TheVat

This is sort of clear, but the measurements by the proton-man are still frame dependent. In his one nanosecond, he travels farther in the star interior which is Lorenz contracted. And temperature is a measure of average kinetic energy. Something seems off, but...as @iNow observes I am afflicted with human fallibility. 😀 Great thread, btw, as many of yours are.

You don't have a proof there. Sounds like the Einstein proof was based on the fact that a right triangle can be decomposed into two similar triangles that are similar to the original. This was well known before Einstein, but he like many smart pupils reinvented it. You extract an equation with fA2 and fB2 and fC2 which i will leave as an exercise...

Hannah Arendt nailed it with her phrase the banality of evil.

It would help (both us and yourself) to label each vertice. Also, think on what the most basic meaning of c squared is, geometrically. Now look at your original hypotenuse. Start with this maybe....

Of course, and I corrected in my subsequent post. I actually meant to say the correct way, I was typing all this distracted and couldn't use the edit in time. If you read my two later posts hopefully it is clear that I understand the reciprocal nature of observations from the FoRs. We had a wildfire nearby, so I'm checking other posts to see if other errors happened. Sorry for confusion.

Okay, then the significant observation is the proton watching the center of dwarf approach at (I checked) .996 c. Using Lorentz, γ = √(1 - v²/c²) the dwarf is now seen by proton as a pancake that is shortened to .089 its rest frame diameter. The proton finds its path is less than a tenth the distance of a rest frame. And all clock-like functions in the dwarf are perceived as slower, happening at 8.93 percent of the dwarf's proper time. The proton is essentially free-falling as it moves in, so would GR be significant? I mean it is already at 99.6 c, so how much would the gravity pull of the star accelerate it?

Then we have something like the muon paradox, don't we? To the muon, time is moving slower on Earth as the Earth speeds towards it at near-c, while to the Earth observers the muon's clock is slower and so it is not decaying as fast as expected. So the cosmic ray observes the WD as speeding towards it near-c, and the WD aging more slowly, therefore cooling more slowly. But the rest frame of the observer sees the CR/muon as aging more slowly. So you can't really reconcile those observations. And, afterthought, there is an almost instantaneous velocity change, because of the vector reversal for the CR muon. One nanosecond, the white dwarf is approaching the muon, but the next it is receding. And there is also a Doppler effect on the WD spectrum that the muon can observe. (edit: I should use proton CR because it will last longer than a muon, right?) So, back to your OP question: the perspective that matters is the muon, which will see the star cooling more slowly due to its relative velocity. To an earth observer, which shares a rest frame with the dwarf, the dwarf will be cooling normally because they (observer and star) are co-moving. Is the instantaneous velocity change important here? Also, would a proton make it through the packed neutrons core of a WD? Would it lose a lot of its velocity if it did?

Well, the cosmic ray's clock is moving more slowly relative to an observer on, say, a nearby planet or space station. So if the ray were passing through an object of negligible mass, then it would observe that's object's clocks as moving faster, therefore cooling faster. But that white dwarf's mass is not negligible, so its clock is also moving slower to an observer on the nearby planet. (even on Earth, with it's small mass, the center of the Earth has aged 2.5 years less than its surface) So it would depend on the competing effects of gravitational time dilation and relative velocity time dilation. Generally, given that cosmic rays (like protons) move very close to c, I would think that would be the stronger effect and the proton would "see" the star as cooling faster.

Yes. I was amused by the wide range of responses to the rooster from different family members (and cats). Also the philosophic thoughts on eating a pet v turning it over to strangers.

Thanks. You probably cited it in a related thread and I missed that. I will borrow it from a nearby college.

Am trying to search what MTW is. Can't see from the page screenshots. A Google search found Mathematics Their Way, but that is a text for K-2, so probably not. A citation would be helpful for some who are following this thread.

Video about living with a rooster... ...in a Mumbai apartment https://www.theatlantic.com/video/index/582871/tungrus/?utm_source=atl&utm_medium=email&utm_campaign=share

Not even wrong.

There is decomposition of a manifold by triangulation. That works on a 3-manifold, but not always on a 4. And there are fractal manifolds, which I don't know much about. Maybe not workable given the boundary of a Mandelbrot set. If the boundary of a manifold is one dimension lower, then....hmm. There is also handle decomposition, which takes balls. Sorry.

A mathematician named Klein Thought the Möbius band was divine. Said he: If you glue The edges of two, You'll get a weird bottle like mine.

Perhaps our recent new Norwegian-speaking member could shed some light on this? And why it took two weeks to react this way. @grayson Perhaps they are pining for the fjords?

Ok, that helps. Thanks.

Is that certain? Why is it not just as valid to have a model in which space does not expand and objects simply move apart under the influence of their mutual gravity and dark energy repulsion? In that case, nothing emerges at large scale, it just becomes easier to observe because you don't have local energy densities obscuring it.

I guess I was trying to ask, with my limited physics, if it could be an intrinsic property at the smaller scale which is just masked by the gravitational attraction of local inhomogeneous clumps so it's only noticeable at the largest scale. Maybe it doesn't make sense outside of QFT? Can zero point energy be the cosmological constant?

A boy stood on the burning decks, mumbling a crust of clotted flecks, an oesophagus lofted to fungible heights, expels a conundrum in bright purple tights, a brother now fits in a microwave dish, though adding galoshes makes it a squish.

I was thinking of dark energy theory, where expansion and vacuum energy are related. As in this... https://www.cambridge.org/core/journals/journal-of-plasma-physics/article/abs/dark-energy-and-dark-matter-as-due-to-zero-point-energy/DFAC4A98338A39DDFD72DA85A6B09F06 An attempt is made to explain dark energy and dark matter of the expanding universe in terms of the zero point vacuum energy. This analysis is mainly limited to later stages of an observable nearly flat universe. It is based on a revised formulation of the spectral distribution of the zero point energy, for an ensemble in a defined statistical equilibrium having finite total energy density. The steady and dynamic states are studied for a spherical cloud of zero point energy photons. The ‘antigravitational’ force due to its pressure gradient then represents dark energy, and its gravitational force due to the energy density represents dark matter. Four fundamental results come out of the theory. First, the lack of emitted radiation becomes reconcilable with the concepts of dark energy and dark matter. Second, the crucial coincidence problem of equal orders of magnitude of mass density and vacuum energy density cannot be explained by the cosmological constant, but is resolved by the present variable concepts, which originate from the same photon gas balance. Third, the present approach becomes reconcilable with cosmical dimensions and with the radius of the observable universe. Fourth, the deduced acceleration of the expansion agrees with the observed one. In addition, mass polarity of a generalized gravitation law for matter and antimatter is proposed as a source of dark flow.

Good question. How would a vacuum energy model of expansion work with emergentism? Though near objects are gravitationally bound, a vacuum energy still weakly repels and so all objects are slightly larger than they would be. Then expansion would be intrinsic? So not emergent?

Haha. When there is a discussion of absurdity, it is hard not to mention Monty Python. That phrase is almost a shibboleth for Python fans.

Haha! A little embarrassed to admit how much fun I had with this webpage... https://www.omniglot.com/language/phrases/hovercraft.htm

Oh, right, Google wouldn't recognize a lot of creole languages. Owat eyfule amei = Oh what a fool am I. And here is a phrase in Morse Code.... -- -.-- / .... --- ...- . .-. -.-. .-. .- ..-. - / .. ... / ..-. ..- .-.. .-.. / --- ..-. / . . .-.. ... Cheers.