat geometry

Yes. FLRW spacetime is a “dust solution” - a universe homogeneously and isotropically filled with energy-momentum that interacts only gravitationally. The choice of coordinate system is arbitrary, it represents no physical assumption. You are basically just picking an observer on whose point of view you base your labelling. You can take the ordinary FLRW metric (usually written in what is called Gauss coordinates) and just perform a valid coordinate transformation to arrive at a different point of view; this can be done directly, and has nothing to do with the field equations or the physics. For example, you could choose an observer that is accelerated at all times - you would get a metric that at first glance looks very different, but still describes the same spacetime. As I said, the choice of coordinates is arbitrary. For example, if you were to base your coordinate system on a clock that is not comoving with the cosmological medium (eg one that is accelerated at all times, possibly non-uniformly), you would get a metric where both the time and space parts explicitly depend on the t-coordinate. So long as the coordinate transformation is a valid diffeomorphism, this is perfectly allowed, though probably an algebraic nightmare to actually work with. It’s important again to realise that this describes the same spacetime, just in terms of different coordinates. What is not possible though is to try and have only the time part expand - there’s no valid transformation that yields this. See above - you could “distribute” the expansion across both time and space parts of the metric by a suitable coordinate transformation, which has no physical consequences. It’s the same spacetime, you’d just label events in it differently. The question is why you would want to do this - it would greatly complicate most calculations relevant to us, since such coordinates wouldn’t straightforwardly correspond to our own clocks and rulers. But of course you can do this, if you really wanted to.

It is wrong to assume that physical processes during acceleration are responsible for the time dilation. Time dilation is a geometrical rather than a physical effect. It is caused by the geometry of Minkowski spacetime. Let me describe the "twin's paradox" when nothing happens during an "acceleration". There is a clock located at 4 lh (light-hours) from Earth which is synchronized with the clock on Earth. Let's call this point in space, T. A ship moves with the speed 0.8c past the Earth. At the moment when a clock on the ship passes the clock on Earth, it is set to whatever is the time on Earth. Let's say, 10:00. The ship reaches the point T in 4/0.8=5 hours in the Earth time. The clock in T, which is synchronized with the clock on Earth, shows 10:00+5=15:00 when the clock on the ship passes it. However, the clock on the ship shows at this exact point in spacetime, i.e., as the two clocks are side-by-side, 10:00+3=13:00, because the time dilation factor for the speed of 0.8c is 0.6, and thus the trip to the point T takes 5*0.6=3 hours in the ship time. At the same exact point in spacetime, another ship passes the point T, going toward the Earth with the speed 0.8c. They grab the ship's clock and take it back to Earth. This trip back takes the same 5 hours in the Earth time and the same 3 hours in the ship time. So, when the clock returns to Earth, the clock on Earth shows 10:00+5+5=20:00, while the returned clock shows 10:00+3+3=16:00. Done.

But homogeneity and isotropy in the cosmological principle is an assumption of spatial distribution of energy momentum. Choosing time coordinates for a solution to EFE such as FLRW, is an assumption of temporal distribution. Isotropy of time would mean there is no preferred direction of time, but all our observations of time show it does have a preferred direction - time goes forwards. Observationally, the universe is temporally anisotropic. Homogeneity of time would mean there is no preferred moment in time. The universe looks different at different coordinates in time - it was pure plasma very early on, and now it isn't. Similarly, observationally, the universe is temporally inhomogeneous. Right, but FLRW is a particular solution that inherently forbids temporal expansion because of the choice of coordinates. Therefore it cannot be used to justify why all expansion is spatial. My position is NOT that the universe is NOT expanding. My position is why all the expansion is attributed to spatial expansion and not temporal expansion. I suspect all the other evidence that supports metric expansion does not directly refute temporal expansion. Cosmological redshift does not refute temporal expansion. But if we use the same FLRW solution to interpret the evidence, then our conclusion will be constrained to the assumptions of the solution we chose. It is the solution that assumes all expansion is spatial, not the evidence. I am really interested in distance measures in cosmology. In particular the margins of error, models and assumptions when interpreting observations. But will ask those questions another day. This is piqued my interest. No transformation that allows time to expand and not space. Why does expansion have to be at least in part spatial? Why can expansion have no temporal component? What does this physically mean?

A few things from above, the Krebs cycle does not provide energy, one of its functions is to generate reducing equivalents. Likewise, the cycle also does not consume or require oxygen. In aerobic organism oxygen is used as terminal electron acceptor. By coupling this redox reaction to an electron transport chain, proton pumps are are used to create a proton gradient, and that is ultimately used to generate energy (via an ATP synthetase). Anaerobic bacteria use alternative electron acceptors, to do pretty much the same. As others have noted, this is not what is happening here. While glycolysis can happen and generate energy, the interesting bit about hydrogenosomes is another process, which is highlighted in the posted figure. ATP is generated via a multi-step process, which looks like a reversal of acetate activation (which then would go into TCA), but requires ferredoxin shuttle at which H2 is formed.

You may be looking for: from the equivalence principle, clocks at the tip and base of an accelerating rocket will measure different times.

Sorry ,didn't see your post. Well I had been thinking about the twins but I was interested generally in an accelersted system ,biological or mechanical. I was thinking how ,in a rocket that was accelerating a beam of light would ,to a person on board to bend. And so it seemed to me that ,since all(I think) interactions between objects inside the rocket would depend upon the em forces then those forces would similarly be bent. So I was wondering if the distortion of the em field inside the accelerating rocket might be responsible for time slowing as compared to the unaccelerated frame of reference of the stay at home twin (not on Earth but somewhere really unaccelerated like ,as per your example in the ISS as a close approximation) If light is curved in an accelerated frame would that have a bearing on the way that objects inside that accelerated frame interact with each other? If they interact less with each other that would mean that they (ie the system as a whole)age less,mightn't it? Am I wrong to see a connection between em radiation and the forces that cause interactions between objects(it would hardly be the first time I have been wrong in our discussions!)

https://en.wikipedia.org/wiki/Floquet_theory for A(x) aka Floquet coordinates https://personal.math.ubc.ca/~ward/teaching/m605/every2_floquet1.pdf https://www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch2/floquet.html

It is the equation. a(t) = V(t)/s(t)^2 or miles/hours^2 aka mph^2 Position=S(t)->(distance over time) Velocity=v(t)->s(t)/time Acceleration=a(t)->v(t)/S(t)->distance/time^2 Time squared, yes it is covering the same distance over more time. Hence the outside world is experiencing a greater passage of time. Whether or not the observer is experiencing more time as well is a matter of debate. We really can't go fast enough to tell.

Where are the Arcturians from or are they from Antares star system

Accelerator physics Frenet-Serret Frame/coordinates Hamilton form reference reference 1) https://arxiv.org/pdf/1502.03238 reference 2) Particle accelerator Physics by Helmut Weidemann third edition particle trajectory r(z)=ro(z)+δr(z) define 3 vectors as ux(z) unit vector ⊥ to trajectory uz(Z)=dro(z)dz unit vector || to beam trajectory uy(z)=uz(z)+ux(z) "to form an orthogonal coordinate system moving along the trajectory with a reference particle at r0(z) . In beam dynamics we identify the plane defined by vectorsux and uz(z ) as the horizontal plane and the plane orthogonal to it as the vertical plane, parallel to uy . Change in vectors are determined by curvatures " dUz(z)d(z)=kxUz(z) dUy(z)dz=kyUz(z) k_x and k_y are the curvatures in the horizontal and vertical plane. gives particle trajectory as \[r(x,y,z)=r_o(z)+x(z)U_x(z)+y(z)U_y(z)\] "where\( r_0(z)\) is the location of the coordinate system’s origin (reference particle) and (x,y) are the deviations of a particular particle from \(r0(z)\). The derivative with respect to z is then \[\frac{d}{dz}r(x,y,z)=\frac{dr_o}{dz}+xz\frac{dU_x(z)}{dz}+\frac{dU_y(z)}{dz}+\acute{x}(z)U_x(z)+\acute{y}(z)U_y(z)\] \[dr=U_xdx+U_ydy+U_zhdz\] \[h=1+k_{0x}x+k_{0y}y\] curvilinear coordinate beam dynamic Langrangian \[\mathcal{L}=-mc^2\sqrt{1-\frac{1}{c^2}(\dot{x}^2+\dot{y}^2+h^2\dot{z}^2)}+e(\dot{x}A_x+\dot{y}A_y+h\dot{z}A_z)=-e\phi\] reference 2) 1.8O and 1.81 see floquet coordinates below

Night

Thanks for your replies, it's over midnight here, so good night.

Lets put it this way. The SM model including QFT has been so successful that just like the Higgs boson. It was able to predict long before detection over 90 % of the standard model of particles. There is still open questions so it's not complete. However it is simply the best fit for predictability and observational evidence. The VeV is part of that for the Higgs. If it weren't for the VeV range prior to Higgs detection. CERN wouldn't have known what range to look for to calibrate it's detectors.

For to refine my concern or primary issue we know that VEV is the probabilistic energy amount needed for mass being established related to Higgs field mechanism. The concern is if this "working" "transition" "current" mainly is originating from the LHC collision kinetic energy. -Or not, if there are some other unknown contributing sources involved? This is, to my view a cosmological central issue, besides being a straight security issue. Maybe a bit "silly" concern, still the average layman may be wondering.

I was wondering the same thing, when I first heard of this I thought they were metabolizing hydrogen but it clearly states that molecular hydrogen is produced not used.

Yes I suppose that must be it. I was thinking of anaerobic bacteria that use alternative chemistry as fuel, like sulphate reducing or iron reducing bacteria.

Those are the units, but not the equation. Is there a point here?

Acceleration is velocity over time. Velocity is distance over time. So, acceleration is distance over time^2

There were Mössbauer experiments done with rotors - the emission/absorption moves out of resonance as you increase the rotation speed. citations 82-84 in https://en.m.wikipedia.org/wiki/Tests_of_general_relativity

It looks like the Higgs field consists of two entwined "parts" one- "mass" and one "electromagnetic" related which is shown from the SU(2) doublet statement. How is situation derived, I mean originally at the early/mid 20th century's indications of a mass establishing field? Is it a qualified assumption first theorized and later evolving to the "final" (mid 1960's) Higgs field and its mechanism. And finally in 2012 proven with the LHC success. How was this interesting "journey" started? I'm a bit embarrassed asking elementary issues, though it is cosmological crucial issue. (And I believe that my starting quest caught your attention, though being a bit confused.) Is the SM and the QFT always to be correct, we know about the cosmological constant problem?

The fact that you ignore my points make me feel you were just wasting time before also. Of course it is; it's in the thread title -why did Truman use the atomic bomb on Japan- The pChemical plant where I work makes and purifies liquid Phosphine. On a regular basis we may have up to 60 000 lbs of Phosphine at 700 psi, on site. That is considered a weapon of mass destruction, even by the FBI, who have been here to investigate our site after 9/11. What we consider weapons of mass destruction would have first been used in WW1, in the form of Chlorine and Phosgene gas attacks. It might also be relevant that certain battles of WW1, and even the Crimean war, regularly had 100 000 casualties; if not from munitions then from infections of wounds afterwards. even earlier when city states in Europe were besieged, flaming catapults may have killed half their inhabitants ( or plague-ridden rats, most of them ). In that historical context, would that have been considered use of WMDs? Or how about when Ghengis Kahn raided central Asian cities, killed most, enslaved the rest, and burned the city to the ground ? Does that make arrows and fire WMDs? If the taking of lives is immoral, Taking them to save economy and culture are also. I, and I'm sure many others ( even MSC ) don't consider taking the life of someone who is threatening the life of others, immoral. Fear is never a justification; an imminent threat is. There is a difference, and its usuaslly called self defense. Have I addressed all your points, or are you still wasting your time.

From what I understand they behave more like this:

This is how the "twins' paradox" is usually set up.

Clear[x, pnp] pnp = 2564855351 Show[ Plot[(( (((pnp^2/x) + x^2)) / x) /pnp), {x, 0, 60000}] Graph this equation. It is the inverse. It should make it easier to find the SemiPrime. It will decrease number of trails, but on small numbers will still be more time than brute force. It will however give you a graphical understanding of the smaller SemiPrime. Remember 2 unknowns should be impossible.