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Superluminal Speeds and All That Jazz 
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#1
Oct3108, 07:22 AM

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A popular prejudice is sometimes expressed as “nothing can travel faster than light”. But Special Relativity (SR), from which this prejudice is derived, in fact teaches only that “nothing can be observed to travel faster than light”. The meaning of ‘observed’ here is technical and can be unpacked by explaining how distances are measured and clocks are synchronized with light signals in SR. It may then come as a relief to realize that SR creates no mysterious speed barrier. SR does not prevent one traveling to a star, measured on Earth to be lightyears away, in just a few hours; SR dictates only that traveltime be measured by the traveler on his/her clock, not by an Earthbound stayathome.
It would be misleading, though, to call the traveler’s speed ‘superluminal’, say because at home on Earth the distance the that the traveler covered was measured as a few lightyears. From an SR point of view, this would be like comparing apples and oranges. In nature as described by SR there are no superluminal speeds that can be measured as such. What about superluminal speeds in General Relativity (GR)? ‘Superluminal speeds’ are certainly talked about when dealing with models of the universe based on GR, in many threads in this forum. Sufficiently distant parts of a model expanding universe are sometimes said to ‘separate at superluminal speeds’. To me, this seems in an inverse sense just as simplistic as saying that “nothing can travel faster than light”. In GR speed is not a simple concept: First, in GR ‘to separate’ is generally taken to mean to increase ‘the proper distance between’. Second, ‘proper distance’ means the sum of a chain of ‘local’ proper distances, measured as in SR, over a span in which spacetime is perceptibly nonEuclidean (‘distance’ could also measured by radar, as in SR, with possibly different results). Third, properdistance measurements are to be made simultaneously, at the same instant of a defined ‘time’ (in consensus cosmology ‘simultaneous’ means when observers measure the same density of mass/energy, locally, in a model universe.) In GR the concept of ‘speed’ needs a lot of unpacking! If, after all this unpacking, one gets an answer that exceeds c, there is in my view nothing to make it worthwhile to describe a speed which in practice you cannot measure or observe as ‘superluminal’. Using 'superluminal' suggests that something special or exceptional is being uncovered. In cosmology, getting an answer for a speed greater than c in an expanding universe means simply that one is extrapolating a model into unknowable regions beyond the (dynamic) red horizon of the observable universe. In observable nature as described by GR there are also]no superluminal speeds that can be measured as such. Why then bother with the word ‘superluminal’ at all, I ask? 


#2
Oct3108, 11:43 AM

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I don't particularly like the word. I use it rarely. I prefer to talk about standard model distances increasing at rates > c. Some other posters use it and when I occasionally do it's mainly just to make contact with other people's way of talking. I'm not sure what you mean by "unknowable regions beyond the (dynamic) red horizon of the observable universe." Could you clarify? Maybe we mean different things by observable universe. For me, when we map the CMB we are looking at matter which is now about 46 billion lightyears away from us. We can't see what that matter is doing at this very moment, but we can tell certain things about it such as variations in its density. To me it's clear that matter is part of our observable universe. The distance estimate is part of the standard LCDM model which I believe we have educational function to help people understandas a home base or common point of departure. If we choose to deviate, it's OK but it's more efficient if as a minimum we all know the basics of the standard picture of cosmology we are deviating from. You mention distance. Distance has always been a complicated issue in astronomy. Everybody should be alert to this. How do we define various distance measures? Which one is the prevailing or foremost, in terms of which others are conveniently expressed? Etc. You give a definition which (perhaps phrased slightly differently) I would basically agree with. It is convenient to use as one's primary idea of presentday distance and the Hubble Law is based on it. In order to sketch out and visualize the universe we live in, we need some primary idea of distance. It's how you talk about geometry. And there is a prevailing definition. Given this measure of distance we are immediately confronted by the question of the rate at which various distances increase and for full many a distance that we deal with in cosmology, for instance the distance to pretty much any object we see with a redshift z > 1.4, that rate of increase is greater than c. I'm not sure if you are having trouble with this, or objecting to it? Should we not use those words? Should we not say that suchandsuch distance is increasing at a rate of 2c or 3c or whatever? Should we use more words every time we need to refer to a rate of change of distancesome caveat or qualifying phrase that you have in mind and would like to recommend? I'm not entirely sure what you are saying in your post, Oldman. How should we be talking about the standard picture of the layout of the universe, according to you? And my earlier question was what do you mean by "unknowable regions beyond the (dynamic) red horizon of the observable universe" ? Do you mean regions beyond, say, 46 billion lightyears? Or do you mean regions beyond, say, 13.7 billion lightyears (the distance which is increasing at exactly c) because in the standard picture we see stuff currently way way out beyond that. Perhaps you'd clarify? 


#3
Nov108, 12:48 AM

P: 622

Here's a quick first reply to your post. Your detailed reply is really helpful. Thanks, Marcus. You asked "How should we be talking about the standard picture of the layout of the universe? " In answer to your question  in a word: "carefully". All I can offer is the opinion of a 'struggle veteran', as we say in these parts. I've found cosmology not an easy subject to understand, but with help I'm getting there. In a way it's like learning Russian, where the first hurdle you have to overcome is unlearning your English alphabet and replacing it with the Cyrillic alphabet. Worse than learning French!With cosmology one has first to unlearn the simple meaning of words like distance and speed. You must then learn to reinterpret them in a relativistic context. Once this is done you can go back to using these words freely, but with implicit caveats. The advantage of Russian is that when it is heard, it is easily recognised. Cosmologyspeak is not so easily recognised because cosmologists use the same vocabulary as Joe the Plumber. But, finally, after overcoming these hurdles, one comes to recognise that Joe's vocabulary is all we have, and that cosmologists and plumbers mean similar things after all. This is why I think cosmology needs to be introduced with a health warning, as it were, and why one should be wary of talking loosely about 'superluminal speeds' in particular. I'll answer the other points you raised 'just now'  in our local patois meaning 'a bit later'. 


#4
Nov108, 02:55 AM

P: 622

Superluminal Speeds and All That Jazz
You may see me as making much ado about nothing, Marcus; if so, you may well be right. But judging from the many confusions that arise in this forum I do believe that the careful presentation of cosmology is worth fussing over. [QUOTE] 


#5
Nov108, 11:49 AM

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As you say, the edge of the observable is about 46 billion lightyears from usthat's where the matter is that we see when we map the microwave background. We are looking at stuff that is currently 46 from here. That's important for noobs to understand, and fortunately we are all on the same page regarding the estimated age of around 13.7 billion. Since coming to PF in 2003, I've seem something on the order of 100 posters bring us their insight that, in standard cosmo, the radius of the observable must be 13.7 billion lightyears because expansion started 13.7 ago and the edge can't receed faster than c. One of the main jobs for the regulars has been to relieve noobs of that misconception. In standard cosmo, the distance to the farthest matter we are looking at currently is 46, not 13.7. I've gradually acquired the viewpoint that the least fuss and bother way to deal with this is to immediately confront it and make a clean break with this endemic misconception. Essentially it is a costbenefit analysis type of choice. 1. It is very CHEAP timewise to picture visually how distances between stationary points can increase at a c+ rate. You simply look at a balloon with glued pennies and with photons wriggling across the surface at a fixed rate of one inch per minute. There will be distances between pennies which are increasing faster than one inch per minute. But no penny ever outraces a photon in its neighborhood. Ned Wright provides the two computer animations of the balloons with wrigglers. To visualize (in an unparadoxical nice consistent way) how distances can increase at c+ rates, that's all you need. 2. It is very EXPENSIVE to leave the endemic misconception in place, because c+ expansion rates are physically built in to Hubble law, and the FLWR metric. Rates of expansion of distance are what Hubble law is about: v = Hd. The v there is a rate of change of distance, the instantaneous distance between two stationary points. Since it's what the basic law is about, if you don't get that up front, you don't ever get to square one. So I find it is actually hazardous to leave that misconception lying around for other posters to stumble on. One person spouting off can get several others confused, if they are vulnerable to thinking there is something funny or suspect about distances increasing at c+ rates. 3. There is a considerable bonus BENEFIT of coming to grips early on with some aspects of cosmology that are integral to the basic framework, like the business of stationary wrt background. You might say a basic cosmological injunction is "Dont move too fast relative CMB or the doppler hotspot will fry you!" And don't let the people in your thought experiments do that either, lest it fry them and fry your mind as well. Stationary basically means rest wrt the matter which emitted the CMB that we are now looking at. And happily we find the other galaxies are not moving much relative to it either. There may or may not be some largescale drift but either way that is a small footnote that you can't even talk about without first getting the idea of approximate rest wrt the expansion process and bulk primordial matter. Also cosmic rest gives you an idea of cosmic simultaneity that is essential to standard cosmology. The Hubble law v = Hd relates v and d defined as if measured instantaneously at some given moment. The d is between stationary points. In other words, the most basic quantities we work with depend on an idea of rest and simultaneity which is special to the field. 4. Dealing up front with the standard cosmo pattern of increasing distances, including rates of increase, gives a handy way to define useful quantities. For example the Hubble radius of 13.7 billion lightyears is defined simply as that distance which is increasing at rate c. The Hubble law is the proportionality between a distance and its rate of increase. So a distance of 27.4 (twice Hubble radius) would be increasing at rate 2c, and so on. These are physical relationships which I think it's good for beginners to assimilate early on. Part of understanding the standard model, which we should all get under our belts for starters. (Then if you want to cast doubt on the standard model and propose some alternative picture of the cosmos at least we all share a common starting point from which to explore variants. I don't object to skepticism and exploratory deviation, they are healthy! But first we all need to understand the basics of what we are being skeptical about and deviating from.) Oldman, I'm hoping very much that you and I can agree on some of these points! 


#6
Nov208, 01:50 AM

P: 622

There is plenty of room for both approaches. One can't have too much of a good thing! I hope that the final version of your sticky thread is a convincing mixture that helps newcomers to a better understanding of what modern cosmology is all about. With this aim in mind, I'll transfer some residual misgivings I have about comments you made here on the balloon analogy, to that thread. 


#7
Nov208, 08:14 PM

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I missed the part where FLRW suggests superluminal velocities. Spacetime is not constrained by special or general relativity.



#8
Nov208, 11:19 PM

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#9
Nov308, 06:05 PM

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E.g. write down the FLWR metric, take the flat case for simplicity, normalize a(present)= 1 which is often done. Look at a spatial interval of length 1/a' where a' is the time derivative of the scalefactor. Then consider the rate at which the length of that interval is increasingit is c by simple algebra. And any longer interval will be increasing faster than c. Just as a consequence of the way the FLWR metric is constructed. Double that length and the metric will tell you it is increasing at 2c. Am I missing something? Seems like a direct math consequence of FLWR, by inspection so to speak. I like switching the letters FLRW around to FLWR so that it spells "flower" Excuse the playful levity. 


#10
Nov308, 11:17 PM

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#11
Nov408, 01:32 AM

P: 2,043

A bit of a leap to map that to our known universe which appears mostly relative vacuum with just a few spots of dense matter would't you say? 


#12
Nov408, 08:32 AM

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Long answer: When you assume homegeneous and isotropic, it practically amounts to an approximation with matter uniformly spread out instead of concentrated in lumps. Cosmologists use the "dust" metaphor. The validity of the FLWR model is not at issue hereit fits the data. The point is if you assume FLWR as a good approx, then you automatically get distances increasing at c+ rate. Approximating a clumpy spangled world by a world with uniformly spread turns out to give a splendid approximation to reality, and of course with matter spread with ideal perfection there is no vacuum, but so what? All one needs to get over that hurdle is a "dustgrain" of motherwit , wouldn't you say? ====================== Oldman, if you are reading, I still recall your description of early universe structure formation as curdling. You enjoy words and it occurs to me that "flower" sounds like "flour". The Friedmann et al solution is sometimes called a dust solution, or dust universe. Matter being uniformly spread and pressureless, like a cloud of dust. FLWR 


#13
Nov408, 09:39 AM

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That is like using astrology to predict stock prices and explain the discrepancies by dark and hidden forces. I would say pretty obvious to the critical mind, not so obvious to those who have built an industry around it and have a history of aversion to be caught wrong. 


#14
Nov408, 10:00 AM

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Come on Jenny, FLWR fits the data excellently well. And it is doing exactly what one hopes a model will doit provides us with two important numbers to explain: the dark energy density and the dark matter density. It is now up to physicists theoretical, and physicists experimental, to find physicist explanations for these two numbers (which may even lead to an improvement in FLWR!). This is an exciting challenge to them and it will be interesting to see what they come up with. So far we have a sweet simple model with two interesting parameters which we adjust (say to 0.73 and 0.27) and it fits masses of data stunningly. It is doing just what a model in a mathematical science is supposed to do, and it might seem foolish to disparage it for doing its job. When FLWR is precisely adjusted to fit (e.g. by plugging 0.73 and 0.27) it is called LCDM or LambdaCDMLamda refers to the 0.73 parameter and CDM (cold dark matter) refers to the 0.27. So FLWR alias LCDM is making us a present of these two fascinating numbers. And from everything I hear, legions of physicists are positively beside themselves with excitement and curiosity, and (finances permitting) the funding funds are flowing as well. Explaining 0.73 and 0.27 is becoming a major major focus of research worldwide. So that's cool. 


#15
Nov408, 10:06 AM

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#16
Nov408, 11:50 PM

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#17
Nov508, 12:16 AM

P: 622

So here's a thought about a 'leap' of a different kind for you: The FRLW metric, which so neatly accounts for the moderncosmologyfounding interpretation of redshift, decribes change in the universe by allowing the the scale factor (which is the spacecoordinate metric coefficient, presently unity) to vary with time. Have you noticed that one could equally well account for the redshift by describing change with a timecoordinate metric coefficient that varies in time? (I don't mean c, which in this context is a unitconversion factor) The accepted choice, made long ago, was the 'leap' I'm referring to. In fact the only thing that the redshift is telling us is that the ratio of metric coefficients changes with time. It'sthehuge amount of other circumstantial evidence accumulated by astronomers that supports the FRLW metric with it's choice of varying scale factor. But then you're sceptical about the effectiveness of this evidence, aren't you? 


#18
Nov508, 01:35 AM

P: 2,043

However that does not help the support of the idea that a FRLW metric is a good approximation for the existing universe. Think about it, does our universe even remotely look like a pressureless fluid? To me it looks like mostly (relatively) empty space and some concentrated blobs of matter. When one develops a model and it turns out that that model does not approximate reality one can do two things, either find a better model or stick with it and introduce things like dark forces and dark matter which, perhaps conveniently, cannot be directly detected. One might as well try to falsify fairies. 


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