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.
I have one more though on this. Consider a traveling to a very distant galaxy. Take a path connecting me to that galaxy. Now imagine I have a magic device which temporarily takes a cylinder around that path, and quickly contracts space tangent to that path only within this cylindrical region, while leaving the rest of space untouched. Then the distance between me and that galaxy would very quickly shrink. I would in effect very quickly speed towards the galaxy, potentially at a speed much greater than that of light for much of the journey (of course as I reach the galaxy my speed would necessarily slow to under the speed of light). I’m not claiming that a warp drive like this is possible (and there would be huge tidal forces at the edge of the cylinder if it was), but I don’t see how it would violate special relativity, or the equivalence principle. I also don’t see how that speed is only apparent (i.e. an illusion?) since I actually get to the galaxy in a short period of time.
@Peter Moomaw – “I’m a bit confused about something. Given two galaxies, there is a distance between them, x.”
See my comment here, there isn’t actually any unique definition of “the” distance between you and another galaxy. Even if you restrict yourself to talking about proper distance along a space-like curve between you and the galaxy (proper distance can be thought of as the distance that would be measured by adding up the lengths of a large number of short rulers–short enough that we can define each one’s individual length in a local inertial frame–whose ends touch one another at a single moment), rather than any arbitrary notion of coordinate distance, there is still the problem that defining the distance “at a single moment” requires a definition of “simultaneity”, and the relativity of simultaneity says there are an infinite number of different but equally valid ways to define which events happen at the “same moment”.
Another question; If light slows, distance shrinks and time is dilated in accelerated and gravitational frames, then on the other side of the equation, what is the frame with the longest distances and fastest clocks and thus light speed? Wouldn’t it be some equilibrium state to the vacuum, against which everything is relative?
Hi Phillip – first to say, by the way, you replied a while back to a comment I made about Greece/Germany. Just to mention no hint of anti-German sentiment beyond that narrow context was intended. Nor any there concealed or not.
Look I don’t agree that Special Relativity puts no constraint on the passage of light in objective terms, which is the meaning of things when said ” the only meaningful definition of the speed of light is …[observer dependent).
Can we help me come around to this, by coming at this matter from a very slightly altered direction. So what about this component “all inertial frames have equivalence….(e.g. can be treated as a single absolute space).
So we’ve got any number of inertial frames of reference each at rest or moving with constant speed relative to one another. Which does matter, they are equivalent and that means for example they can all be treated as the same inertial /absolute space.
Is that postulate observer dependent…as in meaningless when not a locally observation
Because that’s another way to say (almost) the speed of light is C in all inertial frames.
When we look back into the light cone, we date the universe by assuming the speed of light is
consistently C for 14 Billion years, when observed and when not. Mass cannot exceed the speed of light. The speed of light over all distances and scales, has the same amplitude and energy as any other instancing at any other distance and scale. Which cannot be absent splendid synchronization., and a constant speed in all cases (inertial frames assuming).
Something is said in relativity of the physical character of light that surely stands on its own? Special Relativity has the further interesting attribute of making the principles and laws of SR accessible for real purposes strictly via an intermediate framework, a ‘mode’
But that’s not a statement about fundamental reality the way it is in QM.
Help me. I’m fond of Germany. So it won’t make you a traitor.
“Which does matter” = “Which doesn’t matter” (inertial frame of reference equivalence paragraph)
How is it possible to see light from the most distant galaxy according to the big bang theory? How does the evidence falsify the steady state theory?
I would be willing to bet no one could name a single galaxy that they could observe that is traveling faster than the speed of light from our frame of reference as it is seen now. If such a galaxy even exist, it should have been made a bigger deal of, and it would only be able to be seen with advancements like the Hubble telescope. Many of astronomers have tried to view such an object before Hubble and failed. It really makes me wonder if the referred article is just theory, and it is not based on any actual observational evidence. There should have been some mention of a particular example or this big discovery that has apparently been made.
Philip,
I guess you are busy. I do find it an interesting conundrum.
@John Barrett – “I would be willing to bet no one could name a single galaxy that they could observe that is traveling faster than the speed of light from our frame of reference as it is seen now. “ Talking about how fast a distant object is moving in “our frame of reference” is only meaningful in special relativity, where the phrase is understood to refer to inertial frame in which you are at rest. In general relativity, as I explained in this comment the only inertial frames are “local” ones covering an infinitesimally small patch of spacetime, no coordinate system covering a large region (large enough to contain both us and another galaxy) would be non-inertial, and there are an infinite number of non-inertial frames you could construct where we are at rest, the equations of general relativity would hold equally well in all of them (a feature called “diffeomorphism invariance”).
There is a common way of defining the recession velocity of distant galaxies in cosmology, though. Different coordinate systems can have different definitions of simultaneity–which pairs of events are assigned the same time-coordinate as one another–and although the laws of physics themselves don’t give a “preferred” definition of simultaneity, in the context of cosmology, cosmologists generally like to define simultaneity in such a way that the density of matter and energy will be approximately uniform throughout the observable universe at each time-coordinate. And as I explained in this comment, once you have a choice of simultaneity convention, you can then talk about the “velocity” of distant objects in terms of the rate that their “proper distance” from you (the distance that would be measured by a series of short rulers that are end-to-end at a single simultaneous instant) increases a rate of your own “proper time” (the time that would elapse according to a clock that is always next to you and at rest in your local inertial frame).
So long story short, if you do define the velocity of distant galaxies in this particular way, there are indeed galaxies that we can see that have nevertheless been moving faster than c throughout their entire history (both when they emitted the light we see now, and still moving faster than light at the current cosmological time coordinate). For example, see p. 42 of the Scientific American article Misconceptions about the Big Bang by physicists Lineweaver and Davis, where it says “In the current standard model of cosmology, galaxies with a redshift of about 1.5—that is, whose light has a wavelength 150 percent longer than the laboratory reference value—are receding at the speed of light. Astronomers have observed about 1,000 galaxies with red- shifts larger than 1.5. That is, they have observed about 1,000 objects receding from us faster than the speed of light.” In the “Running to Stay Still” section on the same page they explain how the light from such galaxies can reach us, and later in that section on p. 43 they note that “we can observe light from galaxies that have always been and will always be receding faster than the speed of light”.
@ Jesse M.
I understand what you are saying, but given a reference frame, there is no issue in defining distance. Even in special relativity, the distance between objects, as well as their relative velocities, depends on the reference frame (they are not Lorentz invariant). Don’t all the simultaneity issues come from special relativity? I don’t think curved space time has anything to do these issues. So wouldn’t what you are saying imply that one shouldn’t talk about distances, or velocities between objects at all, even in flat space time (special relativity)?
@Peter Moomaw “I understand what you are saying, but given a reference frame, there is no issue in defining distance.”
Given a reference frame (or even just a definition of simultaneity without any choice about what lines of constant position coordinate should look like), that’s correct. But as I said, the phrase “our frame of reference” doesn’t have any specific non-local meaning in GR, since for any large region of curved spacetime all coordinate systems defined over the entire region must be non-inertial ones, and there are an infinite number of different non-inertial frames in which we are at rest. Whereas in SR the phrase does have a specific meaning, since it’s understood to refer to our unique inertial rest frame.
“Even in special relativity, the distance between objects, as well as their relative velocities, depends on the reference frame (they are not Lorentz invariant).”
Yes, as I said I was just making a point about your use of the phrase “our reference frame”–although distance depends on reference frame, “our reference frame” would always refer to a specific one in SR, whereas it wouldn’t in GR.
“Don’t all the simultaneity issues come from special relativity? I don’t think curved space time has anything to do these issues.”
All the simultaneity issues are already present in SR, if that’s what you mean–but they are also present in GR, in both theories there are many different ways to define simultaneity and the laws of physics don’t “prefer” any specific one.
“So wouldn’t what you are saying imply that one shouldn’t talk about distances, or velocities between objects at all, even in flat space time (special relativity)?”
In SR you can’t talk about distances in a frame-independent way (unless you are talking about proper distance along a specified space-like worldline), but whenever a physicist speaks of the “relative speed” of two inertial objects in SR, it’s generally understood they mean the speed of one in the other’s inertial rest frame (and the value is the same regardless of which one’s rest frame you pick), so given that definition of the phrase inertial objects in flat spacetime do have a unique relative speed.
@Peter Moomaw – Sorry, I got confused–when I replied to your last comment I though the previous comment I had just replied to was also from you, but I just realized that one (which contained the phrase ‘our reference frame’ that I was objecting to) was actually from John Barrett, not you. If only we could delete our own comments here…anyway, I agree that the distance between objects can’t be defined in either SR or GR without choosing a reference frame or at least a simultaneity convention, but as I said in my last mixed-up comment, the notion of “relative speed” between inertial objects in SR is usually defined to mean the speed of either one in the other’s inertial rest frame. Really just a matter of semantics I suppose.
“Thank you for the reply, but I see it as fudging the issue. To use your analogy, the speed of the ant is one metric and the expanding balloon is another. These are two different metrics. Which is the “real” measure of space?”
It depends on what you want to do. We don’t normally experience expanding space, so intuition is not a good guide. If you want to define the distance as the speed of light times the propagation time, fine, but then everything else has to be consistent with this definition. It is more useful to define the speed to be the locally measured speed and take into account expansion of space if appropriate.
“Philip,
I guess you are busy. I do find it an interesting conundrum.
“
Always.
Jesse, Peter,
Assuming it’s possible to tell which frame has the faster clock and which is dilated by gravity/acceleration, wouldn’t that mean the one with the faster clock is closer to the inertial state of the vacuum in which they both exist? Such that if a large number of frames are compared, the one with the fastest clock would be closest to the inertial state of some background vacuum.
Philip,
Thanks for the effort. I can’t seem to find anyone to clear this up for me.
@John Merryman
“Assuming it’s possible to tell which frame has the faster clock …”
I don’t think that the phrase “has the faster clock,” by itself, expresses a coherent concept in relativity. Consider two people, Alex and Jill, traveling past each other at near the speed of light without accelerating. Since they are passing each other, gravitational effects will be effecting them the same, and hence can be ignored (in other words, we are in the realm of special relativity). Now in this situation, from Alex’s reference frame Jill’s clock is going slower, while from Jill’s reference frame, Alex ‘s clock is going slower. So which is running faster is frame dependent.
@Jesse M.
Thanks for your thoughts. You make a good point about there being an infinite number of noninertial reference frames which contain an observer’s local inertial frame, but I will need to think on this further. My gut tells me that one should be able to take a local inertial Cartesian frame of an observer, pick some spacelike direction, and simply “move along it”. Doing this for all tangent vectors in the subspace spanned by the spacelike coordinate vectors seems, to me, to be a natural way to extends the coordinate system in a physically meaningful sense. I think what I am describing may simply be taking the subspace spanned by the spacelike coordinate vectors of the local inertial frame, and then mapping it to the manifold via the exponential map. Wouldn’t this give a natural physical coordinate system for the observer? I’m pretty sure this would give a global inertial Cartesian coordinate system in a flat space time. Is there some ambiguity I am missing? Granted this might miss some points, but I would be willing to say that distance is not well defined for those points.
ouch, I’ve got that exact textbook from Cheng…
Peter,
That is why I asked whether it could be determined which is the one most affected.
The problem is that several decades ago, when I was first studying this, the explanation given was that C is the speed of light in a vacuum and any motion of the frame in the vacuum has to be subtracted from the light moving in the frame, so the combination doesn’t exceed C and since any atomic structure comprising that frame would also be compressed(remember the elevator and moving train thought experiments), that C would remain the same.
So it seems to me there is an explicit zero bound vacuum underlaying these frames, that has become lost as the debate has grown ever more abstract.
One of the main problems I’ve had with the notion of four dimensional spacetime as being physically real, is that if you think of time, not as the point of the present moving from past to future, which physics codifies as measures of duration, but the changing configuration of what is present, that turns future into past, as in tomorrow becoming yesterday because the earth turns, than time is actually only an effect of action, more like temperature, than some underlaying mathematical framework. So the energy manifesting these events is naturally conserved as the present, not having to explain how an eternity of events physically exist in block time.
What is actually being measured is frequency and duration is the state of the present, as the events form and dissolve. So different clocks can run at different rates and remain in the same state of the present, because they are separate actions.
So, to me, it seems physics has fallen into the trap of building its theories around what amounts to the “naive intuition” of treating time as the narrative timeline that we cognitively experience. Just as we still experience the sun rising in the east and setting in the west, even though we know it is an effect of the earth turning the opposite direction..
So with spatial dimensionality, be it one, two or three, it is actually space being measured. While with time, it is action within space being measured. Aka a particular frequency. Just as temperature is a combination of masses of amplitude and frequency.
We could even use ideal gas laws to formulate a thermalvolume, similar to spacetime, but temperature is only foundational to our emotional and biological processes, not our cognitive ones and so we can be more objective.
The three spatial dimensions are really the xyz coordinate system and no more foundational to space than longitude, latitude and altitude are foundational to the surface of the planet. A handy mapping device, no more, no less. Naturally we can apply many such frames to the same space, but they all reference from different points of view. In the political world, they are also backed by different narrative timelines. As witness various deep conflicts in the middle East.
I suppose I’ve caused some ire, but just putting out some observations.
Philip,
This came through my email feed, but hasn’t shown up on the thread, so I have time now, I’ll reply.
(If it does show up after, I suppose it would be time traveling.)
“It depends on what you want to do. We don’t normally experience expanding space, so intuition is not a good guide. If you want to define the distance as the speed of light times the propagation time, fine, but then everything else has to be consistent with this definition. It is more useful to define the speed to be the locally measured speed and take into account expansion of space if appropriate.’
The problem is they are being directly related. In order for the light to be redshifted, it has to take longer to cross between the galaxies. That makes the speed of this intergalactic light the denominator. So if there are more units as defined by this method of measurement, than what is being measured is the numerator. As per my example of the car, it goes from 1/1, to 2/1.
If we go back to the beginning, it was originally assumed that this was normal motion in space, but then they realized that as redshift increased proportional to distance in all directions and there was no apparent lateral motion, it created the impression that we must be at the exact center of this expanding universe. Then the argument became that space itself is expanding and so every point appears as the center. Which, as I pointed out previously, overlooks the premise of Spacetime, that in accelerated or in gravitational fields, both the frame is compressed and the speed of light slows proportionally, so it remains constant. Yet if it takes light longer to cross between galaxies, then it’s not constant to this space.
Now we are at the center of our view of the universe, so if redshift is an optical effect, like gravitational lensing, then it would explain why we appear at the center. If it compounds on itself, then it would explain why the rate increases with distance.
As it is, both Inflation and Dark Energy are enormous patches to explain gaps between the predictions the theory makes and what is observed. How can a theory be disproved, if every gap becomes an reason to invent another enormous force of nature, the only evidence of which is the mismatch between theory and observation?
The primary prediction that matched observation was the existence of the background radiation, yet it still needed Inflation to actually match what was observed. If redshift is an optical effect, then light from over the horizon of visibility would be shifted to the microwave and that would explain the CMBR. As such, it would be the solution to Olber’s paradox. the light of infinite sources, shiftinging to zero.
So the question would be whether Hubble actually discovered evidence of Einstein’s original Cosmological Constant? An expansion to balance the contraction of gravity. So then we would have what expands between galaxies balanced by what falls into them, resulting in the overall flat space that is actually observed, by COBE and WMAP.
@John Merryman – You have not caused me any anger. I’m sorry if my reply seemed curt (it wasn’t meant to).
Ah, heck… I’ll never be able to use my smart-alec explanation of inflation ever again: “According to the theory of relativity, nothing can move faster than the speed of light. According to inflation theory, that’s exactly what the nothing did.”
Maybe I can revise it…
Peter,
Nothing personal taken or meant. I’ve just had a fair amount of negative previous responses to looking at the evidence from different points of view, than what many people have spent their lives studying. I can well understood why anyone from outside the field are looked on as uninformed, but I do think I bring up some valid observations.
As it is, the field is in a bit of a quandary and it is doubtful that pursuing multiverses will solve it, so some review will become necessary at some point.
“But the fundamental issue relevant to this post is that the application of any Doppler formula won’t make sense when galaxies are so far away that light from them hasn’t gotten to you in the whole history of the universe. (I.e. they are outside the particle horizon.) ”
And that’s all there is to it. I’ve taken 2 introductory astronomy classes and even I gathered this from my intro textbook. It’s just another form of physical singularity where physics breaks down. It’s another limit to the physics we know.
@John Merryman: “Assuming it’s possible to tell which frame has the faster clock and which is dilated by gravity/acceleration, wouldn’t that mean the one with the faster clock is closer to the inertial state of the vacuum in which they both exist? Such that if a large number of frames are compared, the one with the fastest clock would be closest to the inertial state of some background vacuum.”
Quantum field theory has the mathematical property of “Lorentz-invariance” meaning that the vacuum obeys the same equations in every inertial frame, so the vacuum doesn’t have a particular rest frame even in a local sense. And in both SR and GR, the relativity of simultaneity means that for any arbitrary time interval one one clock, different frames may not agree about whether another distant clock elapsed more or less time during the “same time period”, and all these frames are equally valid, so there is no general truth about whether a distant clock is ticking slower or faster.
Note that there can be specific cases where all frames do agree about which of two clocks elapsed more time, even if this isn’t true in general–the obvious one is that if two clocks depart from a common location and reunite at a common location, all frames agree about how much time elapsed on each clock in total between the moments of departure and reuniting. Also, even if they don’t depart and reunite from a common location, if you restrict yourself to coordinate systems where no event in a single simultaneity surface can be in the past or future light cone of another event in the same surface (i.e. you can’t have two events that happen “at the same time” but causally influence one another), then there may be cases where if you have two clocks A and B, and you pick two readings on A with a sufficiently large interval of proper time between them, then all coordinate systems that respect this rule must agree B elapsed less time, even if they disagree on exactly how much. (For example, if you picked two readings T1 and T2 on a clock A orbiting around a gravitating body which had a second clock B sitting on its surface, and the separation between the readings was such that A had completed many orbits between them, it could be the case that all frames with these kinds simultaneity surfaces would agree B had elapsed more time between the simultaneity surfaces that include T1 and T2. For those who want more detail, the idea is that in this situation it could happen that even if you pick the first reading T1′ on B that lies in the future light cone of T1, and the last reading T2′ on B that lies in the past light cone of T2, T2′ – T1′ might still be larger that T2 – T1. And T2′ – T1′ is the lower bound on the proper time interval that can elapse on B during the same amount of coordinate time that A advanced from T1 to T2, in any coordinate system that respects the rule that events in the same simultaneity surface don’t lie in one anothers’ light cone). But even with this restriction, if you pick a sufficiently short interval on one clock, I’m pretty sure it would always be possible to find some frames where another clock ticked more time during that interval, and other frames where that same other clock ticked less time during that interval.