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.
Chris M (and anyone else),
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?
It would seem there is some void being assumed and what is measured is occurring in it. Geometry maps space, it doesn’t create it. No more than longitude, latitude and altitude create the surface of the planet, only map it.
Inflation is just a way to shoehorn an apparently overall flat space into the current model. What expands between galaxies, is balanced by what contracts into them. Hubble actually found Einstein’s Cosmological Constant, a balancing force to the contraction of gravity.
“Can’t the expansion of the universe can’t be measured by the decrease of the net density of the universe? So couldn’t its units be kg/(m^3)/second ?”
Sure. Or the temperature of the CMB Or many other proxies. But they involve additional assumptions and I don’t see how they would help here.
Kevin:
At any given point (including points very far away from us), the local expansion is very very tiny. It’s only “greater than c” when you consider two points very far away from each other (roughly, 14 billion lightyears apart). So if you were sitting on a planet at the edge of Earth’s observable universe, the sun you’re orbiting would not be expanding away from you any faster than our sun is expanding away from us,* and your flashlight would work exactly the same way it works here. Put another way, it’s worth remembering that we are at the edge of that planet’s observable universe.
*Roughly 0.0004 mm/sec as I calculate it.
I feel a little foolish for having never asked what could possibly be meant by the universe expanding faster than the speed of light. I guess I need to think a little more critically during the next colloquium I attend.
Cosmology makes a little more sense today. Thanks.
@David C. — Your point about the speed of light limit only applying locally is correct, but objects in different frames of reference are not “beyond the scope of GR’s predictions”–did you mean to say SR’s predictions there? In curved spacetime, the laws of SR (including the law saying that light travels at c in any inertial frame, and all massive objects travel slower) only work in “local inertial frames”, as dictated by the equivalence principle, and objects far apart in curved spacetime cannot share a common local inertial frame, because “local” in this context basically means “defined on an infinitesimally small patch of spacetime”. But you can define a larger non-inertial coordinate system that includes various faraway objects, and the equations of GR can still be used in any such coordinate system, as long as you correctly express the metric in terms of those coordinates. But there is no rule saying that light must travel at a constant coordinate speed in non-inertial coordinate systems, in fact even in SR it’s possible to define non-inertial coordinate systems where it does not (look up ‘Rindler coordinates’, for example).
@Jesse,
Thanks for the correction. As I disclaimed before, I am not a physicist and I’m drawing on what I learned back in college, along with what I think I’ve read from others here. I clearly have not completely understood what I’ve read.
WRT your comments, would it therefore be fair to say that, even in GR, there is no concept of C being a speed-limit when you’re dealing with non-inertial coordinates, as you would have to be when dealing with distant objects, like galaxies?
In other words, it would seem that the colloquial phrase “nothing can travel faster than light” is really an inaccurate oversimplification, and in the case of cosmology (and especially the rate of expansion of the universe – whatever that means), we’re dealing with conditions where that phrase is simply wrong.
Does that sound right to you?
Two helpful additions for non-GR physicists:
The Lineweaver article also exists as a simplified, well illustrated version for the Scientific American, available at: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
In addition, there is a real masterpiece of introductory teaching on that subject, with no more than high school math: Cosmology, by E. Harrison, Cambridge Univ. Press, Ch.21, entitled: Horizons in the Universe. Harrison most definitely gets it right!
Enjoy!
Indeed. There is simply no point in asking questions if you haven’t read Davis and Lineweaver and Harrison.
I would have to say that it is very common for books for laymen to suggest that the expansion of the universe can be superluminal during inflation and possibly outside of the observable universe. I say possibly, because the apparent velocity of galaxies traveling near the edge of the visible universe is very close to the speed of light. Then if one was to assume that the actual universe was larger than the visible universe and the rate of expansion remained constant, then galaxies outside of the visible universe would be traveling faster than the speed of light away from the Milky Way galaxy, so to speak. Then it is actually rare to read about a definitive claim that there are galaxies traveling faster than the speed of light relative to the Milky Way galaxy today or that there is even something beyond the visible universe for that matter. The observational evidence is simply not there, if you really wanted to nit-pick it. Then I am not sure if there is really any experimental proof that shows that inflation had to be superluminal. Then a lot of times it is just told as a well known fact that is thrown around.
David C says “Your talk of light cones only describes what we can observe.”
It’s the legitimate starting point in science. If you are saying we can observe objects moving away from us faster than C, then you are saying the light cone is greater than the age of the universe.
@David C.:
“WRT your comments, would it therefore be fair to say that, even in GR, there is no concept of C being a speed-limit when you’re dealing with non-inertial coordinates, as you would have to be when dealing with distant objects, like galaxies?”
Yes, that would be accurate–in non-inertial coordinate systems in both GR and SR, there is no general rule that light travels at a constant coordinate speed (though in some GR spacetimes you can construct a special non-inertial coordinate system where it does, like Kruskal-Szekeres coordinates for a Schwarzschild black hole spacetime).
The part I don’t understand is that if redshift is a consequence of the intergalactic light taking longer to reach us, as the galaxies move away, what is the basis of the speed of light, if it isn’t “space?”
If a galaxy is x lightyears away and the universe were to expand so that it is 2x lightyears away, that means there is a distance metric, based on the speed of light, that is distinct from the expansion. So there is one metric based on the speed of intergalactic light and another based on the redshifted spectrum metric of the very same intergalactic light.
In my simple understanding of math, since the distance is being denominated in lightyears, that makes the metric based on the speed of light the denominator, so the metric based on the redshift would be the numerator. Which would mean it is not expanding space, but increasing distance.
Keeping in mind as well the premise of spacetime is that the speed of light remains CONSTANT to the distance. So presumably if this were really expanding spacetime, the speed of light would have to increase to match and so the lightyears would be stretched, not just more units. But that would cancel it causing redshift, as the light would still arrive at the same rate.
Is it not true though that the extent to which the universe is expanding (in some places relative to our location) keeps light from those locations from ever ever reaching us?
That given, I think as long as one provides the caveat that expansion isn’t really a speed, it doesn’t hurt us lay folk so much to think of it that way. If anything it seems a crude analogy that can get the general point across from which interested individuals can explore further.
Maybe someone here can answer questions I have. I have read that the expansion of space creates more space; each unit volume of space has a quantity of inherent energy and behaves like a substance with constant energy density; therefore, the expansion of space increases the sum total of the inherent energy without limit. Assuming that the total energy + matter of the universe is conserved, where does the additional energy come from? If the source of the energy is “external” to the universe, isn’t there the possibility that once the source nears exhaustion, the expansion of space will slow down or stop? If the source of the energy is “internal” to the universe, does that not imply that the universe has regions of space that are contracting?
“the apparent velocity of galaxies traveling near the edge of the visible universe is very close to the speed of light”
This is simply wrong. Please read Harrison, Davis and Lineweaver, or Rindler’s 1950s paper in MNRAS. (Yes, this confusion was cleared up more than half a century ago!)
The part I don’t understand is that if redshift is a consequence of the intergalactic light taking longer to reach us, as the galaxies move away, what is the basis of the speed of light, if it isn’t “space?”
The speed of light is always defined as measured locally.
In case anyone missed it… so does this mean Bohmian Mechanics is dead? or long live the Copenhagen Interpretation? Still waiting for the quaesar version…
http://www.nytimes.com/2015/10/22/science/quantum-theory-experiment-said-to-prove-spooky-interactions.html?ribbon-ad-idx=4&src=me&module=Ribbon&version=context®ion=Header&action=click&contentCollection=Most%20Emailed&pgtype=article
“Assuming that the total energy + matter of the universe is conserved, where does the additional energy come from?”
Your assumption is wrong; energy isn’t conserved in GR.
“does this mean Bohmian Mechanics is dead? or long live the Copenhagen Interpretation? “
False dichotomy. Also, completely off-topic here.
Philip,
“The speed of light is always defined as measured locally.”
Yes, but lightyears are still being used as the cosmic ruler and in order for the light to be redshifted, there have to be an increase in these units, as it has to take light longer to cross between galaxies. So how can there be this stable unit, if the very fabric of space is being stretched?
Also, if General Relativity is the reason for space expanding, why doesn’t the speed of light remain constant to this space, instead of taking longer to cross it?
That light-years are the units is neither here nor there. You could just as easily use furlongs. It doesn’t matter.
You haven’t found some contradiction in relativity. In relativity, the only meaningful definition for the speed of light is one measured locally. That’s all you need to know. You can, if you like, interpret various effects in GR as slowing the speed of light, or as increasing the space. Take your pick. What matters is whether you get the right answers when you calculate something.
Think of it this way: Locally the speed of light is constant, but the expansion means that more space appears between the source and the destination. It’s not always a good analogy, but it is in this case: think of an ant crawling along an expanding balloon: You measure his crawling speed locally, and it is the same speed you always measure with ants. But the balloon is expanding. Some points he can never reach, no matter how long he crawls.
Philip,
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?
Let me put the issue in a different frame; Say you have a car that always travels at fifty miles an hour. Let’s call it C. Then you have two points fifty miles apart. Call them Galaxy, North Dakota and Galaxy, South Dakota. So at time A, say 7 billion years ago, it takes one hour to drive between these towns. Now today though, it takes two hours.
So either the towns are now a hundred miles apart, as measured by the car traveling at C, or the car only travels at twenty five mph. Since the argument is that space expands, not that the speed of light slows, otherwise known as “tired light theory,” it would seem the denominator being assumed is the speed of light remaining constant and so it is the galaxies that are moving apart. Therefore making that the numerator. Which would make it increased distance, as measured in lightyears, not expanding space, since it is still being implicitly assumed that space is defined by C.
I’m a bit confused about something. Given two galaxies, there is a distance between them, x. For distance galaxies that distance is increasing as time progressed. So what prevents us from using the usual definition for the recession speed, s=d x/d t. It seems to me to be a well defined quantity. Of course it can also be greater than c. I would argue that the confusion comes from the fact that, in my opinion, it is incorrect to say that no objects can ever be moving relative to each other with a speed greater than the speed of light. What I would argue is correct is the statement, which you make above, that no objects can pass each other with a speed grater than that of light.
I think this might all be semantics. We have the following three statements:
A) “No objects can ever be moving relative to each other with a speed greater than the speed of light”
B) “Speed isn’t defined for objects not at the same place”
C)”two objects in the same position can never have a relative speed greater than light”
You seem to be clamming that A and B are true, which implies that C is true as well. I would claim that B and C are true, but A is false.
Maybe I am missing something. If so would you point out my confusion?
Thanks,
Peter
Actually rereading your post. I think what I am calling speed, is what you are calling apparent speed. But why is it only apparent?
In terms of the velocity of distant objects, one can connect the themselves to a distant object via a geodesic. Then one can also measure the angles that geodesic intersects them at, relative to some reference, like the earth’s horizon. Then as the distant object moves the two angular coordinates will vary continuously, as will the length of the geodesic connecting the observer to the object being observed. Why can’t this vector be used to define positions and velocities. I think this is what you are referring to as “apparent velocity”. But this method is how we measure velocities for near by objects. It seems perfectly generalizable to curved space time, so why call it apparent velocity when spacetime is curved? The only issue I see is if there is some lensing effect where there is more than one geodesic to the distant object. Then the position and velocity of the object will be multivalued, which I guess is a bit weird. Maybe I am missing something.