Dark energy is superfluous First, the current state of affairs: Observations in 1998 first gave evidence that the expansion of the universe is accelerating. What causes this acceleration is unknown and is one of the biggest mysteries in physics. The most popular proposed solution is an ad hoc form of energy called “dark energy”, which is theorized to work against gravity and overpower it on large scales. Now I will give a far simpler solution that shows that dark energy is superfluous. I will show that general relativity (GR) already predicts that the expansion of an expanding universe can accelerate as observed. In another thread I proved that GR predicts that the universe can expand arbitrarily fast (in defiance of what cosmologists currently believe). Here is another take on that, which better serves our purpose here: The proper distance between the Milky Way and Andromeda galaxies is two million light years. Let a rocket traverse between the Milky Way and Andromeda, passing by Earth and decelerating relative to Earth the whole way. Let the trip take three million years on a clock on Earth. In the frame of some hypothetical planetary observer X somewhere in the Milky Way, can the elapsed time for the rocket’s trip be only one year? Sure, GR allows that via gravitational time dilation. All that’s required is for X’s clock to run at a rate that is one three-millionth of the rate of a clock on Earth, and gravitational time dilation allows such a difference in clock rates. Then in X’s frame the rocket can recede all the way to Andromeda in just one year. This proves that in principle there’s no upper limit to the proper distance an object can recede from a planetary observer in a given elapsed time in the observer’s frame. Any given proper distance corresponds to one and only one distance that X measures. And the greater the proper distance, the greater the distance that X measures. Then it is proven that, in the frame of a planetary observer, there’s no upper limit to the distance an object can recede in a given elapsed time. And then there is no upper limit to the rate at which the universe can expand in the frame of an observer, in terms of distance to some receding object, over time. Yet the velocity of the rocket need not and does not exceed c, the speed of light, as directly measured. In the frame of a planetary observer, there’s no upper limit to the distance an object can recede in a given elapsed time. Then in such frame there’s no upper limit to an object’s change in distance in a given change in time. If the rocket passed right by X on its way to Andromeda, we know that its directly measured velocity in X’s frame would be less than c. Velocity is a change in distance over a change in time. Then we know that the rocket’s change in distance over a given change in time, a velocity, would be less than c in X’s frame, when that velocity is directly measured. And we know that its change in distance over a given change in time can be more than c in X’s frame—indeed there is no upper limit—when X measures the distances from afar (and that does not violate GR). Then we can incontrovertibly infer that an object’s rate of change in distance over change in time, when the observer measures the distance from afar, can accelerate as the object decelerates relative to the observer. When cosmologists observe via supernovae that the universe is accelerating in its expansion, they are not directly measuring velocities of those supernovae. Rather they infer a change in their distance from us over a change in time, both in our frame, and the result indicates acceleration. But we’ve established that GR can predict acceleration in that case, even as the object decelerates relative to the observer. Then dark energy is superfluous. It isn’t needed to explain the observations of the supernovae. See also the related topic "Widespread misconceptions about cosmic expansion".
I have considerable respect for you ability and feel a little guilty that I never made it thru you version of SR (relativistic rocket etc many months ago) but.... Also I do not know much about the obseravtional basis for dark energy but... As I understand you it, is the large local gravity near the observer that can make the motion of distant objects appear to be accelerating, but this also would make the motion of near by ones appear to be accelerating to, would it not? Perhaps your more complete version of SR theory leads to an alternative to "dark energy" (I do not much like it either) but with this simple analogy, you seem to be violating Einstein's strongest rule (not anything about relativity, etc. but his rule: "Make everything a simple as possible, not not simplier.") On the dark matter question: - I again know too little to comment, but claim the same privledges as most others here do, so I will: I think there are many more small (few stellar masses) black hole than all the stars that have ever existed. They do not make quasars and have such brief* and tiny gravitational lens effect that they are undetectable, except if they happen to pass close by our solar system and perturb the orbit of planets. In late 1920s something perturbed the most distant planet then known (Neptune). The search for what perturbed Neptune lead to the discovery of Pluto; but to make the observed perturbation from Pluto's position at the time, Pluto must be much larger than the Earth. For this reason, it was thought to be much larger than Earth for more than a decade. Now we know Pluto is smaller than the moon, but no longer have any explanation for the observed perturbation of Neptune. A passing small Black hole could have made the perturbation (and tilted the orbit plane of then unknown Pluto.) This is part of the basis for my book, Dark Visitor - See more about it, why I wrote it, a list of all the physics I hid in it, and HOW TO READ FOR FREE at the web site under my name. What do you think dark matter is? Do you think, like me, it could be a great multitude of small black holes? I have explained how (and why one should expect) each of the very large first generation stars to produce at least a dozen of these small black holes. (Has to due with not exactly symmetric collapse resulting from the fact fusion rate depends much more strongly on the local temperature than upon the density.) ----------------------------------- *Because they are small, they must be essentially exactly on the line of sight to the "background star" to have any noticable effect and they are only briefly, if ever, there. Any brighting they would produce would be considered atmospheric "star twinkle" even if noticed.
zanket, You did no such thing. You just kept repeating the same unsupported assertian, even though I pointed out your misconception in your off-thread 'paper' Please Register or Log in to view the hidden image! . correct so far... Here is where you begin to mix reference frames. The two million light year distance between the Milky Way and Andromedia is measured by the time it takes on an Earth clock for light to travel between the Milky Way and Andromeda, reference frame 1. The time required for light to travel between The Milky Way and Andromedia by X's clock will be less than one year, reference frame 2. You are mixing the distance as measured by an Earth clock (frame 1) with the time as recorded on X's clock (frame 2). The 'proper distance' between the Milky Way and Andromeda is about 10 million light years for a clock at rest in Earth's frame of reference. The 'proper distance' between Earth and Andromedia according to an observer at rest in X's frame of reference is 10 million light years only when measured by proper time, not the observer's local clock. The observer's local clock will measure less than one million years for light to transit between the two galaxies. A clock in motion in either frame 1 or frame 2 will not measure proper distance for either frame, but relative distance as measured by that particular clock. Proper distance can only be measured by a clock counting proper time. 'Proper' coordinates are just another way of staying comoving coordinates. Comoving coordinates are taken from a frame of reference in which the cosmic microwave background is at rest (no Doppler shift in any direction) and clocks are unaffected by gravitational redshifts. A clock on Earth is only very slightly affected by gravitational time dilation wrt the comoving frame. A clock on Earth is only very slightly affected by the Milky Way's velocity through the comoving frame (the CMB frame, again) and beats almost identically with a comoving clock in the Andromeda galaxy because for the very small relative velocity between these two galaxies. Again, you do not understand the definitions 'proper time' and 'proper distance', which are comoving coordinates as used in cosmology and astronomy.
Thanks and no worries, I got lots of input elsewhere. Yes, nearby ones would appear to accelerate too; I say they “seemingly accelerate away”. Any local gravitational acceleration will cause the observation, even the gravitational attraction of an observer floating alone in deep space. The object seemingly accelerates away as long as its velocity is relativistic. (I don’t show this above, but it’s in my paper.) Do you think it’s too complicated? I keep trying to think of ways to make it simpler (usually finding a new way only after I post, unfortunately). That is my favorite advice of Einstein's. I’ve given dark matter a lot of thought but I still consider myself weak on the subject and have only some loose ideas. I think black holes can be refuted, but even if I were right, perhaps small dense & highly-redshifted (i.e. nearly black) objects could substitute in your idea. I don’t see why dark matter could not be something like that. I’ve never understood why cosmologists think that dark matter must be exotic matter (like “machos” or “wimps”) rather than ordinary matter that is simply dark and hard to detect more directly, like you propose. Dark matter is proposed in part because of galactic rotation curves. One consideration that I haven’t seen mentioned anywhere is that there are two masses possible for every one rotation velocity. Maybe cosmologists are getting faked out, observing that the rotation velocity they observe is x when it’s really much larger but slowed down by gravitational time dilation, in which case the mass below that point is larger than they infer from the misleading observed-from-afar rotation velocity.
As I saw it, my rebuttals refuted all of your refutations of my arguments. But let’s see what you say below... Agreed. I assume that a single inertial frame can exist all the way from Earth to Andromeda, so that two million light years is the proper distance between them. I don’t mix them. I mention them both; that’s all. “Mixing” implies that I invalidly include both of them in some equation. I don’t do that. You’re misusing terminology here. There is only one proper distance between the Milky Way and Andromeda, for every observer in the universe. They all agree on what that proper distance is. A proper distance between two given objects at a given moment applies to all frames. I’ve mentioned this before, and gave a supporting link, but you seem to think otherwise. Can you support your claim with a reference or other logic? My argument depends on the invariant property of a proper distance. If you don’t understand what an invariant is, you won’t understand my argument. The easiest way to understand proper distance is to imagine it measured by a ruler floating in an inertial frame. Everyone in the universe will agree on what value the ruler displays for the distance. Where did you get “10 million light years” from? Proper time in X’s frame is the time elapsed on X’s local clock. The easiest way to understand proper time is to imagine it measured by a wristwatch of a particular observer. Everyone in the universe will agree on what value the wristwatch displays for an elapsed time between events. You don’t have to say “an observer at rest in X's frame of reference”, because X is already such an observer. You can just say “X”. No, it’s the other way around. I believe you do not really understand these terms. We can try to resolve that before continuing, if you want. I could be wrong, but my references disagree with you.
zanket, You mix them to explain your claim that an observer would see objects accelerate away from X number of light years to Z number of light years when the observer decelerates. The proper distance and the physical location of the viewed object never changes. For instance, you cannot accelerate toward a galaxy to make it appear 'closer' for a larger view. You cannot accelerate to very near 'c' to make an object millions of light years away appear to be 'close' for a view like looking through a powerful telescope. This is a common misconception. It also does not appear to recede back to the original distance of millions of light years when you slow to 0 relative velocity. That was the point I was making in the other post about not appearing to recede. I meant no 'additional' recession, obviously. Sure, that's fair enough. Here is an excerpt and link to wiki, which you quoted from earlier: http://en.wikipedia.org/wiki/Comoving_distance Sorry, the equations do not cut & paste as usual. I put the part about 'constant cosmological time' in bold. Edit: By the way, I do not like the idea of Dark Energy either and am not convinced the accelerating rate of expansion is a physical fact. I mentioned my speculation in the other thread, so won't repeat.
Well, I don’t talk about what an observer sees, but rather what they measure. (But I suspect that’s what you meant anyway.) I don’t see how referring to measurements of distance or time individually can be mixing frames. The only question is whether the measurements are valid. I think I understand your viewpoint completely now: You think that length-contraction, and length expansion from a length-contracted state, have no physical meaning. You think the only true distance is the proper distance. I’ve seen nothing in any source on relativity that supports your viewpoint. And your viewpoint is contradicted by experimental tests. For example, in the muon experiment, the only way the muon can traverse the Earth’s atmosphere before decaying is if the atmosphere’s depth is physically less for the muon than what an observer on the Earth’s surface measures for that. The principle of relativity says that who is moving in that scenario (Earth or muon) is indeterminate (i.e. movement is relative only, so no experimental test can tell who is stationary and who is moving). Then the muon must experience that lesser depth for the atmosphere in every measurable way. Any experiment done by the muon, even a visual one, like how close the Earth’s surface appears to the muon, must support the length-contracted distance the muon measures, or else the principle of relativity is violated. I believe that your viewpoint, not mine, is the common misconception. Your viewpoint requires dark energy and expanding space (or alternative additional assumptions) to explain what we observe, and violates the principle of relativity, the heart of relativity theory. My viewpoint adheres to relativity theory and requires no additional assumptions to explain what we observe. Unfortunately “proper distance” is a term used in multiple ways. The link you posted for it obfuscates the issue. It discusses proper distance as that term is used in the expanding space paradigm. Above I’m talking about proper distance only in terms of SR and GR, as described here, and described in the link you gave with: My example above applies even when space itself does not expand. A correction to something I said above: The easiest way to understand proper distance is to imagine it measured by a ruler floating in an inertial frame, by an observer at rest with respect to the ruler. Everyone in the universe will agree on what that observer sees the ruler display for the distance.
zanket, Yes, that is correct. It is my viewpoint that objects in the universe do not physically change locations due to moving observers' observations. Yes, proper distance is 'true' distance. Observers moving within this 'special' frame do not measure proper distance because their clocks are counting time slower. This frame is also known as the International Celestial Reference Frame (the ICRF). It is used extensively in advanced cosmology in conjunction with both General Relativity and competitive theories. No, the muon's local clock (time in its FOR)) is ticking slowly, allowing it to cover a greater proper distance in a shorter period of 'time'. Newer models of the decay process of cosmic rays and other relativistic particles have the decay modeled as a cascade, with leptons and muons produced sometimes in secondary decays. The old experiment of measuring excessive muons on the surface of the Earth is subject to many factors ignored in that simple model used to support length contraction. Here you seem to be restating the position I support. Ever observer in the universe will agree to the measure carried out by the observer in the ruler's frame of reference. This ruler is measured in the comoving frame, the ICRF frame. I do not see any reason for us to keep stating our viewpoints, you are welcome to yours if it differs from mine. I just wanted you to understand there IS another viewpoint. And, yes, that viewpoint is used in advanced cosmology.
Hello all If EM radiation does not contribute to the stress-energy-tensor of GR (I have yet to find an experiment that proves this contribution) then the universe is loosing mass which reduces the stress-energy-tensor in the universe's space-time. The reduction of the stress-energy-tensor will increase the rate of time flow. Therefor, over time, the rate of time flow increases. A possible contribution to the red shift we see. Please Register or Log in to view the hidden image!
Montec, Hello all I agree with this. It is essentially what I was speculating about in another thread when I said the said the 'density' of spacetime may decrease (the permittivity and permeability increase) as the universe expands.
How do you reconcile your viewpoint with its violation of SR’s principle of relativity? If length-contraction is not physically meaningful, then an experiment can tell who is moving vs. who is stationary; that contradicts the principle. Do you agree that you are describing a theory that contradicts SR? If they measure a distance that differs from the proper distance, how is that difference not physically meaningful? After all, a measurement is a physical experiment, and you agree that the measurement can show that the distance differs from the proper distance. What experiment could support your viewpoint that “objects in the universe do not physically change locations due to moving observers' observations”, if an experiment that simply measures distance contradicts that viewpoint? OK, but I don’t see anything about the ICRF that supports your viewpoint. I see that it is just an arbitrarily chosen inertial frame, for convenience only. That is a valid interpretation in SR for the Earth observer. But how do you explain the result from the muon’s perspective? In its frame, its clock does not tick slower. Then if the distance to the ground is not physically less than what the Earth observer measures, the muon will decay before it reaches the ground. I’ve done extensive research on this experiment, and have not seen anything to suggest that it does not (or no longer) supports the conclusion that length contraction is physically meaningful. Can you please provide a reference? Where we disagree is that you think it is mixing frames to mention the proper distance in the context of an observer who is not in the ruler’s frame. I say that the proper distance has meaning to such an observer, as a standard by which his own measurement of distance can be compared. My original post uses the proper distance in that way. If your viewpoint was consistent, I could accept it as an alternate. But it seems inconsistent, as I note above. Can you reconcile the inconsistencies?
zanket, My position does not violate the principle of relativity, nor the special principle of relativity. The principle of relativity states the laws of nature are the same regardless the the person measuring them. The special principle of relativity states the laws of physics are the same across all inertial frames, but may vary across non-inertial ones. Comparing the measurements obtained by an observer in an extreme gravity enviroment with the same measurenents obtained in a gravity-free inertial frame will differ. You are basing your arguements on the unwarranted assumption that the measurements would be identical. I did not state that. I stated objects in the universe do not physically change locations because a moving observer changes his velocity. Can you not actually understand the difference, or are you just distorting my statements to argue against a constructed strawman? My viewpoint is not contradicted by distance measurement. As I have already stated, distance measurement between 'galaxies' is a product of velocity and accumilated 'time' on a clock. The clock in extreme gravity ticks slower than a clock in an inertial frame. You are assuming the two clocks beat at the same rate and the two galaxies have physically moved closer together in one frame. No, it is a 'special' inertial frame in which proper distance and proper time hold true. Comoving coordinates hold true in this frame of reference. Correct, in the muon's frame of reference, appox. 2.2 microseconds pass on its clock before it decays. But it measures the distance between two points as less when compared with the same distance as measured by an Earth observer. If you state distance only contracts in the moving frame, then you are stating it is necessary to identify which frame is in motion. If you state the clock ticks slower in the moving frame, then it is necessary to identify the moving frame. Why do you state 'slow clocks' belong to only one frame and 'contracted distance' to the other frame? You are violating the special principle of relativity. Please Register or Log in to view the hidden image!
There are inertial frames all the way down to any planetary surface, so says the equivalence principle, so a proper distance can be measured to any desired precision between any two objects’ surfaces, regardless of the strength of gravity. I do think you make a good point that shows a loophole in my argument in my original post, which I'll close in a better example later. But for now my question to you can be limited to a single inertial frame. More on this below. What else am I to think from the following exchange? I really do want to understand your viewpoint here, before moving on. But your comments are confusing to me. Reading your post a couple times, I think I’m getting what you’re saying. Let’s see if I’ve got it: Let’s forget about gravity, which only obfuscates the issue. Let’s revisit this example of mine: By definition in my paper, a “relativistic rocket” exists in flat spacetime of indefinitely large extent, so gravity is not an issue. You say that the beacon does not physically change its location. For example, if the beacon was initially floating stationary at a specific location in the International Celestial Reference Frame (ICRF), it remains at that location regardless how the rocket changes its velocity relative to the beacon. Of course I agree with that; it’s okay to declare that the beacon remains stationary. But it remains true that “they observe the beacon recede to a distance of ten light years in one year”. You can say that the beacon did not change its location, but in that case the rocket must have changed its location relative to the beacon—the rocket would end up at a location in the ICRF that is a proper distance of ten light years away from the beacon. And the proper distance to the beacon changed at a rate of ten light years per year as the crew observes. (The crew measures zero distance to the beacon when they pass it, the same as the proper distance. One year later on their clock, when they are at rest with respect to the beacon, they measure the distance to the beacon to be ten light years, the same as the proper distance.) From the crew's perspective this change cannot be due solely to the rocket’s velocity, which accounts for less than 10% of the change (1 year on their clock times a velocity less than c = a distance less than one light year). From the crew's perspective, the length expansion (uncontraction from a length-contracted state) caused the other 90+% of the change in distance they observe, the same as the change in proper distance. (Talking about the rate at which the proper distance changes during time elapsed on the crew's clock is not mixing frames. That rate is just as meaningful in the beacon's frame as it is in the crew's frame.) Now it seems that you disagree with the statement in bold. I’d like to know how you can refute that. If you argue that the beacon’s location did not change, then I will argue that the rocket’s location must have changed, and vice versa. So your location argument will fail. As I understand it, your whole argument (excepting about gravity) is based on an object’s location being unchanging. It is “special” in that most of the objects in the frame are essentially stationary. But it is not truer than an inertial frame in which most of those objects are moving. In the muon’s frame, the entire Earth including its atmosphere is moving, so the entire Earth including its atmosphere is length-contracted and time-dilated. In the Earth observer’s frame, only the muon is moving, so only the muon is length-contracted and time-dilated. Distance is contracted and time is dilated in both frames, but only for the object that is moving. Then to explain the experiment’s results it is not necessary to identify a moving object except relatively speaking, and the principle of relativity holds. When discussing the experiment, both the muon’s length contraction (in the Earth observer’s frame) and the Earth’s time dilation (in the muon’s frame) are ignored because they are irrelevant to the conclusion. As I now understand your argument, and considering only a single inertial frame (i.e. tabling your arguments about gravity for now, to simplify the issue), you think I have not proven my case because, while you agree that length contraction affects a distance measurement, you think that a receding object does not change its location due to length contraction or length expansion from a length-contracted state. I have shown above that, if one adopts this position (and it is okay to adopt it), then one must accept that the location (e.g. a specific location within the ICRF) of the observer itself must change due to length contraction or length expansion, so that your argument fails. Can you refute that?
zanket, zanket, you are distorting my post by quoting only part of my response. My response was, quote: "Yes, that is correct. It is my viewpoint that objects in the universe do not physically change locations due to moving observers' observations." Yes, that is the definition of comoving coordinates, the frame of reference that proper distance and proper time is relative to. No, the ten light year distance is the proper distance only in the comoving frame. The one light year distance was the relative distance in the rocket's frame while it was traveling at close to 'c' relative to the beacon. Do you not understand that the comoving frame is neither the rockets rest frame not the beacon's rest frame. It is a third frame of reference. Either the rocket or the beacon may be at rest in the comoving frame, but only if they have no velocity relative to the comoving frame. After your relativistic rocket comes to rest relative to the comoving frame, then proper distance is the same as relative distance, but not while the rocket is in motion. While the relativistic rocket is in motion relative to the beacon, there will be a Doppler shift of the light corresponding to whatever the velocity happens to be at that instant. However acceleration/deceleration does not cause any additional redshift in and of itself, only gravitational fields do that. It has been proven in supercollider experiments that there is no additional slowing of clocks due to mechanical acceleration over what is predicted by relative velocity alone. Look up 'the clock postulate' in GR. It also is not completely true that free-falling frames are the exact equivalent of inertial frames in flat spacetime. A free-falling frame will measure a frequency shift from the light emitted from the gravitational source in addition to the Doppler shift of the light due to relative velocity. So you are stating only moving objects are length contracted, and not the distance between those objects. Didn't you just refute your whole thread?
I’m not trying to distort anything. I’m just saying that you agreed to what I said you agreed to, and that’s how I misunderstood you. I can’t know that your subsequent statement contradicted you unless you tell me that. Let the beacon be at rest in the comoving frame. Let the rocket come to rest in that frame. When the rocket passes the beacon, we know that its proper distance to the beacon is zero. The distance to the beacon that the crew subsequently measures while they move relative to the comoving frame is irrelevant. All that matters is that the rocket’s proper distance to the beacon changes by ten light years in one year on the crew’s clock. To conclude this, the crew need not make a measurement between passing the beacon and coming to rest with respect to it. The crew can attribute only less than one light year of that change to their velocity. What do you think causes the other 90+% of the change, if not length expansion? The question can be put simpler: if you pass something, and one year later on your clock you measure it to be ten light years away, how do you account for the 9+ light years that cannot be explained by a velocity always less than c? You've told me about the 1- light year portion. I want to know what you think caused the 9+ portion. I understand and accept the clock postulate. But it doesn’t answer my question above. The crew could start decelerating only the moment after they pass the beacon, and make their next measurement of distance to the beacon when they are at rest with respect to it and have their engines off. Then the clock postulate, which relates to measurements made during acceleration, is not an issue here. Taylor and Wheeler define an inertial frame as a frame in free fall that is small enough that the tidal force throughout it is negligible. Then a free-falling frame can be made as close to equivalent to an inertial frame as desired, by reducing the size of the frame. Maybe that is the difference you described. But if you disagree, please provide a reference. An object X can be a system that contains other objects. For example, X can be a galaxy containing stars. When I move relative to X, it is a given that the distances between the objects that X contains contract in length, because X as a whole contracts in length.
Hi zanket How do you measure speed from inside a moving frame? Distance traveled divided by the time it takes to travel said distance? The speed of light measured in a moving frame is still the speed of light. A problem arises when you try to use the same "second" from a moving frame to compute a speed in a stationary frame. Your only "one year" is the time from a moving frame. The "ten light years" is in a stationary frame. Please Register or Log in to view the hidden image!
zanket, Simply because the crew's local clock was ticking slow relative to the clock in the comoving frame where the proper distance was measured. Again, proper time and proper distance is measured in the comoving frame. The rocket is moving relative to this comoving frame and the crew measures relative time and relative distance. If you understand the clock postulate, then you understand there is no additional frequency shift due to acceleration. The only frequency shift the crew sees is due to relative velocity wrt the beacon. Astronomers and cosmologists measure an additional frequency shift that they attribute to an accelerating expansion rate, the 'stretching' of the wavelength of light while it is in transit from the distant source to us observers on Earth. Your gedanken only speaks of Doppler shift due to relative velocity. It does not solve the problem of where this additional redshift arises. Tidal forces have nothing to do with frequency shifts of light. You simply do not understand what I stated. As for a reference, please provide an outside reference to back up your argument as to the cause of the precieved accelerating rate of expansion of the universe. Please Register or Log in to view the hidden image! Your extire gedanken was about two separate galaxies located at a proper distance of ten million light years apart. Also, if the muon observer considers himself inside the object (Earth and atmosphere) in that frame, you must also consider the Earth observer sees the muon moving within its frame. Tell me, when we have two objects, frame A and frame B, moving toward each other at relativistic velocity, which frame is length contracted and which has the slow clock? Why must the Earth observer 'see' the muon's clock as beating slow and the muon 'see' Earth as length contracted in it's frame? Why not the other way around if the frames are equilavent?
Yes, where both distance and time are measured in your frame, using measuring equipment at rest with respect to you. Agreed. Nowhere above is a speed computed invalidly by me. When I say that the rocket’s proper distance changes by ten light years in one year on the crew’s clock, that is not meant to imply a speed greater than the speed of light.
That addresses the scenario only from the perspective of the beacon. I’m asking you to explain the situation from the perspective of the crew. From their perspective, their clock runs at a normal rate. The elapsed times involved (zero, and one year) were measured in their frame. The distances involved (zero, and ten light years) were measured in their frame. When they measured the distance of ten light years, they were at rest in the comoving frame, so they measured the distance to be the same as the proper distance; other than that relationship, the comoving frame is irrelevant to my question. How does the crew explain that the beacon they passed one year ago on their clock is now ten light years away as they measure? No answer that involves a slow clock will suffice. You must stick to the crew's frame only. The additional redshift comes from length expansion, which is a physical expansion of space, but it’s a relativistic effect (it cannot rip apart atoms, for example). If you disagree with Taylor and Wheeler, then yes, I do not understand you. That’s why I asked for a reference in that case. Or is it a new idea of yours? There is no reference for that, because I’m explaining something new here, my own idea. I'm backing it up right here in this thread. Two million light years. I don’t know where you got ten from. I already answered this. In the Earth observer’s frame, the muon’s clock runs slow and the muon is length-contracted. In the muon’s frame, the Earth including its atmosphere is length-contracted and the Earth observer’s clock runs slow. In both frames, the other object is both length-contracted and time-dilated.
zanket, No, I explained the scenario from the perspective of the comoving frame, the frame in which proper distance and proper time is measured. That frame is a third frame of reference, not either the 'crew' frame or the 'beacon' frame. The crew's local clock accumilated one year of time since passing the beacon. That does not mean they traveled less than one light year. They traveled a distance of ten light years in the comoving frame while their clock only advanced one year. The clock in the comoving frame will accumilate over ten years on it. Assume the rocket never decelerated during the trip. In this case, the crew would travel less than one of the crew's light years in one of the crew's years. Those distances and times are in the crew's frame of reference. In the the comoving frame (the ICRF) the rocket will travel a proper distance of ten light years in over ten proper years. Relativity theory says the crew can move between the two points without exceeding 'c' in the rocket's frame of reference because the rocket measures time and distance differently. The universe never contracts nor do clocks ever beat slowly in the comoving frame, only in the rocket's frame. The comoving frame (the ICRF) closely corresponds to an Earth frame of reference. The distant objects we observe from Earth are not decelerating to a stop nor is the Earth decelerating to a stop. The distant objects appear to be accelerating in velocity relative to us. If distances contract as relative velocities increase, shouldn't the universe appear to be contracting instead of expanding? Edited to clarify. I was going to let zanket point out my previous delibrate mistake concern the comoving frame, but decided against it.
