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I Rovelli on the notion of "now"

  1. Apr 29, 2017 #1
    Carol Rovelli recently claimed :
    "in physics there is nothing that corresponds to the notion of the ‘now’. Compare ‘now’ with ‘here’. ‘Here’ designates the place where a speaker is. For two different people, ‘here’ points to two different places. Consequently ‘here’ is a word whose meaning depends on where it is spoken. The technical term for this kind of utterance is ‘indexical’. ‘Now’ also points to the instant in which the word is uttered and is also classed as indexical."

    i think this is normal relativity. But I was recently reading a philosopher saying Rovelli has it wrong:

    "When scientists say that the universe is around 14 billion years old, they are not talking just in Earth-time. They don’t mean relative to our reference frame. Rather, this cosmic time parameter is independent of space. It is independent of spatial coordinates. Therefore, cosmic time is the same for every hypothetical observer in the universe regardless of his state of motion. In other words, cosmic time is a kind of reinstatement of Newton’s absolute time. It measures the duration of the universe in a frame-independent way."

    Read more: http://www.reasonablefaith.org/black-holes-and-the-arrow-of-time#ixzz4fdKYoUIz

    My suspicion is that Rovelli know more about relativity than this philosopher but perhaps someone can elaborate on what is going on, is Rovelli wrong? if not, is it false to say the cosmic time is measure the same by all observers?
  2. jcsd
  3. Apr 29, 2017 #2


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    Cosmological time is the time coordinate in a very particular coordinate system on a FLRW universe and is the typical implied quantity when a cosmologist refers to "age of the Universe". This does not mean that it is a universal or absolute time. The statement that the cosmic time is the same for every hypothetical observer in the Universe is either wrong or a tautology depending on what you imply by it. If you are saying that observers on the coordinate surfaces of cosmological time have the same cosmological time, then it is a tautology. If you are saying that all observers regardless of where and when they are located will have the same cosmological time, then it is utterly false. Coordinate systems are not observer-dependent, but we can often find "natural" coordinate systems based on some set of observers. An observer moving relative to the comoving frame would not consider cosmological coordinates "natural", at least not locally.

    Edit: TLDR; Don't trust philosophers to tell you about physics.
  4. Apr 29, 2017 #3


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    Cosmological time is a bit like the rest frame of the surface of the Earth. It's 6×1024kg of important, and includes a natural choice of z direction. But it's not physically special. It's just a frame, and seeing it as "the" rest frame is just conventional. And nothing forces you to care about it except ease of communication with other people.

  5. Apr 29, 2017 #4


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    Your suspicion is correct.

    Yes. Only comoving observers will agree on the cosmic time. Comoving observers are observers who always see the universe as homogeneous and isotropic. Note that we, on Earth, are not comoving observers: we do not see the universe as homogeneous and isotropic--for example, we see a dipole anisotropy in the CMBR. So the comoving coordinates that cosmologists use to describe the universe are a theoretical construct; we do not make any direct observations that correspond to them.
  6. Apr 29, 2017 #5
    This is very interesting. But Im a little confused. I've heard a lot of cosmologists say the universe is homogenous and isotropic at large scale. so If we can dont see it as such, whats the justification for that view?
  7. Apr 29, 2017 #6


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    The fact that, once we correct our observations for the dipole anisotropy we observe, the universe does look homogeneous and isotropic at large scale. That means we can interpret the dipole anisotropy as our own motion relative to a comoving observer.
  8. Apr 30, 2017 #7


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    My analogy with the surface of the Earth frame wasn't an idle one. If you are driving along a road in a car you are perfectly entitled to consider yourself as being at rest and the whole world as moving past you ay 30mph. In fact, that's exactly what you do see if you look at your dashboard (it's not moving) and out of the window (the trees rush past you). However, it's conventional for most purposes to consider the ground to be stationary and to specify what the world looks like in that frame - and not to say that you've done so.

    Similarly, cosmologists usually work in co-moving coordinates but leave out the "as seen in the comoving frame" for the same reason you don't say "I was doing 30mph relative to the local surface of the Earth when I was hit by someone travelling to my left at 30mph relative to the local surface of the Earth and then we both skidded and came to a stop relative to the local surface of the Earth". This kind of convention confuses laymen sometimes because experts forget to spell all of that out when talking to non-experts. Your philosopher really ought to know better if claiming to speak as any kind of authority - so well spotted.

    Edit: to be fair to Craig, I don't believe it's possible to completely rule out the existence of an undetectable "really real" frame. However, it's not required by the maths or physics we understand, and in any case we could only guess at which frame it is (there is no experiment even theoretically possible to detect it) with infinitely many possible wrong guesses. Craig's reasons for believing as he does are not rooted in physics - so are out of bounds for discussion here.
    Last edited: Apr 30, 2017
  9. Apr 30, 2017 #8
    Thanks guys, this is very helpful.
  10. Apr 30, 2017 #9


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    Let's put it more physically. We know that there is the cosmic microwave background radiation (CMBR). It was discovered by accident by Penzias and Wilson when the constructed a microwave antenna at the Bell labs and could not get rid of some "background noise" (legend has it that they even cleaned their antenna from pidgeon droppings to check whether this might be the reason for this noise).

    Now, given the famous Friedmann-Lemaitre-Robertson-Walker solutions of General Relativity you could come to the conclusion that this CMBR might be the remnant of thermal radiation in an early epoque of the evolution of the universe, before the electromagnetic radiation decoupled from the then still charged matter (plasma). Then the universe expanded but as one can show after decoupling the em. spectrum still stays a Planck spectrum with lower temperatures due to the cosmological redshift of the radiation. This is so, because the em. field is massless and thus free electromagnetics is scale invariant. So all that can happen is that the temperature (the only characteristic scale in the black-body spectrum).

    Now a system in thermal equilibrium leads to a physically preferred reference frame, where this black-body radiation is homogeneous and isotropic, following a Planck spectrum. Since this is a local notion, we can argue with special relativity here to make the argument simpler. In this rest frame the photon spectrum is given by a Bose-Einstein distribution function (in natural units of thermal QFT, where ##\hbar=c=k_{\text{B}}=1##)
    $$\frac{\mathrm{d} N_{\gamma}}{\mathrm{d}^3 \vec{x} \mathrm{d}^3 \vec{k}}=\frac{1}{(2 \pi)^3} 2 f_{\text{B}}(k^0),$$
    $$f_{\text{B}}(k^0)=\frac{1}{\exp(k^0/T)-1}, \quad k^0=|\vec{k}|.$$
    Now this is a scalar distribution, and we can write it in a manifest covariant way. Since this is in the restframe of the radiation we can define the four-velocity of this frame relative to an observer at rest as ##(u^{\mu})=(1,0,0,0)##, and thus we can write
    $$\frac{\mathrm{d} N_{\gamma}}{\mathrm{d}^3 \vec{x} \mathrm{d}^3 \vec{k}}=\frac{1}{(2 \pi)^3} 2 f_{\text{B}}(u_{\mu} k^{\mu}),$$
    which is already manifestly covariant.

    If a black body moves with velocity ##\vec{v}## relative to an observer in his/her frame we have
    $$(u^{\mu})=\gamma \begin{pmatrix} 1 \\ \vec{v} \end{pmatrix}, \quad \gamma =\frac{1}{\sqrt{1-\vec{v}^2}}.$$
    Thus we have
    $$u_{\mu} k^{\mu}=\gamma (k^0-\vec{v} \cdot \vec{k})=\gamma k^0 (1-v \cos \vartheta),$$
    where ##\vartheta## is the angle of the photon momentum to the direction of ##\vec{v}##. Comparing the argument in the Bose distribution with the one in the rest frame one sees that in any direction such an observer sees a Planck spectrum but with an effective "temperature" that is dependent on the direction he looks, namely
    $$T_{\text{eff}}(\vartheta)=\sqrt{1-v^2} \frac{T}{1-v \cos \vartheta}.$$
    A photon running in direction of the fluid cell's velocity ##\vartheta=0## leads to the largest temperature ##T_{\text{eff,max}}=T \sqrt{\frac{1+v}{1-v}}##, and in opposite direction ##\vartheta=\pi## it's the minimal temperature ##T_{\text{eff,max}}=T\sqrt{\frac{1-v}{1+v}}##, which is due to the corresponding Doppler blue and redshift. In the directions in between it varies according to the given formula with the characteristic cosine.

    In other words for an observer, for whom the fluid element runs towards him/her (away from him/her) sees the photons blue (red) shifted, as expected, but he/she sees still a planck spectrum but with an apparent "temperature" that is larger (smaller) than the proper temperature ##T## (which by the way is the only temperature one should use in relativistic physics, as one should exclusively use the invariant mass of an object, which both are scalar quantities).

    So to calculate the CMBR invariant temperature ##T## out of observations on Earth (or by satellites like Planck) one has to correct for the motion of the Earth relative to the rest frame of the CMBR, and indeed this leads to the conclusion that an observer on Earth moves with about ##360 \mathrm{km}/\mathrm{s}## in direction of the constellation Lion.
  11. May 1, 2017 #10
    The cosmological model has a preferred time coordinate: In this time coordinate, as well as in comoving space coordinates, the solution of a homogeneous isotropic universe looks much simpler than in other coordinates, namely homogeneous and isotropic.

    So, of course, if cosmologists talk, they use these preferred coordinates in their talk. Nobody will use other coordinates.

    But this does not mean that in principle other coordinates cannot be used. One is allowed to use them. All what makes the coordinates above special is the distribution of matter. And this distribution is only approximately, for very large distances, really homogeneous.

    So, from a pragmatic point of view, that of the usual cosmologist, where the coordinates matter which are really used, your philosopher is correct. From a philosophical point of view, where the fundamental principles matter, and not what these cosmologists do in that particular accidental universe we live in, Rovelli is right.
  12. May 1, 2017 #11


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    If describing the Universe as a whole, no. However, local measurements are often referred to using local normal coordinates in a patch small enough to be essentially flat. These differ from the preferred cosmological coordinates in just such a way that objects at rest relative to the CMB frame move apart at a velocity ##v = Hd##, where ##d## is the distance and ##H## the Hubble constant. It is a rather fun exercise to derive this result and it was an eye-opener for me at least.
  13. May 1, 2017 #12
    Julian Barbour and a number of his students have developed a model based on 3-space called Shape Dynamics, which is a Hamiltonian formulation of 3-geometry evolving in "time". He has been able to show that the propagation of massless fields in the model still move at a constant speed for all observers, showing that local observers will reproduce Special Relativity. As far as I can tell, and I have studied his papers closely, this shows that an evolving present is compatible with all observations, including the predictions of General Relativity. Block time is not necessary to describe the universe as we observe.


    Theological musings aside, Craig also makes good some good points about time and experience. I take the position that unless there is a contradiction between physics and elements of experience, there is no justification to label our psychological or sense experience as "an illusion", and to invent an entire ontology which goes against our mental model based on sensory information. [The Libet experiments do not provide an argument against presentism after the fact either.] If Barbour has a theory, which can be shown to be equivalent or indistinguishable from GR through observation, then I agree with Craig that there is no justification for jettisoning the present moment. In fact, Hamiltonian theories of Quantum Gravity as Rovelli would know, produce quantum states of Space, not space-time. Rovelli's co-creator of Loop Quantum Gravity, Lee Smolin is also a strident critic of the idea of time as a dimension, and goes further to argue that even the laws of physics themselves have evolved according to some evolutionary principle. Smolin says that the whole time-dimension fallacy began when someone first drew a t-axis on a graph.


    PS Never trust physicists to tell you about philosophy or the 'true' nature of reality. I can say that the amount of philosophy of science, or otherwise, I was exposed to in my ten years at university was less than about 1 Planck unit. Such things had to wait until retirement. I think it may be designed to keep the best minds from criticising the nonsense which comes out of the cultural studies departments.
    Last edited: May 1, 2017
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