Christoph Wetterich has put out a paper in which the universe isn't always expanding; it can be static or expanding just some of the time or even shrinking. And then there is an interaction which makes the masses of fundamental particles change in a complementary way, so as to preserve the properties of atoms, etc.

Now here is what I don't understand. An electron gets its mass through the Higgs mechanism. A nucleon gets its mass through QCD effects. The quarks also get their masses from the Higgs mechanism and that makes a very small contribution to the nucleon mass, but mostly the nucleon mass arises in a different way. So I just don't see how any simple mechanism of varying mass can preserve e.g. the electron/proton mass ratio. Is this a tremendous problem for his theory, or is there something I have overlooked?

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    $\begingroup$ The paper says : "The masses of atoms or electrons vary proportional to the Planck mass.". Assuming the change of the Planck mass is really a physical change (and not a change of unit) the questions are : is Higgs v.e.v. proportionnal to the Planck mass ?, and : what is the behaviour of QCD coupling constants if Planck mass is changing ?. $\endgroup$
    – Trimok
    Commented Aug 26, 2013 at 8:03
  • $\begingroup$ related: physics.stackexchange.com/q/71849 $\endgroup$
    – user4552
    Commented Aug 26, 2013 at 20:20
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    $\begingroup$ @Trimok: Assuming the change of the Planck mass is really a physical change... None of these changes are really physical changes. They are not observable, even in principle. All Wetterich is doing is a change of variables. What is observable is if a unitless constant changes, e.g., the ratio of the electron's mass to the proton's mass, or the fine structure constant. $\endgroup$
    – user4552
    Commented Aug 26, 2013 at 20:23

2 Answers 2


First a correction: Wetterich's paper doesn't say the universe is expanding or shrinking. All it says is that physics is invariant under scale changes and that a perspective in which the universe is static or shrinking (depending on the evolution stage) can lead to a simpler description.

The scale change applied consists of applying a factor $\lambda$ to all lengths and all time intervals, a factor $1/\lambda$ to all masses, and a factor $\lambda^2$ to the gravitational coupling $G$. Such a rescaling induces a factor $1/\lambda$ scale change in all interactions (including the Higgs mechanism). All this boils down to is that in terms of a description of the physics in dimensionless parameters, the scale change should not incur any changes.

  • $\begingroup$ -1: From the abstract: "We discuss a cosmological model where the universe shrinks rather than expands during the radiation and matter dominated periods." $\endgroup$
    – MarkWayne
    Commented Nov 15, 2013 at 18:34
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    $\begingroup$ @MarkWayne - suggest you read the whole paper. I have discussed the paper with Wetterich personally (over e-mail). There is no doubt that his model does not contain an absolute length scale and Wetterich certainly does not deny that. What he does show is that viewing the universe as shrinking (at least during certain phases) renders a natural view. $\endgroup$
    – Johannes
    Commented Nov 16, 2013 at 5:19

Varying electron mass (via e.g. varying Higgs VEV) alone can cause red shift (reflected as the changed photon frequency while an electron jumps from one quantum state to another, with electron-mass-dependent orbiting energy levels) without resorting to the commonly accepted expanding universe scenario.

That being said, one must substitute the reduced mass for the mass of the electron to take into account the fact that the mass of the atomic nucleus is not actually infinite compared to the mass of the electron. The reduced mass reads $$ \mu= \frac{M m_e}{M + m_e} = m_e\frac{1}{1 + \frac{m_e}{M}}, $$ where $M$ is the total mass of the nucleus.

Hence, in order to nudge the energy levels in a uniform way for different atoms, one is expecting to hold ratio $m_e/M$ constant. There are two ways to achieve this,

  1. A scale change is applied consistently to all length and time intervals. Then the whole proposal amounts to an exercise of rescaling.
  2. The spontaneous symmetry breaking scales of electroweak symmetry (Higgs mechanism) and quark chiral symmetry (NJL + Skyrmion?) are somehow in lockstep.
  • $\begingroup$ See section 3 of nat.vu.nl/en/sec/atom/Publications/pdf/JMS-Quas-07.pdf ... in which apparent redshift of a spectral line is analysed into cosmological redshift plus the effect of a change in the mass ratio. In effect, you propose to account for the entirety of apparent redshift with the cosmological redshift set to zero. But there's no way that that's going to work - the energy levels will bunch up or separate in a non-uniform way. $\endgroup$ Commented Jun 12, 2018 at 7:23
  • $\begingroup$ @MitchellPorter, Thank you for pointing it out. I have updated the answer. $\endgroup$
    – MadMax
    Commented Jun 12, 2018 at 14:59

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