Halc

The interval cannot be invariant between observers at different gravitational potentials. Consider a light blinking at the top of a radio tower (on a non-spinning planet if we want to be more precise). We have an observer at the top and one on the ground, each measuring the interval between the blinks. They're both stationary relative to the tower, so the interval is trivially just the time between the blinks, but the two observers will measure different elapsed times on their local clocks because they're at different potentials and don't run in sync. So the spacetime interval being invariant is a property only of flat Minkowskian spacetime.

Dandelions and Homo are genetically similar enough to be connected, but that doesn't mean that either is descended from the other. It just means we share a common ancestor at some point. The more recent that common ancestor, the closer we are related to a thing.

Gifts of silver and gold will vir- ginity tend to put an end to. The tortithe and rabbit rathed theee timeth thith month. The rabbit won twithe and the torithe onthe. Started choking, turning purple, A hardy slap and one good burp'll put you to rights. Quoted from memory. Credit: James Hogan. There was one with orange as well, but it was really reaching, and I don't remember it.

Accelerating an electron to nearly light speed is regularly done in particle accelerators, which then go on to add momentum to said electron perhaps another thousand-fold, and the electron still doesn't go faster than c. I think that is a practical example of verification that's been done. I cannot parse what you have in mind with the M and the little m's. A rock is composed of a bunch of molecules, which is a set of smaller masses making up a larger mass. That fact seems totally irrelevant to the limit the separation rate of a pair of rocks. GR limits separation speed locally to c, but non-locally, this is not the case. Hence there are distant galaxies increasing their proper distance from us at a rate greater than c. No object can have a peculiar velocity greater than c. Peculiar velocity is local in a sense: it is its velocity relative to the center of mass of all matter within some radius (typically the size of the visible universe, or possibly the Hubble radius) centered at the location of the object.

I said no such thing. Either your reading comprehension skills are completely absent or your are deliberately twisting everybody's replies. I suspect the latter. I said that since the 'traveler' considers himself stationary in his own frame (by definition no less), clock 2 rushes towards him from 36 light minutes away, and this takes 45 minute, which is less than SoL. That makes no statement about what he sees while this is going on. 10 years away as measured in a different frame than your own, yes. If I have a fast enough ship, I can get to the far edge of the galaxy in my lifetime, despite it being 70,000 LY away in the frame of the galaxy. That speed is called proper velocity (dx/dt') and there is no limit of c to it. Normal velocity (dx/dt, or distance and time measured in the same frame) is bounded locally by light speed.

That error has already been pointed out. The example shows clock 3 traveling the light hour in 5/4 hours. That's what it means to be moving at 0.8c. Due to time dilation, clock 3 just happens to have logged only 3/4 hours during that trip. Relative to the clock's own frame, only 45 undilated minutes pass, but it is stationary (by definition), which is hardly traveling faster than SoL. In that frame, clock 2 comes to it at 0.8c, and moves 36 light-minutes during those 45 minutes, which is also less than SoL. 2: As seen some observer A, the incoming clock is seen to go from a light hour away to 'here' in 15 minutes, yes. That's the difference between its actual speed in that frame and the speed of the light the observer is observing.

Yes, it takes 1:15 in the frame of 1st/2nd clock for the 3rd clock to get one LH away. In the frame of that 3rd clock, it is stationary, so it isn't traveling anywhere in the 45 minutes it logs, so it isn't moving faster than light.

Because one and a quarter hours is an hour and 15 minutes, not an hour and 25 minutes.

Not going to watch a 6 minute video to look for where he says that. As swansont points out, there is no such thing as 'the gravity'. It needs to be more specific. The gravitational potential above the surface of some mass is -GM/r, which is proportional to M/r, so perhaps by 'the gravity' he means gravitational potential. It can be expressed in the same units as velocity.

Janus is describing the ballistic theory of light, which is actually a much better fit to Galilean relativity which asserts no preferred frame. One cannot 'continue to see B as "frozen"' '. Light from that moment can at best be measured once, not continuously. Oddly enough, if the missile moves at 2c, with either theory, if they look at a 'stationary' Earth from the missile, Earth will appear to run backwards. At 11:00 missile time, it will see Earth at 9:00 given a 10:00 departure. The 9:00 light from Earth gets to the same location as where the missile is at that time. Funny thing is, the image of Earth will appear in front of the missile, not behind it like intuition suggests. Sound works the same way. The post of mine discussed both, but the part to which you responded involved more of a Newtonian preferred-frame ether theory which denies Galilean relativity. Don't get the question. The only measurements you describe are both of them in each other's presence at the time of departure. They both measure 10:00 on both clocks at that time. Not sure what it would mean for those identical observations to 'cancel'.

It depends on what theory Galileo uses. Using the ballistic theory of light, the missile is immediately invisible at A because it is going faster than light, and thus light emitted by it cannot propagate towards A. It can only fall behind. Using a pre-relativity ether theory (Newtonian), and assuming A is stationary in that ether, the missile clock reads 11:00 when it passes C and it takes 2 hours for that light to go back and reach A, so A sees the missile clock ticking at 1/3 rate. In both cases, the missile can see nothing behind it because it is superluminal, similar to how a supersonic aircraft cannot hear any noise from behind. Both theories predict different results than what is actually observed, but the actual theory has no different answer for the problem since it forbids the missile from having a space-like worldline. As you say, relativity forbids that you go there, but the other two theories do not.

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.