There seems to be something in the air these days that is making people speak out against the idea that space is expanding. For evidence, check out these two recent papers:
The kinematic origin of the cosmological redshift
Emory F. Bunn, David W. HoggA diatribe on expanding space
J.A. PeacockExpanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis
Admittedly, my first sentence is grossly unfair. The correct thing way to paraphrase the underlying argument here is to say that “space is expanding” is not the right way to think about certain observable properties of particles in general-relativistic cosmologies. These aren’t crackpots arguing against the Big Bang; these are real scientists attacking the Does the Earth move around the Sun? problem. I.e., they are asking whether these are the right words to be attaching to certain indisputable features of a particular theory.
Respectable scientific theories are phrased as formal systems, usually in terms of equations. But most of us don’t think in equations, we think in words and/or pictures. This is true not only for non-specialists interested in science, but for scientists themselves; we’re not happy to just write down the equations, we want sensible ways to think about them. Inevitably, we “translate” the equations into natural-language words. But these translations aren’t the original theory; they are more like an analogy. And analogies tend to break under pressure.
So the respectable cosmologists above are calling into question the invocation of expanding space in certain situations. Bunn and Hogg want to argue against a favorite cosmological talking point, that the cosmological redshift is not an old-fashioned Doppler shift, but a novel feature of general relativity due to the expansion of space. Peacock argues against the notion of expanding space more generally, admitting that while it is occasionally well-defined, it often can be exchanged for ordinary Newtonian kinematics by an appropriate choice of coordinates.
They each have a point. And there are equally valid points for the other side. But it’s not anything to get worked up about. These are not arguments about the theory — everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words. For example, the motivation of B&H is to do away with confusions in students caused by the “rubber sheet” analogy for expanding space. Taken too seriously, thinking of space as an expanding rubber sheet convinces students that the galaxy should be expanding, or that Brooklyn should be expanding — and that’s not a prediction of GR, it’s just wrong. In fact, they argue, it is perfectly possible to think of the cosmological redshift as a Doppler shift, and that’s what we should do.
Well, maybe. On the other hand, there is another pernicious mistake that people tend to make: the tendency, quite understandable in Newtonian mechanics, to talk about the relative speed between two far-away objects. Subtracting vectors at distinct points, if you like. In general relativity, you just can’t do that. And realizing that you just can’t do that helps avoid confusions along the lines of “Don’t sufficiently distant galaxies travel faster than light?” And reifying a distinction between the Doppler shift and the cosmological redshift is a good first step toward appreciating that you can’t compare the velocities of two objects that are far away from each other.
The point is, arguments about analogies (and, by extension, the proper words in which to translate some well-accepted scientific phenomenon) are not “right” or “wrong.” The analogies are simply “useful” or “useless,” “helpful” or “misleading.” And which of these categories they fall into may depend on the context. Personally, I think “expanding space” is an extremely useful concept. My universe will keep expanding.
October 6th, 2008 at 1:09 pm
So can you explain *why* the GR space expansion point-of-view doesn’t apply to solar-system scale objects or galaxies? Every explanation I’ve heard throws around terms like “gravitationally bound”, but doesn’t say why that effects anything. So what if they’re gravitationally bound?
Is it just so long as the metric closely approximates, say, the Schwarzschild metric, that the deviations due to the large scale changes are small enough that they don’t matter, or are they even in principle not there? If the first, okay, but what’s so special about these cases that they should be called out that way, rather than any other case where the effects just happen to be too small? If the second, how does that come about that the local perturbation completely suppresses the large scale structure?
October 6th, 2008 at 2:22 pm
@aaron
If I’m not totally muddled, I think it’s because gravity and the other forces hold closely grouped objects such as the stars in galaxies (and of course anything smaller) together in clumps that don’t expand, even though the ‘fabric’ in which they exist is technically expanding. It would be like having some stones suspended in a gel that expands, carrying them further apart. Obviously the stones wouldn’t expand with the gel.
I understand all of this from a perspective that consists of nothing but analogy though, not knowing much of the underlying maths.
October 6th, 2008 at 2:41 pm
Paul: but what’s holding together the solar system, or a galaxy is just gravity — warped space-time — which is the gel in your analogy.
October 6th, 2008 at 2:48 pm
@Paul
I think that the point the physicists Sean has mentioned above are trying to get across is that such an analogy does not hold for localized clusters of matter. Unfortunately, I’m as muddled as you are. I don’t quite see why the analogy doesn’t hold locally. The only answer that has ever been offered to me by my teachers is that “gravity holds them together”, which never made sense to me.
I’m with Aaron. It would be absolutely great if someone could explain this better.
October 6th, 2008 at 2:50 pm
@(Aaron, Paul); There is an attempt at addressing this in Secs. 2.3-4 of the third paper to which Sean links. Section 2.3 is an extended mathematical argument using results from an earlier work, but it culminates in: “[o]bjects will not expand with the universe when there are su?cient internal forces to maintain the dimensions of the object;” while Section 2.4 is all prose and addresses the question of gravitationally-bound systems directly.
October 6th, 2008 at 3:23 pm
The section numbering in comment 5 is incorrect: I mean 2.6.2 and 2.6.3; please forgive my not double-checking! The reason an explanation such as “gravity holds them together” might be confusing is that it isn’t clear what is meant by ‘gravity’: the Newtonian picture of forces or the GR picture of an expanding space-time—it seems like these two must be competing for primacy. But there is only one gravity!
The gravitational motions here are the governed by solutions to the Einstein field equations, given a particular choice of ‘metric’ (a measure of distance between points). In the solution used for cosmology, the metric is changing with time (the distance between points is getting larger), and this is what is generally meant by ‘expanding space.’ But this says nothing of the galaxies themselves, which are usually put on the other side of the field equations to the metric. The Friedman equations, which are the stock and trade of theoretical cosmology, are a reduction of the field equations under the assumption of this expanding metric and a particular description of matter, both agreed not to be accurate on the scales of galaxy clusters or the Solar system. Instead, the metric on these scales must be some kind of strange admixture of the very-large scale cosmology form (expanding space) with the small-scale metric for isolated clumps of matter (like the Schwarzschild metric). But working that out has so far proved too difficult!
I hope that is some help; additionally, the passage I had in mind is: “Unsurprisingly then, the resulting picture the student comes away with is is somewhat murky and incoherent, with the expansion of the Universe having mystical properties. A clearer explanation is simply that on the scales of galaxies the cosmological principle does not hold, even approximately, and the FRW metric is not valid. The metric of space-time in the region of a galaxy (if it could be calculated) would look much more Schwarzchildian than FRW like, though the true metric would be some kind of chimera of both.”
Sorry again about the numbering; I feel like a dunce.
October 6th, 2008 at 3:39 pm
[…] and Physics and Science and Science and the Public and The Universe Berian 8:39 pm Sean Carroll provides a dégustation of recent literature on expanding space, including one work from the proprietors of […]
October 6th, 2008 at 3:41 pm
I think it is very very important for Scientists to be concerned about producing useful analogies. They need to to do this to an even greater extent so that it reaches the general public. This needed communication of ideas and concepts to the general public is so very important, otherwise all this good science and information stays locked away in ivory towers and those of us in the unwashed and unlearned masses are left with nothing but the traditional analogies; myths and religions.
It would be great if everyone was able to think in terms of higher mathematics but that is not the reality. Today the entrenched ancient analogies are still influencing political debate with the potential to curb funding in some areas of study.
Albert Einstein made the effort to publish a book for the general population, “Relativity: The Special and the General Theory”.
Perhaps I have not searched hard enough but now that I am retired I am searching for reading that will bring me up to date on all the current research in Physics.
October 6th, 2008 at 3:44 pm
Great post as always Sean. Way off topic: As we all know tomorrow the Nobel prize in physics will be announced and there is not a single post in CV about predicting the winner. Come on people, what´s wrong with you?
October 6th, 2008 at 3:46 pm
Berian: thanks. Of course I should have thought to *gasp* actually read the papers, and that they might discuss these points.
This description of the local metric as a mixture of FRW and Schwarzschild is exactly how I was trying to think of things.
Thanks.
October 6th, 2008 at 4:47 pm
Isn’t is true that for a wide range of cosmological models the total volume of space is finite and increasing with time, no matter how you slice it, right?
So how could anyone deny that space is expanding in this scenario?
October 6th, 2008 at 5:30 pm
To a first approximation, matter is uniformaly distributed in the universe. Precisely at that level of approximation, “space is expanding”. The “expansion” of the universe is really a statement about homogeneity, isotropy, etc. (of coarse-grained distributions of matter in the universe.)
Glaxies are test particles moving in the ambient spacetime curved by everything else in the Universe. When we look at local structure at the level of galaxies, we are already far from the regime of the original approximation.
October 6th, 2008 at 7:48 pm
There are two distinct issues here, and it’s very confusing to mix them.
Issue 1: The “rubber sheet” story is definitely an *analogy*. As Sean says, there is no right or wrong here, only misleading and not misleading. And this particular analogy really IS misleading, particularly when people are discussing Inflation. When you stretch a rubber sheet, you really do flatten out the inhomogeneities. Inflation is not like that: it just makes everything bigger, it doesn’t flatten anything out. Of course, to “small” beings like ourselves, making everything big makes it difficult for us to detect the inhomogeneities, but they are still there.
Issue 2: Is the universe “really” expanding? Is this too a matter of opinion, as some of the authors of these papers state or imply? Well, to say that the universe is expanding means that you have modified Pythagoras’s theorem to include an increasing function of time. Technically, the extrinsic curvature of the relevant spacetime foliation is non-zero. This is a question of fact, not opinion or convenience. So I think I have to part company with Sean here: several of these papers are either *wrong* or so close to it that it makes no difference. Certainly any idea that GR can be understood in terms of Newtonian mechanics is quite nonsensical. The essence of FRW cosmology is isotropy, and a vector cannot be isotropic unless it vanishes. So you will never understand cosmology if you insist on thinking in Newtonian terms. [In particular, thinking of cosmic acceleration in terms of “gravitational repulsion” is a terrible mistake — vacuum energy cannot point in any direction, it is intrinsically isotropic.] Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.
What I find strange about this Doppler business is this. The “correct” explanation of cosmic redshift, in terms of the extrinsic curvature, is really beautiful and, as students say, “cool”. You are directly observing the curvature of spacetime every time you measure a redshift. The alternative “explanation” in terms of the Doppler effect is contrived, clunky, and boring. Why do these people prefer boring to cool?
October 6th, 2008 at 7:56 pm
> Why do these people prefer boring to cool?
We don’t - we prefer accurate to cool. Breaking redshifts into three “different” kinds actually confuses the beautiful E=-p.u underpinning all redshifts, and as we know, we can play around with the metric to do the dot product and so your “interpretation” will be different.
October 6th, 2008 at 8:00 pm
>Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.
Hmm - it seems we do disagree - are you arguing that the standard FRW metric is the “correct” metric for the universe? If so, then I disagree and point you towards discussions in
Coordinate Confusion in Conformal Cosmology
Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, J. Berian James
http://arxiv.org/abs/0707.2106
and
Cosmological Radar Ranging in an Expanding Universe
Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, Juliana Kwan, J. Berian James
http://arxiv.org/abs/0805.2197
There is more than one way to skin a cat (luckily).
October 6th, 2008 at 8:14 pm
Thanks Sean! This is my absolute favorite question! And I crave for answers!
On Science Saturday: Cosmic Bull Session, John Horgan asks you to explain how the universe can expand faster than the speed of light, and you answer: There is no such thing as expanding faster than the speed of light.
http://bloggingheads.tv/diavlogs/9433?in=11:09&out=12:43
At my very basic non-mathematical-amateur-level we seem to have a “problem” here, or maybe two:
1) The universe is about 14 billion years old, and we observer objects that is 27 billion light years away. How on earth can that ever be possible?
2) If you are right Sean (and Mr Einstein of course!), what will happen with the expansion speed in the future? We know today at that the expansion of the universe is actually accelerating (measuring quasars)? Will the “mass” of the universe increase due to acceleration, and slowing down the speed, or what? Otherwise, we will eventually expand at the speed of light (or more!), right?
Okay, I trust you Sean as a serious scientist. I also trust this guy, Michael S. Turner and you are on a sort of “supernova collision course”, as far as I can see.
Michael S. Turner writes; How Can an object we see today be 27 billion light years away if the universe is only 14 billion years old? And the answer is:
According to Einstein’s general theory of relativity, the expansion of the universe is actually an expansion of space itself, and galaxies are moving away from each other because they are “being carried along by space.” The theory does NOT limit the speed at which space expands, only the motion through space. Thus, the distance to this quasar can be greater than 13 billion light years. In fact, if we ask the question, “How fast is the distance between us and this quasar increasing?” we get the seemingly amazing answer of 540,000 km/sec or about 1.8 times the velocity of light. This number is ultimately not very interesting, both because this is not the best way to think about distant objects, and because there are objects farther away whose distance is growing even faster. To quote Fermilab’s Judy Jackson, “There is no speed limit on the universe.”
So what is actually going on here, what is the right way to tackle this question?
October 6th, 2008 at 8:52 pm
Points of space and spacetime slide around. J. A Wheeler called general relativity geometrodynamics to bring this point out. The FRW metric
ds^2 = -dt^2 + R(t)(dr^2 + r^2 d(Omega)^2)
has the radius R(t) changing with time and curvatures determined by derivatives of it. We all know or have seen these. As way of analogy it is the old picture of points on a balloon being blown up.
However, how points move is given by a gauge condition. How one shoves points on a spatial manifold is entirely given by the coordinate gauge-like choice one imposes on the problem. For a given point p one can define one spatial surface (a surface where one has set all clocks to synchronicity) and how this point along with others are lapsed into the future. Similarly one can chose another surface and push the same point into a completely different point by this change of coordinate condition on the second spatial surface of choice. So the points on a “rubber sheet” moving apart really only makes sense when one is talking about the relative deviation between two points — the geodesic deviation equation.
We can well enough say that space expands in a cosmology, or that galaxies are on comoving frames with this expansion and the rest. However, I do think this is in some ways a model construction. General relativity as a theory of general covariance only makes reference to moving points or coordinate systems when one imposes a gauge-like coordinate condition on a problem. Of course this condition is freely chosen by the analyst.
Lawrence B. Crowell
October 6th, 2008 at 9:41 pm
I think analogies are very useful. More useful than simply a means of communication with non-scientists. Analogies also can lead to the construction of actual experiments that can tie mathematics to the physical.
Unless I’m wildly mistaken, being directly tied to the physical is still something important to physics.
This was a wonderful post. I’m very happy seeing things that shine a light upon orthodoxy. It needs to be lit up.
October 6th, 2008 at 10:26 pm
Well, the nice thing about the “expansion of space” description, for physics students at least, is that it translates extremely well to the mathematics.
As for why the local universe isn’t expanding, another way to look at it is this. First, remember that the force that is driving this expansion is gravity. The universe as a whole is expanding on average because the initial conditions combine with gravity to make this occur. But the action of gravity depends upon the distribution of matter, and this expansion depends upon an approximately homogeneous distribution of matter.
Here near the Earth, we don’t have anywhere close to a homogeneous distribution of matter. So gravity acts differently, and doesn’t drive any expansion. On the contrary, gravity supports a nearly steady state set up due to the fact that matter near us isn’t distributed uniformly.
As is alluded to above, one could examine this explicitly by embedding a Schwarzschild metric as a perturbation on top of an expanding space-time, and see how orbits behave.
October 7th, 2008 at 12:51 am
I don’t like encouraging people not to think of the possibility that space can expand between say atoms. Strictly speaking you can only make a manifold flat around some epsilon.
The point is a general manifold (not necessarily FRW) can and does feel this expansion, via tiny tidal forces, which are suppressed by many orders of magnitude.
The reason I insist on making that point, is that this can be important in understanding the role of the cosmological constant. If its too big, gravitationally bound systems will find it difficult to form. Theres a bit of a word game here with what we mean by expansion (a FRW concept) vs negative pressure density, but thats semantics.
The point is, this sort of game is what allowed people to put anthropic bounds on the size of the CC, and its a very real effect.
October 7th, 2008 at 5:18 am
You have to first solve the appropriate gravitational equation, i.e. the appropriate GR field equation and then comment on it using an analogy to communicate what this means with ‘joe public’, your students and yourself.
For example, Peacock in his “A Diatribe on Expanding Space” uses the Schwarzschild solution to show that ‘expanding space’ is an inappropriate analogy for the cosmological solution and that space therefore does not expand.
However as the Schwarzschild solution is that of a static spherical mass embedded in Minkowski space-time, i.e. non-expanding space, I find this criticism unconvincing.
What happens if the Schwarzschild solution, such as that describing the gravitational field of the Sun, is embedded in expanding cosmological space? Would not the solar system, and by extension the galaxy, not expand with it?
Garth
October 7th, 2008 at 5:34 am
Perhaps it is time for a general audit of some of the outstanding interpretations in theoretical physics.
October 7th, 2008 at 6:16 am
Off-topic: The 2008 Nobel Prize in Physics goes to Yoichiro Nambu, “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” and to Makoto Kobayashi and Toshihide Maskawa “for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature”.
Congratulations!
October 7th, 2008 at 8:46 am
Expanding Space: the Root of all Evil?
No, no, no, that’s all wrong. It is Love of expanding space that is the root of all evil.
October 7th, 2008 at 8:46 am
See this article:
Solar system effects in Schwarzschild–de Sitter spacetime
October 7th, 2008 at 9:00 am
With all due respect to all very intelligent theoretical physicists and mathematicians, it seems that we have a slight Blind Men and an Elephant problem here.
I hope we all can agree that we are living is this real physical world, and not in an equation on a piece of paper, right? I can use my physical eyes to look at this fantastic and beautiful Hubble Ultra Deep Field Image, right? In this picture I can see about 100 small red galaxies, existing when the universe was just 800 million years old. The larger, brighter and well-defined galaxies thrived about 1 billion years ago, when the cosmos was 13 billion years old.
Theoretical physicists have calculated (redshift) that some of these small red galaxies are at the mind-boggling distance of 27 billion light years away from the lens of the Hubble Space Telescope. Yes yes, I know the red galaxies aren’t in “this moment” 27 billion light years away, we only see the light that was emitted… wait!? 27 billion years ago!? That’s impossible!? The universe is only 14 billion years old!? Help!?
And now there’s an academic discussion on highest level on which proper words should be used to get around this “problem”.
Sean claims that this is a “well-accepted scientific phenomenon” and that “you can’t compare the velocities of two objects that are far away from each other”. Okay, it would be more than bold to question this, but I still can NOT get this in to my simple little hillbilly brain, and I still have simple unanswered questions that wouldn’t be that hard to answer if what you are saying is correct:
1) Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?
2) Are Michael S. Turner/Judy Jackson right when claiming; “There is no speed limit on the universe.“, or is Sean right when claiming; “There is no such thing as expanding faster than the speed of light.“?
(I sure hope that everybody agrees that No. 2 is perfectly contradictory?)
Please, can anybody explain this in plain English!?
October 7th, 2008 at 9:57 am
you make approximations like that all the time.
the distance from me to the door is a strait line
measuring about 3 meters. (i can neglect the
curvature of the earth)
the distance from me to a door in the southern hemisphere
would need to take the curvature of the earth into account.
things measured on large scales have to take cosmological
curvature into account
October 7th, 2008 at 10:05 am
I wrote my “diatribe” on expanding space to address many of the confusions and disagreements aired in these comments - which are arguments I’ve heard so often. I encourage people who still think expanding space is trying to rip the Earth away from the Sun to read my note.
The only other thing I would add is that the virtue of GR is that you can calculate things from any point of view and still explain what you see. So there is no unique right viewpoint - but if a viewpoint leads you to get the wrong answers unless you are very very careful, then its use should be discouraged. I’d say it’s clear that the idea of *locally* expanding space falls into this category. Experts can use it correctly, but we should certainly ban it from public talks, since it so easily leads people to incorrect conclusions.
October 7th, 2008 at 11:14 am
(— from Annie Hall)
October 7th, 2008 at 12:12 pm
jpd, even I can use elementary math to calculate the circumference for a trip to the southern hemisphere (c=pi*d) but it doesn’t change the speed of my car anyhow.
There seems to be some mix-up in using plain English.
My (stupid) understanding of physicists saying “well guys here is a supernova 27 billion light years away” was that this is not where the object is “now”, but how far the light has traveled. But after reading this Understanding the expansion of space, this seems to be totally wrong!?
Oh man! Take me back to earth. This picture of embedded Lambda-CDM geometry explains it all. It’s not complicated and you don’t have to grasp miles of mathematical hieroglyphs to understand what’s going on. It’s just a woolly use of plain English that lead to this confusion.
The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.
It’s perfectly clear and as easy as taking your car to the southern hemisphere. Sure, the supernova is 28 billion light years away. But we are never going to see any emitting light at this point in worldline! It’s forever beyond our reach and Einstein can rest in peace, as always.
Why are physicists creating this kind of “pseudo confusion”? Or is it me?
Yea yea, I know you all Gurus out there is laughing you pants of right now!
October 7th, 2008 at 2:38 pm
i wasn’t saying anything about your abilities, i was
addressing your comment:
“Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?”
we (you and me) make adjustments depending on scale all the time,
my example was distance on the earths surface.
October 7th, 2008 at 4:34 pm
One minor point - Sean says
> For evidence, check out these two recent papers:
but lists three. Should we read anything into this (considering ours is number 3)?
October 7th, 2008 at 5:11 pm
jpd, it’s all okay and forgot to say, thanks man!
My “exasperation” falls back on my own stupidity and fixation with the fact that there was something weird going on with the speed of light. Your thoughts about curvature, took me back to earth for some “reconciliation”.
And I must apologize to both Sean and Michael S. Turner, it was all perfectly correct, if I just had examined all text carefully. My only excuse is that this is not my native language and I’m a complete “Swedish Chef” in physics.
Well, nice to be back on track again with the universe and the speed of light. It took me four (light) years, but it was worth every second!
Oh, and by the way, I have no problems what so ever that Brooklyn Is Not Expanding, i.e. Steady State Brooklyn.
October 7th, 2008 at 5:26 pm
Hi John,
Your analysis seems a bit fishy. You say Birkhoff’s theorem implies that a test particle at distance r0 from us at time t0 in an isotropic universe should fall towards us. If the universe is isotropic, why does it choose to fall towards us?
I don’t intuitively understand the idea that local stuff doesn’t respond to the expansion. If it’s purely kinematic and driven by initial conditions, why do peculiar velocities of galaxies damp out over time? Why wouldn’t the same damping of peculiar velocities occur on the small scale, does the analysis leading to that damping formula depend on scale?
October 7th, 2008 at 5:29 pm
[ Of course I understand the effect on the scale of the solar system is totally negligible/unmeasurable and swamped by local gravitational fields, but still finite ]
October 7th, 2008 at 7:23 pm
My understanding of “space expanding” is, that in such a case particles have rates of separation based on successive distances in a way that resembles classical kinematics. IOW, it’s not like special relativity, and we can actually assign rates of recession to extremely distant objects in principle, and those rates of recession can be indeed greater than c. Space could be huge, even infinite, and if the galaxy at distance X goes 0.1c then the one at 10X goes c, and the one at 100X goes 10c.
Here is how it could be rightly defined: increase in “distance” means what it intuitively suggests, defined in terms of successive adjacent increments. So, I see a galaxy 100 MLY from me, critters there see another one 100 MLY from them, opposite me; and so on and so on. This works because those distances can be all defined and calibrated in terms of “cosmic time” - how long since your own proper clock ticked from the big bang, the time when things started receding. Everyone notes local distances at such and such moment of CT. No, it doesn’t matter whether they can get together to compare notes since we consider an objectively realist view of the universe. The very large distances are simply what the increments all add up to at successive moments of CT whether anyone is around to understand or deal with it or not. Isn’t this the basic concept you can tease out of the Robertson-Walker metric? The only problem I see is, space is not perfectly uniform and things are moving a bit to and fro, ruining the perfection of cosmic time and the regimentation of the progression of increments and local relative recessions.
As for red shift, this is usually put as: the ratio of wavelength equals the ratio of the “size of space” (benchmarks like two galaxies each “at rest” relative to CMB) between reception and emission.
One issue though, is that apparently one can pretend that SRT still applies. Imagine that the receding material is ever-more Lorentz contracted with distance and speed, relative to any self-appointed “central observer.” Supposedly the results are the same as “expanding space” only if the rate of recession stays the same, and there’s no way to slow things down and run them back together. This is what Milne tried in his off-beat cosmology. It’s fun to play with, and imagine what happens if one properly “infinite” but limit-Lorentz-contracted edge bashes into another …
Since the properties of “space” depend on material relations and the existence of gravity, I can get the idea of “space expanding” because there is a difference in effect as I said (the unbound extent possible for collections of mutually receding or approaching vantage points.) However, what bothers me instead is how to demarcate a given “space” from another “space” in which it supposedly can be embedded, like a soap bubble in the air - but what keeps it constrained as a separate thing? See my comment, at Backreaction thread “100 Years of Space-Time” at https://www.blogger.com/comment.g?blogID=22973357&postID=5978898531609158226. No one gave me an answer. Better luck here?
October 7th, 2008 at 7:33 pm
In case it wasn’t clear, we concatenate successive separations and relative velocities all together, calibrated under “cosmic time” (I didn’t make up that term, it’s out there.) Then we can get a “cosmic” definition of both separations and recession velocities over boundless extents of space. So add up the little distances to get the big distances, and add up the little relative velocities to get the big velocities at big distances (and other derivatives by extension - so for example, acceleration should be a = -(4/3)pi*rho*R relative to a given observer. It doesn’t make direct physical sense anymore as the gravity from the sphere “under” the shell of matter beyond the point you’re looking at, but it has to be consistent with the kinematics all the way out (well, not counting overall curvature.))
BTW this is an over-simplification since it only makes good sense over the region space is reasonably flat, but if expansion is about the right rate then that is the case - well, dark energy has made this all a mess, so I’m not sure anymore.
October 7th, 2008 at 7:40 pm
Geraint said “Hmm - it seems we do disagree - are you arguing that the standard FRW metric is the “correct” metric for the universe? If so, then I disagree”
Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.
If that’s what you meant, consider the following. An FRW spacetime has the property that it can be sliced up into spacelike pieces which are isotropic about each point. This statement has nothing to do with any choice of coordinates. Now it turns out that in GR a set of timelike geodesics perpendicular to these distinguished slices necessarily have non-zero geodesic deviation if the stress tensor is not zero. [I’m including the cosmological constant in the stress tensor.] This geodesic deviation is what we call, very naturally [look at any textbook picture of geodesic deviation] “the expansion of the universe”. Again, no coordinates. So yes, space is expanding. An observation of cosmic redshift is a direct observation of geodesic deviation. Nothing to do with Doppler effects of course, though the random motions of galaxies does give rise to an ordinary Doppler effect which is superimposed on and should not be confused with geodesic deviation.
October 7th, 2008 at 9:37 pm
> Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.
No - I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway.
The point is that the observable, the observed redshifts at a particular time for a particular observer are the same, irrespective of how we chose to slice and dice spacetime in terms of coordinates.
I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!
October 7th, 2008 at 10:03 pm
Geraint: “I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!”
What?! Are you saying space is not some thing?
In fact, I emphatically declare that space is some thing! I would go further to state that space is essentially every thing! (at least in our observable patch of reality)
So, what are you saying space is, if it is not some thing?
October 7th, 2008 at 10:53 pm
> So, what are you saying space is, if it is not some thing?
Nothing
October 8th, 2008 at 12:44 am
“No - I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway. ”
But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.
I think you are missing the point, which is that FRW spacetimes have a very special property which corresponds precisely to [the rate of] “the expansion of space”, AND this property has nothing to do with how you choose your coordinates, or indeed whether you choose any particular coordinates at all. Again, whether one thinks of space as a “thing” [whatever that is] is completely beside the point, though I agree with an earlier commenter that the rubber sheet business is really horribly misleading. Still, it is not a good idea to replace one horribly misleading statement [”galaxies are like bumps on a rubber sheet”] with another [”the universe is not *really* expanding — it depends on how you look at it.”]
Again: the key point here is geodesic deviation of geodesics corresponding to galaxies. Maybe you can twist words in some ingenious way so that geodesic deviation is not describable in terms of “expansion” [which by the way has a technical definition], but what you hope to gain from such a strange exercise escapes me. Whatever it is, “clarity” is in a different world.
The problem with all of these papers seems to be an obsession with the freedom to choose different coordinates. It would be better to just ignore coordinates altogether, neither they nor the freedom to choose them are of any importance fundamentally.
October 8th, 2008 at 1:07 am
> But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.
I am not talking about any approximations anywhere - when you say “metric” do you mean geometry? the FRW “metric” is a coordinate system on the underlying geometry. But it is not special in anyway and there are may ways you can cover the same geometry with different “metrics” (same geometry). The important thing is the observables are the same.
I do understand the FRW metric - have a read of the papers above.
October 8th, 2008 at 8:55 am
Heh… I just came down strongly on the side of expanding space here:
http://www.sonic.net/~rknop/blog/?p=66
Hogg once took me to task for using the “space expanding” picture, even warning me that he was afraid people were going to think me ill-informed for speaking out against the “galaxies flying apart” picture…. But, to my mind, the “galaxies flying apart” picture introduces *more* confusions and problems and misconceptions than the “space expanding” picture. That’s part of what my blog post is all about.
Another important point about the “space expanding” picture… if you live in a Universe that has vacuum energy… and, there is some reason to suspect that just perhaps our Universe is like that… saying that there is “more space” between galaxies, as opposed to thinking about the galaxies as moving apart from each other, conceptually fits closer to the mathematics of what’s going on in GR when you have something whose density is constant. Dark Energy is becoming an ever more important dynamical contributor all the time. Really, there is something *physical* between the galaxies that there is more and more of as the Universe expands. Saying there is more “space itself” is perhaps a nebulous concept… but there is most definitely more Dark Energy between the galaxies as the Universe expands.
October 8th, 2008 at 9:32 am
There’s an incorrect statement in the Burns & Hogg paper:
that “hydrogen atoms, the solar system, and the Milky Way Galaxy must all constantly “ressit the temptation” to expand along with the Unvierse. … is an erroneous consequence of the reaification of the rubber sheet: there is no such temptation, because there is no expanding rubber sheet.
First, to be fair to them, there is no such temptation for a matter dominated Univesre; there, the expansion is the left over coasting from the Big Bang, and there’s no ongoing “force” driving the expansion any more than a golf ball flying through the air continues to feel the force of “the hit”.
However, in our Unvierse, there is a temptation, and that is Dark Energy. I don’t want to comment on the scale of the hydrogen atom, since that would probably involve quantum gravity, but on the scale of the Solar System and the Galaxy, without the gravitational forces that hold those systems together, test particles placed initially at rest with respect to each other on those spatial scales would begin to move apart from each other due to the negative gravity effects of Dark Energy. Those effects are tiny compared to the gravitational binding of the systems, but the temptation exists.
My problem with viewing cosmological redshifts as an infinite number of infinitesimal Doppler shifts is that it’s *more* confusing than the other picture. You have to implicitly consider the infinite (or at least one over epsilon) of reference frames between source and observer in that picture… whereas the “space itself has expanded” picture doesn’t require implicit consideration of all of that. E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer… but, as even Burns and Hogg agree, that relative “velocity” is ill defined if there’s no single special relativistic frame that is valid at both events.
October 8th, 2008 at 11:39 am
Mentioned in CV - that’s probably as close to immortality as I’ll ever get …
One of the main points of our paper was that even though the “expanding space” analogy is open to misinterpretation and can be pushed too far, it is still the most useful way of thinking about the RW metric. John Peacock is right to point out its flaws, especially in the local universe, but I don’t think a “global vs. local” dichotomy is perfect either, even though it is rigorous (the RW metric can be approximated locally by Minkowski spacetime).
To JP: John’s analysis is correct. From the standpoint of “space is not expanding locally”, the particle falls toward us because a particle that is not moving away with the exansion will be pulled back toward the origin by gravity - what’s not going up will start coming down. From an exanding space perspective the expanation is slightly more subtle. We have to analyse the situation from the perspective of Bob, who is in the hubble flow, but wayy out there next to the particle. From Bob’s perspective, the particle is being shot out into the universe, in our direction. It will approach us because, even though the particle’s peculiar velocity and our expansion velocity are initially equal, the expansion of the universe is decelerating in this scenario, and so the particle starts to catch up with us as we both race away from Bob.
Also, the issue of dampening peculiar velocities and joining the hubble flow isn’t as straightforward as you might think. I’ll refer you to one of our earlier papers:
Joining the Hubble Flow: Implications for Expanding Space
Authors: Luke A. Barnes, Matthew J. Francis, J. Berian James, Geraint F. Lewis
October 8th, 2008 at 4:45 pm
> E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer…
Tempting, but clearly wrong
Just thinking of two observers who are spatially at rest at two different radii in the schwarzschild metric shows this.
Personally, I feel the problem lies with the with to label redshifts as being “different” - gravitational, cosmological, doppler - when in reality E=-p.u is it and the components of g, p and u depend on which coordinate system you choose -
i.e. in the FRW u has zero spatial components (for a comoving observer) and so people say the redshift is “cosmological”, where as the conformal representation of the same spacetime has non-zero spatial component for the same observer and now there is a doppler component to the redshift - but it’s exactly the same situation, with exactly the same observable - the only thing that changed was the coordinate system you threw down.
October 8th, 2008 at 4:55 pm
Rob Knop, I’m going to be a little bit rough here because I have been going through a sort of intellectual core meltdown in this post here, here and here, but it’s nothing personal, just physics.
Before I start, I must proudly announce the birth of a new acronym; Hazy English Language of Physicists - HELP
I have also formulated a pseudoscientific law saying: HELP = HELP, and I urge everyone to shout for HELP when physicists talks woolly in the hazy smog.
Okay Rob, there seems to be a clear case of HELP in your post about Randall Munroe and the Size of the Observable Universe.
Why then isn’t the observable Universe at most 28 billion light-years? If something emitted light and it took 14 billion years to reach us, and it was moving the other way as fast as it could, it would only be 28 billion light-years away right now. What’s with the 46?
For physicists it’s probably clear what the observable Universe represents mathematically, for all others observable correspond to a visual object that you can see with your eyes.
I hope that you are not saying that we can receive photons here on earth that has been travelling for 46 billion years? Alternative; that you are not saying that we can receive photons here on earth that has been travelling for 14 billion years at 3.28 times the speed of light in vacuum?
A picture is worth a thousand words and this one is the best I’ve seen explaining the observable universe and Understanding the expansion of space.
It’s high time to demystify our universe and use a proper language for everyone!
October 8th, 2008 at 5:00 pm
Actually - I find Tamara Davis’s conformal representation as the best for explaining why the observable universe is 46 billion LY in radius.
http://www.dark-cosmology.dk/~tamarad/astro/scienceimages/Spacetime_diagrams.pdf
As for use of proper language, we do already.
October 8th, 2008 at 5:21 pm
Geraint, when saying “observable universe”, are you saying that we can see (receive photons) from an object that is 46 billion years away?
October 8th, 2008 at 5:26 pm
No - as shown in the conformal picture, more most distant objects we can see (effectively the lumps in the CMB) are *now* 46 billion light years away.
October 8th, 2008 at 6:04 pm
Thanks Geraint, that’s a relief!
My guess is that there are plenty of people (made of ordinary matter
) out there who just give up on trying understand the universe because of this “lost in translation” situation. I have talked to science journalists about this “46 billion question” (those who are supposed to bring this info to the public) and they are besides “lost in translation” completely “lost in space” as well…
It’s probably a tricky problem to find one or two words that say; The largest piece of universe that we can know anything about is at visual distance of 14 billion light years, which represents an actual present physical position of 46 billion light years away, even if it’s problematical to talk about *now* according to Einstein’s general theory of relativity.
Did I get that right?
October 8th, 2008 at 7:30 pm
> Did I get that right?
Yeah - except the bit of the universe we can ever know something about is given by the event horizon, and is currently at a radius a little over 60 billion Lyrs away.
October 8th, 2008 at 7:39 pm
I hope that you are not saying that we can receive photons here on earth that has been travelling for 46 billion years? Alternative; that you are not saying that we can receive photons here on earth that has been travelling for 14 billion years at 3.28 times the speed of light in vacuum?
Er.
You are slamming on me by quoting the question from a blog post that’s written in a “hypothetical questioner and answer” format. I invite you to read the next paragraph after the one that you quoted, in which I explain what’s going on.
October 8th, 2008 at 7:42 pm
And, in any event, talking about the *distance* to very distant objects is troubling, because there are lots of different distances involved… proper distance at the time the photon was emitted, proper distance now, both of those measured by setting the FRW t parameter to constant; or the distance the photon travelled…
When I give public talks, I talk about lookback time, because it’s conceptually a lot cleaner.
October 8th, 2008 at 8:28 pm
The speed of light determines a relationship for a distance and a time locally. There can exist two frames F and F’ where observers in both will see that d = ct works. However, the two frames F and F’ may have their lightcones oriented differently. And the further away an observer on the frame F detects things on frame F’ this deviation may become more extreme. It is because of this with cosmology that as one observes further out the general relativistic physics of particles comoving in a frame becomes significant. The lightcone on the frame of a distant galaxy has an orientation different than the lightcone for your local frame. This corresponds to points on the spatial surface that galaxy is embedded in are being “slid” away. This then can lead to the discrepancy between time and distance (13.7 billion years vs 47 billion light years).
This 47 billion light years is only the distance to the CMB region some 370,000 years after the big bang. If we could get the neutrino telescopes or gravity wave interferometers to peer much further back to the inflationary period of the universe this distance will become far greater. On a local frame the light cone defines the projective space and the local projective Lorentz group. This is naturally defined because of the null property of light rays, ds^2 = 0. Globally, where these local frames “mesh together” on the whole spacetime, this projective spacetime has a more complex geometry, so that the distance “infinity” is parameterized by a finite time interval. That distance “infinity” is, or close to, the initial quantum event giving rise to the observable universe. That might be a quantum fluctuation of some vacuum state, the collision of branes or … , which is infinitely far (or approximately so), but is also the single point from which the universe emerged.
Lawrence B. Crowell
October 8th, 2008 at 8:53 pm
Geraint said: “the FRW “metric” is a coordinate system on the underlying geometry.”
At this point I can only say: “Huh?”
“The important thing is the observables are the same.”
If we are really going to be hard-headed positivists then we should give up all talk about hypothetical objects like “galaxies” and confine ourselves to discussions of optics in telescopes etc. The point of these discussions is to find a way of *thinking about* what we mean when we say “space is expanding”.
Let’s try this. Pythagoras came up with a formula for the distance between two points. Naturally enough it did not occur to him that his formula should include any functions of time. But fascinatingly enough it turns out that he was wrong: the corrected version of Pythagoras’ formula *really does* have an *intrinsic* time dependence. So in order to understand the distance between two objects, it is no longer enough to know where they are and how they are moving: *superimposed* on that, the laws of geometry are dependent on time. This time-dependence of the laws of geometry is what we call “the expansion of space”.
I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc. It is just a translation into English of the mathematics of GR applied to cosmology. It has also the virtue of being true.
October 8th, 2008 at 9:39 pm
> At this point I can only say: “Huh?”
You may say huh, but the statement is correct. The FRW metric is a coordinate choice, but there are others that can equally be thrown over the geometry of the universe. In FRW (comoving) galaxies are stationary, in others they are not.
The point is that all of these coordinate systems are equal, FRW is no more “fundamental” or special than any other (like choosing cartesian over polar on a piece of paper - both are just coordinate systems).
I know what I think about “the expansion of space” - if you look at the 3 papers at the start of this thread, I wrote one of them.
October 8th, 2008 at 9:43 pm
>I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc.
Again, the point is that this viewpoint is as valid as anyone elses.
October 8th, 2008 at 9:54 pm
Geraint on Oct 8th, 2008 at 9:39 pm
You may say huh, but the statement is correct. The FRW metric is a coordinate choice,
That is true, the metric is given by a coodinate choice, which underlies the connection coefficients, which in turn are used to compute curvatures. The metric is a tool, and points defined in a particular metric are calculational entities of sorts.
Lawrence B. Crowell
October 8th, 2008 at 11:14 pm
Geraint: “I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!”
neophyte “So, what are you saying space is, if it is not some thing?”
Geraint “Nothing”
Oh yeah? Where’s the geometry then?
October 8th, 2008 at 11:23 pm
>Oh yeah? Where’s the geometry then?
It’s a mathematical construct, just like the wave function, magnetic fields and all the other constructs.
October 8th, 2008 at 11:30 pm
i.e. - it’s nowhere.
October 9th, 2008 at 5:43 am
Before I give up, I have to correct
“You may say huh, but the statement is correct. The FRW metric is a coordinate choice,”
A metric is a particular kind of tensor. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
Likewise the fact that a particular spacetime has the FRW structure is a property of that spacetime’s geometry. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
Everything about FRW spacetimes can be stated without ever mentioning any coordinates. With a few [extremely non-generic] exceptions, namely the ones with maximal isometry groups, one can say definitely whether they are expanding or not. Generically they do expand or contract. This statement is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
October 9th, 2008 at 5:47 am
LB Crowell said “That is true, the metric is given by a coodinate choice”
No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.
October 9th, 2008 at 8:10 am
I can try.
At any distance. Comparing velocities at different spatial locations is simply not a valid operation in General Relativity. Doesn’t matter whether it’s a millimeter, a light year, or a billion light years.
Now, then, that said, it is something that you can do in special relativity, which assumes perfectly flat space-time. So you can go ahead and compare relative velocities in different locations as long as the area has an approximately flat space-time.
Therefore, since the curvature of the universe is essentially set by its expansion rate, the expansion rate of the universe determines how far away assuming special relativity works (which is typically as far as the expansion is negligible, so within a megaparsec or so, and also far away from any really dense objects, such as black holes or neutron stars). So as long as you stick with special relativity, and as long as that works as an approximation, you’re golden.
Now, does this mean that in General Relativity there is no speed of light limit? Certainly not! The speed of light limit in General Relativity just means something different: no object with mass can ever outrun a light ray. That is to say, if I use a laser to pulse a beam of light off in some direction, and at the same time launch a rocket ship from that same location, that rocket ship, provided it takes the same path as the laser beam, can never ever catch up to the beam of light, no matter how much acceleration it has or how fast it moves.
Of course, if the space ship was launched before the beam of light, in some special circumstances it is possible for the beam of light to never catch up either. This depends entirely upon the curvature of the space-time through which the ship travels, and it’s exactly why we can see things today that are some 20 billion light years away: when that light was emitted, they were much, much closer than that. But the universe has expanded since then, and they’ve moved so far away in the intervening time that we can no longer ever reach them with a beam of light, nor they us.
Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?
As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.
October 9th, 2008 at 8:15 am
Geraint,
While it may be true that things like wave functions, magnetic fields, manifolds, metrics, etc. are mathematical constructs, mathematics is the most specific and accurate way which we know to describe the universe around us. A “magnetic field” exists in the exact same way that a tree exists. While the mathematical equations that describe the status and behavior of a magnetic field are not in and of themselves the field, they are a description of a real, physical system which we call by the name “the magnetic field”.
October 9th, 2008 at 9:52 am
H.M. Amir … King of the Yemen. on Oct 9th, 2008 at 5:47 am
LB Crowell said “That is true, the metric is given by a coodinate choice”
No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.
—————————-
What is invariant is the interval ds^2 = g_{ab}x^adx^b. However, for a particular spacetime problem how one assigns coordinates is given by a coordinate condition or a gauge-like choice.
Lawrence B. Crowell
October 9th, 2008 at 10:47 am
Jason Dick, thanks a lot for taking time! I must let this sink in to my little brain
this is not easy stuff for a layman.
Geraint, thanks and I’ll be back with some questions about - Expanding Space: the Root of all Evil?
Rob Knop, sorry man. It was not my intention to slam on *you*, just to “stir the pot” of language confusion. The real nutcase here is *me*, not understanding. Physicists are my heroes!
October 9th, 2008 at 2:49 pm
Yes, FRW is a coordinate choice on a particular geometry. There is nothing special about the choice.
I disagree on the magnetic field statement above - The classical “magnetic field” of Maxwell is not observable, only its consequences. Is it “there” filling space with little red field lines (with little blue field lines of its friend, the electric field)? I suggest you have a read of a little Feynman and the development of QED on that one.
October 9th, 2008 at 3:12 pm
The question might be asked whether the electric or magnetic field in quantum mechanics are Hermitian operators. Of course they are not being of the form
E ~ int dk a^*e^{i@} + a e^{-i@}, @ = kx - omega*t,
and so the matrix elements are off diagonal. Strictly speaking an observable in QM is determined by a Hermitian operator.
I indicated yesterday how the global relationship between distance and time can be seen according to projective geometry of null rays. One is from there free to hang the spatial surfaces on this framework as one want (shift functions) and how they foliate together (lapse functions).
Lawrence B. Crowell
October 9th, 2008 at 5:02 pm
“Everything should be as simple as it is, but not simpler.” — Einstein
Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
October 9th, 2008 at 5:11 pm
> Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
No - you can’t “see” the magnetic field - you see an interaction - in QED the “magnetic interaction” is mediated by photons, which, in the large number limit, looks like a “classical magnetic field”. If there were no iron filings there, there would be no photons mediating the magnetic interaction and hence no classical magnetic “field”.
October 9th, 2008 at 6:42 pm
Jason Dick:
Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?
As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.
No, it’s not the units that’s the point. At a large enough distance (added up successive “steps” of concatenated local separations) that still generates a separation rate of c, and farther away the rate is even higher. You’re just hiding the separation velocity itself under a rug (making the ration seem to be the point.) There is no limit because we are talking about the rate of change in total distances between various galaxies in a case with no true physical edge (no place where anyone can’t see yet more galaxies in all directions) nor is there a small-enough closed universe (e.g. hypersphere.) Like I said, you imagine this as a “realist” thinking that those galaxies exist and next to one far from us is another one, and from them yet another, and so on - even if we can’t see all of that and never will.
You just have to get out of thinking in terms of SRT and being able to compare local objects that can move *right past* each other. Yes, it is like a “rubber sheet” because as the whole sheet expands, the bumps on it separate accordingly in a classical-type way (I mean, effectively in context, don’t go thinking I meant it literally is a classical process.) Of course this has to be thought of in terms of “cosmic time” to make sense. I am surprised not to hear more about CT in this discussion, do you guys appreciate its significance? Check out the Wikipedia piece:
Cosmic time
From Wikipedia, the free encyclopedia
Cosmic time (also known as “time since the big bang”) is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). Measure the passage of time using clocks moving with the Hubble flow. Choose the big bang singularity as the origin of the time coordinate.
Cosmic time is the standard time coordinate for specifying the Friedmann-Lemaître-Robertson-Walker solutions of Einstein’s equations.
October 9th, 2008 at 7:11 pm
Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
————–
A charged particle will move according to
F = g(E + vxB)
in the presence of an electric and magnetic field. This does not tell us that these fields are “real” as such. They might just be ways in which we organize things to account for the motion of charged particles.
This is one of those frustrating things about physics. A lot of what we use as tools, methods and mental images and constructions might not have quite the hard reality we would like them to have.
Lawrence B. Crowell
October 10th, 2008 at 12:21 am
>>I disagree on the magnetic field statement above - The classical “magnetic field” of Maxwell is not observable, only its consequences. Is it “there” filling space with little red field lines (with little blue field lines of its friend, the electric field)? I suggest you have a read of a little Feynman and the development of QED on that one.<<
Geraint and I had an ongoing argument about the reality of magnetic fields years ago, the conclusion of which is (in my mind) that his criteria for something being called “real” are far too strict and excludes things like trees, as a previous poster mentioned. I think restricting the word that much is unhelpful.
From hearing these expanding space discussions over the last couple of years, I summarise it to myself in the following way. Yes, space is expanding*.
* May not mean exactly what you think it means.
October 10th, 2008 at 4:50 am
Brendon - I still suggest you read a little QED and think again (I said this last time also
October 10th, 2008 at 6:12 am
Except that’s not a valid operation to perform in General Relativity. You can’t do it.
October 10th, 2008 at 6:17 am
Okay. Now why not consider Maxwell’s equations? In Maxwell’s equations, we find that a changing magnetic field can cause an electric field. And a changing electric field can cause a changing magnetic field. Change one or the other in the right way, and you start off a traveling wave. This wave can be shown to carry momentum: if it reflects off an object, it imparts momentum to said object.
And whenever there is an electric field, magnetic field, or both, they carry energy (equal to the integral of E^2 + B^2, modulo units, over the region in question).
So what, exactly, isn’t real here? The electric and magnetic fields describe a real phenomenon that has real effects upon the world around us. As Brandon mentions, saying that the electromagnetic field is not real would also exclude a tree as being real.
October 10th, 2008 at 6:54 am
>As Brandon mentions, saying that the electromagnetic field is not real would also exclude a tree as being real.
No - it is not quite the same question. If you think Maxwell’s B and E are “real” there are red and blue lines threading the room, even when there is no charge there to interact with. What I mean by “real” is that they are there - something physical, even if we are not trying to interact with them. Clearly, this is not the case in QED - which is amongst our most accurate pictures, so where are the B and E if they don’t appear in QED (except when pushed to the classical limit)
October 10th, 2008 at 9:03 am
What is real or directly observable about the EM field is contained in the momentum-energy tensor, which for T^{00} is the energy T^{ii} the momentum and off diagonal terms are Poynting vector terms. The fields are in a way the “square roots” of these terms. In QM the momentum energy terms are of the sort a^dagger times a, which are hermitian, while the square root involves linear equations in a and a^dagger terms, which are not hermitian.
The E and B fields, as is the case with all Yang-Mills field theories, simply reflect symmetries of the energy-momentum of the field. These fields we have been told have all sorts of pretty vector field interpretations, with some nice mathematics such as Gauss’ law, Stokes law and so forth. In these mathematics we have all types of ideas of vector fields crossing imaginary surfaces, vector fields in vortices and others radially arrayed, vector potentials associated with loops and currents and so forth. Yet these are really just mathematical ways of representing symmetries of the field.
These symmetries are internal symmetries, and so things such as fields are curvatures on a principal bundle F_{ab} = D_bA_a - D_aA_b, for D_a a covariant differential. As such these fields are really in a way “lifted” off the base manifold. Their connections to measurable physics on the base manifold is with the motion of charged particles, energy and momentum.
It is interesting to reflect on the fact that position and momentum are also represented according to linear equations in a and a^dagger. Yet these quantities are “observables.” The difference is that they are external symmetries — ultimately involved with the Lorentz group. So there appears to be two different types of symmetries here, which are extended to three symmetries with the CPT discrete symmetry. That physics has these three symmetries is the Coleman-Mandula theorem. Yet what ties the apparent dichotomy between internal and external symmetries is supersymmetry.
I REALLY am looking for the LHC to find evidence of SUSY, at least some particle physics for broken SUSY.
Lawrence B. Crowell
October 10th, 2008 at 2:04 pm
Geraint, do you believe space is static? If not, what is space doing? Justify your answer.
October 10th, 2008 at 3:02 pm
> Geraint, do you believe space is static? If not, what is space doing? Justify your answer.
Yes. My justification is written for all to see in paper number 3 up there at the start of the thread. Please have a read.
October 10th, 2008 at 3:06 pm
ps - the paper was refereed and has appeared in an international journal.
October 10th, 2008 at 3:07 pm
> What is real or directly observable about the EM field is contained in the momentum-energy tensor, which for T^{00} is the energy T^{ii} the momentum and off diagonal terms are Poynting vector terms
I don’t quite agree - what is observable is how charged particles move.
October 10th, 2008 at 3:17 pm
“I have asked you to imagine these electric and magnetic fields. What do you do? Do you know how? How do I imagine the electric and magnetic field? What do I actually see? What are the demands of the scientific imagination? Is it any different from trying to imagine that the room is full of invisible angels? No, it is not like imagining invisible angels. It requires a much higher degree of imagination (…). Why? Because invisible angels are understandable. (…) So you say, “Professor, please give me an approximate description of the electromagnetic waves, even though it may be slightly innacurate, so that I too can see them as well as I can see almost-invisible angels. Then I will modify the picture to the necessary abstraction.”
I’m sorry I can’t do that for you. I don’t know how. I have no picture of this electromagnetic field that is in any sense accurate. (…) So if you have some difficulty in making such a picture, you should not be worried that your difficulty is unusual.”
Feynman Lectures
October 10th, 2008 at 3:22 pm
“Suppose there was no field. Then perhaps the circularity could be broken. Each electron would act directly on another. Only the direct interaction between charges would be permitted. … The interaction was light, in the form of radio waves, visible light, X rays, or any other manifestations of electromagnetic radiation. “Shake this one, that one shakes later, “Feynman said later.
No field; no self-interaction”
Genius; Richard Feynman and Modern Physics
October 10th, 2008 at 3:28 pm
[ps - I see students dearly hanging onto ideas learnt at school when they enter university, so electrons are “really” particles that sometimes have wave-like properties, while photons are “really” waves that sometimes have particle-like properties, that the classical magnetic fields of maxwell’s equations “really” permeate space and that space “really” expands]
October 10th, 2008 at 5:16 pm
Geraint wrote
1) Q) Geraint, do you believe space is static? If not, what is space doing? Justify your answer.
A) Yes. My justification is written for all to see in paper number 3 up there at the start of the thread. Please have a read.
2) I don’t quite agree - what is observable is how charged particles move.
3)”Suppose there was no field. Then perhaps the circularity could be broken.
———-
When it come to #1) I’d say that we might ask whether space even fundamentally exists. What we might say has a concrete reality in physics are null rays, congruences of null geodesics and projective geometries. These are invariants of the theory. These projective spaces, or null congurences can then have a fibration over then from which connection terms and curvatures are computed. BTW, this is how I in fact have been reworking GR. This then makes general relativity similar in structure to quantum mechanics according to the Fubini-Study metric. In this approach the metric is not that fundamental. Anything which might be called space or spacetime is then something which we hang on projective geometry or sets of null congruences. How we want to do this “decorating” is up to the analyst.
When it comes to #2) I can meet you half way. I tend to think of the expectation of a Hermitian operator as observable. The most important observable is the EM field of a photon H = 1/2a^dag a. The photon is a particle and I tend to think of particles as observable. The photon has a helicity or spin, momentum and energy. So I would consider the photon as observable.
When it comes to something such as a static field, of course we don’t observe them! We might say that in a region of a magnetic field we can insert a Hall probe and measure the magnetic field. However, all we are doing is calculating what might be called a field effect because we have found that an electric current has been effected. Charged particles in motion are all we really measure. The B field is then inferred. This becomes of course particularly interesting with quantum hall effects.
Much the same holds for quantum waves. We really observe particles. The wave is more of a complex valued field effect which models how quantum particles behave. But interestingly we really don’t measure the wave at all.
Oh and while we are at it about things which don’t exist in the way we might think we might throw in vacuum energy as well.
With respect to #3) The fields are useful only as calculational devices for computing propagators. If the field is just a way of computing the symmetry of the bosonic field, such as with photons, then there are no real fields which couple back on the electron. Feynman got this one right.
Lawrence B. Crowell
October 10th, 2008 at 5:37 pm
Geraint,
What I mean by “real” is that they are there - something physical, even if we are not trying to interact with them.
Does this imply that this Cup of Levitron uses an “unreal magnetic field” to hold the spinning top floating in the air?
Or, does this imply that the magnetic field is real while the top is spinning, and become unreal when the top stops? If so, how can a spinning top decide what’s real or unreal?
October 10th, 2008 at 5:44 pm
Hehe, found this one with more “unreal music”!
October 10th, 2008 at 5:47 pm
The cup of levitron floats due to the electromagnetic interaction which is a direct propagation of photons (a’la QED) - In the large number limit, this looks like the classical B field in maxwell’s equations.
October 10th, 2008 at 5:48 pm
> But interestingly we really don’t measure the wave at all.
Exactly - the “wave function” is the QM equivalent of the B field (and of course are when you look at quantized em field they are the same
October 10th, 2008 at 8:13 pm
“If you can’t explain it simply, you don’t understand it well enough” — Einstein
Geraint, have done some more reading. Can we say that?
magnetic field = electromagnetic field (or electromagnetic waves)
And, that the “mechanical force” that hold the Levitron Spinning Top floating in the air is photons?
If this is the case I think I can understand: Magnetic field - doesn’t exist - is unreal - is not observable - because it belongs to the quantum world of approximations, right? And an approximation can never be a “real” thing; it’s just an approximation, right?
If my “hobby speculation” is anywhere near scientific truth, I have 2 questions:
1) Light is “made off” photons, I can see the light with my eyes. Is light a real thing?
2) According to Einstein matter and energy is the same thing E=MC2, and matter can be regarded as “frozen energy”. Energy/matter cannot be destroyed. We all agree a tree as being a real thing. If have a “container” for burning trees that would not let anything out. Could one say that after burning a real tree, we get a “tree” in the form of light, heat and carbon, which is also real? Or is it just the carbon that counts for real?
If it’s NO on both questions I suggest we make it very simple for everyone and say:
All that is not matter is unreal because Quantum Mechanics has to big influence, so the best we can do is give (pretty god) predictions and approximations.
October 11th, 2008 at 12:34 am
Geraint, to what extent, if any, in your opinion, is curvature real?
October 11th, 2008 at 8:09 am
Curvatures on a bundle define the fields. The electromagnetic field tensor constains the electric and magnetic fields, and this is the curvature on the principal bundle. The difference with spacetime curvatures is that it is given on a fibre bundle of connections pertaining to the base manifold, or that it is an extrinsic curvature. It this curvature real? Well we can use that curvature to compute the deflection of light around a gravitating body, and find that measurements confirm the prediction. Does this mean the curvature “exists,” or does this mean that it is a geometrical calculational device for predicting a measurement?
When it comes to points moving apart in an expanding cosmology, say with a deSitter (like) metric, we might say that this moving of points is a solution to the Einstein field equations. As I indicated the main thing which might be real in gravitation are projective and congruent configurations from null geodesics. Spacetime is what we dress this framework with. If so then on the Hubble frame (a convenient coordinate condition) points are found to be sliding away from each other on a large scale. Is this business of points moving apart real? Maybe it is just a solution which permits us to compute some things about the universe, such as comoving of frames.
Remember, general relativity is not about points! Given a point in spacetime one can chose two spatial metrics which contain that point and then “evolve” that point into two different points. What matters in general relativity is the relative motion of particles or massive bodies.
As for waves and the rest, of course physics has lots of wave equations. Maxwell’s equations for waves of electric and magnetic fields, Schrodinger wave equations, and on and on. These are nifty mathematical devices, and they permit us to predicts lots of stuff. Even general relativity for N-type of Petrov-Pirani solutions are wave equations (gravity waves). There is nothing wrong with talking about fields and waves and all the rest, including points sliding apart in cosmology. It is however, important to remember that these things do appear to be more mathematical representations of nature than how nature herself actually operates.
Lawrence B. Crowell