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.
>>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.
Brendon – I still suggest you read a little QED and think again (I said this last time also 🙂
Except that’s not a valid operation to perform in General Relativity. You can’t do it.
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.
>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)
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
Geraint, do you believe space is static? If not, what is space doing? Justify your answer.
> 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.
ps – the paper was refereed and has appeared in an international journal.
> 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.
“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
“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
[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]
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
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?
Hehe, found this one with more “unreal music”!
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.
> 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 🙂
“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.
Geraint, to what extent, if any, in your opinion, is curvature real?
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
(1) Is there any form of mathematics that pertains in any way whatsoever to reality?
(2) Is there a reality for mathematics to pertain to?
(3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?
neophyte, I’m going to try to answer in a “layman way”, surely the “real” guys are going to correct me. 😉
(1) Is there any form of mathematics that pertains in any way whatsoever to reality?
A: Yes, one popular formula is: If you take one banana and then one more banana, you have two real bananas. Mathematically that would represent the famous equation: 1 +1 = 2 (which allows you to go bananas). 🙂 Seriously, of course there is lots of mathematics that connects direct to reality.
(Some mathematician gurus say that mathematics is the reality, but I cannot comment on that.)
(2) Is there a reality for mathematics to pertain to?
A: Yes, the whole universe.
(3) Is there any reasonable sense in which a (healthy growing) tree is expanding, but space is not expanding?
A: No, therefore both the healthy tree and space is expanding, but in a very different way, and for very different reasons.
Ah, yes. Good common sense answer.
Now let’s see what the “experts” have to say.
Oh, and Sean, feel free to chime in.