Halc

That was sort of my thinking at the OP, but I wasn't sure. Energy is conserved, so where does it go? The 'expansion' doesn't seem like a form of energy that can receive it. Maybe all the slowing down stuff powers the dark energy, translated into acceleration of expansion. Energy is conserved in an inertial frame, but not from one frame to another, so the rock has no kinetic energy in the frame in which it is stationary, but has KE in the frame of Earth from which it was launched. Relative to the curved FLRW frame (also known as cosmological or comoving frame), the rock has been imparted with a sort of absolute KE which is derived from its peculiar velocity. The reply from @swansont thus made some sense in that light. KE relative to an inertial frame makes sense only for a local object. What's the KE of some star receding from us at 2.3c?* It isn't computable, but its KE based on its peculiar velocity does make sense. This is why I was willing to accept that answer, even though it wasn't my initial guess. *recession velocities are not measured in units that add relativistically, but rather add linearly, per the FLRW frame, so 2.3c doesn't have the usual meaning when computing something like KE. Good argument, but I've heard that the photon doesn't lose energy since relative to Earth it was always red-shifted to its observed measurement,. But as I said, 'relative to Earth' loses meaning over these sorts of distances. The universe isn't Minkowskian. The photon definitely does lose energy in the FLRW frame. Its peculiar velocity must be c, so its peculiar energy (is there such a term??) must be lost to something in that frame. That or the curved frame does not have the property of conservation of energy. How do the absolutists (which typically select this frame as the absolute one) deal with that? Violation of thermodynamic law has sunk an awful lot of theories. I'm not going to disagree, but I'm getting conflicting answers. Is there an article or other page somewhere that discusses this? I didn't know how to frame a search on stack exchange. Anyway, you seem to address one question in the OP: "Two such ballistic objects are ejected, one at .9999c and the other at .999999c. Is there a major difference in when the two get here? " Apparently the number of 9's makes a significant difference. The speed is nearly identical, but the energy/mass is not. That's good, since it would be harder to swallow a view where the rock lost proper mass along the way, fading to dust... Why not? A neutrino seems to be a very small and typically fast rock. It has proper mass. It has an inertial frame in which it is stationary, all just like the rock. The photon has none of this. That would seem to need more justification than just an assertion. I thought it was a valid point, and cannot easily think my way around it, especially when it is expressed as 'peculiar energy' as I put it.

Well, that's my question. I'm not asserting anything here. Suppose I launch a rock at half light speed. The proper distance between it and some object 7 GLY away is constant, making it sort of stationary relative to it in a way. But over time, the Hubble 'constant' goes down, and that distant object is no longer stationary relative to our rock, so the rock starts gaining on it. Given that logic, perhaps it will not only eventually get there, but it will pass by it half light speed. That would imply that expansion has no effect on peculiar velocity over time. If so, then our neutrino gets here pretty much the same time as the light. Not sure if that logic holds water.

I know that, but that supernova occurred barely outside our galaxy, hardly enough distance for cosmic expansion to play a role. I'm asking about a hypothetical event 5 orders of magnitude further away than that, from a source with a recession speed greater than c.

I am trying to figure out ballistic trajectories over cosmological distances. All the literature seems to speak only of light, and shows worldlines only of comoving objects, not objects with motion relative to the comoving frame. So suppose some early galaxy exists 1.7 billion years after the big bang, 12 billion years ago. Some star emits light and neutrinos at that event. The light gets here today, so the galaxy at the time was something on the order of 4.7 GLY away (proper distance measured along line of constant cosmic time) from here (the place where our solar system will eventually be). Due to expansion, the star is increasing its proper distance from us at something like 2.5c at the time, although the same galaxy is currently receding at more like 2.1c today. My question is about the neutrino, which is not light, but rather a simplistic ballistic object. It is moving at nearly light speed relative to the star that emitted it. Does it get here? When? If it doesn't get here close to today, how far does it get in the 12 billion years (cosmic time)? I don't know how to apply expansion of space into an integration of its movement, and special relativity is not help whatsoever. The light is easy because it always moves locally at c. Both light and neutrino increase their proper distance from 'here' at first since they're both well beyond the Hubble distance at the time but still well inside the particle horizon. Does the speed matter? Two such ballistic objects are ejected, one at .9999c and the other at .999999c. Is there a major difference in when the two get here? The neutrino has a lot of 9's.

Closest approach (about 16 au) is still well outside the Roche limit of Sgr-A (about 1/30th that distance). So imagine the speed of an object getting that close. Just outside that limit, I imagine a passing star would still get pretty torn up.

Neither view posits a special role for humans. You're thinking the Wigner interpretation which has a special role for humans, but even Wigner backed off support for it since it can be shown to lead to solipsism. If humans (or biological consciousness) are necessary, then the universe never collapsed into say the existence of Earth until humans came along to do the first measurement. Kind of a chicken/egg problem there.

Out of curiosity, why? What possible evidence do you have against it? Or is this just a statement of your lack of warm fuzzies for the view? This statement presumes that there is one 'the Buddha' that experiences one of the worlds and not any of the others. This is not what MWI is all about. That would be a supernatural philosophy, otherwise known as religion. Wrong forum to discuss that. Under MWI, all versions of a person are self-experienced (and yes, none experiences death), and there is no epiphenomenal entity that 'follows' one of them.

No argument there. But since they made my own topic out of this diversion, I might as well defend what I'm doing. Can I edit the topic title? I never said anything on the order of "This is an SR effect". More like "How the universe could be 30 GY old". I may be using the wrong theory, but I'm wielding it correctly. Using the wrong theory gets me some empirical contradictions, but nobody has pointed out any of them. I think perhaps we can explore some of them. You can tell me precisely where I'm using the theory incorrectly. The universe can be described by an inertial frame iff expansion was inertial (the scalefactor was linear). The scalefactor function isn't linear, so the theory is misapplied. No argument there. I'm considering the universe only in a local context. I just drew an unusually large box around my system. In such a coordinate system, the big bang happened at the origin of the inertial frame, the location where a comoving object is stationary. Everything is moving away at a rate that is a linear function of its distance, up to the speed of light. A Lorentz transformation can be applied making any point in space that center of the universe, so there is no preferred location until an inertial frame is chosen. The graph I showed has superluminal speeds. It measures speed as comoving proper distance per unit time, and that kind of speed accumulates additively, not relativistically, so you get speeds arbitrarily high. By accumulating additively, I mean if I observe Bob in his galaxy receding at 0.6c, and Bob is looking at Charlie in the same direction receding from Bob at 0.6c, then I am going to observer Charlie recede at 1.2c, not 0.88c. Under SR rules, Bob is receding at 0.54c from me and Charlie is moving at 0.83c. Different coordinate systems yield different speeds. The graph I showed plots the redshift to speed conversion for both coordinate systems as well as a few others. Redshifts have always mapped to speeds, even if it took a lot of (ongoing) work to generate that graph. Also note that the graph shows redshift to current recession speed, not recession speed at the time of emission of the light we're measuring. Under the SR system, the two speeds are the same because I'm ignoring the expansion rate changing, which is one of the ways SR is wrong. Sorry, but the line is drawn for SR as well. The speed of a spaceship leaving Earth can be measured by its redshift. So what are some empirical problems with doing what I'm doing? For one, there is no event horizon under SR, so light can get here from anywhere given enough time. This is true if expansion is not accelerating, and I said I was ignoring expansion rate changes, and besides, you can't empirically see the event horizon. We see plenty of objects that have long since passed beyond it. A big problem is the angular size of galaxies. Under SR, the faster something is receding, the further away it is from us when the light we see now is emitted, and the galaxy appears smaller much in the same way that Saturn appears smaller than Jupiter when they're more or less aligned like they are not. Not so under the standard model. GN-z11 for instance (redshift z=~11) appears twice the angular size as a similar size object with redshift 2, because the light from it was emitted from half the proper distance from here compared to the lower redshift galaxy. SR just cannot account for that appearance. Light travel time is also significantly different, but that cannot be directly measured, so I'm not sure if it counts as an empirical difference. Observing gravitational effects like lensing is an obvious difference between SR and GR, but I'm not suggesting otherwise. I'm assuming that on a large scale, the universe is essentially flat. I drew a crude picture of the universe using inertial coordinates, and except for the constant expansion rate, it pretty much worked. I can post it if you like. It had a finite size (an edge), but was nevertheless everywhere isotropic to any observer. The angular-size thing really sinks it, because I couldn't immediately think of other immediate empirical problems. If you put our solar system way off center in the picture, you can make the current age of the universe as old as you like, and that's what I was doing when I made my initial comment which is its own OP now.

Newton showed this to be true only for spherically symmetrical objects, in which case the center of the planet is the same as its center of mass. I just wanted to point this out. For another shape (a barbell or a hoop for instance), an object nearby may well be attracted away from the center of gravity of the object/system. E.g, if it is noon and a rock is dropped from a tower at the equator (a location between Earth and Sun), the rock will accelerate away from the mutual center of gravity of the sun and Earth. The moon is beyond the point where this is true, so during a solar eclipse, the moon still accelerates towards the sun, not towards Earth. At half-moon, it accelerates in a direction that points at neither Earth, sun, nor the center of gravity of anything. The moon's path through the solar system is always convex. That means the sun always exerts more force on the moon than does Earth, but this is not the case with our dropped rock. Center of mass of our solar system is often not within the sun, such as is the case right now. It doesn't take much mass of the minor star in a binary system to pull the center of gravity of the system outside the larger star.

Your statement implies a preferred moment. A clock is a worldline and it reads all times along that worldline and doesn't say that the universe is any one particular time. Yes, this is a better destruction of my argument. As I said above, it is quite a stretch to use SR on the scale I chose. There are empirical differences (such as the angular size of rapidly receding objects) that falsify the SR view on those scales. I was just trying to illustrate a coordinate system that put our current event simultaneous with an event with a clock that measures 30 GY since the BB. I don't think you pointed out any blatant errors before. Redshifts do actually map to speeds. Galaxies don't recede at superluminal speeds under SR where velocities add via the relativistic rule instead of the simple addition that is commonly used at cosmological scales. The entire universe could be mapped in an inertial frame iff expansion was forever constant (inertial), but it isn't. It was decelerating and now it is accelerating, which forms an event horizon that cannot exist in a flat SR model. That right there falsifies the model. I'm not asserting that what I've done is legal. As for GR, not even GR suggests a way to foliate all of spacetime, something I pointed out in rjbeery's thread. I can have an observer that asks the question: "What is the age of the universe now?" and GR gives no meaningful reply to the question.

Stationary relative to the inertial frame in which they are stationary. It is completely symmetric. In their frame, we're moving fast and our clock says it's been 13.8 GY since the BB, instead of 30. In our frame, when our clock says the universe is 30 GY old, their fast moving clock will read 13.8 GY. That's simple relativity of simultaneity.

I'm using the SR definition. They're stationary, we're moving fast enough in their frame that 30 years dilates down to 13.8, which is somewhere around 0.9c. So I picked a galaxy relative to which we're moving away at that speed, and if we see 13.8 GY with our dilated clocks, they must see 30 GY. Yes, it is a stretch to use special relativity at such a non-local scale. Times over cosmological distances are never considered in our inertial frame (they use a comoving frame), which is why it sounds strange to consider a frame where the age of the universe is 'currently' much more than the figure we usually hear. Red shifts of galaxies do very much correspond to speeds. The shift-to-speed conversion (consensus is near the .3, .7 line) only works with objects with negligible peculiar velocity, which is true of any galaxy, but not true of the space ship receding from Earth at 0.9c, the speed of which would follow the SR line to the lower right. The v=cz is Newtonian physics. OK, the graph above is admittedly a graph of recession speed in comoving coordinates, not inertial coordinates. That means it is the rate at which the proper distance between us and them increases per unit of comoving time. That's pretty different than the inertial definition, the increase per unit of inertial time. Point is, there is very much a galaxy relative to which we're moving at 0.9c, even if I computed its redshift incorrectly.

Quite plausible actually, not just in principle. In the inertial frame X of some planet in a galaxy 27 billion light years from here (distance measured in frame X), the universe is currently (simultaneous with us now) about 30 billion years old. Yes, the universe for such an observer would be quite different from what we see here since for one thing it appears to be over twice as old. Much more mature galaxies and such. Yes, we do know of galaxies moving at sufficient speed for this. The one I mention above would have a redshift of about z=1.3 as viewed from here, and the record holder is over z=11. Yes, I realize I'm replying to posts from January, before I registered I think.

In general, a superposition of states is known through demonstration of interference between the two states: Refraction patterns, positive/negative interference and such. I want to know how it is done for more macroscopic scenarios. They put a macroscopic object (one visible to the naked eye) into superposition. It was a sliver of material suspended in some kind of field, and in superposition of vibrating (like a xylophone bar) and just sitting there. What test was performed on such a system that couldn't be used to determine which of the two states it was in, but nevertheless demonstrated (over the course of multiple iterations of course) a pattern different than what would have been measured if the system was simply in one unknown state or the other, but not in superposition? The article I originally read on the subject was just based on a press release and did not report such details, but it seems to be the only one that matters. A different scenario will do as well, but firing buckyballs through slits does not count as a sufficiently macroscopic superposition.

Speed has nothing to do with it, since in your example, the situation is no different than the ship being stationary and the observer watching it go by being what moves at relativistic speed. Unruh radiation is observed in an accelerating reference frame, and has nothing to do with speed. Hawking radiation can be measured at any distance from an event horizon, but only by a hovering observer, not by one falling in.

Unruh radiation is not emitted by an accelerating ship. There is also no collision of matter going on in that scenario. There's merely a coordinate singularity inherent in a continuous accelerated reference frame, which, only in that ARF, emits faint radiation at the singularity similar to the Hawking radiation (which is also not emitted by any ship) emitted in say an inertial reference frame at the coordinate singularity of the event horizon of a black hole In both cases, the radiation is not emitted in coordinate systems where there exists no coordinate singularity there.

Einstein did not beg his conclusions. He posited two lightning strikes, but posited neither their simultaneity nor the absolute motion of either observer. The simultaneity of the strikes was concluded only after the respective observers took measurements of the events in question. Neither observer measured the motion (absolute or relative) of any object in that particular though experiment.

I am talking about universal time, and while I agree that there's no such thing, there seems to be no contradiction arising by postulating it. I'm proposing such a contradiction here. If the choice is relative to a particular observer, it's hardly objective. Another clock cannot be set to the universal time without agreeing on this privileged observer or privileged location in space. Points in space 50 billion light years away do not exist at all relative to a given observer, so his personal choice of coordinates do no in fact foliate all of spacetime. There is a choice that does foliate all points in an arbitrarily large scale, but as pointed out in this topic, it doesn't work for excessive local curvature such as black holes. There seems in fact to be no possible coordinate system that does, and that's the contradiction that arises from postulating universal (objective/absolute) time/space.

I'm talking about interpretations that deny the principle of relativity. There seem not to be infinitely many possible foliation schemes. As a matter of fact there doesn't seem to be any that foliate all of spacetime. The typical one suggested is the curved (non inertial) comoving frame corresponding locally to the inertial frame in which the CMB appears isotropic, but any frame like that does not properly foliate local deviations from flat space like black holes. If they did, then rjbeery would have grounds to stand on when trying to objectively determine if event X inside a black hole occurs before or after event Y somewhere outside it, particularly after the BH has evaporated. An objective foliation scheme should not in any way depend on an observer. Any two observers, no matter how separated and unable to communicate, should be able to sync their clocks simply by setting said clock to the current objective time, and then I suppose having the clock running at some rate which depends on the speed of the clock and its current gravitational potential. The latter requires a standard 'zero', which also seems undefined. For example, what is the gravitational potential at the surface of Earth? Nobody publishes that. They only publish the potential if Earth was in an otherwise empty universe, which it obviously isn't. Anyway, point is, there is no viable objective foliation scheme that includes all spacetime events. The lack of a viable scheme means that time and motion cannot be objective. The principle of relativity cannot be denied. Correct me if I'm wrong.

It seems that there is no coordinate system that foliates all of spacetime. This seems to be an interesting argument against any philosophy of time that posits an absolute coordinate system (a preferred frame of one sort or another). Presentism is only a subset of these philosophies. The inability to identify any coordinate system that can consistently map any pair of events as to which occurs first seems to me to be a fatal flaw in such a philosophy.

You've not given any indication of what you've done or what your current understanding of these terms is, so I don't know where help is needed. If you don't know the difference between an interrupt and a subroutine call, it seems you have to re-read the chapter(s) preceding this question.

Unclear how you might think so. Simple substitution yields 1-1/1 which is zero. Even if you ignore precedence rules and evaluate it as (1-A^2)/B^2 you still get zero. I can prove that 1 equals 2 using some sleight of hand, but not in the equation you present.

I've seen it demonstrated with a Kruskal-Szekeres diagram that an infalling observer can only witness a finite future as measured by an outside observer. He cannot see the universe end.

I never said any particular coordinate system wasn't meaningful. It isn't meaningful to compare the times of the two events you indicate. The Penrose diagram demonstrates the same thing in this case. An event within the black hole (an event that doesn't exist in the coordinate space discussed in my prior post, but does exist in the Penrose diagram) has no causal connection with the event after the evaporation. That makes it like any pair of events separated in a space-like manner: There is no objective comparison of their times. A-before-B is a relation dependent on the foliation of choice, because neither event is in the past or future light cone of the other.

No, I do not. It is not meaningful to compare the time of an event to an event not in your coordinate space. Use different coordinates if you want to do this.