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 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 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.
> Geraint, to what extent, if any, in your opinion, is curvature real?
As we say in our papers, “curvature of space” is as “real” as the “expansion of space”. Space is not a thing that curves and expands.
Weinberg has a great section in his (IMHO fantastic) textbook on “The Geometric Analogy” (which I keep bookmarked to show students) that because the maths looks like curved space-time that there actually is a curved space-time.
‘Imagine looking at a galaxy which is, say, a billion light years away. Then imagine a fellow in that galaxy looking at a galaxy along the line of sight which is another billion light years further away. Imagine, the galaxy you are looking at is travelling at 10 000 kilometres per second. But the fellow in the second galaxy must also see the third galaxy travelling at 10 000 kilometres per second. So the third galaxy, which is twice as far away from you as the second galaxy, is travelling away at 20 000 kilometres per second – twice as fast from you.
‘You can build this up into a proof that the speed of a galaxy is proportional to its distance,’ says Weinberg. ‘And it’s all derived from the principle that the Universe looks the same from all positions.’
Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space, which is utterly empty, to expand? How can ‘nothing’ expand?
‘Good question,’ says Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’
(Steven Weinberg quoted in New Scientist)
> (3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?
The universe is expanding (things are moving apart) but it’s not because the space between them is stretching.
> 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?
Not quite. In QED, the thinkgo floats because there is an exchange of virtual photons between the base and the floating thing. Now, this is a classical device and so there are quadrabazzilions of photons being exchanged, mediating the EM force between the two.
Now, take away the floaty thing – what does classical physics say – well, Maxwell’s equations would say that there is a magnetic field there, even when there is nothing there to interact with, little red lines with arrows on them looping through.
What does QED say – well, with nothing there to interact with, there are no virtual photons flying around (there will be between the atoms in the base, but not up to where the floaty was. The classical B-field is not there. Now, bring a compass in, the exchange of virtual photons begin in earnest, and viola, it “feels” a magnetic force.
Geraint, thanks a lot! I was just reading about virtual photons!
The debate of the magnetic field is close to end, and then we should all be proper “on-topic guys”. 😉
But, before I stop rambling I must go in to virtual photons (which should have a lot in common with virtual particles in empty “expanding” space).
Questions:
1) Just imagine that the carrying force of the magnetic field was ordinary (real) photons. Would those photons have to “go any ware”, i.e. excite on the Levitron Spinning Top and making it glow like a light bulb (if the wavelength was in the visual spectrum)?
2) Could ordinary (real) photons ever have this “mechanical momentum” as virtual photons have, i.e. if I would try to make the Levitron Spinning Top float in the air using a real powerful laser, it’s would just burn a hole in the poor thing, or?
3) In vacuum (or empty space) there are vacuum energy “made off” quantum fluctuations in virtual particles. My understanding is that this is “okay” only because it’s an extremely short “loan” from reality, so if you borrow 100 bucks – you must repay 100 bucks immediately – ending up with zero, right? In what way does quadrabazzilions of virtual photons in the classical magnetic field get “unlimited credit” (like Wall Street! 😉 ) to create a real mechanical force that holds real matter floating in the air (and even lift up heavy cars in the junkyard)?
PS – Brilliant Weinberg quote.
Sorry for misspelling, my “soft-where” is taking me “any ware”…!? 🙂
“Virtual” photons are normal photons, it’s just this issue of borrowing and giving back energy that makes them somewhat different (basically, for a virtual photon, both the energy and momentum are not conserved at a vertex in a feyman diagram, but these quantities are conserved overall). Yes, all photons carry momentum and so can push on things (even the classical em-waves of maxwell’s equations carry and transfer momentum).
Photons are only exchanged, so they arn’t randomly fired off with the hope of meeting an absorber, they can only be transfered from one particle to another (sometimes that other is in your eye so you “see” the photon).
Cool, even if I feel that the feyman diagrams are “above” my capabilities. In “my world” it feels like if I’m a virtual photon – forced to undo everything I do, not to mess-up with reality – if I push a real thing 1 cm forward, I have to immediately pull it back 1 cm, to repay my “loan”, or?
It’s completely new to me that all photons carry momentum, fascinating! But it’s also weird since momentum the product of the mass and velocity of an object (p = mv), and photons don’t have any mass??
By the way; I’ve found the Feynman’s lectures on QED on video! Better start learning!
“Imagine, the galaxy you are looking at is travelling at 10 000 kilometres per second. But the fellow in the second galaxy must also see the third galaxy travelling at 10 000 kilometres per second. So the third galaxy, which is twice as far away from you as the second galaxy, is travelling away at 20 000 kilometres per second – twice as fast from you.”
Brilliant and simple enough for everyone to understand, thanks Steven Weinberg!
If we call them G1, G2 and G3 for galaxy one, two and three and space is — it would look like this:
G1 — G2 — G3
The weird thing is that we who lives in G1 are perfectly sure that we are at rest. And the folks in G3 think the same, so when they look at us we are moving away at 20 000 kilometers per second!?
AND, the folks in G2 think absolute the same, so when they look at G1 and G3 they are moving away at 10 000 kilometers per second!?
Weird and unreal, but a fact.
Geraint said
Well it’s possible for a neophyte to be right and a nobelist to be wrong (assuming you’re correctly portraying him as agreeing with you). I think it’s clear that it is the people who confuse “empty space” with “nothingness” who are the ones getting confused by their own bad intuition.
> I think it’s clear that it is the people who confuse “empty space” with “nothingness”
General relativity doesn’t say than empty space is anything but nothingness. It is those that attribute empty space with physical properties are those going askew.
That’s the point of the three papers quoted at the start of the thread. No, I am not misquoting Weinberg (or Rees) – in fact, it’s these comments that started our thoughts on this issue (see Expanding Space: The Root of All Evil?)
Where are all the physical constants stored?
> Where are all the physical constants stored?
What does that mean?
Everything that exists is information, and information is everything that exists. That includes all the physical constants and the physical laws . And if you want any kind of locality these physical constants and physical laws have to be essentially everywhere, permeating all of space, as are rulers and clocks.
That’s how I see it.
How do you see it? (I’m guessing you have a different view.)
Sorry Neo – but I have not idea what you are talking about. The “fundamental constants” describe things – they don’t “exist” anywhere. There is no Harry Potter like Gringolts (sp?) where their values live.
The expansion of space is just a solution to the Einstein field equation. The spatial surface might be flat in the Hubble frame, a particularly convenient coordinate (gauge-like) choice, but these surfaces are not embedded in a flat spacetiime. As such the local time direction (or lapse parameter chosen) is not equal to the time direction at some distance region. More importantly null directions are not universally the same. Because of this we get this model of points of space moving apart.
This is not that different from what happens with black holes. In the case of a Kerr metric the rotation of the black hole is often seen according to points of space being rotated around (frame dragging) the black hole. The comotion of frames in the universe is analogous to this frame dragging, though there are some departures due to the difference in the isometries of the spacetime (Killing fields etc) in the two examples.
The point here is that space and spacetime are similar to fields in electromagnetism. These are inferred quantities which we don’t measure directly. The existential qualities of these types of entities is of course a matter of some debate, but these things do not have the same physical observable status as other directly observables. Things which are directly observable might simply only be those things which are associated with Hermitian operators in quantum mechanics.
Lawrence B. Crowell
>The expansion of space is just a solution to the Einstein field equation.
You mean FRW is a solution of the field equations, and the interpretation of a(t) is that space is expanding – but other solutions of field equations for exactly the same geometry (but sliced differently) behave differently and have a more complex form for a(t) than FRW – and would not necessarily be interprested as “expanding space”.
We, therefore, return to the question of what a(t) is (which I guess is the point of this thread) – and what the papers at the start basically say is that you can’t embody space with physical properties and say that it is actually expanding.
The spatial portion of the metric is well known and the solution involves spatial surfaces in a foliation where volumes contain there in are variable. This is a well understood. For spatial slices according to an inconvenient coordinate condition will result in oddball solutions. These might correspond to what an observer on a highly relativistic spaceship would see of the universe.
Again the problem is not so much whether space expands, but the physical reality of space. Space is a geometric quantity, and its dynamics in general relativity is similar to the dynamics of field-waves in electromagnetics. These fields are not directly measurable, but are inferred from the measurements of other quantities. In EM we talk a lot about fields, waves and we design attenna to couple to electric or magnetic field components of a wave and so forth. So these things are a part of the language we use. In fact we could not get away from them, even if these things exist only according to inferences from certain measurements.
Within the solution of GR on the Hubble frame points of space do separate. It is similar to points of space being frame dragged around a rotating black hole, or points on a spatial surface moving towards a Schwarzschild black hole.
Lawrence B. Crowell
Lawrence B. Crowell, this sends shivers down my spine:
“The point here is that space and spacetime are similar to fields in electromagnetism. These are inferred quantities which we don’t measure directly.”
I’m no physicist or mathematician, but I have always “felt” that there must be a “connection” between gravity/spacetime and (electro)magnetism, and here is obviously one similarity.
I know that the Graviton is not discovered get (maybe at LHC?) but if it exists, wouldn’t gravity have a lot in common with electromagnetism, in the way virtual particles make up the carrying force?
(of course gravity must be “monopole” only)
If they find the Graviton would that mean the end of curved spacetime as a model/explanation of gravity?
I love Einstein, he is one of the greatest genius we ever had, and for me curved spacetime looks like an excellent solution when talking about objects like the Earth and the Moon (where one can use the “terrible” rubber sheet to make a working picture).
But when you stand on the Earth and try to imagine a spacetime that “warps” you to the ground, it doesn’t give you the same “intuitive” feeling.
I would be much more pleased if gravitons “glued” me to the Earth like a magnet.
And that would also solve a much greater problem; Quantum gravity/TOE. Please, LHC hurry up! 😉
Wait… the Higgs boson and the Graviton is the “same” particle, right? And the Higgs boson works like a syrupy and thus slowing down particles with mass… right? So it will not “glue” me to the Earth like a magnet… or? I prefer magnets before syrupy, syrupy is messy…
Geraint, sorry I missed to address to you, but do you have any comments on virtual photons and the mass of photons, and the weird things that goes on with G1 – G2 – G3?
The monopole of the gravity field is the black hole, the Petrov-Pirani type D solution. This is analogous to the near field solution of the Maxwell equations. The analogue of the far field solution in electromagnetism in general relativity are the type N solutions, which correspond to gravity waves. There are other solution types, some which define intermediate field solutions, and one called type O for cosmologies. The solution types are determined by eigenvectors of the Weyl curvature and their eigenvalues.
The type N solutions are not dipole as can be the case with an electromagnetic wave. The type N solutions are vectors V^d which are eigenvectors of the Weyl tensor by
C_{abcd}V^d = 0,
which by zero eigenvalue means they are null. Gravity waves move at the speed of light. Further momentum is an isometry of this spacetime, so momentum is conserved. Hence a dipole p = mx (mass along a distance) is constant and does not oscillate in order to conserve momentum. Gravity wave are generated by quadrupole moments or higher.
For a weak gravity wave, say a metric of the form
$latex
g_{ab}~=~eta_{ab}~+~h_{ab}
$
for the perturbation h_{ab} small one gets a Maxwellian-like sort of wave equation with helicity 2. This can be quantized in this weak linearized form, which then defines what might be called the graviton.
As for the graviton being a Higgs, well that is speculation which is somewhat outside the domain of physics. A Higgs particle is spin-0, and the graviton as described above is spin-2. So there is a problem right away with this idea. If the Higgs in a technicolor like theory is composed of something it might be a top-quark condensate.
Lawrence B. Crowell
Thanks Lawrence B. Crowell, it’s absolutely amazing; gravity and electromagnetism do have a something in common!
To continue with “expanding” space: There seems to be some “disagreement” among physicists whether space is expanding or not (finally on-topic!), and I have one question:
1) No one could argue with the fact that the distance between galaxies are increasing, we do have physical hard proof as this picture of The 2dF Galaxy Redshift Survey from John Peacock’s personal webpage. Why can we not skip the discussion on “expanding space” and just say; The distances between galaxies are increasing – or maybe even simpler – The Universe is getting bigger – or maybe even better – The Universe is in a state of universal expansion?
(For those who like 3D there is also an amazing 2dF redshift survey Rotating Slice Movie)
The redshift factor for special relativity and cosmology exhibit some departures from each other. The standar defintion for the redshift factor is
$latex
z~+~1~=~lambda_o/lambda_e,
$
where the right hand is the observed wavelength -:- the emitted wavelength. In special relativity this is given by the formula
$latex
z~+~1~=~sqrt{frac{1~+~v/c}{1~-~v/c}}.
$
The hubble relationship was demonstrated by Cepheid variables that have a precise relationship between their average absolute luminosity and periodicity of luminosity (they pulsate). Using the well known relationship between absolute and apparent luminosities Hubble found that the velocity of galaxies, based on redshift, and their distance measured by Cepheid variables was
v = Hd
where the velocity and distance (v, d) are related by this constant H = 64km/sec/Mpc. For for every megaparsec (1pc = 3.26 ly and the distance out to where one AU subtends a one second arc) the further out one observes that galaxies are moving an average of 64 km/sec faster. This law works best the further out you look where galaxies are not subject to local gravity of the local group of galaxies — the Andromeda galaxy is actually moving towards us! Further the obsered redshift when factored into the Hubble relationship indicates that 1 + z = exp(v/c). Yet clearly there are some departures with the special relativistic rule. If you take a binomial rule on the special relativistic formula you do get to first order v = cz + …, which conforms to the Hubble law. However, the two exhibit departures for larger velocities. Hence the special relativistic coordinates of Minkowski spacetime are not the same as cosmological coordinates.
It is tempting to say that maybe the Hubble law breaks down for large distances. If we directly look at the Hubble relationship it is easy to see that for d = 4687.5 Mpc or 15.3 billion light years that galaxies would be moving faster than light! It is tempting to think that something is going awry here. However, let us consider the CMB. This is due to the deionization of the plasma of material at the end of the radiation dominiated period. The photons emitted were comparable to optical photons ~ 1 micron wavelength, and now are redshifted into microwave wavelengths. Just ballparking this is clearly a z ~ 10^6. For the Hubble law this gives a v ~ 6c for the velocity of the material we are observing. We see stuff reach us from emitters traveling at an apparent velocity faster than light!!! More on this later, and how we actually detect photons from this material. The distance to this material is also
$latex
d~=~(c/H)ln(1~+~z)~simeq~6c/H~=~90 billion ly.
$
this is one reason for this much larger distance to the CMB opacity barrier than predicted by d = ct.
Now let us assume that there is some departure from the Hubble law which folds cosmology into a Minkowski spacetime. If we compute this redshift using the special relativistic rule then the velocity of this stuff is moving at v/c ~ 1 – 10^{-12}, or very very close to the speed of light. The distances also fold in accordingly as well so we no longer have this huge distance to the CMB opacity barrier.
So is there a special relativistic recovery? No, for these departures would show up much closer to home than at these distances. Even for 100Mpc distant galaxies these departures would be apparent. With the Hubble space telescope and some of the other mega-scopes it has become clear that these departures do not exist. In other words Cepheid variables and other standard candles used to benchmark distances would exhibit these departures, but our direct observations have not found them. For better or worse, even as the “root of all evil,” observations bear out the reality of the Hubble relationship to incredibly large distances.
So how is it that we can detect photons from material flying away at velocities which appear to be faster than light? Remember that the “no faster than light” rule is a local rule which holds in a local Lorentz frame. The Hubble relationship tells us that the spacetime of the universe is curved. In fact it means that the time direction of a distant galaxy is different from our local time. Further, the light cone centered at that distant galaxy is pointed mostly away from our direction — it is squashed relative to our light cone. Thus locally a photon on this cone centered at an emitted with v > c will indeed receed away from us! Yet a photon emitted towards us by an emitter way out there with an apparent v > c will travel on the local light cone that connects up with different local light cones. That local light cone is a local tangent to the null geodesic of the photon, where these local tangents (light cones tangent to the photon path) become more oriented in the same way our local light cone is. As a result that photon which may initially receeed away from our position will enter into local regions where it receeds less and less and then eventually approaches us.
So the Hubble law appears pretty solid. There are however deviations, but not those which recover special relativity. These deviations in fact do the opposite. We might call the year 1997 the year of breaking a cosmic barrier. Two big developments happened. The first is that Perelmutter found that not only is there a law which breaks down special relativity, but that velocities are receeding faster than thought. This means that the universe is a deSitter-like cosmology with the line element
$latex
ds^2~=~-dt^2~+~e^{Lambda t/3}(dr^2~+~r^2dOmega^2),
$
which is an exponentially expanding space. The Omega just stands for spherical angular coordinates. The “Lambda-factor ” is of the form
$latex
Lambda~=~3H^2Omega/c^2,
$
for H the Hubble factor and Omega the infamous factor which accounts for all the mass-energy in the universe. The total Omega turns out to be near unity, where only 5% of it is ordinary matter, another 25% is dark matter and the rest is dark energy. The dark energy part has some strange properties, in particular it appears to give a negative pressure on space, which expands things ever faster.
The other development in 1997 of great interest is something called the AdS/CFT correspondence of Maldacena. This result hinges upon the dual of the deSitter cosmology, the Anti-deSitter spacetime, which is dual by having a negative Gaussian curvature and two time directions in its embedded 5 dimensions. On the horizon of this spacetime, where time increments become huge or “infinite” is a barrier to the outside with field theory. The horizon provides a conformal map or boundary, and this leads to a fascinating result that the AdS and conformal field theory are equivalent. Further, since the Gaussian curvature is negative a black hole is repelled from the horizon, and so maintains an “eternal” equilibrium with the horizon and conformal fields define there. That the observable universe is deSitter-like and this AdS/CFT result has taken us considerably closer to an understanding of quantum gravity.
This post has been much longer than I had intended, but I wanted to write on some of these issues to attempt to clarify some things. Now as I have previously said, things like space, spacetimes, field etc are inferred and in someways appear to be constructions. Yet in doing physics it is nearly impossible not to refer to them — they appear to be lasting aspect of our lexicon.
Lawrence B. Crowell
> Space is a geometric quantity, and its dynamics in general relativity is similar to the dynamics of field-waves in electromagnetics.
Well, the metric is, but space does not have physical properties in GR – it does not bend, stretch or expand.
Speedy – Everyone is happy saying the universe expands – but some of us are saying that this is because “space expands” is not the best way of putting it (cos it leads to horrible misconcetions)
[Several of my posts did not appear – hope I haven’t upset someone so am now moderated :/ ]
The matter of a metric changing or the space or spacetime changing does not matter much. The standard old fashioned way of writing a line element is with Gaussian coordinates
$latex
ds^2~=~g_{ab}dx^adx^b,
$
but I can just as well write this as
$latex
ds^2~=~eta_{ab}{underlineomega}^aotimes{underlineomega}^b,
$
which is according to the basis one-forms of the spacetime. In the first approach we can say that a metric tensor is what is changing, but in the second case the basis elements of the space or spacetime are the dynamical entities. Both views are reasonable.
Again as I have said space and spacetime are inferred quanitities when it comes to measurement. They are model dependent quantities. Yet within general relativity it is perfectly acceptable to talk about points moving around, such as points moving in a black hole geometry. The motion of galaxies by the outward motion of points of space is a form of frame dragging, similar to the Penrose-Kerr effect of particles moved inside the ergosphere of a rotating black hole. One might be more precise and talk about the relative structure of local light cones and avoid all this discussion of moving points. In fact in some ways I do prefer that language. The classic text by Misner Thorne and Wheeler has in chapter 21 a good discussion of the “space plus time” or ADM approach to general relativity and the nature of lapse and shift functions on points of a spatial surface.
As I indicated above the motion of galaxies outward simply can’t be reduced to the motion of particles in a Minkowski spacetime. Observational data pretty stronly rules that out. So we are pretty much forced into the idea of space, as the classical field or model, in a dynamical evolution.
Lawrence B. Crowell
> As I indicated above the motion of galaxies outward simply can’t be reduced to the motion of particles in a Minkowski spacetime. Observational data pretty stronly rules that out. So we are pretty much forced into the idea of space, as the classical field or model, in a dynamical evolution.
I don’t think anyone suggests that a general FRW universe can be globally represented as motion through a minkowski metric – which is obvious as the underlying geometries are not the same. But the point is that the choice of FRW and the interpretation “that its because space expands” is one choice of many.
But saying “cos space expands” also leads some to adopt the rubber sheet analogy as being somehow “real” and hence inferring that whacky things happen cos space expands, pushes, pulls, twists, bends or wobbles it. Space doesn’t do any of these things to objects. That’s the point of the papers at the top.