Breaking my radio silence here to get a little nitpick off my chest: the claim that during inflation, the universe “expanded faster than the speed of light.” It’s extraordinarily common, if utterly and hopelessly incorrect. (I just noticed it in this otherwise generally excellent post by Fraser Cain.) A Google search for “inflation superluminal expansion” reveals over 100,000 hits, although happily a few of the first ones are brave attempts to squelch the misconception. I can recommend this nice article by Tamara Davis and Charlie Lineweaver, which tries to address this and several other cosmological misconceptions.
This isn’t, by the way, one of those misconceptions that rattles around the popular-explanation sphere, while experts sit back silently and roll their eyes. Experts get this one wrong all the time. “Inflation was a period of superluminal expansion” is repeated, for example, in these texts by by Tai-Peng Cheng, by Joel Primack, and by Lawrence Krauss, all of whom should certainly know better.
The great thing about the superluminal-expansion misconception is that it’s actually a mangle of several different problems, which sadly don’t cancel out to give you the right answer.
1.The expansion of the universe doesn’t have a “speed.” Really the discussion should begin and end right there. Comparing the expansion rate of the universe to the speed of light is like comparing the height of a building to your weight. You’re not doing good scientific explanation; you’ve had too much to drink and should just go home.The expansion of the universe is quantified by the Hubble constant, which is typically quoted in crazy units of kilometers per second per megaparsec. That’s (distance divided by time) divided by distance, or simply 1/time. Speed, meanwhile, is measured in distance/time. Not the same units! Comparing the two concepts is crazy.
Admittedly, you can construct a quantity with units of velocity from the Hubble constant, using Hubble’s law, v = Hd (the apparent velocity of a galaxy is given by the Hubble constant times its distance). Individual galaxies are indeed associated with recession velocities. But different galaxies, manifestly, have different velocities. The idea of even talking about “the expansion velocity of the universe” is bizarre and never should have been entertained in the first place.
2. There is no well-defined notion of “the velocity of distant objects” in general relativity. There is a rule, valid both in special relativity and general relativity, that says two objects cannot pass by each other with relative velocities faster than the speed of light. In special relativity, where spacetime is a fixed, flat, Minkowskian geometry, we can pick a global reference frame and extend that rule to distant objects. In general relativity, we just can’t. There is simply no such thing as the “velocity” between two objects that aren’t located in the same place. If you tried to measure such a velocity, you would have to parallel transport the motion of one object to the location of the other one, and your answer would completely depend on the path that you took to do that. So there can’t be any rule that says that velocity can’t be greater than the speed of light. Period, full stop, end of story.
Except it’s not quite the end of the story, since under certain special circumstances it’s possible to define quantities that are kind-of sort-of like a velocity between distant objects. Cosmology, where we model the universe as having a preferred reference frame defined by the matter filling space, is one such circumstance. When galaxies are not too far away, we can measure their cosmological redshifts, pretend that it’s a Doppler shift, and work backwards to define an “apparent velocity.” Good for you, cosmologists! But that number you’ve defined shouldn’t be confused with the actual relative velocity between two objects passing by each other. In particular, there’s no reason whatsoever that this apparent velocity can’t be greater than the speed of light.
Sometimes this idea is mangled into something like “the rule against superluminal velocities doesn’t refer to the expansion of space.” A good try, certainly well-intentioned, but the problem is deeper than that. The rule against superluminal velocities only refers to relative velocities between two objects passing right by each other.
3. There is nothing special about the expansion rate during inflation. If you want to stubbornly insist on treating the cosmological apparent velocity as a real velocity, just so you can then go and confuse people by saying that sometimes that velocity can be greater than the speed of light, I can’t stop you. But it can be — and is! — greater than the speed of light at any time in the history of the universe, not just during inflation. There are galaxies sufficiently distant that their apparent recession velocities today are greater than the speed of light. To give people the impression that what’s special about inflation is that the universe is expanding faster than light is a crime against comprehension and good taste.
What’s special about inflation is that the universe is accelerating. During inflation (as well as today, since dark energy has taken over), the scale factor, which characterizes the relative distance between comoving points in space, is increasing faster and faster, rather than increasing but at a gradually diminishing rate. As a result, if you looked at one particular galaxy over time, its apparent recession velocity would be increasing. That’s a big deal, with all sorts of interesting and important cosmological ramifications. And it’s not that hard to explain.
But it’s not superluminal expansion. If you’re sitting at a stoplight in your Tesla, kick it into insane mode, and accelerate to 60 mph in 3.5 seconds, you won’t get a ticket for speeding, as long as the speed limit itself is 60 mph or greater. You can still get a ticket — there’s such a thing as reckless driving, after all — but if you’re hauled before the traffic judge on a count of speeding, you should be able to get off scot-free.
Many “misconceptions” in physics stem from an honest attempt to explain technical concepts in natural language, and I try to be very forgiving about those. This one, I believe, isn’t like that; it’s just wrongity-wrong wrong. The only good quality of the phrase “inflation is a period of superluminal expansion” is that it’s short. It conveys the illusion of understanding, but that can be just as bad as straightforward misunderstanding. Every time it is repeated, people’s appreciation of how the universe works gets a little bit worse. We should be able to do better.
Jesse,
Thank you for the reply.
Yes, we would never be able to tell if one particular clock runs quicker than all other frames, but it would seem the increments would get increasingly smaller, thus at least pointing toward an upper bound.
I suppose my deeper position is that geometry only maps space, it doesn’t create it. Currently it seems as if space is simply being treated as an effect of matter and energy moving around and so defined in terms of spacetime, the mathematical description of this activity. Yet as I argued previously, I see time as an effect of that activity. Now if we were to eliminate all physical properties, would the vacuum of space cease to exist? How can space rise from a dimensionless point, if anything multiplied by zero is zero? Wouldn’t an infinite number of dimensionless points still be a dimensionless point? So wouldn’t you need some increments of dimensionality to project anything?
If we were to eliminate all physical properties from space, than wouldn’t it still have the non-physical qualities of infinity and equilibrium, as it would have nothing to bound, locate, or disturb it?
Smolin argues that time is the primordial factor, given the argument that laws emerged and evolved over time, but I think a better argument could be made for space as the essential state; Given that the existence of space is the basis for quantum vacuum fluctuation. Which as an elemental wave action, gives us the frequency and amplitude of energy that is basis for both time and temperature. Then you get feedback, as this energy expands toward infinity and collapses back to equilibrium, starting the process of creating radiation and mass, as emergent.
Now this is speculation, but I do think we need to consider time as something more than a measure of duration and presumably existent as block time. There are just so many contradictions in it.
For instance, the premise of determinism is based on the inertia of energy leading from one event to the next, such as a batter hitting a ball, or a rock hitting water. The very transfer of energy manifesting one event to the next, means the prior event ceases to exist. Unlike with space, where both ends of a line can co-exist.
As for determinism, while we think of the present moving from past to future, this also means those events which were in the future, become past. So events are first in the present, before in the past. Therefore they have to occur, in order to be determined.
Now given energy, even light, travels at finite speeds, it would take a point of view outside of time and space to fully acknowledge all input into an event before it occurs and if you cannot know the input, you cannot know the output, which seriously undermines the premise of determinism, for all but a God’s eye view.
So while events and forms go future to past, as they come into being and dissolve, the energy manifesting this process goes past to future, as it creates and dissolves these events.
So in this dichotomy of energy and the forms it manifests, time is an effect, as well as the laws emerging from the activity they define, since there would be nothing to describe and model in a void. The primary quality of law being regularity/repeatability.
So then the question of General Relativity is whether it is the physical structure underlaying reality, or a mathematical description of the patterns emerging from it?
Remember epicycles were very predictively accurate, because they were based on direct observation, but the mechanism, the cosmic clockworks, to explain this regularity was mistaken. I suspect we will find the same with General Relativity and spacetime. The math is effective, but the mechanism extrapolated from it is flawed.
So, yes, as frames move about, their clocks slow, but there is still some underlaying assumption of what that is movement in. So far, all our efforts to limit and define space, seem to require additional spaces in an increasingly infinite network. Multiverses have some inescapable premise. To paraphrase an old saying about war; You may not like infinity, but infinity likes you.
John Merryman says “If the edge of the universe recedes at C, this means there are increasingly more lightyears between our point and it. So that assumes the vacuum, which is defined by the speed of light, is independent of this expansion. As Einstein said, “Space is what you measure with a ruler,” and the ruler is not being stretched, just more units are added. How do you even get space from a dimensionless point, if even infinite multiples of zero are still zero?”
If you’re point is that all the model does is replace an explicit spacetime-expansion that works, with an implicit assumption of a pre-existing and unexplained vacuum?
Answer: The conceptual basis of a scientific assumption is something ‘not obvious empirically nor implied by what is. Space is empirical. Empiricism is the assumption. But ‘if it’s observed, it’s understood’ is not implied by empiricism and not sensible assumption to make. Best.
Chris,
For one thing, how can it even be “spacetime,” if the speed of light doesn’t remain Constant? If it is explicitly taking light longer to cross the space, in order to be redshifted, that’s not spacetime, just increased distance.
The entire premise is that it takes light longer to cross the distance between galaxies, as the cause of redshift. This is not an assumption. It is a relationship, between what is measured by the speed of light, to what is deduced from the redshifted spectrum of the same intergalactic light. Do you understand the difference between a denominator and a numerator? In this case, the speed of light is the denominator and the distance between galaxies is the numerator.
If it were the other way around and the space between galaxies were considered the denominator, then it would be an issue of tired light, as the question would be why does it take light longer to cross between these points.
Word salad is not an answer. Regards.
Sean-
Your explanation is superb. I wonder how you would apply that same skill to quantum mechanics/quantum field theory. I ask because I recently watched a panel where you were a participant that discussed formulations/interpretations of quantum mechanics. I also hope you might shed some light on the issue in your new book.
The issue is the physical meaning of the quantum wave function or even the quantum fields in QFT. Or as Brian Greene called it the “probability wave.” Now I appreciate that many physicists think such questions are unnecessary or not applicable. However, when communicating physical theories to laypeople like myself, I believe it is critical. Now in all standard quantum formulations aside from Bohmian mechanics, the so-called wave function has no physical meaning in 4D space-time. So that’s why I think this analogy of the Schrodinger equation describing a “probability wave” in physical space ( 4D space time) is misleading. Similarly, you described particles a “disturbances” of quantum fields; however, I feel that is just as misleading since these fields have no physical reality. So, in the end, QFT just like quantum mechanics cannot explain the basic paradoxes of nature like the double slit experiment in a physical sense.
Now I ask or pose all these questions respectfully. But as an avid follower of the history of physics, it seems to me that to abandon a realist explanation of the behavior of matter and light is premature. After all, Schrodinger was attempting to expand de Broglie’s notion of matter waves into a formal dynamical formula. Interestingly, Madelung derived an equation from Schrodinger’s that in some sense describes mass and/or charge density in a hydrodynamic way and thus distributed over space and time. My point is that there are consistent mathematical models that can now explain wave particle duality as a consequence of the real vacuum electromagnetic field and the interaction of light and matter (waves) with it. Even so called quantum spin states can now be explained via new understandings of angular momentum and rotations in hydrodynamic states. (Foundations of Physics October 2009, Volume 39, Issue 10, pp 1177-1190)
Not to mention new experiments exhibiting violations of Bell’s Inequalities through purely macroscopic means, i.e. two classical volumes of water.(Professor Aerts) The point there is that Bell’s Theorem rests on certain assumptions and that these so-called non-local connections may be a consequence of purely physically real states. (arXiv:quant-ph/0007044) In fact, additional examples of entanglement emerge in purely classical optics. The insight is not about the probabilistic nature of matter but of our understanding of probability itself. It makes quantum theory seem more and more as an approximation like statistical mechanics.
I guess my point is that acceptance of quantum field theory (QFT) as it is now fails to assert any claims about how the physical universe operates on a Realist level. It cannot explain the double slit experiment in a physical sense. Not to mention its mathematical defects via Haag’s Theorem. Thus, I implore physicists like yourself who already have the unique skills to communicate complex physical concepts to the uninitiated, to be frank when describing quantum theory and thus physics in general. Let people know that you do not have a physical picture of how the universe operates, only an abstract mathematical one that physicists postulate then somehow magically collapses or reduces into classical reality. I am not too familiar with Everett’s formulation, but postulating that all the values of the wave function exist still does not seem to explain where the wave function evolves or what physical process causes the evolution of the wave function. Thus, I hope that you could comment on this approach especially some of the theories and experiments that offer classical or physical explanations for the behavior of matter and light.
@Sean Carroll,
“Logic” cannot help us when we use the wrong concept. The right concept will make it possible to derivate the universal properties of nature. Of course, there is a restriction. A universal property (physic law; physic constant; overall behaviour) is not limited to a specific category of phenomena, so these properties must be existent at the lowest level of reality (otherwise, it is just some kind of empiric physics).
Hi Jesse M – you’re making posts with general value regardless of who, in the moment, may be agreeing or disagreeing or what the specific subject is.
However, if I could just point out an issue in the current context that is in play here.
As you say there is a standard way to talk about distant velocities that does in some sense draw on the ‘relativity of simultaneity’ thing.
But typically, for reasons you also gave, this tends to involve simultaneity assumptions along the lines of ‘where that distant galaxy is NOW as we observe it”. This is usually graphed along the lines of…imagine two parallel lines in the horizontal. The bottom is the distant object, the top line represents all the simultaneous observers. Then draw as many (parallel, evenly spaced) vertical lines as you like, connecting the horizontals. They represent individual galaxies. Then choose a point on the top horizontal line, that point as a observer. Then draw two diagonals from that point on the top line to two points with separate z on the bottom line. That’s the light-cone ‘look back’. So it’s very clear galaxies that we can observer the further back, leave our light cone.
Invert the graph (change the context) and it’s clear that a galaxy in our light cone from the perspective of another observer light cone, can be travelling at faster than light speeds relative to our observer in our light cone.
However, that does not mean that we can observe an object receeding from us at faster-than-light speeds. The reason is that even without Einstein’s relativity, the forerunner effects are still there in the form of redshift. Whether Doppler or cosmological, the redshift slows, in effect, time as we receive or observe it from our position.
Redshift keeps the speed that is observable inside the speed of light. This is an empirical fact besides being theoretical since Maxwell. Observables with a known duration like some supernova, are MEASURED to run for longer periods with more distant observations.
So the people saying that you can’t observe objects faster than light are absolutely correct. And everything you said was also absolutely correct. Because two contexts were in play.
Hi John Merriman,
It sounds like you are pursuing an alternative possibility, or considering doing so. Personally IMHO I think nascent, fledgling, ideas if they inspire another human being, should be left alone. It’s too easy to shoot down a seed idea
which yours is…it’s a seed idea. IMHO you should not be waving it around for others to ignore (and frustrate and demoralize you) and/or shoot down (and infuriate, frustrate and demoralise you).
If you believe it, and you’ve got the energy and commitment that it takes to see where it goes. Then do it.
That particular one I’ve seen a few times in comments sections on the Internet. Which may be you in different names, or you may be one of those who like me has seen the point. Or you may be the originator of the point. Or any number of other possibilities.
That’s why it’s better to keep personal seed ideas private, at least until one is sure one is not going to be pursuing it. FWIW the seed idea in question is flawed in context of incumbent meanings of words and theories. Best.
I said “So it’s very clear galaxies that we can observer the further back, leave our light cone. ”
to be clear though, not from our perspective. From another ‘simultaneous’ observer perspective, but not ours.
Nothing ever leaves our light cone that was there to begin with. It doesn’t matter how much faster than light the object accelerates toward.
This because all that happens from our perspective is the photon gets more and more stretched out. At a certain theoretical point, it just stops. That’s because we are talking about an ‘event horizon’ type conception.
It’s not the same thing as with a black hole, but it is a close relation of the same thing. Time stops at the horizon from the perspective of the observer.
@Chris Mannering:
But typically, for reasons you also gave, this tends to involve simultaneity assumptions along the lines of ‘where that distant galaxy is NOW as we observe it”. This is usually graphed along the lines of…imagine two parallel lines in the horizontal. The bottom is the distant object, the top line represents all the simultaneous observers.
I don’t understand, when you say the bottom line “is the distant object”, do you mean the line represents its worldline, or something else? And by “the top line represents all simultaneous observers” do you mean it represents a surface of simultaneity in the cosmological coordinate system we’re using? If the bottom line is a worldline and the top line is a simultaneity surface, I don’t see how they can both be horizontal, since that means they will never intersect on the diagram, but every worldline of a bit of matter (or a light ray) should intersect every simultaneity surface is cosmology. Perhaps you meant the bottom line to just represent a different simultaneity surface? For example the bottom line could be the time when the distant galaxy emitted some light (from a distinct event like a supernova, say), and the top could be the time when we received that same light (seeing the supernova in our telescopes).
Then draw as many (parallel, evenly spaced) vertical lines as you like, connecting the horizontals. They represent individual galaxies.
If you draw the galaxy worldlines as vertical, that implies the horizontal axis represents comoving distance–that’s fine as long as you keep in mind that this is a different notion of “distance” than the one used when talking about how fast galaxies are moving away from us (in that case we are talking about their proper distance in each simultaneity surface, and how that changes with our own proper time). It might help if we had some actual diagrams to refer to in this discussion, so take a look at Figure 1 on p. 3 of the paper Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe by Davis and Lineweaver–in that figure we have three diagrams, the top one is the most relevant since it uses proper distance as the horizontal axis and proper time as the vertical axis, so the slopes of the dotted lines (representing galaxy worldlines) tell us their recession velocity in terms of proper distance/proper time. Meanwhile, the middle and bottom diagram use comoving distance as the horizontal axis, so all the galaxy worldlines are vertical; the middle one uses proper time as the horizontal axis, while the bottom one uses a “conformal” time coordinate which ensures that all light rays travel at 45 degree angles, so light cones become particularly easy to interpret.
Then choose a point on the top horizontal line, that point as a observer. Then draw two diagonals from that point on the top line to two points with separate z on the bottom line. That’s the light-cone ‘look back’. So it’s very clear galaxies that we can observer the further back, leave our light cone.
The sides of a light cone would only be diagonal if you assume a coordinate system where this is true, like the combination of comoving distance and conformal time in the bottom diagram. But when cosmologists talk about galaxy’s recession velocity, they are typically not using such a coordinate system, but again using “velocity” in terms of proper distance/proper time, and in this sense light itself does not travel at a constant velocity (look at our past light cone in the top diagram, you can see the light rays aren’t straight lines, and the light cone looks more like a teardrop shape).
Invert the graph (change the context) and it’s clear that a galaxy in our light cone from the perspective of another observer light cone, can be travelling at faster than light speeds relative to our observer in our light cone.
What do you mean “in our light cone from the perspective of another observer light cone”? If an event, such as a supernova in a distant galaxy, lies in our past light cone, then this is a coordinate-independent physical fact which does not depend on which observer’s “perspective” we choose to assume–do you disagree?
However, that does not mean that we can observe an object receeding from us at faster-than-light speeds. The reason is that even without Einstein’s relativity, the forerunner effects are still there in the form of redshift.
I don’t understand what you mean by “forerunner effect”. And things can be receding faster than light but have a finite redshift, presuming you are defining recession speed in terms of proper distance/proper time–this is mentioned specifically in the Davis/Lineweaver paper on p. 2, where they say first mention that they are using D to represent the proper distance, then say:
“Using Hubble’s law (v_rec = HD), the Hubble sphere is defined to be the distance beyond which the recession velocity exceeds the speed of light, D_HS = c/H. As we will see, the Hubble sphere is not an horizon. Redshift does not go to infinity for objects on our Hubble sphere (in general) and for many cosmological models we can see beyond it.”
(note that c here is actually a variable rather than a constant, since the rate that a light ray’s proper distance changes with proper time depends on both the cosmological time and its proper distance at that time; and H, the Hubble “constant”, varies with time in most cosmological models)
Davis and Lineweaver also wrote a simpler version of this article for Scientific American titled Misconceptions about the Big Bang, and as I already mentioned in a previous comment, they also stated plainly on p. 43 of that article that “we can observe light from galaxies that have always been and always will be receding faster than the speed of light.” Are you arguing that the authors are mistaken in the two statements I quoted, or would you agree these statements are correct as long as we define recession velocity in terms of proper distance/proper time?
Redshift keeps the speed that is observable inside the speed of light. This is an empirical fact besides being theoretical since Maxwell.
The redshift equation you will see in the context of Maxwell’s electromagnetic theory is one that holds in inertial coordinate systems in flat spacetime, a different equation is required if you want to calculate redshift using proper distance and proper time as your spacetime coordinates, in the context of the curved spacetime in cosmology. Davis and Lineweaver give the cosmological redshift equation on p. 5 of the “Expanding Confusion” paper, equation (1), and they also give the special relativistic redshift equation (i.e. the one you’d see in the context of Maxwell’s theory) as equation (2), you can see the equations are quite different. In equation (2), the redshift z goes to infinity as v approaches c, but the same is not true in equation (1)–they mention on p. 6 that “Recession velocities exceed the speed of light in all viable cosmological models for objects with redshifts greater than z ∼ 1.5.”
So the people saying that you can’t observe objects faster than light are absolutely correct. And everything you said was also absolutely correct. Because two contexts were in play.
It isn’t clear to me what context you are using when you say it’s true that “you can’t observe objects faster than light”. Are you just talking about the context of inertial coordinate systems in flat spacetime, or do you argue there is a sense this is true in cosmology as well? If so, when you say “objects faster than light”, are you defining their velocity in terms of proper distance/proper time, or using some other coordinates, and if the latter which ones?
Chris,
Thanks for the advice and concern. I do post as brodix on occasion, as that is my middle name. I have originated various aspects of this proposal and have evolved it through discussions over the internet. I’m certainly willing to consider logical rebuttals and respond and adapt to them. Given it falls under what would be considered a steady state model, I also realize such positions are usually dismissed out of hand. As I’m not professionally engaged in this, but find it an interesting hobby and mental exercise, I can sense the conflicts and politics, without taking them too personally. If I was professionally engaged, I also realize I would be unemployed, to hold such a position.
I actually started studying physics some decades ago, as a way to better understand politics, given that when billions of people are involved, it is more a matter of the physics, than the sociology. So having come from that perspective in the first place, I am only moderately surprised by how much politics dominates the fields of physics.
That said, if anyone does find my ideas interesting, I suppose I am open sourcing them, given I lack both the time and the professional standing to pursue them. Otherwise, I’m just one more crank among many.
Awesome. I’d only gotten as far as dimensional analysis. The expansion of space has the wrong dimensions for speed. I had not gotten as far as my weight. Well, i’m an engineer. The good news is that my kids were introduced to dimensional analysis recently in high school. Why not?
There’s also another bit to wrap your head around. During Inflation, the Universe is supposed to expand by a huge amount in a very short period of time (or instantly or something). It might be when the Universe is a millionth of a second old, and if you start out at a point, not very large, but you see a small ball (a meter in radius?) grow to a large ball in what seems to be all at once. It’s very hard to wrap your head around this as something other than speed. Of course, what’s wrong is that you tend to imagine it from outside. There is no outside. But inside the ball is even worse on the imagination. The best i can come up with is that we are pretty much at the same spot that, uhm, our atoms were at near the start of the Universe. Nothing has moved much. Space has been added around us. And that’s what it looks like inside the ball. The ball that has no edge, and may be infinite in size. Or not infinite, but still without an edge. Or something.
Hi Jesse M – I rode roughshod on the schematic because I figured I only had to do enough for you to figure out the schematic I was recalling. It’s not mine it’s just one of the bog-standard schematics. I think. Anyway I should be able to find it on youtube somewhere and will link it before I post this comment.
You wrote a hell of a post and I’m appreciative. But if it reduces to “You are being incoherant to my eye”. An option might have been spend the time/energy, making inferrances what I’m saying, from common sense and what disagreement has been the central theme of this thread.
A few of us, you and I included, have been throwing comments on the bonfire of [killing] time, where the theme is you and some others have been saying we OBSERVE red-shift galaxies – over 1.5 I think you said – in superluminal recession. Fair enough?
And a few other of us have been objecting that it’s impossible – due to the terms, definitionally, of the light cone, to observe object in superluminal recession. All good…have we two lazily killed time in the same unnoteworthy thread? I mean, it’s forgettable sure, but so soon??!!
So anyway, are you happy so far? If you are then all I was saying in the last comment was that the point about the light cone does not ASSUME anything one way or the other, about galaxies in superluminal recession relative to us.
The objection was that we cannot OBSERVE a galaxy in superluminal recession. And that it cannot be said in any physical sense that a red shift galaxy is observably in superluminal recession.
The reason that I gave was that Red Shift is synominous with time slowing down in the red-shift galaxy RELATIVE to time experienced by us from our observational coordinate FROM our PERSPECTIVE. The last part about perspective is a throwaway, if it makes anything clearler.
Red Shifted electro-magnetism is the physical messaging in play between the distant red-shift galaxy (any ARBITRARY red-shift galaxy satisfying THRESHOLD criteria for, in your view, observable superluminal recession
Is this ok so far?
As your galaxy crosses into superluminal recession it simultaneously moves further into red-shift, which is a quantity that is fully exchangable with clockspeed. We empirically confirm this by listening to what was going down in that galaxy at the time the photons began their journey over to us. We turn in to the radio waves and listen to standard candle catacalisms of KNOWN duration, and measure everything in slow motion.
In the limit, at a certain theoretic point, time just stops in that distant redshift galaxy relative to where we are standing. It stops. And that is why nothing ever OBSERVABLY departs the light cone, that was previously there. It dims and reddens, you need a bigger telescope, you need a longer exposure, or a new technology, but it remains detectable in principle.
I tied off by mentioning another line of reasoning using the fact there is an Event Horizon in play. These objects theoretically stand on their own. They show up at BlackHoles not because of anything intrinsic, other than the criteria for an event horizon is satisfied.
The thought experiment that gives rise to the holographic principle – that a displaced observer of a friend of whatever falling into a blackhole, never makes that observation because the hapless chappie’s clock slows from the perspective of the displaced observer, and continues to slow forever at closer approximation to time just stopping.
That’s an attribute of event horizons in certain criter met, which galaxies in superluminal recession satisfy.
I’m not asserting authority. You can agree or disagree. I do hope though, I’ve managed enough that you at least do understand, what I think is correct, correction pending.
@Chris Mannering: Hi Jesse M – I rode roughshod on the schematic because I figured I only had to do enough for you to figure out the schematic I was recalling. It’s not mine it’s just one of the bog-standard schematics. I think. Anyway I should be able to find it on youtube somewhere and will link it before I post this comment.
It looks like you forgot to include that youtube link when you posted—but did you look at the three diagrams I talked about in my previous comment, the ones from Figure 1 on p. 3 of the Expanding Confusion paper I linked to? If not, could you please take a look now and see if any matches what you’re thinking of? All diagrams depict the same expanding universe with the same definition of simultaneity, but the three diagrams differ in what position coordinate they use on the horizontal axis (the first uses proper distance, the next two use comoving distance), and/or what time coordinate they use on the vertical axis (the first two use proper time in our own galaxy, the last one uses a ‘conformal’ time coordinate which together with comoving distance has the nice property that all light rays then have the same constant coordinate speed, so all light cones have straight-line sides at 45 degree angles from the vertical on the diagram, whereas the coordinate speed of light is variable in the first two diagrams so light cones don’t have straight sides in those).
You wrote a hell of a post and I’m appreciative. But if it reduces to “You are being incoherant to my eye”. An option might have been spend the time/energy, making inferrances what I’m saying, from common sense and what disagreement has been the central theme of this thread.
My post wasn’t intended to make any final pronouncement that your position is incoherent, it was intended to be part of a more open-ended dialogue, that’s why so much of my post consisted of questions about statements you had made that seemed unclear to me, but perhaps would become more clear if you clarified them. It was a long post so I’ll understand if you don’t feel you have time to address every question, but in general could you try to address at least one or two of whatever seem to be the most significant questions I ask you?
The main “theme” of my difficulty understanding the meaning of your comments is that I don’t think it’s meaningful to talk about the “speed” of anything (including a galaxy) unless it is clear what notion of distance and time one is using—for example, the speed of a faraway object will generally be different if we are talking about (proper distance)/(proper time) than if we are talking about (comoving distance)/(conformal time). This also applies to the relationship between speed and redshift, since the idea that redshift goes to infinity as something approaches the speed of light is only true with certain measures of distance and time (like distance and time in an inertial frame), but not true in others. So if you only have time to answer one question, I would ask that you answer this one: when you argue that there is some sense in which it’s impossible to see galaxies which have a speed greater than light, are you talking about “speed” in terms of proper distance and proper time, or some other notion, and if some other, can you specify what it is?
The reason that I gave was that Red Shift is synominous with time slowing down in the red-shift galaxy RELATIVE to time experienced by us from our observational coordinate FROM our PERSPECTIVE. The last part about perspective is a throwaway, if it makes anything clearler.
Well, again the actual “observational coordinate” needs to be specified for this to be clear, but I would agree that if “time slowing down” means a slowdown in the rate of the galaxy’s clock as compared to our own clock (our own proper time), then more redshift does correspond to more slowdown. However, you can’t assume the time dilation factor approaches infinity as the galaxy’s speed relative to us approaches light speed, that would be true in an inertial coordinate system in special relativity, but it isn’t true in a cosmological context where “speed” is being defined in terms of the rate the galaxy’s proper distance from us changes as a function of our own proper time.
In the limit, at a certain theoretic point, time just stops in that distant redshift galaxy relative to where we are standing. It stops. And that is why nothing ever OBSERVABLY departs the light cone, that was previously there. It dims and reddens, you need a bigger telescope, you need a longer exposure, or a new technology, but it remains detectable in principle.
The phrase “departs the light cone” is not entirely clear, since we have different past light cones at different moments. At any given moment, any event we can see at that moment must by definition lie in our past light cone at that moment, but it’s not true that an event which lies right on the boundary of our past light cone has infinite redshift. However, there is another context in which your statement would be correct. In cosmology, if the universe is expanding fast enough, the theoretical model also implies that some events will never enter our past light cone at any moment—in the third of the three diagrams from Figure 1 at that paper, our infinite future proper time is compressed into a finite height on the graph by the conformal time coordinate, so we can see what our past light cone “at infinity” looks like, consisting of all the events that will ever enter our past light cone at any finite proper time in the future. On the graph, this past light cone at infinity is labeled “event horizon”. And as a receding galaxy approaches this cosmological event horizon, we will see it getting more and more redshifted, and see its clock running slower and slower, never quite reaching whatever time T that its clock actually shows at the moment it crosses our event horizon (of course any observers in that galaxy would experience time to continue as normal past T, but light from any events at T or later in that galaxy will never reach us).
But although your comment is correct in this point, my question would be: How does this have anything to do with superluminal recession velocities? Are you assuming that the point at which a galaxy crosses our cosmological event horizon is synonymous with the point at which its recession velocity reaches the speed of light? If so, then assuming we’re defining recession velocity in terms of proper distance/proper time, that idea is not correct. The “point at which its recession velocity reaches the speed of light” is the point it crosses an entirely separate boundary, known as the boundary of our Hubble sphere, and the boundary of the Hubble sphere lies within the cosmological event horizon—within our past light cone “at infinity”; and for sufficiently early times, it even lies within our past light cone today. Again just look at the diagrams I linked to, particularly the third one where past light cones are easy to spot since they like cones with sides at 45 degrees, as they do in special relativity, and all galaxy worldlines are just straight vertical lines since the diagram is using comoving coordinates. The boundary of the Hubble sphere is also labeled on the diagram, and you can see that all of its boundary lies within our event horizon, while part of its boundary lies within our current past light cone. You can also see that there are some vertical galaxy worldlines, like the one just past the “20” mark on the bottom horizontal axis, which never cross into the Hubble sphere (meaning they always have a recession velocity greater than the speed of light, in terms of proper distance/proper time), and yet there are plenty of points along these worldlines that lie within our current past light cone, meaning we can see much of the history of these galaxies with only a finite redshift, and with any astronomical clocks in these galaxies seen to be “ticking” at a finite rate.
That’s an attribute of event horizons in certain criter met, which galaxies in superluminal recession satisfy.
Any galaxy outside our cosmological event horizon would have a superluminal recession velocity, but the converse is not true, assuming “recession velocity” is defined in terms of proper distance/proper time. A galaxy can be within our cosmological event horizon and have a superluminal recession velocity, and it can also be within our current past light cone and have a superluminal recession velocity at every point within that past light cone (including the intersection between the galaxy’s worldline and our current past light cone, which of course is the point on the galaxy’s worldline that we are seeing right now). Do you disagree?
I note that you have referenced in this article: http://nautil.us/issue/29/scaling/will-quantum-mechanics-swallow-relativity
The article concludes: “But the best thing it can do is create deeper meaning that connects back to us, the observers, who get to define ourselves as the fundamental scale of the universe.”
It is with both considerable trepidation and temerity that I suggest that a possible solution to reject the anthropic fallacy that we are the only observers of the universe and that the scale at which we observe things is the only scale that “observers” can “observe”. Maybe the solution is to consider that the quantum effect is scalable, depending on the “observer”. A galaxy and a photon can both “observe” things – but what they can observe are very different. A galaxy can “observe” other galaxies, but not individual stars in those other galaxies. A photon can observe other photons, but cannot “observe” the star that it is from. Until something can “observe” and be “observed” there is no before and after of the observation – there is no time. It is in a “quantum state” to the “observer”. Maybe mass is the sum from all the actual positions that something is in until the moment that it is then “observed”? Hence the apparent discrepancy of mass in the universe from our singular point of observation.
“Thinking like a mountain” (Aldo Leopold) means that you have to “think” like a galaxy, or “think” like a photon or muon. What do you experience, feel, or observe from that perspective? Doing the maths from that perspective should be relatively simple (or am I being naive here?). Trying to explain from “our” position as observers is as pointless and futile as epicyclists trying to use their theories and maths to deconstruct Copernicus’s insights. Just as Copernicus caused a paradigm shift I believe a paradigm shift in thinking is required about how we think about physics at macro and micro scales. Today’s physics requires greater and greater flights of fancy – epicycles upon epicycles.
More unstructured “observations” on treating the quantum effect as scalable: https://docs.google.com/document/d/1upBUuNOAEG5Ue1RwW8e_3AFZ1xOredTftzOFSHa_5gM/edit
Since you can’t step outside the universe, it seems to boil down to a frame of reference issue.